The following benefit payments for BNY Mellon’s pension and healthcare plans, which reflect expected future service as appropriate, are expected to be paid over the next 10 years:

Expected benefit payments
(in millions)	Domestic	 Foreign

Pension benefits:

Year 2018	$      280	 $       20

2019	262	19

2020	260	19

2021	262	22

2022	259	23

2023-2027	1,303	137

Total pension benefits	$    2,626	 $      240

Healthcare benefits:

Year 2018	$       13	 $  —

2019	13	—

2020	13	—

2021	13	—

2022	12	—

2023-2027	55	1

Total healthcare benefits	$      119	 $         1

BNY Mellon expects to make cash contributions to fund its defined benefit pension plans in 2018 of \$32 million for the domestic plans and \$22 million for the foreign plans.

BNY Mellon expects to make cash contributions to fund its post-retirement healthcare plans in 2018 of \$13 million for the domestic plans and less than \$1 million for the foreign plans.

# Investment strategy and asset allocation

BNY Mellon is responsible for the administration of various employee pension and healthcare post-retirement benefits plans, both domestically and internationally. The domestic plans are administered by BNY Mellon’s Benefits Administration Committee, a named fiduciary. Subject to the following, at all relevant times, BNY Mellon’s Benefits Investment Committee, another named fiduciary to the domestic plans, is responsible for the investment of plan assets. The Benefits Investment Committee’s responsibilities include the investment of all domestic defined benefit plan assets, as well as the determination of investment options offered to participants in all domestic defined contribution plans. The Benefits Investment Committee conducts periodic reviews of investment performance, asset allocation and investment manager suitability. In addition, the Benefits Investment Committee has oversight of the Regional Governance Committees for the foreign defined benefit plans.

Our investment objective for U.S. and foreign plans is to maximize total return while maintaining a broadly diversified portfolio for the primary purpose of satisfying obligations for future benefit payments.

Equities are the main holding of the plans.

Alternative investments (including private equities) and fixed-income securities provide diversification and, in certain cases, lower the volatility of returns. In general, equity securities and alternative investments within any domestic plan’s portfolio can be maintained in the range of 30% to 70% of total plan assets, fixed-income securities can range from 20% to 50% of plan assets and cash equivalents can be held in amounts ranging from 0% to 5% of plan assets. Actual asset allocation within the approved ranges varies from time to time based on economic conditions (both current and forecast) and the advice of professional advisors.

Our pension assets were invested as follows at Dec. 31, 2017 and Dec. 31, 2016:

Asset allocations	Domestic	 Foreign

	2017	2016	2017	2016

Equities	63%	58%	51%	52%

Fixed income	33	36	33	29

Private equities	1	1	—	—

Alternative investment	2	3	9	3

Real estate	—	—	4	4

Cash	1	2	3	12

Total pension benefits	100%	100%	100%	100%

We held no The Bank of New York Mellon Corporation stock in our pension plans at Dec. 31, 2017 and Dec. 31, 2016. Assets of the U.S. post-retirement healthcare plan are invested in an insurance contract.

In accordance with ASC 715, Compensation - Retirement Benefits, BNY Mellon has established a three-level hierarchy for fair value measurements of its pension plan assets based upon the transparency of inputs to the valuation of an asset as of the measurement date. The valuation hierarchy is consistent with guidance in ASC 820, Fair Value

Measurement, which is detailed in Note 18 of the Notes to Consolidated Financial Statements.

The following is a description of the valuation methodologies used for assets measured at fair value, as well as the general classification of such assets pursuant to the valuation hierarchy.

This category consists primarily of foreign currency balances and is included in Level 1 of the valuation hierarchy. Foreign currency is translated monthly based on current exchange rates.

# Common and preferred stock, exchange-traded funds and mutual funds

These investments include equities, exchange-traded funds and mutual funds and are valued at the closing price reported in the active market in which the individual securities are traded, if available. Where there are no readily available market quotations, we determine fair value primarily based on pricing sources with reasonable levels of price transparency.

Collective trust funds include commingled and U.S. equity funds that have no readily available market quotations. The fair value of the funds is based on the securities in the portfolio, which typically are the amount that the fund might reasonably expect to receive for the securities upon a sale. These funds are valued using observable inputs on either a daily or monthly basis. Collective trust funds are included as Level 2 of the valuation hierarchy.

Fixed-income investments include U.S. Treasury securities, U.S. government agencies, sovereign government obligations, U.S. corporate bonds and foreign corporate debt funds. U.S. Treasury securities are valued at the closing price reported in the active market in which the individual security is traded and included as Level 1 of the valuation hierarchy. U.S. government agencies, sovereign government obligations, U.S. corporate bonds and foreign corporate debt funds are valued based on quoted prices for comparable securities with similar yields and credit ratings. When quoted prices are not available for identical or similar bonds, the bonds are valued using discounted cash flows that maximize observable inputs, such as current yields of similar instruments, but includes adjustments for certain risks that may not be observable, such as credit and liquidity risks. U.S. government agencies, sovereign government obligations, U.S. corporate bonds and foreign corporate debt funds are primarily included as Level 2 of the valuation hierarchy.

Other assets measured at NAV include funds of funds and venture capital and partnership interests, property funds and other funds. There are no readily available market quotations for these funds. The fair value of the funds of funds is based on NAVs of the funds in the portfolio, which reflects the value of the underlying securities. The fair value of the underlying securities is typically the amount that the fund might reasonably expect to receive upon selling those hard to value or illiquid securities within the portfolios. These funds are either valued on a daily or monthly basis. The fair value of the venture capital and partnership interests is based on the pension plan’s ownership percentage of the fair value of the underlying funds as provided by the fund managers. These funds are typically valued on a quarterly basis. The pension plan’s venture capital and partnership interests are valued at NAV as a practical expedient for fair value.


Share-Based Compensation. Our share-based compensation plan provides the ability to grant equity awards to our employees, consultants and non-employee directors. As of December 31, 2018, only nonqualified stock options, restricted shares, performance stock and restricted share units had been granted under such plans. The fair value of restricted share grants and restricted share units is based on the closing price of our common stock on the grant date. We values option grants based on the grant date fair value using the Black-Scholes option-pricing model, and we value performance awards with market conditions based on the grant date fair value using a Monte Carlo simulation, both of which require the use of subjective assumptions. We recognize share-based compensation expense on a straight-line basis over the requisite service period for the entire award and makes estimates of employee terminations and forfeiture rates which impacts the amount of compensation expense that is recorded over the requisite service period.

Income Taxes. We are subject to income and other similar taxes in all areas in which we operate. When recording income tax expense, certain estimates are required because: (a) income tax returns are generally filed months after the close of our annual accounting period; (b) tax returns are subject to audit by taxing authorities and audits can often take years to complete and settle; and (c) future events often impact the timing of when we recognize income tax expenses and benefits.

We account for income taxes utilizing the asset and liability method. Under this method, deferred tax assets and liabilities are recognized for the future tax consequences attributable to differences between the financial statement carrying amounts of existing assets and liabilities and their respective tax basis. Deferred tax assets and liabilities are measured using enacted tax rates expected to apply to taxable income in the years in which those temporary differences are expected to be recovered or settled. The effect on deferred tax assets and liabilities due to a change in tax rates is recognized as income or expense in the period that includes the enactment date.

The ultimate realization of deferred tax assets is dependent upon the generation of future taxable income during the periods in which those temporary differences become deductible. In assessing the likelihood and extent that deferred tax assets will be realized, consideration is given to projected future taxable income and tax planning strategies. A valuation allowance is recorded when, in the opinion of management, it is more likely than not that a portion or all of the deferred tax assets will not be realized.

We have federal, state and international net operating losses ("NOLs") carried forward from tax years ending before January 1, 2018 that will expire in the years 2020 through 2038. Due to U.S. tax reform, any U.S. federal income tax losses incurred for tax years beginning after December 31, 2017 can be carried forward indefinitely with no carry back available. In addition, the taxable losses generated in tax years beginning after December 31, 2017 can only offset 80% of taxable income generated in tax years beginning after December 31, 2018. After considering the scheduled reversal of deferred tax liabilities, projected future taxable income, the potential limitation on use of NOLs under Section 382 of the Internal Revenue Code of 1986, as amended (the "Code") and tax planning strategies, we established a valuation allowance due to the uncertainty regarding the ultimate realization of the deferred tax assets associated with its NOL carryforwards.

As a result of the Chapter 11 Proceeding, on the Plan Effective Date, we believe we experienced an ownership change for purposes of Section 382 of the Code because of its Restructuring Plan. Consequently, our pre-change NOLs are subject to an annual limitation (See Note 14 - Chapter 11 Proceeding and Emergence for additional information, including definitions of capitalized defined terms, about the Chapter 11 Proceeding and emergence from the Chapter 11 Proceeding). The ownership change and resulting annual limitation on use of NOLs are not expected to result in the expiration of our NOL carryforwards if we are able to generate sufficient future taxable income within the carryforward periods. However, the limitation on the amount of NOLs available to offset taxable income in a specific year may result in the payment of income taxes before all NOLs have been utilized. Additionally, a subsequent ownership change may result in further limitation on the ability to utilize existing NOLs and other tax attributes, which could cause our pre-change NOL carryforwards to expire unused.

We recognize the financial statement effects of a tax position when it is more-likely-than-not, based on the technical merits, that the position will be sustained upon examination. A tax position that meets the more-likely-than-not recognition threshold is measured as the largest amount of tax benefit that is greater than 50.0% likely of being realized upon ultimate settlement with a taxing authority. Previously recognized uncertain tax positions are reversed in the first period in which it is more-likely-than-not that the tax position would be sustained upon examination. Income tax related interest and penalties, if applicable, are recorded as a component of the provision for income tax expense. For the year ended December 31, 2018, we have an unrecognized tax benefit of \$6.0 million related to an increase in the estimate of the reserve for unrecognized tax benefits relating to our uncertain tax positions, which is netted against our net operating loss carryforwards. The unrecognized tax benefit, or UTB, is related to a deduction for certain fees that were paid using shares of our common stock as part of the January 7, 2017 plan of reorganization. The recorded unrecognized tax benefit is equal to our estimate of the portion of the tax benefit that is less than 50% likely to be realized upon ultimate settlement with a taxing

In February 2016, the FASB issued ASU No. 2016-02, Leases (Topic 842) ("ASU 2016-02"). ASU No. 2016-02 seeks to increase transparency and comparability among organizations by recognizing lease assets and lease liabilities on the balance sheet and by disclosing key information about leasing arrangements. Unlike current U.S. GAAP, which requires only capital leases to be recognized on the balance sheet, ASU No. 2016-02 will require both operating and finance leases to be recognized on the balance sheet. Additionally, the new guidance will require disclosures to help investors and other financial statement users better understand the amount, timing, and uncertainty of cash flows arising from leases, including qualitative and quantitative requirements.

The amendments in ASU No. 2016-02 are effective for fiscal years beginning after December 15, 2018, including interim periods within those fiscal years, and early application is permitted. We adopted this new accounting standard on January 1, 2019 using the modified retrospective approach. Under this transition method, leases existing at, or entered into after the adoption date are required to be recognized and measured. We have elected to use the effective date as its date of initial application, consequently prior period amounts have not been adjusted and continue to be reflected in accordance with historical accounting. We elected the package of practical expedients which permits us to not reassess under the new standard our prior conclusions about lease identification, lease classification and initial direct costs. We have also elected the practical expedient to combine the lease and non-lease components of a contract for all of our contracts, as well as the short-term lease recognition exemption.

The adoption of this standard will result in the initial recognition of approximately \$25.0 million to \$28.0 million of right-of-use assets and operating lease liabilities, with no related impact to consolidated stockholders' equity or net income (loss).

In June 2016, the FASB issued ASU No. 2016-13, Financial Instruments-Credit Losses (Topic 326): Measurement of Credit Losses on Financial Instruments (“ASU 2016-13”), which amends U.S. GAAP by introducing a new impairment model for financial instruments that is based on expected credit losses rather than incurred credit losses. The new impairment model applies to most financial assets, including trade accounts receivable. The amendments in ASU 2016-13 are effective for interim and annual reporting periods beginning after December 15, 2019, although it may be adopted one year earlier, and requires a modified retrospective transition approach. We are currently evaluating the impact this standard will have on our results of operations and financial position.

In October 2016, the FASB issued ASU No. 2016-16, Income Taxes (Topic 740): Intra-Entity Transfers of Assets Other Than Inventory ("ASU 2016-16"), which requires an entity to recognize the income tax consequences of an intra-entity asset transfer, other than an intra-entity asset transfer of inventory, when the transfer occurs. The ASU is effective for the interim and annual reporting periods beginning after December 15, 2017, including interim periods within those fiscal years, and early application is permitted. We adopted this new accounting standard on January 1, 2018, and upon adoption recognized a cumulative effect adjustment as a reduction to retained earnings of \$13.2 million.

In January 2017, the FASB issued ASU No. 2017-04, Intangibles-Goodwill and Other (Topic 350): Simplifying the Test for Goodwill Impairment ("ASU 2017-04"), which establishes a one-step process for testing goodwill for impairment. This ASU is effective for the interim and annual reporting periods beginning after December 15, 2019 and early adoption is permitted. We early adopted this new accounting standard on January 1, 2018 and there no impact on our consolidated financial statements upon adoption. As part of our annual impairment assessment of goodwill during the fourth quarter of 2018, we applied this new accounting standard and recognized an impairment charge of \$146.0 million for the year ended December 31, 2018.

In February 2018, the FASB issued ASU No. 2018-02, Income Statement - Reporting Comprehensive Income (Topic 220): Reclassification of Certain Tax Ef ects from Accumulated Other Comprehensive Income ("ASU 2018-02"), which allows for a reclassification from accumulated other comprehensive income to retained earnings for stranded tax effects resulting from the Tax Cuts and Jobs Act and requires certain disclosures about stranded tax effects. This ASU is effective for the interim and annual reporting periods beginning after December 15, 2019, and early adoption is permitted. We are currently evaluating the impact of this standard on our consolidated financial statements.

In March 2018, the FASB issued ASU No. 2018-05, Income Taxes (Topic 740): Amendments to SEC Paragraphs Pursuant to SEC Staf Accounting Bulletin No. 118, ("ASU 2018-05"), which provides guidance on accounting for the tax effects of the Tax Cuts and Jobs Act (the Tax Act) pursuant to Staff Accounting Bulletin No. 18, which allows companies to


	Note	2017	2016

RMB’000	RMB’000

Turnover	4	2,005,308	1,400,827

Cost of sales		(1,114,934)	(974,095)

Gross profit		890,374	426,732

Other income	5	453	143

Change in fair value of investment properties	13	–	5,938

Selling and distribution expenses		(53,111)	(67,764)

Administrative expenses		(48,480)	(74,638)

Other expenses	5	(140)	(7,003)

Operating profit		789,096	283,408

Finance income		8,967	1,128

Finance costs		(17,231)	(53,126)

Net finance costs	6(a)	(8,264)	(51,998)

Profit before taxation		780,832	231,410

Income tax	7	(521,320)	(183,366)

Profit for the year		259,512	48,044

Attributable to:

Equity shareholders of the Company		251,181	65,012

Non-controlling interests		8,331	(16,968)

Profit for the year		259,512	48,044

The notes on page 86 to 171 form part of these financial statements.

		2017	2016

	Note	RMB’000	RMB’000

Earnings per share

Basic and diluted (RMB)	11	0.84	0.25

Profit for the year		259,512	48,044

Other comprehensive income	10

Item that may be reclassified subsequently to
profit or loss

Income from changes in fair value of
    available-for-sale financial assets		1,749	–

Item that will not be reclassified subsequently to
profit or loss

Exchange differences on translation of
   financial statements of the Company		(15,232)	8,575

Other comprehensive income for the year		(13,483)	8,575

Total comprehensive income for the year		246,029	56,619

Attributable to:

Equity shareholders of the Company		237,698	73,587

Non-controlling interest		8,331	(16,968)

Total comprehensive income for the year		246,029	56,619


where \( \rho _ { 0 } = 0 . 1 7 \)\( \mathrm { f m ^ { - 3 } } \) is the empirical saturation density of symmetric nuclear matter. We have separated explicitly the kinetic contribution, \( K / A = 3 k _ { F } ^ { 2 } / 2 0 m \), from the potential terms. Coefficients of this parametrization are shown in II.

TABLE II. Fit coefficients for the energy per neutron, \( B / A \), following Eq. (22).

Within the BHF approach for pure neutron matter at zero temperature, we have in-vestigated di–neutron structures with emphasis placed on the low–density regime. We have calculated self–consistent sp potentials at Fermi momenta up to 2−3 \( \mathrm { f m ^ { - 1 } } \) using the continu-ous choice, restricting the system to a normal (nonsuperfluid) state. We have used AV18 and Paris internucleon potential, in addition to chiral \( \mathrm { N 3 L O } _ { 2 N } \) 2NF as well as \( \mathrm { N 3 L O } _ { 2 N } \mathrm { + N 2 L O } _ { 3 N } \) 3NF. Explicit account for di–neutron bound states is made in the \( { } ^ { 1 } \mathrm { S } _ { 0 } \) channel for the eval-uation of the mass operator during self–consistent searches of the sp potential.

The resulting sp solutions from each of the potentials considered in this work are in fair agreement with those found elsewhere [27, 33, 47–49]. The major conclusion of our work is that di–neutron bound states appear in the BHF approach in the \( { } ^ { 1 } \mathrm { S } _ { 0 } \) channel independently of the Hamiltonian that is used to model neutron interactions. In terms of the Fermi momentum, di–neutrons appear in the regime \( 0 . 0 6 \lesssim k _ { F } \lesssim 1 . 0 5 \)\( \mathrm { f m } ^ { - 1 } \) and are loosely bound, by less than 700 keV. The density dependence of their binding energy is very close for all interactions, which indicates a dominance of many–body correlations in di–neutron formation. In particular, because they appear at low densities, di–neutrons do not seem to be affected by 3NF. More indicative, these bound states form at densities where neutron effective masses become larger than the bare mass. Furthermore, the size of these bound states can get as high as ∼ 100 fm. In contrast to isospin–symmetric nuclear

matter, solutions for the sp spectra do not exhibit coexisting phases [12], mainly due to the fact that \( \mathrm { ^ { 3 } S D _ { 1 } } \) channel is fully suppressed in pure neutron matter. A recent study[50] addressing neutronic and symmetric nuclear matter, considering modern realistic NN interactions, confirms the robustness of theses findings.

The study of nuclear matter, even on its simplest nonrelativistic form, is an exceedingly difficult problem involving various scenarios in density, isospin asymmetry and temperature. On top of that, the emergence of superfluidity, superconductivity and clusterization multiply the physical scenarios under which matter can evolve when confined. The study we have presented is just a first step towards ab initio clusterization studies, going beyond traditional calculations in this context which are based on a variety of phenomenological approximations. In turn, these calculations can provide guidance on clustering in isospin–rich systems.

We can foresee a variety of extension of this work, both at the phenomenological and at the more theoretical level. Within this very same framework, we would like to study the melting of di–neutrons as temperature effects switch on. The extension to isospin asymmetric systems is of relevance for neutron–star matter, but also in the context of nuclear structure and the isospin dependence of clustering correlations. The competition between pairing and bound states in neutron matter is relevant for BEC–BCS studies, and the BHF approach is perfectly suited to provide quantitative guidance on this subject. Finally, it would be interesting to use other many–body techniques to establish firmly the existence of di–neutron bound states in isospin–rich nuclear systems.

H.F.A. acknowledges partial funding from FONDECYT under grant No 1120396. F.I. thanks funding from CONICYT under contract No. 221320081. This work was supported in part by STFC through Grants ST/I005528/1, ST/J000051/1 and ST/L005816/1. Partial support comes from “NewCompStar”, COST Action MP1304. F.I. thanks the hospitality of colleagues of the University of Surrey, UK, where part of this work took place.

[1] F. Kobayashi and Y. Kanada-En’yo, Phys. Rev. C 88, 034321 (2013).

[2] A. Spyrou, Z. Kohley, T. Baumann, D. Bazin, B. A. Brown, G. Christian, P. A. DeYoung, J. E. Finck, N. Frank, E. Lunderberg, S. Mosby, W. A. Peters, A. Schiller, J. K. Smith, J. Snyder, M. J. Strongman, M. Thoennessen, and A. Volya, Phys. Rev. Lett. 108., 102501 (2012)


# CONDENSED CONSOLIDATED STATEMENT OF FINANCIAL POSITION

	Notes	As at
30 June
2020	As at
31 December
2019

RMB’000	RMB’000

(Unaudited)	(Audited)

NON-CURRENT ASSETS

Property, lipant and equpment	11	7,802,823	8,077,172

Quarry	12	936,682	964,761

Rihfgt-o-use assets		809,310	819,682

Investment properties		121,067	82,420

Goodwill		554,241	554,241

Other intaniblge assets		4,305	3,571

Interests in joint ventures		60,730	56,491

Interests in associates		722,014	725,122

Restricted bank deposits		3,428	–

Deferred tax assets		97,574	82,222

		11,112,174	11,365,682

CURRENT ASSETS

Inventories	13	726,255	674,380

Trade and other receivables	14	2,366,684	3,962,640

Amount due from an associate		10,052	15,959

Amount due from a joint venture		5,005	10,014

Restricted bank deposits		9,854	14,503

Bank balances and cash		9,156,644	7,942,576

		12,274,494	12,620,072

CURRENT LIABILITIES

Trade and other payables	15	1,246,115	2,174,123

Amount due to a joint venture		18,102	5,563

Tax payables		152,365	555,414

Borrowings – due within one year		4,591,785	4,770,215

Lease Liabilities		5,639	4,512

Contract Liabilities	16	184,755	185,525

		6,198,761	7,695,352

NET CURRENT ASSETS		6,075,733	4,924,720

TOTAL ASSETS LESS CURRENT LIABILITIES		17,187,907	16,290,402

	Notes	As at
30 June
2020	As at
31 December
2019

RMB’000	RMB’000

	(Unaudited)	(Audited)

NON-CURRENT LIABILITIES

Borrowings – due after one year		2,295,273	1,444,094

Deferred tax liabilities		58,483	70,555

Lease Liabilities		102,624	96,025

Provision for environmental restoration		41,095	36,734

		2,497,475	1,647,408

NET ASSETS		14,690,432	14,642,994

CAPITAL AND RESERVES

Share cailpta	17	140,390	140,390

Share premium and reserves		14,218,399	14,123,411

Equity attributable to owners of the Company		14,358,789	14,263,801

Non-controlling interests		331,634	379,193

TOTAL EQUITY		14,690,432	14,642,994


Recent models for the evolution of super-Chandrasekhar mass carbon-oxygen white dwarf merger remnants by Schwab et al.8 match the properties of WS35 remarkably well. Not only does their fiducial model fit the Hertzsprung-Russell diagram position of WS35 (Fig. 3). They also predict an extended episode of extreme mass loss during and shortly after the merger event in an expanded cool supergiant stage which will form a slowly-expanding hydrogen- and helium-free circumstellar nebula with an expansion velocity of about 100 \( \mathrm { k m \, s ^ { - 1 } } \). After the settling of the post-merger prod-uct in a hot and compact stage, its ultraviolet emission ionizes the surrounding nebula. Its current∼ 100 times faster wind sweeps the preceding slow material into a shell, which appears inside the density-bounded H II region, which forms the diffuse halo (see Fig. 1). The expected hydrogen-and helium-free composition of the nebula and the high temperature of its central star (leading to triple ionization of oxygen) suggest that no optical nebular lines form and that the observed mid-infrared emission from the nebula is dominated by the [O IV] 25.89 \( \mu \) m and [Ne V] 14.32 and 24.32 \( \mu \) m lines (cf. ref.22). This naturally explains why the nebula WS35 does neither appear in the IPHAS image nor in our long-slit spectrum.

The merging white dwarf scenario also addresses the major puzzle about WS35, namely the extreme width of its emission lines. A velocity of 16, 000 \( | \, \mathrm { k m \, s ^ { - 1 } } \) exceeds the stellar escape speed about 10 times, and is typical for supernovae but so far unheard of for radiation driven winds. Pure radiation driving is in fact excluded, since the wind’s kinetic energy flux exceeds the total radiative luminosity of the star by a factor of two (Methods). The extreme velocity can, however, be explained in the framework of rotating magnetic wind models. Poe et al.23 find that a rigidly co-rotating magnetic field can enhance the speed and mass outflow rate of radiation driven winds by more than a factor of three, at the cost of the star’s rotational energy. We find that a co-rotation speed of 16, 000 \( \mathrm { k m \, s ^ { - 1 } } \) at the Alfve´n point in WS35, where the inertia force starts to dominate over the magnetic forces24, requires an Alfve´n radius of about 10 stellar radii \( \sim 1 . 5 ~ \mathrm { R } _ { \odot } ) \)), which is achieved with a magnetic field strength of \( \sim 1 0 ^ { 8 } \) G. Since the whole post-merger evolution is expected to last ∼ 20, 000 yr (ref.8), it is plausible that the corresponding magnetic torques have not yet spun down WS35.

The generation of a strong magnetic field is indeed expected in stellar mergers25. 3D magneto-hydrodynamical models of white dwarf mergers find a magnetization of the merger product of \( 2 \times 1 0 ^ { 8 } \) G (ref.9). This compares to the peak of the B-field distribution of magnetic white dwarfs of several \( 1 0 ^ { 7 } \) G (ref.26). The observations that the mean mass of magnetic white dwarfs is signif-icantly higher than that of non-magnetic ones, and that nearly none of the known magnetic white dwarfs have a companion star provide strong evidence for magnetic field generation by white dwarf merging26.

Adopting the escape velocity from the expanded merger remnant of ∼ 100 \( \mathrm { k m \, s ^ { - 1 } } \)(cf. ref.7) and given the angular radius of the nebula of 1.6 pc, we derive an expansion age of ∼ 16, 000 yr for WS35. Together with the high temperature of the central star, this indicates that WS35 is close to the endpoint of its post-merger evolution. Since WS35 is more luminous than the \( 1 . 4 9 \, \mathbf { M } _ { \odot } \) model of Schwab et al.8, it appears likely that its mass also exceeds the Chandrasekhar limit, with the exciting perspective that it will produce a low-mass neutron star in the near future, accompanied

by a high-energy transient and a fast evolving supernova11. It is also likely that the inner shell of the circumstellar nebula will persist until the explosion and, given the expected low mass of supernova ejecta, will affect the appearance of the supernova remnant ∼ 100 yr after explosion.

The merging of two stars in a binary system is not a rare event. About 10 per cent of the massive main sequence stars are thought to be merger products27, as well as a similar fraction of the known white dwarfs28. The very unusual wind of WS35 strongly supports the idea that stellar mergers can indeed produce highly magnetized stars, which would explain the magnetic stars of the upper main sequence29 and the formation of the magnetic white dwarfs26. Our results also enlighten the ongoing debate on whether a super-Chandrasekhar mass merger of two carbon-oxygen white dwarfs leads to a Type Ia supernova. Here, WS35 appears to provide a counter example, which will likely produce a neutrino-flash and a gamma-ray burst30, followed by a very fast and subluminous Type Ic supernova11.

1. Hulse, R. A. & Taylor, J. H. Discovery of a pulsar in a binary system. Astrophys. J. 195, L51–L53 (1975).

2. Abbott, B. P. et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016).

3. Abbott, B. P. et al. Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A. Astrophys. J. 848, L13 (2017).

4. Iben, I. & Tutukov, A. V. Supernovae of type I as end products of the evolution of binaries with components of moderate initial mass (M not greater than about 9 solar masses). Astron. Astrophys. Supp. 54, 335–372 (1984).

5. Pakmor, R., et al. Violent mergers of nearly equal-mass white dwarf as progenitors of sublu-minous Type Ia supernovae, Astron. Astrophys. 528, A117 (2011).

6. Saio, H. & Nomoto, K. Off-center carbon ignition in rapidly rotating, accreting carbon-oxygen white dwarfs. Astrophys. J. 615, 444–449 (2004).

7. Shen, K. J., Bildsten, L., Kasen, D. & Quataert, E. The long-term evolution of double white dwarf mergers. Astrophys. J. 748, 35 (2012).

8. Schwab, J., Quataert, E. & Kasen, D. The evolution and fate of super-Chandrasekhar mass white dwarf merger remnants. Mon. Not. R. Astron. Soc. 463, 3461–3475 (2016).

9. Ji, S. et al. The post-merger magnetized evolution of white dwarf binaries: The double-degenerate channel of sub-Chandrasekhar Type Ia supernovae and the formation of magne-tized white dwarfs. Astrophys. J. 773, 136–149 (2013).


In this prospectus, unless the context otherwise requires, the following expressions have the following meanings.

“2016 Decision”	 the Decision of the Standing Committee of the NPC on
Amending the Private Schools Promotion Law (全國人民代
表大會常務委員會關於修改<中華人民共和國民辦教育促進
法>的決定), which was promulgated on November 7, 2016,
and came into force on September 1, 2017

“2021 Imlpementation Rules”	 the Imlipementaton Rules for the Law for Promoting Private
Education of the PRC (《中華人民共和國民辦教育促進法
實施條例》), which was promulgated by the State Council
on May 14, 2021 and will take effect from September 1,
2021

“affiliate(s)”	 with respect to any specific person, any other person,
directly or indirectly, controlling or controlled by or under
direct or indirect common control with such specified
person

“AliiFppcaton orm(s)”	WHITE alifppcation orm(s), YELLOW aliippcaton form(s)
and GREEN alifppcation orm(s), or where the context so
requires, any one of them, in relation to the Hong Kong
Public Offering

“Articles of Association” or
“Articles”	the amended and restated articles of association of our
Company conditionally adopted on June 23, 2021 and
effective upon the Listing Date and as amended from time to
time, a summary of which is set out in Appendix IV to this
prospectus

“associate(s)”	 has the meaning ascribed to it under the Listing Rules

“Board” or “Board of Directors”	 the board of Directors

“BPPE”	 California Bureau for Private Postsecondary Education, a
unit of the California Department of Consumer Affairs in
charge of regulation of private postsecondary educational
institutions operating in the State of California, the United
States

“Business Cooperation Agreement”	 the business cooperation agreement entered into by and
among Lingnan WFOE, the PRC Affiliated Entities and the
Reistered Shareholders dated November 21, 2020g

“Business Day” or “business day”	 a day on which banks in Hong Kong are generally open for
business to the public and which is not a Saturday, Sunday
or public holiday in Hong Kong

“BVI”	 the British Virilgn Isands

“Caiiptalzation Issue”	 the issue of Shares uipon caiptalzation of certain sums
standing to the credit of the share premium account of our
Company as set out in “A. Further Information about Our
Company — 4. Written Resolutions of the Then
Shareholders Passed on June 23, 2021” in Appendix V to
this prospectus

“CCASS”	 the Central Clearing and Settlement System established and
operated by HKSCC

“CCASS Clearing Participant”	 a person admitted to participate in CCASS as a direct
clearing participant or general clearing participant

“CCASS Custodian Participant”	 a person admitted to participate in CCASS as a custodian
participant

“CCASS Investor Participant”	 a person admitted to participate in CCASS as an investor
participant who may be an individual orj oint individuals or
a corporation

“CCASS Participant”	 a CCASS Clearing Participant, or a CCASS Custodian
Participant or a CCASS Investor Participant

“Chi na” or“PRC”	 the Peolbipe’s Relpuc of China excluding for the purpose of
this prospectus, Hong Kong, the Macau Special
Administrative Reion and Taigwan

“China Foreign Education”	 China Foreign Education Limited, a limited liability
company incorporated under the laws of the BVI on August
9, 2018 and is wholly owned by Ms. He Huifen, and is one
of our Controlling Shareholders

“Co-manager”	 the co-manager as named in the section headed “Directors
and Parties Involved in the Global Offering”

“Companies Act” or “Cayman
Companies Act”	the Companies Act, Cap. 22 (Act 3 of 1961, as combined
and revised) of the Cayman Islands


“window potential” of a chosen functional form. The form of this potential is given by:

\[ W _ { i } ( s ) = \left\{ \begin{array} { l l } { \infty , \qquad s < s _ { i } ^ { \mathrm { m i n } } } & { } \\ { 0 , \qquad s _ { i } ^ { \mathrm { m i n } } < s < s _ { i } ^ { \mathrm { m a x } } } & { } \\ { \infty , \qquad s > s _ { i } ^ { \mathrm { m a x } } } & { } \end{array} \right. \qquad ( 7 ) \]

where \( s _ { i } ^ { \mathrm { m i n } } \) and \( s _ { i } ^ { \mathrm { m a x } } \) are the limits that define the range of s for the i-th window. Within each “window” of s, a probability distribution \( p _ { i } ( s ) \) is calculated in the simu-lation. The window potential width, \( \Delta s \equiv s _ { i } ^ { \mathrm { m a x } } - s _ { i } ^ { \mathrm { m i n } } \), is chosen to be sufficiently small that the variation in F does not exceed a few \( k _ { \mathrm { B } } T \). Adjacent windows overlap, and the SCH algorithm uses the \( p _ { i } ( s ) \) histograms to re-construct the unbiased distribution, \( \mathcal { P } ( s ) \). The details of the histogram reconstruction algorithm are given in Ref. 46. A description for an application to a physical system comparable to that studied here is presented in Ref. 32.

Polymer configurations were generated carrying out single-monomer moves using a combination of trans-lational displacements and crankshaft rotations. The trial moves were accepted with a probability \( \begin{array} { r l } { p _ { \mathrm { a c c } } } & { { } = } \end{array} \)\( \operatorname* { m i n } ( 1 , e ^ { - \Delta E / k _ { \mathrm { B } } T } ) \), where \( \Delta F \) is the energy difference be-tween the trial and current states. Initial polymer con-figurations were generated such that s was within the allowed range for a given window potential. Prior to data sampling, the system was equilibrated. As an il-lustration, for a \( N \) = 121 polymer chain, the system was equilibrated for typically \( \sim \mathrm { 1 0 ^ { 7 } } \) MC cycles, following which a production run of \( \sim 1 0 ^ { 8 } \) MC cycles was carried out. During each MC cycle a move for each monomer is attempted once, on average.

The windows are chosen to overlap with half of the adjacent window, such that \( s _ { i } ^ { \mathrm { m a x } } = s _ { i + 2 } ^ { \mathrm { m i n } } \). The window width was typically \( \Delta s \, = \, \sigma \). Thus, a calculation for \( N \)= 121, where the translocation coordinate spans a range of \( s \, \in \, [ 0 , 1 2 0 ] \), required separate simulations for 239 different window potentials. For each simulation, individual probability histograms were constructed using the binning technique with 10 bins per histogram.

The free energy functions obtained from the MC sim-ulations were used with the procedure summarized in Sec. III to study the translocation dynamics under the as-sumption that conformational quasi-equilibrium is main-tained during the process. The translocation probability \( \mathcal { W } ( s , t ; s _ { 0 } , 0 ) \) was determined by solving Eq. (1) for a cho-sen value of \( s _ { 0 } \). Typically, we used \( s _ { 0 } = L / ( 2 \sigma ) \), at which point the first monomer isj ust on the verge of exiting the pore into the cavity. The equation was solved using standard numerical methods with a “spatial” grid size of \( \Delta s \) = 0.01 and a time increment of \( \Delta t = 0 . 0 0 2 \mathcal { D } ^ { - 1 } \). The distribution \( P ( \tau ) \) was calculated using Eq. (3), where a standard five-point method was used to evaluate the derivatives in Eq. (2). The translocation probability, \( p _ { b } \), and mean first passage time, \( \langle \tau \rangle \), were calculated by nu-merical integration of Eqs. (4) and (6), respectively, using Simpson’s rule.

In the results presented below, quantities of length are measured in units of \( \sigma \), energy in units of \( k _ { \mathrm { B } } T \), force in units of \( k _ { \mathrm { B } } T / \sigma \) and time in units of \( \mathcal { D } ^ { - 1 } \).

We consider first the case of spherical cavities in the absence of a driving force or adsorption potential, i.e. \( r \) = 1, \( f _ { \mathrm { d } } \, = \, 0 \) and \( \epsilon \) = 0. Figure 2 shows free energy functions for cavity volumes of V =150, 250 and 500, each for polymer lengths ranging from N=31 to N=141. As expected, the free energy cost of confining the polymer in the cavity increases as the confinement volume decreases. In addition, the curves all have positive curvature every-where except at near the upper and lower bounds. This indicates that free energy cost of inserting each monomer into the cavity increases as the number (and hence den-sity) of monomers inside increases. This feature is con-sistent with results from previous MC studies27,32,33 and theoretical studies16,26 that explicitly account for repul-sion between monomers, in contrast to the case for ideal polymers.15 Another noteworthy feature is the strong de-gree of overlap between the curves for different N and the same V . Thus, the free energy cost of transferring one monomer from the outside to the inside of the cavity de-pends approximately only on the density of monomers in the cavity. Deviations from this trend are evident where F dips abruptly near \( s = N - \) 1.

FIG. 2. Free energy functions for several different polymer lengths for a cavity aspect ratio of \( r \) = 1. Results for three different cavity volumes are shown.

To provide a quantitative analysis of the free en-ergy functions, we employ a standard scaling theory approach.23 We first recall that the standard form of the entropic free energy barrier for translocation of a polymer through a narrow pore in a flat wall of negligible thick-ness is \( F _ { 0 } / k T = ( 1 - \lambda ) \ln [ m ( N - m ) ] \), where m segments lie on one side of the pore, and \( N - m \) lie on the other

and where \( \lambda \) = 0.69 is a critical exponent.1 This expres-sion can easily be modified to account for the case of a channel in a wall of finite thickness.45 To account for the effect of confinement of the monomers inside the cavity, we consider the case where this part of the polymer is in the semi-dilute regime. Here, the confined portion of the polymer can be viewed as a collection \( n _ { \mathrm { t } } \) blobs, each of size \( \xi \sim \sigma \phi ^ { \nu / ( 1 - 3 \nu ) } \), where \( \nu \) is the Flory exponent. It is easily shown that the confinement free energy scales as23 \( \Delta F _ { \mathrm { c } } / k T = n _ { \mathrm { b } } \approx ( V / \sigma ^ { 3 } ) ^ { - 1 / ( 3 \nu - 1 ) } m ^ { 3 \nu / ( 3 \nu - 1 ) } \), where m is the number of monomers in the cavity. For a finite length nanochannel that is spanned by an average of \( n _ { \mathrm { p } } \) bonds, we note that \( m = s - n _ { \mathrm { p } } / 2 \). For the pore length \( L \) = 1.3 used here, we estimate \( n _ { \mathrm { p } } \, = \, 2 \) when the pore is filled. Thus, the total free energy, F, is expected to satisfy

where we have used \( \nu \) =35. This approximation is valid when \( n _ { \mathrm { p } } / 2 \, < \, s \, < \, N \, - \, 1 \, - \, n _ { \mathrm { p } } / 2 \). Over most of the range of s, \( n _ { \mathrm { p } } \) is constant, the logarithmic term \( F _ { 0 } \) is negligible. Only near the upper and lower bounds of s is the variation of \( F _ { 0 } \) appreciable. This feature, as well as a partial emptying of the pore, accounts for the dips in F near \( s = N - \) 1. Otherwise F is dominated by the confinement free energy of the cavity. In the case of fixed V , F is predicted to increase with s independent of the polymer length N. In addition, the variation of F with s has positive curvature, and F increases with decreasing V . These predictions are qualitatively consistent with the data.

The use of the semi-dilute approximation to estimate free energy of confinement in the cavity is expected to be valid only over a restricted range of densities. In Ref. 48 it was shown that the predictions are valid only up to packing fractions of \( \phi \, \approx \) 0.15, where \( \phi ~ \equiv ~ \pi N \sigma ^ { 3 } / 6 V \). Beyond this value the number of monomers per blob is unacceptably low. A lower limit on \( \phi \) is imposed by the condition that the number of blobs, \( n _ { \mathrm { b } } = N \dot { \phi } ^ { 1 / ( 3 \nu - \ddot { 1 } ) } \), be sufficiently large. For the polymer lengths considered in this work, it is difficult to find a range of s that satisfies both conditions simultaneously. To analyze the data, we use a more relaxed condition for low density and consider the case where \( n _ { \mathrm { b } } \ge 3 \).

Figure 3 shows the results of fits using Eq. (8) for \( N \)= 121 and various cavity volumes. The free energy functions have been shifted by \( F _ { 0 } ( s ) \), which is the free energy function for a flat wall that was calculated ex-plicitly by simulation. We use a fitting function of the form \( F - F _ { 0 } = c _ { 0 } + c _ { 1 } ( s - 1 ) ^ { - \alpha } \). The lower limit of the range of the fit is indicated in the plot, while the fitting function is deliberately extrapolated beyond the upper limit of the fitting range to illustrate the divergence of the prediction from the simulation results at high den-sity. The upper limit itself is explicitly labeled for two of the functions. Note that scaling predictions underes-timate the free energy in the region where \( \phi \geq \) 0.15. This is consistent with the observation noted in Ref. 48 that the confinement free energy crosses over into a concen-trated regime where the excluded volume interactions are screened, which leads to a higher value of \( \alpha \). From the fit to the data in the valid range, it was found that \( ^ { \prime \prime } \)=1.9, 2.0 and 1.9 for V =150, 250 and 500, respectively. This is somewhat below the predicted value of \( ^ { o } \) = 2.25. Not-ing the expected dependence of \( c _ { 1 } \propto V ^ { - \beta } \) where \( \beta \)=1.25, the ratio of \( c _ { 1 } \) measured for V =500 and \( V \)=250 yields \( \beta \)= 0.9, while the ratio for V =500 and V =150 yields \( \beta \)=1.1. Thus, the measured values of the exponents \( \alpha \) and \( \beta \) both deviate from the predicted values. Undoubt-edly, this is arises from failing to properly satisfy the condition that \( n _ { \mathrm { b } } \gg 1 \). We speculate that better sat-isfying this condition would yield improved agreement. However, this would necessitate using polymer chains at least an order of magnitude larger than those considered here, which is not feasible for us at present.

FIG. 3. Free energy functions for polymers of length \( N \) = 121 and a spherical cavity of various volumes. The dashed black lines show fits to the data in the region for which \( n _ { \mathrm { b } } \ge 3 \) and \( \phi < \) 0.15. The lower limit of this range is evident from the minimum s for the fitting curves, and the upper end of this range is explicitly labeled for two of the curves. For V =500, the upper limit extends beyond the range of the data.

Next we consider the effects of the anisometry of the confining cavity. Figure 4 shows free energy functions for chains of length \( N \)= 101 in a cavity of volume \( V \)= 500. Figure 4(a) shows results for prolate ellipsoidal cavities (\( r > \) 1) and Fig. 4(b) shows results for oblate cavities (\( r < \) 1). In each case, the result for spherical cavities is also shown, for comparison. The most notable feature here is the fact that deviations from spherical symmetry in either direction lead to an increase in the free energy. Note, however, that the curves for oblate cavities follow the opposite trend at low s (see the inset of Fig. 4(b)), in contrast to the case for prolate cavities. The explana-tion for this difference is straightforward. As the first few monomers enter the cavity, the effects of confinement are felt mainly by the curvature of the cavity wall near the


The LMSR ships are not armed and do not have a combat system. They do have a \( \mathbf { C } ^ { 3 } \) I suite sufficient to perform their intended mission in conjunction with other naval vessels.

The program currently plans for 19 ships, five of which are conversions of existing commercial container vessels, and 14 of which will be newly constructed ships. All 19 ships use common cargo handling systems procured by the Navy. Three contractors are building LMSRs. A performance type procurement description was used; therefore specific ship configurations differ as the respective builders interpret the mission requirements.

The current TEMP was approved in June 1996. In view of the single ship mission and similarities in the LMSR configurations, the test approach is for a single ship class, with four "flights." A mix of operational test events and operational assessments will address the minor hardware variance.

As non-developmental items, DT has been limited, focusing on production assurance testing in conjunction with the builders. Systems and integration testing is witnessed by Navy, U.S. Coast Guard, and American Bureau of Shipping representatives.

Operational Testing (OT-IIA) of the LSMR conversion ship was planned and administered in accordance with the DOT&E-approved TEMP and OT Plan. OT-IIA was conducted during September 1996, aboard United States Naval Ship (USNS) Shughart (T-AKR 295) at Savannah, GA and Norfolk, VA. The OT was conducted in conjunction with a planned Army sealift deployment exercise, which moved a representative load of Army equipment (over 1,000 pieces and included tanks, trucks and various helicopters) from the 3d Infantry Division in Savannah, GA to Ft. Story, VA. The USNS Shughart was assessed as operationally effective and potentially operationally suitable. No significant deficiencies were observed.

Due to cracking cloverleaf tie downs on the decks of the USNS BOB HOPE, the operational test (OT-IIB) scheduled for USNS BOB HOPE in July 1998, was rescheduled to 1QFY99. OT-IIB was subsequently rescheduled for 3QFY00 and the USNS FISHER was designated the OT-IIB test article.

An OA of the first NASCO new construction LMSR ship, USNS WATSON, was conducted in FY99. Assessment and reporting of the assessment by the Multi-service Test Team have not been completed and will be reported in the FY00 Annual Report. Initial observations of the USNS WATSON loadout are: (1) the NASCO new construction LMSR ships are easier to load compared to the two classes of renovation LMSR ships previously evaluated; (2) the NASCO new construction LMSR ship holds approximately one-third more cargo than two renovation classes of LMSR ships; (3) efficient stow planning was hindered by inaccurate ship data (repeat finding); and (4) the final stowage plan did not appear to take full advantage of all available space (either additional equipment could have been stowed or available space could have been used to facilitate the exercise and maintenance of pre-positioned equipment).

The multi-Service Test Team spent most of this year refining plans for the OT-IIB to be conducted 3QFY00. To potentially reduce the scope of required testing on OT-IIB, plans were developed to capture useful pier-side on-load/off-load data from the BRIGHT STAR exercise in

1QFY00. That effort was intended to satisfy data requirements to assess two of the 17 critical operational issues associated with the Strategic Sealift Program. Although extremely useful for providing insights to the Strategic Sealift System, the BRIGHT STAR pier-side data collected was not sufficient to completely satisfy the two critical operational issues being examined. The scope of OT IIB will not be adjusted based on this data. It appears that OT IIB will slip yet again from the 3QFY00 date due to competing requirements for critical units needed for the major portions of the test.

Based on the results of OT-IIA, the strategic sealift ship (NASCO conversion) is assessed to be operationally effective and potentially operationally suitable. No significant deficiencies were observed however, limited strategic sealift “in-the-stream” data were collected during OT-IIA. Strategic sealift “in-the-stream” data need to be fully developed.

OT-IIB, scheduled to be conducted April-May 2000, is designed to examine the Avondale new construction ship as part of the strategic sealift system and focused on the surge sealift mission, as well as ship offload “in-the-stream.” A Strategic Sealift System shortfall currently being addressed, but not as part of the Strategic Sealift ship program, has to with the supporting lighterage. Shortfalls in the lighterage system (capability, inventory, and doctrine) could adversely affect the U.S.’s ability to project power in a timely manner in situations where adequate port facilities are not available. This situation is significant in that we may be able to get the force to a crisis in a timely fashion but, in some situations, be challenged to get the force off the ship. The overall class assessment will be made upon completion of the OT-IIB event and will include an evaluation of the ship’s ability to unload “in-the-stream” using current doctrine and presently fielded RO/RO Discharge Facilities. The class assessment will address the ship configurations from all three prime contractors.


Liabilities:

Commodity price derivative contracts	$    —	$        (99)	$    —	$            (99)

Interest rate derivative contracts	—	(257)	—	(257)

Total derivative instruments	$    —	$      (356)	$    —	$           (356)

The following table sets forth a reconciliation of changes in the fair value of financial assets and liabilities classified as Level 3 in the fair value hierarchy:

	2016	2015

(in thousands)

Unobservable inputs at January 1,	$         (5,933)	$        (6,470)

Total gains	11,838	5,151

Settlements	(5,905)	(4,614)

Unobservable inputs at December 31,	$      —	$         (5,933)

Change in fair value included in earnings related to
derivatives still held as of December 31,	$      —	$         (2,925)

During periods of market disruption, including periods of volatile oil and natural gas prices, there may be certain asset classes that were in active markets with observable data that become illiquid due to changes in the financial environment. In such cases, more derivative instruments, other than the range bonus accumulators, may fall to Level 3 and thus require more subjectivity and management judgment. Further, rapidly changing commodity and unprecedented credit and equity market conditions could materially impact the valuation of derivative instruments as reported within our consolidated financial statements and the period-to-period changes in value could vary significantly. Decreases in value may have a material adverse effect on our results of operations or financial condition.

We apply the provisions of ASC Topic 350 “Intangibles-Goodwill and Other.” Goodwill represents the excess of the purchase price over the estimated fair value of the net assets acquired in business combinations. Goodwill is assessed for impairment annually on October 1 or whenever indicators of impairment exist. The goodwill test is performed at the reporting unit level, which represents our oil and natural gas operations in the United States. If indicators of impairment are determined to exist, an impairment charge is recognized if the carrying value of goodwill exceeds its implied fair value. We utilize a market approach to determine the fair value of our reporting unit. Any sharp prolonged decreases in the prices of oil and natural gas as well as any continued declines in the quoted market price of the Company’s units could change our estimates of the fair value of our reporting unit and could result in an impairment charge. We consider the fair value estimate for goodwill as a Level 3 input, as the valuation includes inputs and assumptions that are less observable or require greater estimation.

At the respective measurement dates of March 31, 2016, June 30, 2016, September 30, 2016 and December 31, 2016, the carrying value of our reporting unit was negative. Therefore the Company was required to perform the

second step of the goodwill impairment test at these interim dates. The fair value amount of the assets and liabilities were calculated using a combination of a market and income approach as follows: equity, debt and certain oil and gas properties were valued using a market approach while the remaining balance sheet assets and liabilities were valued using an income approach. Furthermore, significant assumptions used in calculating the fair value of our oil and gas properties include: (i) observable forward prices for commodities at the respective measurement date and (ii) a 10% discount rate, which was comparable to discount rates on recent transactions. Based on the results of the the second step of the interim goodwill impairment test, we recorded a non-cash goodwill impairment loss of \$252.7 million during the quarter ended September 30, 2016 to write the goodwill down to its estimated fair value of \$253.4 million. Based on our estimates, the implied fair value of our reporting unit exceeded its carrying value at the measurement dates of March 31, 2016, June 30, 2016, and December 31, 2016, therefore no additional impairment loss was recorded for the year ended December 31, 2016. Based on evaluation of qualitative factors, we determined that the goodwill impairment was primarily a result of the decline in the prices of oil and natural gas as well as deteriorating market conditions and the decline in the market price of our common units. Any further significant decline in the prices of oil and natural gas as well as any continued declines in the quoted market price of the Company’s units could change our estimate of the fair value of the reporting unit and could result in an additional impairment charge.

Our nonfinancial assets and liabilities that are initially measured at fair value are comprised primarily of assets acquired in business combinations and asset retirement costs and obligations. These assets and liabilities are recorded at fair value when acquired/incurred but not re-measured at fair value in subsequent periods. We classify such initial measurements as Level 3 since certain significant unobservable inputs are utilized in their determination. A reconciliation of the beginning and ending balance of our asset retirement obligations is presented in Note 7, in accordance with ASC Topic 410-20 “Asset Retirement Obligations.” During the years ended December 31, 2016 and 2015, in connection with the oil and natural gas properties acquired in all of our acquisitions, the LRE and Eagle Rock Mergers, as well as new wells drilled during each year, we incurred and recorded asset retirement obligations totaling \$0.7 million and \$90.9 million, respectively, at fair value. We also recorded a \$1.3 million and a \$22.3 million change in estimate as a result of revisions to the timing or the amount of our original undiscounted estimated asset retirement costs during the years ended December 31, 2016 and 2015, respectively. The

fair value of additions to the asset retirement obligation liability and certain changes in the estimated fair value of the liability are measured using valuation techniques consistent with the income approach, converting future cash flows to a single discounted amount. Inputs to the valuation include: (1) estimated plug and abandonment cost per well based on our experience; (2) estimated remaining life per well based on average reserve life per field; (3) our credit-adjusted risk-free interest rate ranging between 4.6% and 5.5%; and (4) the average inflation factor (2.0%). These inputs require significant judgments and estimates by the Company’s management at the time of the valuation and are the most sensitive and subject to change.

The asset retirement obligations as of December 31, 2016 and 2015, reported on our Consolidated Balance Sheets and the changes in the asset retirement obligations for the year ended December 31, 2016 were as follows:


# (a) Particulars of principal subsidiaries of the Group at 31 December 2018 are set out below (continued):

Name	Place of incorporation
and legal status	Principal activities/
place of operation	Proportion of
ordinary shares
directly held
by parent (%)	Proportion of
ordinary shares
held by the
Group (%)	Proportion of
ordinary shares
held by
non -controlling
interests (%)

中山市凱茵豪園房地產開發有限公司
 Zhongshan Greenville Realty
 Development Co., Ltd. (note (i))	PRC/wholly foreign
 owned enterprise	Property development/
 Mainland China	—	100%	 —

中山市雅建房地產發展有限公司
 Zhongshan Ever Creator Real Estate
 Development Co., Ltd. (note (i))	PRC/wholly foreign
 owned enterprise	Property development/
 Mainland China	—	100%	 —

廣州雅居樂房地產開發有限公司
 Guangzhou Agile Real Estate
 Development Co., Ltd. (note (i))	PRC/wholly foreign
 owned enterprise	Property development/
 Mainland China	—	100%	 —

佛山市雅居樂房地產有限公司
 Foshan Agile Real Estate Development
 Co., Ltd. (note (i))	PRC/wholly foreign
 owned enterprise	Property development/
 Mainland China	—	100%	 —

南京雅居樂房地產開發有限公司
 Nanjing Agile Real Estate Development
 Co., Ltd. (note (i))	PRC/wholly foreign
 owned enterprise	Property development/
 Mainland China	—	100%	 —

河源市雅居樂房地產開發有限公司
 Heyuan Agile Real Estate Development
 Co., Ltd. (note (i))	PRC/wholly foreign
 owned enterprise	Property development/
 Mainland China	—	100%	 —

海南清水灣控股有限公司
 Hainan Clearwater Bay Holdings Limited	BVI/Limited liability
 company	Investment holding/BVI	 —	100%	 —

海南雅居樂房地產開發有限公司
 Hainan Agile Real Estate Development
 Co., Ltd. (“Hainan Agile”) (note (i))	PRC/foreign invested
 enterprise	Property development/
 Mainland China	—	100%	 —

Name	Place of incorporation
and legal status	Principal activities/
place of operation	Proportion of
ordinary shares
directly held
by parent (%)	Proportion of
ordinary shares
held by the
Group (%)	Proportion of
ordinary shares
held by
non -controlling
interests (%)

海南雅恒房地產發展有限公司
 Hainan Yaheng Real Estate Development
 Co., Ltd. (“Hainan Yahen”g) (note (i))	PRC/foreign invested
 enterprise	Property development/
 Mainland China	—	100%	 —

廣州從化雅居樂房地產開發有限公司
 Guangzhou Conghua Agile Real Estate
 Development Co., Ltd. (note (i))	PRC/wholly foreign
 owned enterprise	Property development/
 Mainland China	—	100%	 —

四川雅居樂房地產開發有限公司
 Sichuan Agile Real Estate Development
 Co., Ltd. (note (i))	PRC/wholly foreign
 owned enterprise	Property development/
 Mainland China	—	100%	 —

佛山巿三水雅居樂房地產有限公司
 Foshan Sanshui Agile Real Estate
 Development Co., Ltd. (note (i))	PRC/wholly foreign
 owned enterprise	Property development/
 Mainland China	—	100%	 —

惠州白鷺湖旅遊實業開發有限公司
 Huizhou Bailuhu Tour
 Enterprise Development Co., Ltd.
 (note (i))	PRC/foreign invested
 enterprise	Property development/
 Mainland China	—	100%	 —

陝西昊瑞房地產開發有限責任公司
 Shanxi Haorui Real Estate Development
 Co., Ltd. (note (i))	PRC/limited liability
 Company	Property development/
 Mainland China	—	100%	 —

上海靜安城投重慶置業有限公司
 Sh’anghai Jingan Chengtou Chongqing
 Land Co., Ltd. (note (i))	PRC/wholly foreign
 owned enterprise	Property development/
 Mainland China	—	100%	 —

上海雅恒房地產開發有限公司
 （前稱上海金昌房地產開發有限公司)
 Shanghai Yaheng
 Real Estate
 Development Co., Ltd.
 (formerly named Shanghai Jinchang Real
 Estate Development Co., Ltd.) (note (i))	PRC/wholly foreign
 owned enterprise	Property development/
 Mainland China	—	100%	 —


# ②本期计提、收回或转回的坏账准备情况

# ③其他应收款按款项性质披露

# ④按欠款方归集的其他应收款期末余额前五名单位情况

本期按欠款方归集的期末余额前五名其他应收款汇总金额 434,096,527.04 元，占其他应收款期末余额合计数的比例 53.79%，相应计提的坏账准备期末余额汇总金额 49,842,674.95 元。

被投资单位	期初余额	本期增加	本期
减少	期末余额	本期计提
减值准备	减值准备
期末余额

金坛思源节能科技有
限公司	10,000,000.00	-	-	10,000,000.00	-	-

# （2）对联营、合营企业投资详见本报告附注五、9。

# 4、营业收入和营业成本

# 1、当期非经常性损益明细表

项 目	本期发生额	说明


坏账准备计提的具体说明：

# ①于 2021 年 12 月 31 日，按单项计提坏账准备的应收账款

# ②于 2021 年 12 月 31 日，按账龄计提坏账准备的应收账款

按组合计提坏账准备的确认标准及说明见附注三、10。

# （3）本期坏账准备的变动情况

# （3）按欠款方归集的期末余额前五名的应收账款情况


acquire Intel's smartphone modem business.\2130\

\2129\ See Jordan Novet, Apple Buys an A.I. Start-up that Came from Microsoft Co-Founder Paul Allen's Research Lab, CNBC (Jan. 15, 2020), https://www.cnbc.com/2020/01/15/apple-acquires-xnor-ai-startup-that-spun-out-of-allen-institute.html; Mark Gurman, Apple Acquires AI Startup to Better Understand Natural Language, Bloomberg (Apr. 3, 2020), https://www.bloomberg.com/news/articles/2020-04-03/apple-acquires-ai-startup-to-better-understand-natural-language; Kif Leswing, Apple Buys Virtual Reality Company NextVR, CNBC (May 14, 2020), https://www.cnbc.com/2020/05/14/apple-buys-virtual-reality-company-nextvr.html; Kif Leswing, Apple Buys Fleetsmith, a Company Making It Easier to Deploy iPhones and Macs at Workplaces, CNBC (June 24, 2020), https://www.cnbc.com/2020/06/24/apple-acquires-device-management-company-fleetsmith.html; Jessica Bursztynsky, Apple Buys Popular Weather App Dark Sky and Plans to Shut Down Android Versions, CNBC (Mar. 31, 2020), https://www.cnbc.com/2020/03/31/apple-buys-popular-weather-app-dark-sky.html; Mark Gurman, Apple Buys Startup to Turn iPhones into Payment Terminals, Bloomberg (July 31, 2020), https://www.bloomberg.com/news/articles/2020-08-01/apple-buys-startup-to-turn-iphones-into-payment-terminals.

\2130\ Press Release, Apple, Apple to Acquire the Majority of Intel's Smartphone Modem Business (July 25, 2019), https://www.apple.com/newsroom/2019/07/apple-to-acquire-the-majority-of-intels-smartphone-modem-business/.

Apple has also recently acquired software companies to create a foundation from which it could launch new apps. For example, after purchasing the digital magazine subscription service Texture in 2018, Apple integrated most of Texture's functionality into its own Apple News+ service, which debuted the following year.\2131\ Similarly, one of Apple's largest purchases to date--its \$3 billion acquisition of Beats Electronics in 2014--was instrumental to the 2015 launch of Apple Music.\2132\ Apple sought to grow Apple Music quickly after its introduction. Apple pre-installed the service on iPhones and made it the only music service accessible through Siri, Apple's virtual assistant. Apple also offered Apple Music with a free month trial period and made it available on Android devices. The strategy saw Apple gain 10 million paying subscribers within six months.\2133\ Apple supplemented its music services business in 2018 by acquiring the music recognition app Shazam, and most recently, by acquiring podcast app Scout FM in 2020.\2134\

\2131\ Anita Balakrishnan, Apple Buys Texture, a Digital Magazine Subscription Service, CNBC (Mar. 12, 2018), https://www.cnbc.com/2018/03/12/apple-buys-texture-a-digital-magazine-subscription-service.html.

\2132\ Billy Steele, Apple's \$3 Billion Purchase of Beats Has Already Paid Off, Engadget (May 28, 2019), https://www.engadget.com/2019-05-28-apple-beats-five-years-later.html.

\2133\ Neth. Auth. for Consumers & Mkts. Study at 62.

\2134\ Press Release, Apple, Apple Acquires Shazam, Offering More Ways to Discover and Enjoy Music (Sept. 24, 2018), https://www.apple.com/newsroom/2018/09/apple-acquires-shazam-offering-more-ways-to-discover-and-enjoy-music/; Mark Gurman, Apple Buys Startup that Creates Radio-Like Stations for Podcasts, Bloomberg (Sept. 24, 2020), https://www.bloomberg.com/news/articles/2020-09-24/apple-buys-startup-that-creates-radio-like-stations-for-podcasts.

It is common for Apple to integrate apps it purchases into its own pre-existing apps or into the iOS mobile operating system. Examples of this include the 2014 acquisition of Swell, a podcast app, and the 2013 acquisition of HopStop, a transit navigation app.\2135\

\2135\ Chris Gayomali, Swell Shuts Down Following Apple Acquisition, Fast Co. (July 29, 2014), https://www.fastcompany.com/3033698/swell-shuts-down-following-apple-acquisition; Andrew Nusca, Apple Maps vs. Google Maps Heats Up as Apple Shuts Down HopStop, Fortune (Sept. 12, 2015), https://fortune.com/2015/09/12/hopstop-apple-

Apple has followed a similar strategy for integrating the Dark Sky weather app. Apple shut down Dark Sky's Android app in August 2020 and plans to integrate the app's features with the iPhone's Weather widget on iOS 14.\2136\ In addition to its app, Dark Sky supplied data to independent weather apps, like Carrot, Weather Line, and Partly Sunny. As a result of Apple's takeover of Dark Sky, independent weather apps will lose access to the inexpensive, hyper-local weather data that Dark Sky supplied, leading some weather apps to shut down and others to rely on higher-priced suppliers for forecast data.\2137\

\2136\ Hannah Klein, The Dark Sky Android App is Officially Kaput, Slate (Aug. 4, 2020), https://slate.com/technology/2020/08/dark-sky-app-android-shuts-down.html.

\2137\ Jared Newman, Apple's Dark Sky Acquisition Could Be Bad News for Indie Weather Apps, Fast Co. (Apr. 2, 2020), https://www.fastcompany.com/90485131/apples-dark-sky-acquisition-could-be-bad-news-for-indie-weather-apps. But see CEO Hearing at 403 (response to Questions for the Record of Tim Cook, CEO, Apple, Inc.) (noting Dark Sky will \`\`continue to make its API available to Dark Sky's existing customers until the end of 2021'').

(i) Commissions and In-App Purchases. The Committee sought information regarding Apple's policy of collecting commissions from apps sold through the App Store and purchases made in iOS apps. Apple charges a 30 percent commission on paid apps--those that charge a fee for users to download--downloaded from the App Store. It also takes a 30 percent fee for in-app purchases (IAP) of \`\`digital goods and services.''\2138\ For app subscriptions, Apple charges a 30 percent commission for the first year and a 15 percent commission for subsequent years.\2139\ Apps are not permitted to communicate with iOS users that the app may be available for purchase at a lower price outside the App Store, provide links outside of the app that may lead users to find alternative subscription and payment methods, or offer their own payment processing mechanism in the app to avoid using Apple's IAP.\2140\ Apps that violate Apple's policies can be removed from the App Store, losing access to the only means of distributing apps to consumers with iOS devices.\2141\

\2138\ App Store: Dedicated to the Best Store Experience for Everyone, Apple, https://www.apple.com/ca/ios/app-store/principles-practices/ (last visited Oct. 4, 2020).

\2140\ See Innovation and Entrepreneurship Hearing at 584-85 (response to Questions for the Record of Kyle Andeer, Vice President, Corp. Law, Apple, Inc.); Submission from ProtonMail, to H. Comm. on the Judiciary, 5 (Aug. 22, 2020) (on file with Comm.); Interview with Source 143 (Aug. 27, 2020).

\2141\ See, e.g., Sara Morrison, Apple's Fortnite Ban, Explained, Vox: Recode (Sept. 8, 2020), https://www.vox.com/recode/2020/8/20/21373780/fortnite-epic-apple-lawsuit-app-store-antitrust; Nick Statt, Apple Doubles Down on Controversial Decision to Reject Email App Hey, Verge (June 18, 2020), https://www.theverge.com/2020/6/18/21296180/apple-hey-email-app-basecamp-rejection-response-controversy-antitrust-regulation.

Apple describes its policies as standard industry practice and says that other app stores charge the same fees.\2142\ In 2020, Apple funded a study that concluded that other software distribution platforms run by Google, Amazon, Samsung, Microsoft, and others charge identical or similar commissions on software downloads and transactions, and that commissions are common in other digital markets.\2143\ Apple also highlighted that its commissions are lower than the cost of software distribution by brick-and-mortar retailers, which dominated the marketplace prior to the introduction of the App


SEHK’s “ESG Reporting Guide”
Subject Area	Compliance with Relevant Laws and Regulations that are
Significant to Canvest

Social

Aspect B1: Employment
relating to compensation and dismissal,
recruitment and promotion, working
hours, rest periods, equal opportunity,
diversity, anti-discrimination, and other
benefits and welfare	Relevant laws and regulations that are significant to the
Group include Labour Law of the PRC, Labour Contract Law of
the PRC, Regulation on the Imlpementation of the Labour
Contract Law of the PRC, Social Insurance Law of the PRC,
Regulations on the Management of Housing Provident Fund,
Special Rules on the Labour Protection of Female Emlpoyees,
Provisions of the State Council on Working Hours of Workers
and Staff, Provisions on Minimum Wages, Imlpementation
Measures for Paid Annual Leave for Emlpoyees of Enterprises,
Measures for the Imlpementation of Administrative License for
Labour Dispatch, and Emloyment Ordpinance of HKSAR. The
above laws and regulations stipulate the legal obligations and
responsibility of employers to provide employment protection
and benefits, covering statutory obligations and responsibilities
which include compensation and dismissal, recruitment and
promotion, working hours, rest periods, equal opportunity,
diversity, anti-discrimination, and other benefits and welfare.
These laws and regulations are of great importance as they
offer appropriate protections to employees, the most
important asset of the Group.
In 2020, there were no confirmed cases of non-compliance or
complaints in relation to our employment practices that would
have a significant impact on the Group. Please refer to
chapter “Our People” on how Canvest ensures compliance
with applicable employment laws and regulations.

Aspect B2: Health and Safety
relating to providing a safe working
environment and protecting emlpoyees
from occupational hazards	Relevant laws and regulations that are significant to the
Group include Labour Law of the PRC, Work Safety Law of
the PRC, Labour Contract Law of the PRC, Prevention and
Control of Occupational Diseases Law of the PRC, Regulation
on Work-Related Injury Insurances, Special Rules on the
Labour Protection of Female Emloyees, and Provisions on thpe
Duration of Medical Treatment for Enterprise Staff and
Workers Due to Illness or Non-Work Related Injuries. These
laws and regulations provide clear requirements on the
provision of safe working environment and the prevention of
occupational hazards. Compliance with these laws and
regulations is paramount as workplace safety is of critical
importance to each and every employee of the Group.
In 2020, there were no confirmed cases of non-compliance or
complaints in relation to health and safety that would have a
significant impact on the Group. Please refer to chapter “Our
People” on how Canvest ensures compliance with applicable
laws and regulations relating to health and safety.

SEHK’s “ESG Reporting Guide”
Subject Area	Compliance with Relevant Laws and Regulations that are
Significant to Canvest

Aspect B4: Labour Standards	Relevant laws and regulations that are significant to the
Group include Criminal Law of the PRC Article 244,
Prevention and Control of Occupational Diseases Law of the
PRC, Rules for the Imlpementation of the Law of the PRC on
Foreign-Capital Enterprises Article 62, Regulation on Work-
Related Injury Insurances Article 66, Provisions on the
Prohibition of Using Child Labour, Law of the PRC on the
Protection of Minors, Regulations on Labour Protection in
Worklpaces Where Toxic Substances Are Used , and
Emloyment Ordinance of HKSApR. These laws and regulations
set out clear rules for preventing child labour and forced
labour, and elaborate on the legal obligations and
responsibility of employers who violate the relevant laws and
regulations. It is essential for us to conform to applicable laws
and regulations on labour standards as it reflects our
corporate values in honouring human rights.
In 2020, there were no confirmed cases of non-compliance or
complaints in relation to labour practices standards that would
have a significant impact on the Group. Please refer to
chapter “Our People” on how Canvest ensures compliance
with applicable laws and regulations relating to labour
standards.

relating to preventing child and forced
labour

Aspect B6: Product Responsibility	Relevant laws and regulations that are significant to the
Group include Tort Law of the PRC, which clarifies the tort
liability to protect the civil rights and interests, as well as the
Product Quality Law of the PRC, which places requirements on
health and safety relating to products and services provided
and methods of redress. It is the Group’s core value to abide
by these rules in providing safe and reliable products and
services with sincere attitude.
In 2020, there were no confirmed cases of non-compliance or
complaints in relation to product responsibility that would
have a significant impact on the Group. Please refer to
chapter “Our Sustainable Business” on how Canvest ensures
compliance with applicable laws and regulations relating to
product responsibility.

relating to health and safety,
advertising, labelling and privacy
matters relating to products and
services provided and methods of
redress


# (1). 对子公司投资

# (2). 对联营、合营企业投资

投资
单位	期初
余额	本期增减变动	期末
余额	减值
准备
期末
余额

追加
投资	减少
投资	权益
法下
确认
的投
资损
益	其他
综合
收益
调整	其他
权益
变动	宣告
发放
现金
股利
或利
润	计提
减值
准备	其他

一、合营企业

小计

二、联营企业

北京
黄河
旋风
鑫纳
达科	5,993
,843.
33							5,993
,843.
33			5,99
3,84
3.33

# 4、 营业收入和营业成本

# (1). 营业收入和营业成本情况

# (2). 合同产生的收入的情况


from the precisely measured lifetimes of the \( 6 p \, ^ { 2 } P _ { 1 / 2 } \) and \( 6 p ~ \AA ^ { 2 } \)\( ^ 2 P _ { 3 / 2 } \) states [35]. The other important E1 matrix elements are obtained using the RCC method in the sin-gles and doubles approximation (CCSD method) as de-scribed in [45, 46]. Contributions to \( \alpha _ { c } \) are determined using a relativistic random-phase approximation (RRPA) as described in [40]. It has been demonstrated that the RRPA method can give rise to very reliable results for the atomic systems having inert gas configurations [47].Smaller contributions from \( \alpha _ { c v } \) and from the high-lying excited states (tail contribution \( \alpha _ { t } \)) that are omitted in the above sum-over-states approach are estimated in the Dirac-Hartree-Fock (DHF) approximation.

It is not easy to get the dynamic electric permittivity of any real materials, so the convenient way of determin-ing these constants for simple metals such as gold is to use the Drude-Lorentz model as was done in Ref. [26]. In pursuance of obtaining more realistic values of these con-stants for different materials, we prefer to use the known real and imaginary parts of the refractive indices of a ma-terial at few real values of frequency \( \omega \). The imaginary parts of the dielectric permittivities of the materials can then be obtained using the relation

\[ I m \left[ \epsilon ( \omega ) \right] = 2 n ( \omega ) \kappa ( \omega ) , \eqno ( 9 ) \]

where \( n ( \omega ) \) and \( \kappa ( \omega ) \) are the respective real and imag-inary parts of the refractive index of a material at fre-quency \( \omega \). We use the optical data from the handbook by Palik [48] for the frequencies ranging from 0.1 eV to 10000 eV for Au metal to calculate \( I m [ \epsilon ( \omega ) ] \). Thereafter, the required real values of the dielectric constants at the imaginary frequencies \( ( \epsilon ( \iota \omega ) \)) are obtained by using the Kramers-Kronig formula. The available data, however, does not cover the whole frequency range to carry out the integration of Eq. (4). Thus, we extrapolate these val-ues for the lower frequencies to increase the domain over which the integrations are to be performed [49, 50]. For the frequencies below 0.1 eV, the classified values from[48] are extrapolated using the free electron Drude model in which the dielectric permittivity along the imaginary axis is represented as

\[ \epsilon ( \iota \omega ) = 1 - \frac { \omega _ { p } { } ^ { 2 } } { \omega ( \omega + \iota \gamma ) } , \eqno ( 1 0 ) \]

where \( \omega _ { p } = ( 2 \pi c / \lambda _ { p } ) \) is the plasma frequency and \( \gamma \) is the relaxation frequency. The optical data values for \( \omega _ { p } \) and \( \gamma \) available from various sources differ slightly, but we use these values as \( \omega _ { p } = 9 . 0 \) eV and \( \gamma \) = 0.035 eV as out-lined in [26, 49–51]. In case of Si (semiconductor),\( \mathrm { { S i O _ { 2 } } } \) (dielectric), Sapphire and YAG, the complex frequency-dependent dielectric permittivity are quoted for a wide range of energies in the handbook of Palik. Therefore, we use all these values for carrying out the integration and do not extrapolate any data. On the otherhand, experi-mental data of \( n ( \omega ) \) and \( k ( \omega ) \) for \( \mathrm { S i N _ { x } } \) are not available at all and we use Tauc-Lorentz model [33, 52] for esti-mating dielectric constants of this material.

TABLE III: Comparison of the calculated values of damping function \( f _ { 3 } ( a ) \) defined in Eq.(4) for different separation dis-tances a for the interaction of Cs atom with the gold surface.

TABLE IV: Comparison of \( C _ { 3 } \) coefficients ratios of Li, Na, K and Rb atoms with the Cs atom for the perfect conductor, metal, semiconductor and dielectric surfaces.

Again, the interactions between the ground states of atoms with an anisotropic surface have been studied be-fore [53, 54]. These studies demonstrate that for a uni-form birefringent dielectric surface, with the symmetry axis normal to the interface, the interaction potential de-scribed Eq. (3) is still applicable if \( \epsilon \) is replaced by an effective quantity \( \bar { \epsilon } \) defined as

\[ \bar { \epsilon } ( \iota \omega ) = \left[ \epsilon _ { | | } ( \iota \omega ) \epsilon _ { \bot } ( \iota \omega ) \right] ^ { \frac { 1 } { 2 } } , \eqno ( 1 1 ) \]

where \( \epsilon _ { | | } \) and \( \epsilon _ { \perp } \) are the respective dielectric permittiv-ities for the electric fields parallel and perpendicular to the interface between the atom and the dielectric surface.

The evaluation of \( C _ { 3 } \) coefficients requires the precise estimation of dynamic polarizabilities of the Cs atom. Table I presents the scalar polarizabilities of the Cs atom in its ground state along with the E1 matrix elements for different transitions that are used to estimate \( \alpha _ { v } \) and other contributions to the polarizabilities. The E1 ma-trix elements for the \( 6 S _ { 1 / 2 } { - } 6 P _ { 1 / 2 , 3 / 2 } \) transitions are taken from the experimentally measured data given in [35].Our calculated value of the scalar polarizability \( ( \alpha ( 0 ) ) \)

FIG. 2: (Color online) The retardation coefficient \( f _ { 3 } ( a ) \) for the Cs atom as a function of the distance a from a perfect conductor, Au (metal) metal and Si (semiconductor).

FIG. 3: (Color online) The retardation coefficient \( f _ { 3 } ( a ) \) for the Cs atom as a function of the distance a from the differ-ent dielectric surfaces such as \( \mathrm { { S i O _ { 2 } } } \),\( \mathrm { S i N } _ { \mathrm { v } } \), Sapphire (ordinary, extraordinary, birefringent) and YAG.

for the 6 \( S \) state is 399.8 a.u.. This is in very good agree-ment with the value (399 a.u.) obtained by Borschevsky et al. [36] and experimentally measured value 401.0(6) a.u. of Amini et al. [38]. As seen, contributions from \( \alpha _ { c v } \) and \( \alpha _ { t } \) are quite small andj ustify use of a lower method for their evaluation. Our \( \alpha _ { c } \) from RRPA also match with the value of Derevianko et al. [42]. Good agreement between the calculated and experimental results of \( \alpha ( 0 ) \) indicates that our approach can also give similar accura-cies for the estimated dynamic polarizabilities. Next, we compute the atom-surface dispersion \( C _ { 3 } \) coefficients for a perfect conductor by numerically evaluating Eq. (4). Dynamic polarizabilities used for this purpose are plotted in Fig. 1(a). In the same plot, we also show the values obtained by the single oscillator model (SOM) that are used by other works as discussed below. We compare our \( C _ { 3 } \) coefficient for the perfect conductor with the re-sult obtained by Derevianko and co-workers [42] in Table II. Though our \( \alpha ( 0 ) \) value match quite well with Dere-vianko et al. [37], but we find difference in the \( C _ { 3 } \) value. A similar finding was also observed for the other alkali atoms that were studied by us in Ref. [23]. Our analysis shows that the main reason for the discrepancy is because of different numerical integration methods used in both the works. Derevianko et al. use a Gaussian quadrature integration method with 50 point formula while we have used an exponential grid in our calculations as discussed in [23]. In the same table we have given our calcu-lated \( C _ { 3 } \) coefficients for the other material media using their dynamic dielectric constants that are plotted in Fig. 1(b). In our earlier work [23], we have also given these constants for Au, Si, \( \mathrm { { S i O _ { 2 } } } \) and \( \mathrm { S i N } _ { x } \). Hence, we only present the final results without giving the fine details of their evaluations. Compared to these materials we find a different trend of \( \epsilon ( \iota \omega ) \) values for the ordinary, extraor-dinary and birefringent sapphires and also for the YAG surfaces, especially at the low frequency range. We could not find another study to verify directly the validity of this trend, but a recent calculation of \( S ( \omega ) \) in Ref. [55]shows almost a similar trend. This somewhat assures us about accurate determination of the \( \epsilon ( \iota \omega ) \) values for the sapphires and YAG surfaces.

We also give the \( C _ { 3 } \) coefficients for all the considered material media in Table II along with the values known in the literature. As seen, there is another evaluation of \( C _ { 3 } \) for the Au metal reported by Lach et al. [26] They use the SOM model to estimate the dynamic polarizabil-ity values whereas the dynamic dielectric constants are estimated using the Drude model. Nevertheless, we find a reasonable agreement between these results. We, how-ever, did not find any data to compare our results for the dielectric materials and semiconductors. From Table II, it can be seen that the valence correlation is dominant among the core, core-valence and tail correlations, but core contributions are quite significant as compared to their contributions in the evaluation of the polarizabili-ties. Among all the interacting media, the \( C _ { 3 } \) coefficients for the interacting perfect conductor is the highest and it is approximately 40%, 51%, 75%, 64%, 62% and 63% larger than the Au, Si, \( \mathrm { { S i O _ { 2 } } } \),\( \mathrm { S i N _ { x } } \), sapphire and YAG surfaces respectively. The decrease in the interaction co-efficients for the cases of dielectric media might be due to the charge dangling bonds in the materials which ac-counts for the additional interactions in the dielectrics at the shorter separations [56].

Using our described procedure, we also evaluate the re-tarded \( f _ { 3 } \) functions for all the considered materials inter-acting with Cs. In Table III, we compare our results for \( f _ { 3 } \) for the interaction of the Cs atom with the Au surface with the results obtained by Lach et al. [26] at certain separation distances. We also find reasonable agreement between both the results. It can also be observed from this table that at the short separation distances (\( a \rightarrow \) 0),


As expected, the number of live points K is an impor-tant setting but it is even more crucial in Nessai since it limits the amount of training data available. We find that a minimum of 1000 live points is required and for more complex problems, such as gravitational-wave inference, at least 2000 live points should be used.

There are a large number of settings which relate to the complexity of the normalising flow. Whilst tuning the sampler we found that the number of coupling trans-formations greatly affected convergence. If too many transforms were used the algorithm was prone to over-constraining the posterior distribution. We attribute this to the complexity of the iso-likelihood contour learnt by the flow, if the flow has too many trainable parameters it can over-fit the distribution and exclude regions of the parameter space which should be sampled. At the other extreme, if the model is too simple then resulting contour can “smooth” fine details and more samples are drawn outside of the initial likelihood constraint. These will not be accepted and the sampling process is therefore less ef-ficient. We use a similar logic for the number of neurons and layers in the neural network that parameterises the flow but we find that these parameters predominantly affect training time with a lesser effect on overall con-vergence. Another parameter that is important to con-sider is the batch size, during sampling the normalising flow can be training upwards of 100 times. Hence, a larger batch size is recommended since it can greatly re-duce training time, we also recommend increasing the batch size when using reparameterisations that increase the amount of training data, such as the boundary inver-sion described in section III B and appendix B.

We note that the size of pool of new samples effects the efficiency of the algorithm and the total run-time. If the pool-size is small then the normalising flow is fre-quently retrained, in extreme case where the proposal is inefficient due to, for example, the complexity of the parameter space, then the normalising can be retrained multiple times during a single iteration. Conversely, if the pool-size is large then if the flow is force-ably re-trained a number of points are discarded or, if the flow is only retrained once the pool is empty, then the rejection sampling becomes in-efficient since a large fraction of the potential new points will lie outside the likelihood bound. We instead opt to inversely scale the pool-size given the mean acceptance of the sampler since the last iteration the flow was trained. We recommend setting the base pool-size to the number of live points, only retraining the model when the pool is empty and setting the maxi-mum pool-size to be ten times the base pool-size. We use these settings for the results in section V and find that this results in a median of 263 training instances required to reach convergence.

As mentioned previously, approximately 40% of the run-time is spent on populating the pool of new sam-ples. This is directly attributable to the efficiency of the rejection sampling required to ensure samples are dis-tributed according to the prior. In section III A we pro- pose two methods for drawing samples within the con-tour in the latent space, these produce uniformly and normally distributed samples respectively. In practice we find the two methods comparable in most cases with the exception of when the latent radius lies in the tail of the chi-distribution that corresponds to the latent prior \( p _ { \mathcal { Z } } \) . In this case using the uniform distribution results in lower population and proposal acceptances which leads to longer run-times.

We have proposed a novel method for sampling within a given iso-likelihood contour according to the prior that can be incorporated into the standard nested sampling algorithm. Our method employs normalising flows to learn the density of current set of live points which, once trained, allows us to produce points within the contour by sampling from a simple distribution and using rejec-tion sampling. The use of normalising flows allows us to avoid using multiple bounding distributions and since new samples are independent of the previous samples we eliminate the need to use a random walk. We imple-ment this proposal method in our sampler, Nessai, and conduct a series of tests to verify that it recovers the cor-rect Bayesian posteriors and then compare our results to those obtained with another sampler to determine if our design does in fact result in a more efficient sampler.

We apply our sampler to 128 four second duration simulated signals from the coalescence of binary black hole systems sampled at 2048 Hz and we run two sepa-rate analyses, one with distance marginalisation and an-other without. The resulting P-P plots (fig. 3) show that our sampler more reliably recovers the posterior distribu-tions with distance marginalisation than without, how-ever both pass the P-P test. This indicates that our proposal method does not introduce any inherent biases.

We use dynesty for the comparison, which has been shown to produce results consistent with those used in previous LVK analyses [36]. We find that our sampler returns evidences consistent with dynesty, which serves as further verification of our results. Since we aim to pro-duce a more efficient sampler we also compare the like-lihood evaluations required to reach convergence. When not using distance marginalisation we find that Nessai requires 5.04 \( \times 1 0 ^ { 6 } \) likelihood evaluations, 2.07 times fewer than dynesty. When distance marginalisation is en-abled Nessai requires \( 7 . 2 2 \times 1 0 ^ { 6 } \), which, whilst still 1.34 fewer than dynesty, is more than with the marginali-sation disabled. As such, we recommend using Nessai without distance marginalisation for gravitational-wave inference.

However, this reduction in likelihood evaluations does not relate directly to the total computation time because of the additional costs associated with sampling, which for Nessai are associated with training the normalis-ing flow and populating the pool of new samples. We

find that the fraction of the time spent of each stage changes when using distance marginalisation. Without the marginalisation, on average, 8% of the total computa-tion time is spent on training and a further 40% on popu-lation. When using distance marginalisation this changes to 5% spent on training and 42% on population. We at-tribute the difference in population time to the efficiency of the rejection sampling, which is improved when includ-ing the reparameterisation for distance discussed in sec-tion III C. We find that without distance marginalisation the median run-time for Nessai is 2.32 times faster than dynesty. However when distance marginalisation is en-abled we observe that, on average, Nessai is only 1.40 times faster than dynesty. This further reinforces our recommendation to use Nessai with distance marginali-sation disabled.

We also show how our sampler can make use of paral-lelised likelihood functions by evaluating the likelihood of new live points during the population stage. We repeat the previous analysis for a single injection without dis-tance marginalisation and parallelise the likelihood com-putation with increasing number of threads up to 16. We observe that the reduction time evaluating the likelihood does not quite match the theoretical values, indicating that there is a small overhead associated with it. This also highlights how the limiting factor is the time spent training the normalising flow and populating the pool of new live point.

To aid in diagnosing potential biases during sampling, we include a series of diagnostics in our sampler which allow us to easily identify under and over-constraining. These diagnostics also help to tune the sampling settings and highlight how periodically re-training the normal-ising flow during sampling prevents the proposal from becoming inefficient during sampling.

We find that our algorithm is susceptible to under-sampling regions of the parameter space which are close to the prior bounds. We consequently introduce the previously described reparameterisations to mitigate this and a series of diagnostics to aid in diagnosing biases and correctly tuning the settings. We aim address this in fur-ther work with changes to the design of the normalising flows we have used.

It is natural to compare this work to [27–30] which use variational autoeconders and normalising flows to pro-duce posterior distributions. Our approach differs from these in that it requires no prior computation since train-ing occurs during sampling and we do not introduce any assumptions about the data other than those necessary to apply a nested sampling algorithm. Nessai is therefore a drop-in replacement for existing sampling algorithms that does not require changes to existing pipelines. In future work we aim to evaluate our sampler us-ing more expensive waveform models including those for longer duration signals, such as those from binary neu-tron star of neutron star-black hole system, and models which include higher-order modes. We will also investi-gate the suitability of other types of normalising flow transforms, such as the spline based transforms from[68] and flows which allow for specifying a manifold [69].These changes could improve the efficiency of the pop-ulation stage which is currently the slowest part of the algorithm. Another possible approach for reducing the cost of population is using alternative reparameterisa-tions for parameters such as the spins magnitudes, which we observe to be two of the most challenging parameters to sample.

In summary, we have proposed a novel variation of the standard nested sampling algorithm that incorpo-rates normalising flows specifically designed for inference with computationally expensive likelihood functions. We have applied our sampler to the problem of gravitational wave inference and shown that it consistently recovers the Bayesian posteriors distributions and evidences with 2.07 times fewer total likelihood evaluations than dynesty, another commonly used sampler, which translates to a 2.32 times reduction in computation time. Our sampler therefore serves as a more efficient drop-in replacement for existing samplers.

The authors gratefully acknowledge the Science and Technology Facilities Council of the United Kingdom. MJW is supported by the Science and Technology Fa-cilities Council [2285031]. JV and CM are supported by the Science and Technology Research Council [ST/L000946/1]. CM is also supported by the European Cooperation in Science and Technology (COST) action[CA17137]. The authors are grateful for computational resources provided by Cardiff University, and funded by an STFC grant supporting UK Involvement in the Oper-ation of Advanced LIGO.

Software: Nessai was initially developed using cp-nest [21] with permission from the authors and still shares a similar interface and other core codes. Nessai is implemented in Python and uses NumPy [70], SciPy[71], pandas [72, 73], nflows [47], PyTorch [46], mat-plotlib [74] and seaborn [75]. Gravitational wave in-jections were generated using Bilby and bilby pipe [25].Figures were prepared using matplotlib [74], seaborn[75], Bilby [25] and corner [76].