Counting Lemma Sample Clauses

Counting Lemma. In this section we state the graph counting lemma for the special case of triangles for ε-regularity introduced by Szemerédi. Roughly speaking it says that a sufficiently ε-regular tripartite graph contains approximately as many triangles as one would expect in a random graph with the corresponding den- sity. Gowers formally showed in [14] a graph counting lemma for quasiran- dom graphs but due to the equivalence of ε-regularity and ε-quasirandomness discussed earlier we may simply apply the well-known graph counting lemma for ε-regular graphs although we consider ε-quasirandom graphs.
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Related to Counting Lemma

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  • Accounting Treatment For accounting purposes, the Merger is intended to be treated as a "purchase."

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  • Accounting and Financial Reporting 7.1 The Trustee shall maintain separate records and ledger accounts in respect of the Contributions deposited in the Trust Fund account and disbursements to Partner Entities made therefrom. 7.2 The Trustee shall furnish to the Donors current financial information relating to receipts, disbursements and fund balance in United States dollars of the Trust Fund with respect to the Contributions via the World Bank’s Trust Funds Donor Center secure website. Within six (6) months after all commitments and liabilities under the Trust Fund have been satisfied and the Trust Fund has been closed, the final financial information relating to receipts, disbursements and fund balance in United States dollars of the Trust Fund with respect to the Contributions will be made available to the Donors via the World Bank’s Trust Funds Donor Center secure website. 7.3 The Trustee shall provide to the Donors, within six (6) months following the end of each Trustee fiscal year, an annual single audit report, comprising: (a) a management assertion together with an attestation from the Trustee’s external auditors concerning the adequacy of internal control over cash-based financial reporting for all cash-based trust funds as a whole; and (b) a combined financial statement for all cash-based trust funds together with the Trustee’s external auditor’s opinion thereon. The cost of the single audit shall be borne by the Trustee. 7.4 If a Donor wishes to request, on an exceptional basis, a financial statement audit by the Trustee’s external auditors of the Trust Fund, the Donor and the Trustee shall first consult as to whether such an external audit is necessary. The Trustee and the Donor shall agree on the appropriate scope and terms of reference of such audit. Following agreement on the scope and terms of reference, the Trustee shall arrange for such external audit. The costs of any such audit, including the internal costs of the Trustee with respect to such audit, shall be paid by the requesting Donor. 7.5 The Trustee shall furnish the Steering Committee and each Donor with: (a) copies of all unaudited or audited financial reports; and (b) any other relevant financial information received from the Partner Entities.

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