Statement of the main results Sample Clauses

Statement of the main results. As anticipated, our main results are not only concerned with the existence of the limits in (4.1.8) and (4.1.9), but also with their universality. In other words, for a Xxxxxx matrix Γ (ω) and a given multiplier τ, we show that under some mild assumptions on τ, see (A)-(C) below, the functions‌ LD (t; Γ (ω)) and LD±(t; Γ (ω)) are independent of the choice of τ. τ ^ τ ^‌ Assumptions 4.1.1. Let us state the following assumptions on τ:
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Statement of the main results. Just as in Chapter 4, the main results of this Chapter not only show the existence of the limits in (5.1.8) and (5.1.9), but also, given some mild assumptions on the couple τ, their universality. Let us now state the following assumptions on the τ:‌ Assumptions 5.1.2.
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Statement of the main results. We recall that for any number field E we write rE for the number of its complex places and δE for its p-adic ‘Leopoldt defect’. We recall also that δE is a non-negative integer which vanishes if and only if Xxxxxxxx’s Conjecture is valid for E at p and that there are equalities p E p E rkZ (BΣ) = rkZ (AΣ) − 1 = rE + δE (4.1) (cf. [33, (10.3.7) Corollary]). We now state the main result that will be proved in this chapter. Theorem 4.1.1. Let L/K and Σ be as above and set G := Gal(L/K). L Then the isomorphism class of the Zp[G]-module AΣ is determined (in a sense to be made precise in Theorem 4.2.1 below) by rK, the Leopoldt defects δLi for each i with 0 ≤ i ≤ n and the diagrams of finite groups T Σ L/L1 T Σ fL1,L2 −→ L/L1 ← − gL2,L1 Σ T L/L2 T Σ fL2,L3 −→ L/L2 ← − gL3,L2
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Statement of the main results. ‌ For an A-lattice X and an idempotent e of A we set Xe := {x ∈ X : e · x = x in F ⊗R X} (so that Xe = e · X if e belongs to A). For any A-module X we write Xtor for the submodule comprising all R-torsion elements. For any element x of X we denote the A-submodule that x generates by ⟨x⟩. The main algebraic result in this section is the following.
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  • Dissemination of own Results 8.3.1.1 During the Project and for a period of 1 year after the end of the Project, the dissemination of own Results by one or several Parties including but not restricted to publications and presentations, shall be governed by the procedure of Article 29.1 of the Grant Agreement subject to the following provisions. Prior notice of any planned publication shall be given to the other Parties at least 45 calendar days before the publication. Any objection to the planned publication shall be made in accordance with the Grant Agreement in writing to the Coordinator and to the Party or Parties proposing the dissemination within 30 calendar days after receipt of the notice. If no objection is made within the time limit stated above, the publication is permitted.

  • Expected Results VA’s agreement with DoD to provide educational assistance is a statutory requirement of Chapter 1606, Title 10, U.S.C., Chapter 1607, Title 10, U.S.C., Chapter 30, Title 38, U.S.C. and Chapter 33, Title 38, U.S.C (Post-9/11 GI Xxxx). These laws require VA to make payments to eligible veterans, service members, guard, reservist, and family members under the transfer of entitlement provisions. The responsibility of determining basic eligibility for Chapter 1606 is placed on the DoD. The responsibility of determining basic eligibility for Chapter 30 and Chapter 33 is placed on VA, while the responsibility of providing initial eligibility data for Chapter 30 and Chapter 33 is placed on DoD. Thus, the two agencies must exchange data to ensure that VA makes payments only to those who are eligible for a program. Without an exchange of enrollment and eligibility data, VA would not be able to establish or verify applicant and recipient eligibility for the programs. Subject to the due process requirements, set forth in Article VII.B.1., 38 U.S.C. §3684A, VA may suspend, terminate, or make a final denial of any financial assistance on the basis of data produced by a computer matching program with DoD. To minimize administrative costs of implementation of the law and to maximize the service to the veteran or service member, a system of data exchanges and subsequent computer matching programs was developed. The purposes of the computer matching programs are to minimize the costs of administering the Xxxxxxxxxx GI Xxxx — Active Duty, the Xxxxxxxxxx GI Xxxx — Selected Reserve, Reserve Educational Assistance Program, and the Post-9/11 GI Xxxx program; facilitate accurate payment to eligible veterans or service members training under the Chapter of the Xxxxxxxxxx GI Xxxx — Active Duty, the Xxxxxxxxxx GI Xxxx — Selected Reserve, Reserve Educational Assistance Program, and the Post-9/11 GI Xxxx program; and to avoid payment to those who lose eligibility. The current automated systems, both at VA and DoD, have been developed over the last twenty-two years. The systems were specifically designed to utilize computer matching in transferring enrollment and eligibility data to facilitate accurate payments and avoid incorrect payments. The source agency, DMDC, stores eligibility data on its computer based system of record. The cost of providing this data to VA electronically are minimal when compared to the cost DMDC would incur if the data were forwarded to VA in a hard-copy manner. By comparing records electronically, VA avoids the personnel costs of inputting data manually as well as the storage costs of the DMDC documents. This results in a VA estimated annual savings of $26,724,091 to VA in mailing and data entry costs. DoD reported an estimated annual savings of $12,350,000. A cost-benefit analysis is at Attachment 1. In the 32 years since the inception of the Chapter 30 program, the cost savings of using computer matching to administer the benefit payments for these educational assistance programs have remained significant. The implementation of Chapter 33 has impacted the Chapter 30 program over the past 8 years (fiscal year 2010 through fiscal year 2017). Statistics show a decrease of 23 percent in the number of persons who ultimately use Chapter 30 from fiscal year 2015 to 2016. The number of persons who use Chapter 33 has consistently been above 700,000 in the past four years. VA foresees continued cost savings due to the number of persons eligible for the education programs.‌

  • Accounts Not Required to Be Reviewed, Identified, or Reported Unless the Reporting Financial Institution elects otherwise, either with respect to all Preexisting Individual Accounts or, separately, with respect to any clearly identified group of such accounts, where the implementing rules in the jurisdiction provide for such an election, the following accounts are not required to be reviewed, identified, or reported as Reportable Accounts:

  • Termination and Results of Termination 24.1. Without prejudice to the Company’s rights under this Agreement to terminate it immediately without prior notice to the Client, each Party may terminate this Agreement by giving at least three (3) Business Days Written Notice to the other Party.

  • Justification and Anticipated Results The Privacy Act requires that each matching agreement specify the justification for the program and the anticipated results, including a specific estimate of any savings. 5 U.S.C. § 552a(o)(1)(B).

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  • Financial Statements Deliver to the Administrative Agent and each Lender, in form and detail satisfactory to the Administrative Agent and the Required Lenders:

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  • FINANCIAL STATUS REPORTS (FSRS Except as otherwise provided, for contracts with categorical budgets, Grantee shall submit quarterly FSRs to System Agency by the last business day of the month following the end of each quarter for System Agency review and financial assessment. Grantee shall submit the final FSR no later than forty-five (45) calendar days following the end of the applicable term.

  • Financial Information Upon written request the Company agrees to send or make available the following reports to the Buyer until the Buyer transfers, assigns, or sells all of the Securities: (i) within ten (10) days after the filing with the SEC, a copy of its Annual Report on Form 10-K its Quarterly Reports on Form 10-Q and any Current Reports on Form 8-K; (ii) within one (1) day after release, copies of all press releases issued by the Company or any of its Subsidiaries; and (iii) contemporaneously with the making available or giving to the shareholders of the Company, copies of any notices or other information the Company makes available or gives to such shareholders.

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