Corollary 4 Sample Clauses

Corollary 4. If ΠHBA is both (p, fAR)-responsive and fAV-valid, then fAV < 1 (1 − fAR).
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Corollary 4. If D is a quaternion division algebra over an Ai(2)-field k and σ is of the first kind, then u+(D) ≤ 3 · 2i−2 and u−(D) ≤ 2i−2; = 3 · 2
Corollary 4. If D is a quaternion division algebra over a global function field k, then u+(D) = 3, u−(D) = 1, and u0(D) = 2. Proof. By Chevalley-Warning theorem [Che35; War35], every finite field is a C1- field. By Xxxx-Xxxx theorem [Lan52], every global function field is a C2-field. Since every C2-field is an A2(2)-field [Lee13, between 2.1 and 2.2], by corollary 4.2.3, u+(D) ≤ 3 and u−(D) ≤ 1. By theorem 4.2.2, u0(D) ≤ 2. The equality follows from lemma 4.1.6 and lemma 4.1.1.
Corollary 4. In the case G = D4, the subgroup of GL(g1) stabilizing both the quartic form and the skew-symmetric bilinear form, Stab(q, ⟨−, −⟩), is SL3 uS3 Proof. The previous theorem and the fact that SL3 and the diagram auto- morphism stabilize both forms yield the following containments: SL3 uS3 ⊆ Stab(q, ⟨−, −⟩) ⊆ Stab(q) = ⟨SL3, µ4⟩ u S3. Since −1 ∈ SL2, we also have −1 ∈ SL3. Thus SL3 uS3 is an index 2 subgroup 2 of ⟨SL3, µ4⟩ u S3. However, the coset containing i, a primitive fourth root of unity, is not in Stab(q, ⟨−, −⟩) since ⟨ix, iy⟩ = −⟨x, y⟩ for any x, y ∈ g1. Therefore Stab(q, ⟨−, −⟩) = SL3 uS3.
Corollary 4. For ∆ = √1 and every distribution PXM , Protocol 6 has a probability of error sn vanishing to 0 as n → ∞ and average length |π|av less than12 nRCO(M|PXM ) + O(√n log n). Furthermore, for a fixed R > 0, the fixed-length variant of Protocol 6 has probability of error sn vanishing to 0 as n → ∞ for all distributions PXM that satisfy R > RCO (M|PXM ) + O .√n−1 log nΣ .‌

Related to Corollary 4

  • Service Providing Methodology 1.3.1 Party A and Party B agree that during the term of this Agreement, where necessary, Party B may enter into further service agreements with Party A or any other party designated by Party A, which shall provide the specific contents, manner, personnel, and fees for the specific services. 1.3.2 To fulfill this Agreement, Party A and Party B agree that during the term of this Agreement, where necessary, Party B may enter into equipment or property leases with Party A or any other party designated by Party A which shall permit Party B to use Party A’s relevant equipment or property based on the needs of the business of Party B. 1.3.3 Party B hereby grants to Party A an irrevocable and exclusive option to purchase from Party B, at Party A’s sole discretion, any or all of the assets and business of Party B, to the extent permitted under PRC law, at the lowest purchase price permitted by PRC law. The Parties shall then enter into a separate assets or business transfer agreement, specifying the terms and conditions of the transfer of the assets.

  • Switching and Tagging Rules Each Party shall provide the other Parties a copy of its switching and tagging rules that are applicable to the other Parties’ activities. Such switching and tagging rules shall be developed on a non-discriminatory basis. The Parties shall comply with applicable switching and tagging rules, as amended from time to time, in obtaining clearances for work or for switching operations on equipment.

  • Grades of Service The Parties shall initially engineer and shall monitor and augment all trunk groups consistent with the Joint Process as set forth in Section 14.1 of this Attachment.

  • COVID-19 Employees of Contractor and/or persons working on its behalf, including, but not limited to, subcontractors (collectively, “Contractor Personnel”), while performing services under this Agreement and prior to interacting in person with City employees, contractors, volunteers, or members of the public (collectively, “In-Person Services”) must be fully vaccinated against the novel coronavirus 2019 (“COVID-19”). “Fully vaccinated” means that 14 or more days have passed since Contractor Personnel have received the final dose of a two-dose COVID-19 vaccine series (Moderna or Pfizer-BioNTech) or a single dose of a one-dose COVID-19 vaccine (Xxxxxxx & Xxxxxxx/Xxxxxxx) and all booster doses recommended by the Centers for Disease Control and Prevention. Prior to assigning Contractor Personnel to perform In-Person Services, Contractor shall obtain proof that such Contractor Personnel have been fully vaccinated. Contractor shall retain such proof for the document retention period set forth in this Agreement. Contractor shall grant medical or religious exemptions (“Exemptions”) to Contractor Personnel as required by law. If Contractor wishes to assign Contractor Personnel with Exemptions to perform In- Person Services, Contractor shall require such Contractor Personnel to undergo weekly COVID-19 testing, with the full cost of testing to be borne by Contractor. If Contractor Personnel test positive, they shall not be assigned to perform In-Person Services or, to the extent they have already been performing In-Person Services, shall be immediately removed from those assignments. Furthermore, Contractor shall immediately notify City if Contractor Personnel performing In-Person Services (1) have tested positive for or have been diagnosed with COVID-19, (2) have been informed by a medical professional that they are likely to have COVID-19, or (3) meet the criteria for isolation under applicable government orders.

  • Fixed Term Employees The only terms of this Agreement that apply to employees who are not regular employees are those that are set out in Articles 31A, 32, 33 and 34. 31A.1 Articles 31A.2 to 31A.16 apply only to fixed-term employees other than seasonal, student and GO Temp employees.

  • Switching System Hierarchy and Trunking Requirements For purposes of routing ECI traffic to Verizon, the subtending arrangements between Verizon Tandem Switches and Verizon End Office Switches shall be the same as the Tandem/End Office subtending arrangements Verizon maintains for the routing of its own or other carriers’ traffic (i.e., traffic will be routed to the appropriate Verizon Tandem subtended by the terminating End Office serving the Verizon Customer). For purposes of routing Verizon traffic to ECI, the subtending arrangements between ECI Tandem Switches and ECI End Office Switches shall be the same as the Tandem/End Office subtending arrangements that ECI maintains for the routing of its own or other carriers’ traffic.

  • Mail Order Catalog Warnings In the event that, the Settling Entity prints new catalogs and sells units of the Products via mail order through such catalogs to California consumers or through its customers, the Settling Entity shall provide a warning for each unit of such Product both on the label in accordance with subsection 2.4 above, and in the catalog in a manner that clearly associates the warning with the specific Product being purchased. Any warning provided in a mail order catalog shall be in the same type size or larger than other consumer information conveyed for such Product within the catalog and shall be located on the same display page of the item. The catalog warning may use the Short-Form Warning content described in subsection 2.3(b) if the language provided on the Product label also uses the Short-Form Warning.

  • Service Scope The following Services are covered by this Agreement; o Manned telephone support o Monitored email support o Remote assistance using Remote Desktop and a Virtual Private Network where available o Planned or Emergency Onsite assistance (extra costs apply) o Monthly system health check

  • Union Activity During Working Hours Solicitation of Union membership or collection or checking of dues will not be conducted during working time. The Company agrees not to discriminate in any way against any employee for Union activity, but such activity shall not be carried on during working time, except as specifically allowed by the provisions of this Agreement.

  • Intercarrier Compensation 5.5.1 Intercarrier compensation for seven (7) or ten (10) digit dialed calls originated by ITC^DeltaCom utilizing Local Switching shall apply as follows: 5.5.2 For calls terminating to a BellSouth End User or to an End User served by BellSouth resold services, BellSouth shall charge ITC^DeltaCom for End Office Switching as set forth in Exhibit A at the terminating end office. 5.5.3 For calls terminating to a CLEC where such CLEC is utilizing a BellSouth switch port or port/loop combination to provide service to its End User, BellSouth shall charge ITC^DeltaCom for End Office Switching as set forth in Exhibit A at the terminating end office. BellSouth will not charge the terminating CLEC for End Office Switching as set forth in Exhibit A at the terminating end office. 5.5.3.1 For calls terminating to third party carriers, such as CLECs, wireless carriers and independent companies, utilizing their own switches to serve their End Users, ITC^DeltaCom is required to enter into interconnection or traffic exchange agreements with such third parties for the exchange of traffic through BellSouth’s network. If ITC^DeltaCom does not have such an agreement with a third party carrier and BellSouth is charged termination charges by a third party terminating a call originated by ITC^DeltaCom, or if such third party carrier bills BellSouth for terminating such calls, despite the existence of such an agreement, then BellSouth may, at its option: 5.5.3.1.1 pay such charges as billed by the third party carrier and charge End Office Switching as set forth in Exhibit A to ITC^DeltaCom for each such call; or 5.5.3.1.2 pay such charges as billed by the third party carrier and ITC^DeltaCom will reimburse the full amount of such charges within thirty (30) days of BellSouth’s request for reimbursement. 5.5.3.2 Intercarrier compensation for seven (7) or ten (10) digit dialed calls terminating to ITC^DeltaCom utilizing Local Switching shall apply as follows: 5.5.3.2.1 For calls originated by a BellSouth End User or by an End User served by resold BellSouth services, BellSouth shall not charge ITC^DeltaCom for End Office Switching at the terminating end office for use of the network component; therefore, ITC^DeltaCom shall not charge BellSouth intercarrier compensation or any other charges for termination of such calls. 5.5.3.2.2 For calls originated by a CLEC where such CLEC is utilizing a BellSouth switch port or port/loop combination to provide service to its End User, BellSouth shall not charge ITC^DeltaCom for End Office Switching at the terminating end office for use of the network component; therefore, ITC^DeltaCom shall not charge the originating CLEC or BellSouth intercarrier compensation or any other charges for termination of such calls. 5.5.3.2.3 For calls originated by third party carriers, such as CLECs, wireless carriers and independent companies,utilizing their own switches to serve their End Users, ITC^DeltaCom is required to enter into interconnection or traffic exchange agreements with such third parties for the exchange of traffic through BellSouth’s network. ITC^DeltaCom may xxxx the third parties according to such agreements and shall not xxxx BellSouth for the exchange of traffic through BellSouth’s network. 5.5.3.3 Intercarrier compensation shall apply as follows for intralata 1+ dialed calls originated by ITC^DeltaCom utilizing Local Switching where ITC^DeltaCom uses BellSouth’s CIC for its End User’s LPIC: 5.5.3.3.1 For calls terminating to a BellSouth End User or to an End User served by BellSouth resold services, BellSouth shall charge ITC^DeltaCom for End Office Switching as set forth in Exhibit A at the terminating end office. 5.5.3.3.2 For calls terminating to a CLEC where such CLEC is utilizing a BellSouth switch port or port/loop combination to provide service to its End User, BellSouth shall charge ITC^DeltaCom for End Office Switching as set forth in Exhibit A at the terminating end office. BellSouth will not charge the terminating CLEC for End Office Switching at the terminating end office. In the event that BellSouth is charged termination charges by the CLEC, BellSouth may pay such charges and ITC^DeltaCom will reimburse BellSouth the full amount of such charges within thirty (30) days following BellSouth’s request for reimbursement. 5.5.3.3.3 For calls terminating to third party carriers, such as CLECs, wireless carriers and independent companies, utilizing their own switches to serve their End Users, ITC^DeltaCom is required to enter into interconnection or traffic exchange agreements with such third parties for the exchange of traffic through BellSouth’s network. If ITC^DeltaCom does not have such an agreement with a third party carrier and BellSouth is charged termination charges by a third party terminating a call originated by ITC^DeltaCom, or if such third party carrier bills BellSouth for terminating such calls, despite the existence of such an agreement, then BellSouth may, at its option: 5.5.3.3.3.1 pay such charges as billed by the third party carrier and charge End Office Switching as set forth in Exhibit A to ITC^DeltaCom for each such call; or 5.5.3.3.3.2 pay such charges as billed by the third party carrier and ITC^DeltaCom will reimburse BellSouth the full amount of such charges within thirty (30) days following BellSouth’s request for reimbursement. 5.5.3.4 Intercarrier compensation shall apply as follows for intralata 1+ dialed calls terminating to ITC^DeltaCom utilizing Local Switching where the originating carrier uses BellSouth’s CIC for its End User’s LPIC: 5.5.3.4.1 For calls originated by a BellSouth End User or by an End User served by BellSouth resold service, BellSouth shall charge ITC^DeltaCom for End Office Switching as set forth in Exhibit A at the terminating end office for use of the End Office Switching network component in terminating such calls. ITC^DeltaCom may charge BellSouth for intercarrier compensation at the End Office Switching as set forth in Exhibit A for such calls. ITC^DeltaCom shall not charge originating or terminating switched access rates to BellSouth for termination of such calls. 5.5.3.5 For calls originated by or terminating to interexchange carriers through a switched access arrangement, ITC^DeltaCom may xxxx the interexchange carrier in accordance with ITC^DeltaCom’s tariff and will not xxxx BellSouth any charges for such call. ITC^DeltaCom shall pay BellSouth applicable charges for the use of BellSouth’s network in accordance with the rates set forth in Exhibit A for originating and terminating such calls.

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