By Klimenok V.I.

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**Extra resources for A BMAP/SM/1 Queueing System with Hybrid Operation Mechanism**

**Example text**

4), [D∗ ]◦(φ1W ×id) extends canonically to a morphism 1 1 1 1 1 [D∗ ] ◦ (φ1W × id) : Σ∞ s A × X × ∆ /(A × X × ∆ / \ |W |) → 11 (1/2) . Threading this extension through the same process as we used to deﬁne, revd yields the A1 Ad + 1 homotopy for the two maps P1 ∧ Σ∞ s HZd → (σ0 1)d+1 in the diagram ΣP1 Σ∞ s HZd rev d / Σ∞ s HZd+1 n / (σ 1)(Ad + 1 ) 0 d+1 (Ad ) ΣP1 (σ0 1)d rev d + 1 n thus completing the proof. 4. The cycle class map We denote the Bloch motivic cohomology spectrum (Z 0 , Z 1 , .

We thus have the open subset of A1 × (P1 )d−1 . Let π weak equivalences (0/1) 10 (d/d+1) |W | (|W |) := 10 (d/d+1) |W | (Ad × X) ∼ 10 ¯ −1 (|π ∗ W |) (1/2) π → 10 (0/1) =: 10 (A1 × X × (P1 )d−1 ) (1/2) |π ∗ W | (A1 × X × (P1 )d−1 ) ∼ 10 (A1 × X) (|π∗ W |), giving the deﬁnition of π∗ . (0/1) Thus, the class rev1 (π∗ W ) gives the class revd (W ) ∈ 10 (|W |). This class is functorial with respect to restriction to the points x1 , . . , xs . To make this canonical, let K = k(P1 )d , let ∗ ∈ (P1 )d (K) be the canonical point and let (P1 )d∞ = (P1 )d \ (P1 \ {∞})d .

Maps are sequences of maps in Spt(k) respecting the bonding morphisms. The P1 -Ω-spectra over X form a full subcategory of Spt(s,p) (X) by replacing the bonding maps with their adjoints. If E = (E0 , E1 , . ) is a P1 -spectrum, a P1 -Ω-spectrum or an (s, p)-spectrum, we have the suspensions ΣP1 E := (E1 , E2 , . ), 1 Σ−1 P1 E := (ΩP E0 , E0 , E1 , . ). 2. Model structure and homotopy categories We recall the category SH(k) and its relation to the three categories of spectra deﬁned above. For details, we refer the reader to [14, 15].