This paper discusses a new principle of int.erronnection network for massively parallel arc,hit,ect,ures in t,he field of numerical comput,at,ion. The principle is motivated by an analysis of the applirat,ion feat,ures and the need to design new kind of rommunication networks combining very high hantlwidt,h, very low latency, performance independence t,o communication pattern or network load an...

It has been recently suggested that gravitons moving in AdS m × S n spacetimes along the S n blow up into spherical (n−2) branes whose radius increases with increasing angular momentum. This leads to an upper bound on the angular momentum, thus " explaining " the stringy exclusion principle. We show that this bound is present only for states which saturate a BPS-like condition involving the ene...

This paper generalizes the mixed extension principle in L2(R) of [50] to a pair of dual Sobolev spaces H(R) and H−s(Rd). In terms of masks for φ, ψ, . . . , ψ ∈ H(R) and φ̃, ψ̃, . . . , ψ̃ ∈ H−s(Rd), simple sufficient conditions are given to ensure that (X(φ;ψ, . . . , ψ), X−s(φ̃; ψ̃, . . . , ψ̃)) forms a pair of dual wavelet frames in (Hs(Rd),H−s(Rd)), where X(φ;ψ, . . . , ψ) := {φ(· − k) : k ∈ Zd} ...

The approximation-solvability of the following class of nonlinear variational inequality (NVI) problems, based on a new generalized auxiliary problem principle, is discussed. Find an element x∗ ∈K such that 〈(S − T ) (x∗) , x− x∗〉+ f(x)− f (x∗) ≥ 0 for all x ∈ K, where S, T : K → H are mappings from a nonempty closed convex subset K of a real Hilbert space H into H , and f : K → R is a continuo...

The signal intensity S is given by: S = γB0NB1g(v)/T Where N is the number of nuclei sampled, B1 is the field due to the applied radiofrequency radiation, and g(v) is the lineshape function. Hence, • S ∝ N (large sample and desirability of high isotopic abundance). • S ∝ γ (signals due to nuclei with large γ easiest to observe). • S ∝ B0 (advantage of maximum B0). • S ∝ 1/T (low temperatures gi...

We write Z for the set of integers, and N = {1, 2, 3, . . . } for the set of natural numbers. I’ll use M 28 Aug the convention where natural numbers are assumed to be positive. I may also write Z>0 for N. We also use the notation Z≥0 = {0, 1, 2, . . . } for the set of non-negative integers. Well-ordering principle (WOP). Every non-empty subset of N contains a smallest element. Explicitly: if S ...

One form of the inclusion-exclusion principle asserts that if A and B are functions of finite sets then the formulas A(S) = ∑ T⊆S B(T ) and B(S) = ∑ T⊆S(−1) |S|−|T A(T ) are equivalent. If we replace B(S) by (−1)B(S) then these formulas take on the symmetric form A(S) = ∑ T⊆S (−1) B(T ) B(S) = ∑ T⊆S (−1) A(T ). which we call symmetric inclusion-exclusion. We study instances of symmetric inclusi...

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