and Applied Analysis 3 and define recursively a∇−nf t ∫ t a a∇−n 1f τ ∇τ 2.4 for n 2, 3, . . .. Then we have the following. Proposition 2.1 Nabla Cauchy formula . Let n ∈ Z , a, b ∈ T and let f : T → R be ∇-integrable on a, b ∩ T. If t ∈ T, a ≤ t ≤ b, then a∇−nf t ∫ t a ̂ hn−1 ( t, ρ τ ) f τ ∇τ . 2.5 Proof. This assertion can be proved by induction. If n 1, then 2.5 obviously holds. Let n ≥ 2 an...

We provide a generalization of Lieb’s triple matrix extension the Golden–Thompson inequality from algebras to setting traces on finite von Neumann algebras. More precisely, assume that ℳ is algebra equipped with tracial state τ. If 1≤p,q≤∞ 1/p+1/q=1, it shown whenever a, b, and c are self-adjoint τ-measurable operators satisfying a∈ℳ, e b ∈L p (ℳ,τ), q then following holds:

This paper is to study what we call twisted regular representations for vertex operator algebras. Let V be a algebra, let σ1,σ2 commuting finite-order automorphisms of and σ=(σ1σ2)−1. Among the main results, any σ-twisted V-module W nonzero complex number z, construct weak σ1⊗σ2-twisted V⊗V-module Dσ1,σ2(z)(W) inside W⁎. W1,W2 σ1-twisted, σ2-twisted V-modules, respectively. We show that P(z)-in...

The formal group law of an elliptic curve has seen recent applications to computational algebraic geometry in the work of Couveignes to compute the order of an elliptic curve over finite fields of small characteristic ([2], [6]). The purpose of this paper is to explain in an elementary way how to associate a formal group law to an elliptic curve and to expand on some theorems of Couveignes. In ...

We provide a fully tensorial approach to bound the Bel-Robinson energy of -order under the assumption ∫ t0+T t0 ( ‖k‖L∞(Σt) + ∑ λ≥0 ‖Pλ∆ 1 2Ric‖L∞(Σt) ) dt <∞, which is our first step to establish local well-posedness for the solution of Einstein vacuum equation in CMC gauge with H2+ data . 1. Geometric set-up and Main result 1.1. Heat flow. Let 4 = g∇i∇j denote the Laplace-Betrami operator on ...

In the last lecture, two terms Average Delay and RMS Delay Spread were defined as below () () ∫ ∫ ∞ ∞ Φ Φ = 0 0 τ τ τ τ τ µ τ d d (1) () () () ∫ ∫ ∞ ∞ Φ Φ − = 0 0 2 τ τ τ τ µ τ σ τ τ d d c c (2) If the power density is discrete like Figure 1, the Average Delay and RMS Delay Spread for the multipath profile could be written in the following way: () () ∑ ∑ = k k k k k p p τ τ τ τ (3) () 2 2 τ τ σ...

We construct solutions for the Shilomis model of ferrofluids in a critical space, uniformly entropic relaxation time τ∈(0,τ0). This allows us to study convergence when τ→0 such solutions.

We study the observability of the τ − τ + decay mode of a Higgs boson produced in the s-channel at a muon collider. We find that the spin correlations of the τ − τ + in τ → πν τ , ρν τ decays are discriminative between the Higgs boson signal and the Standard Model background. Observation of the predicted distinctive distribution can confirm the spin-0 nature of the Higgs resonance. The relative...