Digital subscriber lines (DSL) are fundamentally limited by crosstalk. The case where all crosstalk is from the same type of DSL has been studied over the years and accurate models have been standardized. However, crosstalk from multiple different types of DSLs is a relatively new area of study and models of summing mixed crosstalk have only recently been postulated. In this contribution, a new...

We generalise results of Ford and Roman which place lower bounds – known as quantum inequalities – on the renormalised energy density of a quantum field averaged against a choice of sampling function. Ford and Roman derived their results for a specific non-compactly supported sampling function; here we use a different argument to obtain quantum inequalities for a class of smooth, even and non-n...

A class < of convex bodies (c-bodies) P,Q, . . . in a k-dimensional Euclidean space R is called convex, when for all P,Q ∈ < always follows αP × βQ ∈ < [α, β ≥ 0, α+ β = 1]. Here we interpret λP (with λ > 0) to be a c-body, obtained from P through a dilatation with respect to a fixed originO of the spaceR; P ×Q refers to Minkowski addition. This property of a class of c-bodies thus not only ref...

We generalise results of Ford and Roman which place lower bounds – known as quantum inequalities – on the renormalised energy density of a quantum field averaged against a choice of sampling function. Ford and Roman derived their results for a specific non-compactly supported sampling function; here we use a different argument to obtain quantum inequalities for a class of smooth, even and non-n...

Digital subscriber lines (DSLs) are fundamentally limited by crosstalk. The case where all crosstalk is from the same type of DSL has been studied over the years and accurate models have been standardized. However, crosstalk from multiple different types of DSLs is a relatively new area of study and models of summing mixed crosstalk have only recently been postulated. As more and more types of ...

We initiate a systematic investigation into the nature of the function αK (L, ρ) that gives the volume of the intersection of one convex body K in Rn and a dilatate ρL of another convex body L in Rn, as well as the function ηK (L, ρ) that gives the (n − 1)-dimensional Hausdorff measure of the intersection of K and the boundary ∂(ρL) of ρL. The focus is on the concavity properties of αK (L, ρ). ...

Two consequences of the stability version of the one dimensional Prékopa-Leindler inequality are presented. One is the stability version of the Blaschke-Santaló inequality, and the other is a stability version of the Prékopa-Leindler inequality for even functions in higher dimensions, where a recent stability version of the Brunn-Minkowski inequality is also used in an essential way. 1 The prob...

This note is devoted to the study of the dependence on p of the constant in the reverse Brunn-Minkowski inequality for p-convex balls (i.e. p-convex symmetric bodies). We will show that this constant is estimated as c ≤ C(p) ≤ C , for absolute constants c > 1 and C > 1. Let K ⊂ IR n and 0 < p ≤ 1. K is called a p-convex set if for any λ, μ ∈ (0, 1) such that λ + μ = 1 and for any points x, y ∈ ...

Suppose that R is an analytically irreducible or excellent local domain with maximal ideal m . We consider multiplicities and mixed of by filtrations -primary ideals. show the theorem Teissier, Rees Sharp, Katz, characterizing equality in Minkowski inequality for ideals, true divisorial filtrations, larger category bounded filtrations. This not arbitrary

in this paper, two new hamilton operators are defined and the algebra of dual split quaternions isdeveloped using these operators. it is shown that finite screw motions in minkowski 3-space can be expressedby dual-number ( 3×3 ) matrices in dual lorentzian space. moreover, by means of hamilton operators, screwmotion is obtained in 3-dimensional minkowski space 3r1