We investigate the constraints imposed on the weak mixing angles by the K "-K " mass matrix and B meson decay in left-right symmetric gauge thee ries. In a class of such theories with manifest left-right symmetry the domain of Kobayashi-Maskawa angles allowed by the Ki-Kz mass difference has no overlap with-that allowed by B meson decay.

A (1, k)-composition of a positive integer n consists of an ordered sequence of the integers 1 and k whose sum is n. A palindromic (1, k)-composition is one for which the sequence is the same from left to right as from right to left. We give recursive equations and generating functions for the total number of such compositions and palindromes, and for the number of 1’s, k’s, “+”signs and summan...

Abstract We prove an inequality that unifies previous works of the authors on properties Radon transform convex bodies including extension Busemann–Petty problem and a slicing for arbitrary functions. Let $K$ $L$ be star in ${\mathbb R}^n,$ let $0<k<n$ integer, $f,g$ non-negative continuous functions $L$, respectively, so $\|g\|_\infty =g(0)=1.$ Then $$\begin{align*} & \frac{\...

A bstract We study the small- x asymptotics of flavor non-singlet T-odd leading-twist quark transverse momentum dependent parton distributions (TMDs), Sivers and Boer-Mulders functions. While leading eikonal function is given by spin-dependent odderon [1, 2], we are interested in revisiting sub-eikonal correction considered us earlier [3]. first simplify expressions for both TMDs at small Bjork...

In this note, we prove the following inequality for norm N(K) of a convex body K in $$\mathbb {R}^n$$ , $$n\ge 2$$ : $$\begin{aligned} \le \frac{\pi ^{\frac{n-1}{2}}}{2 \Gamma \left( \frac{n+1}{2}\right) }\cdot {{\,\mathrm{length}\,}}(\gamma ) + ^{\frac{n}{2}-1}}{\Gamma \frac{n}{2}\right) } \cdot {{\,\mathrm{diam}\,}}(K), \end{aligned}$$ where $${{\,\mathrm{diam}\,}}(K)$$ is diameter K, $$\gamm...

One can prove the following propositions: (1) For every set X and for every finite sequence p of elements of X such that p 6= ∅ holds p↾1 = 〈p1〉. (2) Let L be a non empty loop structure, p be a finite sequence of elements of L, and n, m be natural numbers. If m ¬ n, then p↾n↾m = p↾m. (3) Let L be an add-associative right zeroed right complementable non empty loop structure, p be a finite sequen...

spherical polyhedron S = (V, F ;E): For a 2-connected planar graph GS = (V,ES), embedded on a sphere (or in the plane), we record the vertices as V and the regions as faces F , and rewrite the directed edges E as ordered 4-tuples e = 〈h, i; j, k〉, where the edge from vertex h to vertex i has face j on the right and face k on the left. (The reversed edge −e = 〈i, h; k, j〉 runs from i to h, with ...

spherical polyhedron S = (V, F ;E): For a 2-connected planar graph GS = (V,ES), drawn without self-intersection on a sphere (or in the plane), we record the vertices as V and the regions as faces F , and rewrite the directed edges E as ordered 4-tuples e = 〈h, i; j, k〉, where the edge from vertex h to vertex i has face j on the right and face k on the left. (The reversed edge −e = 〈i, h; k, j〉 ...

Let H be a semisimple Hopf algebra over an algebraically closed field k. It is assumed that either char k = 0 or char k > dimH . Semisimplicity of H means that H is a semisimple left H-module. In that case H has finite dimension. Throughout the paper we shall keep to notations from [M]. For example H stands for the dual Hopf algebra with the natural pairing 〈−,−〉 : H ⊗ H → k. The algebra H is a...

expand both sides, and compare the terms on both sides in which k of the terms are among the ai. On the left, one has the product of each kelement subset of {1, . . . , n}; on the right, one has ( n k ) (a1 · · · an) · · · (b1 . . . bn), which is precisely ( n k ) times the geometric mean of the terms on the left. Thus AM-GM shows that the terms under consideration on the left exceed those on t...