for all complex z. The space is introduced in [7], where it is characterized by three axioms. If E(a, z) and E(b> z) are entire functions which satisfy (1), then 3C(E(&)) will be contained isometrically in 3C(E(b)) if these functions satisfy the hypotheses of Theorem VII of [8]. Isometric inclusions of spaces of entire functions are a basic idea in [9] and [lO]. A fundamental property of these ...

The Brunn Minkowski theory of convex bodies and mixed volumes has provided many tools for solving problems involving projections and valuations of compact convex sets in Euclidean space. Among the most beautiful results of twentieth century convexity is Hadwiger's characterization theorem for the elementary mixed volumes (Quermassintegrals); (see [3, 5, 9]). Hadwiger's characterization leads to...

Let T be a Tannakian category over a field k of characteristic 0 and π(T ) its fundamental group. In this paper we prove that there is a bijection between the ⊗-equivalence classes of Tannakian subcategories of T and the normal affine group sub-T -schemes of π(T ). We apply this result to the Tannakian category T1(k) generated by motives of niveau ≤ 1 defined over k, whose fundamental group is ...

We give a direct proof of the existence of mixed fiber bodies which is not based upon the reduction to polytopes by continuity. It uses an explicit formula for the support function of a mixed fiber body instead. With the aid of this formula one can also compute the support function of a Newton polytope of a multidimensional resultant and prove a certain monotonicity property for mixed fiber bod...

In this article, we introduce a new concept of general mixed width-integral of convex bodies, and establish some of its inequalities, such as isoperimetric inequality, Aleksandrov-Fenchel inequality, and cyclic inequality. We also consider the general width-integral of order i and show its related properties and inequalities. c ©2016 All rights reserved.

Three-dimensional mathematical problems of the elasticity theory of anisotropic piecewise homogeneous bodies are discussed. A mixed type boundary contact problem is considered where on one part of the interface, rigid contact conditions are given (jumps of the displacement and the stress vectors are known), while on the remaining part screen or crack type boundary conditions are imposed. The in...

Abstract. A sharper L-error estimate is obtained for the non-Fickian flow of fluid in porous media by means of a mixed Ritz–Volterra projection instead of the mixed Ritz projection used in [R. E. Ewing, Y. Lin, and J. Wang, Acta Math. Univ. Comenian. (N.S.), 70 (2001), pp. 75–84]. Moreover, local L superconvergence for the velocity along the Gauss lines and for the pressure at the Gauss points ...

In this paper we show that mixed finite element methods for a fairly general second-order elliptic problem with variable coefficients can be given a nonmixed formulation. (Lower-order terms are treated, so our results apply also to parabolic equations.) We define an approximation method by incorporating some projection operators within a standard Galerkin method, which we call a projection fini...

Associated with the notion of the mixed Lp-affine surface area for multiple convex bodies for all real p (p 6= −n) which was introduced by Ye, et al. [D. Ye, B. Zhu, J. Zhou, arXiv, 2013 (2013), 38 pages], we define the concept of the mixed Lp-dual affine surface area for multiple star bodies for all real p (p 6= −n) and establish its monotonicity inequalities and cyclic inequalities. Besides, ...

The striking analogy between mixed volumes of convex bodies and mixed discriminants of positive semidefinite matrices has repeatedly been observed. It was A. D. Aleksandrov [1] who, in his second proof of the Aleksandrov–Fenchel inequalities for the mixed volumes, first introduced the mixed discriminants of positive semidefinite quadratic forms and established some of their properties, includin...