An upper bound on operator norms of compound matrices is presented and special cases that involve the l l and l norms are investigated The results are then used to obtain bounds on products of the largest or smallest eigenvalues of a matrix The research was started while the rst author visited the Technion in It was continued during a visit of the second author at Universit at Bielefeld and at ...

Casimir effect of a topologically nontrivial two-dimensional space-time, through Krein space quantization [1, 2], has been calculated. In other words, auxiliary negative norm states have been utilized here. Presence of negative norm states play the role of an automatic renormalization device for the theory. The negative norm states (which do not interact with the physical world) could be chosen...

A short review on infinite-dimensional Grassmann-Banach algebras (IDGBA) is presented. Starting with the simplest IDGBA over K = R with l 1-norm (suggested by A. Rogers), we define a more general IDGBA over complete normed field K with l 1-norm and set of generators of arbitrary power. Any l 1-type IDGBA may be obtained by action of Grassmann-Banach functor of projective type on certain l 1-spa...

In this paper we consider the problem of scattering of time-harmonic acoustic waves by a bounded sound soft obstacle in two and three dimensions, studying dependence on the wave number in two classical formulations of this problem. The first is the standard variational/weak formulation in the part of the exterior domain contained in a large sphere, with an exact Dirichletto-Neumann map applied ...

In this paper, we introduce a new family of mixed finite element spaces of higher order (k ≥ 1) on general quadrilateral grids. A typical element has two fewer degrees of freedom than the well-known RaviartThomas finite element RT[k], yet enjoys an optimal-order approximation for the velocity in L 2-norm. The order of approximation in the divergence norm is one less than the velocity, as is com...

Let p be a prime integer, F a field of characteristic not p, T the norm torus of a degree p extension field of F , and E a T -torsor over F such that the degree of each closed point on E is divisible by p (a generic T -torsor has this property). We prove that E is p-incompressible. Moreover, all smooth compactifications of E (including those given by toric varieties) are p-incompressible. The m...

In applying clustering to multivariate data, in which there are some largescale variables, clustering results depend on the variables more than the user’s needs. In such cases, we should standardize the data to control the dependency. For high-dimensional data, Doherty et al. (Appl Soft Comput 7:203–210, 2007) argued numerically that data standardization by variable range leads to almost the sa...

In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

Let F be a field of characteristic 0 or greater than d. Scharlau’s norm principle holds for separable field extensions K over F , for certain forms φ of degree d over F which permit composition. Introduction Let d ≥ 2 be an integer and let F be a field of characteristic 0 or > d. Let φ : V → F be a form of degree d on an F -vector space V of dimension n (i.e., after suitable identification, φ i...

Motivated by some applications in signal processing and machine learning, we consider two convex optimization problems where, given a cone K , a norm ‖ · ‖ and a smooth convex function f , we want either (1) to minimize the norm over the intersection of the cone and a level set of f , or (2) to minimize over the cone the sum of f and a multiple of the norm. We focus on the case where (a) the di...