We present a Weyl-type relative bound for eigenvalues of Hermitian perturbations A + E of (not necessarily definite) Hermitian matrices A. This bound, given in function of the quantity η = ‖A−1/2EA−1/2‖2, that was already known in the definite case, is shown to be valid as well in the indefinite case. We also extend to the indefinite case relative eigenvector bounds which depend on the same qua...

This paper concerns the maximum genus orientable surface upon which a given graph cellularly embeds. Classical theorems of Xuong and Nebesk y give exact values for the maximum genus. The former is suited to constructing embeddings while the latter is suited to forbidding embeddings of larger genus. However, using either theorem alone requires an exhaustive search to establish the exact value. H...

Let M be a closed manifold, ρ a representation of π1(M) on an A-Hilbert model W of finite type (A a finite von Neumann algebra) and μ a Hermitian structure on the flat bundle E → M associated to ρ. The relative torsion, first introduced by Carey, Mathai and Mishchenko, [CMM], associates to any pair (g, τ), consisting of a Riemannian metric g on M and a generalized triangulation τ = (h, g), a nu...

The aim of this paper is to improve a theorem of János Kollár by a different method. For a given smooth Complex projective threefold X of general type, suppose the plurigenus Pk(X) ≥ 2, Kollár proved that the (11k + 5)-canonical map is birational. Here we show that either the (7k+3)-canonical map or the (7k+5)-canonical map is birational and the (13k+6)-canonical map is stably birational onto i...

By introducing the notion of relative derangements of type B, also called signed relative derangements, which are defined in terms of signed permutations, we obtain a type B analogue of the well-known relation between the relative derangements and the classical derangements. While this fact can be proved by using the principle of inclusion and exclusion, we present a combinatorial interpretatio...

In this paper, we present a semi-analytical model for determining the magnetic and electromagnetic characteristics of spoke-type permanent magnet (STPM) machine considering magnet segmentation and finite soft-material relative permeability. The proposed model is based on the resolution of the Laplace’s and Poisson’s equations in a Cartesian pseudo-coordinate system with respect to the relative ...

This article reconsiders the relative-velocity-dependent approach to modeling electromagnetism that was proposed initially by Weber before data from cathode-ray-tube (CRT) experiments was available. It is shown that identifying the nonlinear, relative-velocity terms using CRT data results in a model, which not only captures standard relativistic effects in optics, high-energy particles, and gra...

This paper considers an Extended Generalized Half Logistic distribution. We derive some properties of this distribution and then we discuss estimation of the distribution parameters by the methods of moments, maximum likelihood and the new method of minimum spacing distance estimator based on complete data. Also, maximum likelihood equations for estimating the parameters based on Type-I and Typ...