Search results for "Theorem"

A Mountain Pass Theorem for a Suitable Class of Functions

2009

About the evaluation of the local kinetic, potential and total energy densities in closed-shell interactions

2001

Abstract The local kinetic G( r ) , potential V( r ) and total E( r ) energy densities, calculated at the critical points of 37 H⋯F closed-shell interactions by quantum mechanical methods, have been compared to their estimated values obtained by using an approximate evaluation of G( r ) and the local form of the virial theorem. The results presented here show very small differences between the corresponding quantities, and therefore support the validity of the estimations. Thus, the equations used in this procedure provide useful information for topological studies of experimental electron densities, permitting the evaluation of those energetic properties from the modelling of the topologic…

Co-simulation and Formal Verification of Co-operative Drone Control With Logic-Based Specifications

2021

Abstract Unmanned aerial vehicle (UAV) co-operative systems are complex cyber-physical systems that integrate a high-level control algorithm with pre-existing closed implementations of lower-level vehicle kinematics. In model-driven development, simulation is one of the techniques that are usually applied, together with testing, in the analysis of system behaviours. This work proposes a method and tools to validate the design of UAV co-operative systems based on co-simulation and formal verification. The method uses the Prototype Verification System, an interactive theorem prover based on a higher-order logic language, and the Functional Mock-up Interface, a widely accepted standard for co-…

Abundance and Distribution Patterns of Thunnus albacares in Isla del Coco National Park through Predictive Habitat Suitability Models

2016

Information on the distribution and habitat preferences of ecologically and commercially important species is essential for their management and protection. This is especially important as climate change, pollution, and overfishing change the structure and functioning of pelagic ecosystems. In this study, we used Bayesian hierarchical spatial-temporal models to map the Essential Fish Habitats of the Yellowfin tuna (Thunnus albacares) in the waters around Isla del Coco National Park, Pacific Costa Rica, based on independent underwater observations from 1993 to 2013. We assessed if observed changes in the distribution and abundance of this species are related with habitat characteristics, fis…

Induction and Character Correspondences in Groups of Odd Order

2002

Abstract Let P be a Sylow p -subgroup of G . By Irr p ′ ( G ), we denote the set of irreducible characters of G which have degree not divisible by p . When G is a solvable group of odd order, M. Isaacs constructed a natural one-to-one correspondence *:Irr p ′ ( G ) → Irr p ′ ( N G ( P )) which depends only on G and P . In this paper, we show that if ξ G  = χ ∈ Irr p ′ ( G ), then (ξ*) N G ( P )  = χ*.

On p-Brauer characters of p′-degree and self-normalizing Sylow p-subgroups

2010

ZEROS OF CHARACTERS ON PRIME ORDER ELEMENTS

2001

Suppose that G is a finite group, let χ be a faithful irreducible character of degree a power of p and let P be a Sylow p-subgroup of G. If χ(x) ≠ 0 for all elements of G of order p, then P is cyclic or generalized quaternion. * The research of the first author is supported by a grant of the Basque Government and by the University of the Basque Country UPV 127.310-EB160/98. † The second author is supported by DGICYT.

Transitive factorizations in the hyperoctahedral group

2008

The classical Hurwitz enumeration problem has a presentation in terms of transitive factor- izationsin the symmetric group. This presentationsuggestsageneralizationfromtypeAto otherfinite reflection groups and, in particular, to type B.W e study this generalization both from ac ombinatorial and a geometric point of view, with the prospect of providing am eans of understanding more of the structure of the moduli spaces of maps with an S2-symmetry. The type A case has been well studied and connects Hurwitz numbers to the moduli space of curves. W ec onjecture an analogous setting for the type B case that is studied here. 1I ntroduction Transitive factorizations of permutations into transposit…

Zur Existenz von Lösungen gewisser Randwertaufgaben

1971

With the aid of some known results about integral equations of the Hammerstein type there is proofed an existence theorem for the following class of boundary value problems−y″−l 2 y′=f(x,y),y(a)=y(b)=0,l 2>0 mit|f(x, y)|=0,l 3 (x)>0. The existence range is determined by the greatest eigenvalue of some linear problem.

Fuzzy $$\varphi $$ -pseudometrics and Fuzzy $$\varphi $$ -pseudometric Spaces

2017

By replacing the axiom \(m(x,x,t) = 1\) for all \(x\in X, t>0\) in the definition of a fuzzy pseudometric in the sense of George-Veeramani with a weaker axiom \(m(x,x,t) = \varphi (t)\) for all \(x\in X, t>0\) where \(\varphi : {\mathbb R}^+ \rightarrow (0,1]\) is a non-decreasing function, we come to the concept of a fuzzy \(\varphi \)-pseudometric space. Basic properties of fuzzy \(\varphi \)-pseudometric spaces and their mappings are studied. We show also an application of fuzzy \(\varphi \)-pseudometrics in the words combinatorics.