Search results for "Theorem"
showing 10 items of 1250 documents
An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications
2020
Author's accepted manuscript. This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Bergelson, V., Knutson, I. J. H. & Son, Y. (2020). An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications. International Mathematics Research Notices, 2021(19), 14965-15018 is available online at: https://academic.oup.com/imrn/article/2021/19/14965/5775499 and https://doi.org/10.1093/imrn/rnaa035. Generalized polynomials are mappings obtained from the conventional polynomials by the use of the operations of addition and multiplication and taking th…
Derived length and character degrees of solvable groups
2003
We prove that the derived length of a solvable group is bounded in terms of certain invariants associated to the set of character degrees and improve some of the known bounds. We also bound the derived length of a Sylow p-subgroup of a solvable group by the number of different p-parts of the character degrees of the whole group.
Degrees of characters in the principal block
2021
Abstract Let G be a finite group. We prove that if the set of degrees of characters in the principal p-block of G has size at most 2 then G is p-solvable, and G / O p ′ ( G ) has a metabelian normal Sylow p-subgroup. The general question of proving that if an arbitrary p-block has two degrees then their defect groups are metabelian remains open.
A primal-dual algorithm for the fermat-weber problem involving mixed gauges
1987
We give a new algorithm for solving the Fermat-Weber location problem involving mixed gauges. This algorithm, which is derived from the partial inverse method developed by J.E. Spingarn, simultaneously generates two sequences globally converging to a primal and a dual solution respectively. In addition, the updating formulae are very simple; a stopping rule can be defined though the method is not dual feasible and the entire set of optimal locations can be obtained from the dual solution by making use of optimality conditions. When polyhedral gauges are used, we show that the algorithm terminates in a finite number of steps, provided that the set of optimal locations has nonepty interior an…
Sylow Normalizers and Brauer Character Degrees
2000
Suppose that G is a finite group. In this note, we show that a local condition about Sylow normalizers is equivalent to a global condition on the degrees of certain irreducible Brauer characters of G. Theorem A. Let G be a finite p; q-solvable group, and let Q ∈ SylqG and P ∈ SylpG. Then every irreducible p-Brauer character of G of q′degree has p′-degree if and only if NGQ is contained in some G-conjugate of NGP. Theorem A needs a solvability hypothesis. If p = 7, then the irreducible p-Brauer characters of the group G = PSL2; 27 have degrees 1; 13; 26; 28. If we set q = 2, then each q′-degree is also a p′-degree.
Regular k-Surfaces
2012
Roughly speaking, a regular surface in \(\mathbb{R}^3\) is a two-dimensional set of points, in the sense that it can be locally described by two parameters (the local coordinates) and with the property that it is smooth enough (that is, there are no vertices, edges, or self-intersections) to guarantee the existence of a tangent plane to the surface at each point.
Induced &#x2113;<inf>2</inf> control of discrete-time Takagi-Sugeno fuzzy systems with time-varying delays via dynamic output feedback
2012
This paper is concerned with analyzing a novel model transformation of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new auxiliary model is proposed by employing a new approximation for time-varying delay state, and then delay partitioning method is used to analyze the scaled small gain of this auxiliary model. A sufficient condition on discrete-time T-S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced l 2 disturbance attenuation performance, is derived by employing the scaled small gain theorem. Then the…
Homogeneous Suslinian Continua
2011
AbstractA continuumis said to be Suslinian if it does not contain uncountably many mutually exclusive non-degenerate subcontinua. Fitzpatrick and Lelek have shown that a metric Suslinian continuum X has the property that the set of points at which X is connected im kleinen is dense in X. We extend their result to Hausdorff Suslinian continua and obtain a number of corollaries. In particular, we prove that a homogeneous, non-degenerate, Suslinian continuum is a simple closed curve and that each separable, non-degenerate, homogenous, Suslinian continuum is metrizable.
Existence of a traveling wave solution in a free interface problem with fractional order kinetics
2021
Abstract In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 α 1 . We turn the free interface problem into a scalar free boundary problem coupled with an integral equation. The main intermediary step is to reduce the scalar problem to the study of a non-Lipschitz vector field in dimension 2. The latter is treated by qualitative topological methods based on the Poincare-Bendixson Theorem. The phase portrait is determined and the existence of a stable manifold at the origin is proved. A significant result is that the settling time to reach the origin is fin…
Integrating functional traits into correlative species distribution models to investigate the vulnerability of marine human activities to climate cha…
2021
Climate change and particularly warming are significantly impacting marine ecosystems and the services they provided. Temperature, as the main factor driving all biological processes, may influence ectotherms metabolism, thermal tolerance limits and distribution species patterns. The joining action of climate change and local stressors (including the increasing human marine use) may facilitate the spread of non-indigenous and native outbreak forming species, leading to associated economic consequences for marine coastal economies. Marine aquaculture is one among the most economic anthropogenic activities threatened by multiple stressors and in turn, by increasing hard artificial substrates …