Track–Monitoring of Wheel–Rail–Systems

Inspection and maintenance of railway networks is a complex and expensive task. Special measurement vehicles are used to record the geometrical properties of railway lines within required time intervals. Due to the extent of measurement data the quality of railway track is evaluated considering only a few parameters. Although safety and comfort of wheel–rail–systems depend on the dynamical behavior, current inspection vehicles are not equipped to measure dynamic properties. In this paper, we will discuss a novel approach to evaluate the quality of railway tracks based on wheel–rail dynamics: Wheelset dynamics of subway trains are analyzed by Karhunen–Loève Transformation to extract the principal dynamics from the collected measurement data. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On theorems of Delsarte–McEliece and Chevalley–Warning–Ax–Katz

We present a theorem that generalizes the result of Delsarte and McEliece on the p-divisibilities of weights in abelian codes. Our result generalizes the Delsarte–McEliece theorem in the same sense that the theorem of N. M. Katz generalizes the theorem of Ax on the p-divisibilities of cardinalities of affine algebraic sets over finite fields. As the Delsarte–McEliece theorem implies the theorem of Ax, so our generalization implies that of N. M. Katz. The generalized theorem gives the p-divisibility of the t-wise Hamming weights of t-tuples of codewords (c ⁽¹⁾, . . . ,c ^(t)) as these words range over a product of abelian codes, where the t-wise Hamming weight is defined as the number of positions i in which the codewords do not simultaneously vanish, i.e., for which ${(c^{(1)}_i,\ldots,c^{(t)}_i)\not=(0,\ldots,0)}$ . We also present a version of the theorem that, for any list of t symbols s ₁, . . . ,s _t , gives p-adic estimates of the number of positions i such that ${(c^{(1)}_i,\ldots,c^{(t)}_i)=(s_1,\ldots,s_t)}$ as these words range over a product of abelian codes.     

Discrete potential Ablowitz–Kaup–Newell–Segur equation

We establish a discrete model for the potential Ablowitz–Kaup–Newell–Segur equation via a generalized Cauchy matrix approach. Soliton solutions and Jordan block solutions of this equation are presented by solving the determining equation set. By applying appropriate continuum limits, we obtain two semi-discrete potential Ablowitz–Kaup–Newell–Segur equations. The reductions to real and complex discrete and semi-discrete potential modified Korteweg-de Vries equations are also discussed.     

Orlicz–Brunn–Minkowski inequalities for Blaschke–Minkowski homomorphisms

Orlicz–Brunn–Minkowski type inequalities for Blaschke–Minkowski homomorphisms and their polars are established.     

On the Carey–Helton–Howe–Pincus trace formula

In this article, we give a new proof of the Carey–Helton–Howe–Pincus trace formula using Kato's theory of “relatively-smooth” operators and Krein's trace formula.     

Multiple Vortices in the Aharony–Bergman–Jafferis–Maldacena Model

Vortices in non-Abelian gauge field theory play important roles in confinement mechanism and are governed by systems of nonlinear elliptic equations of complicated structures. In this paper, we present a series of existence and uniqueness theorems for multiple vortex solutions of the BPS vortex equations, arising in the dual-layered Chern–Simons field theory developed by Aharony, Bergman, Jafferis, and Maldacena, over ${\mathbb{R}^2}$ and on a doubly periodic domain. In the full-plane setting, we show that the solution realizing a prescribed distribution of vortices exists and is unique. In the compact setting, we show that a solution realizing n prescribed vortices exists over a doubly periodic domain ${\Omega}$ if and only if the condition $$n < \frac{\lambda |\Omega|}{2 \pi}$$ holds, where ${\lambda >0 }$ is the Higgs coupling constant. In this case, if a solution exists, it must be unique. Our methods are based on calculus of variations.     

Rota–Baxter Hom-Lie–Admissible Algebras

We study Hom-type analogs of Rota–Baxter and dendriform algebras, called Rota–Baxter G-Hom–associative algebras and Hom-dendriform algebras. Several construction results are proved. Free algebras for these objects are explicitly constructed. Various functors between these categories, as well as an adjunction between the categories of Rota–Baxter Hom-associative algebras and of Hom-(tri)dendriform algebras, are constructed.     

Set-Valued Kurzweil–Henstock–Pettis Integral

It is shown that the obvious generalization of the Pettis integral of a multifunction obtained by replacing the Lebesgue integrability of the support functions by the Kurzweil–Henstock integrability, produces an integral which can be described – in case of multifunctions with (weakly) compact convex values – in terms of the Pettis set-valued integral.Mathematics Subject Classifications (2000) Primary: 28B20; secondary: 26A39, 28B05, 46G10, 54C60.     

Dual Orlicz–Brunn–Minkowski theory

In this paper, a dual Orlicz–Brunn–Minkowski theory is presented. An Orlicz radial sum and dual Orlicz mixed volumes are introduced. The dual Orlicz–Minkowski inequality and the dual Orlicz–Brunn–Minkowski inequality are established. The variational formula for the volume with respect to the Orlicz radial sum is proved. The equivalence between the dual Orlicz–Minkowski inequality and the dual Orlicz–Brunn–Minkowski inequality is demonstrated. Orlicz intersection bodies are defined and the Orlicz–Busemann–Petty problem is posed.     

Homogenized Diffusion Limit of a Vlasov–Poisson–Fokker–Planck Model

The approximation by diffusion and homogenization of the initial-boundary value problem of the Vlasov–Poisson–Fokker–Planck model is studied for a given velocity field with spatial macroscopic and microscopic variations. The L¹-contraction property of the Fokker–Planck operator and a two-scale Hybrid-Hilbert expansion are used to prove the convergence towards a homogenized Drift–Diffusion equation and to exhibit a rate of convergence.     

Realisations of Kummer–Chern–Eisenstein-motives

Inspired by work of G. Harder we construct via the motive of a Hilbert modular surface an extension of a Tate motive by a Dirichlet motive. We compute the realisation classes and indicate how this is linked to the Hodge-1-motive of the given Hilbert modular surface.     

Cohen–Macaulay Multi–Rees Algebras

Let A be a local ring, and let I ₁,...,I _r A be ideals of positive height. In this article we compare the Cohen–Macaulay property of the multi–Rees algebra R _A (I ₁,...,I _r ) to that of the usual Rees algebra R _A (I ₁ ··· I _r ) of the product I ₁ ··· I _r . In particular, when the analytic spread of I ₁ ··· I _r is small, this leads to necessary and sufficient conditions for the Cohen–Macaulayness of R _A (I ₁,...,I _r ). We apply our results to the theory of joint reductions and mixed multiplicities.     

On Fano and weak Fano Bott–Samelson–Demazure–Hansen varieties

Let G be a simple algebraic group over the field of complex numbers. Fix a maximal torus T and a Borel subgroup B of G containing T. Let w be an element of the Weyl group W of G, and let $Z(\stackrel{?}{w})$ be the Bott–Samelson–Demazure–Hansen (BSDH) variety corresponding to a reduced expression $\stackrel{?}{w}$ of w with respect to the data $(G,B,T)$.In this article we give complete characterization of the expressions $\stackrel{?}{w}$ such that the corresponding BSDH variety $Z(\stackrel{?}{w})$ is Fano or weak Fano. As a consequence we prove vanishing theorems of the cohomology of tangent bundle of certain BSDH varieties and hence we get some local rigidity results.     

Edgeworth–Cornish–Fisher–Hill–Davis expansions for normal and non-normal limits via Bell polynomials

Cornish and Fisher gave expansions for the distribution and quantiles of asymptotically normal random variables whose cumulants behaved like those of a sample mean. This was extended by Hill and Davis to the case, where the asymptotic distribution need not be normal. Their results are cumbersome as they involve partition theory. We overcome this using Bell polynomials. The three basic expansions (for the distribution and its derivatives, for the inverse of the quantile, and for the quantile) involve three sets of polynomials. We give new ways of obtaining these from each other. The Edgeworth expansions for the distribution and density rest on the Charlier expansion. We give an elegant form of these as linear combinations of generalized Hermite polynomials, using Bell polynomials.