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)     

Cardinality of the Set of Delta–Closed Classes of Functions of Multi–Valued Logic

A closure under composition operation and weak version of inversion operation is considered on the set of functions of k–valued logic. The cardinality of the set of all such closed classes is calculated.     

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.     

Construction of Runge–Kutta methods of Crouch–Grossman type of high order

An approach is described to the numerical solution of order conditions for Runge–Kutta methods whose solutions evolve on a given manifold. This approach is based on least squares minimization using the Levenberg–Marquardt algorithm. Methods of order four and five are constructed and numerical experiments are presented which confirm that the derived methods have the expected order of accuracy.     

Identifiability issues of age–period and age–period–cohort models of the Lee–Carter type

The predominant way of modelling mortality rates is the Lee–Carter model and its many extensions. The Lee–Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age–period or plug-in age–period–cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realizations, we investigate whether the expected values and covariances of the plug-in Lee–Carter models are identifiable. It will be seen, for example, that even if in both steps of the estimation procedure we have identifiability in a certain sense it does not necessarily carry over to the plug-in models.     

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.     

Representations of Khovanov–Lauda–Rouquier algebras and combinatorics of Lyndon words

We construct irreducible representations of affine Khovanov–Lauda–Rouquier algebras of arbitrary finite type. The irreducible representations arise as simple heads of appropriate induced modules, and thus our construction is similar to that of Bernstein and Zelevinsky for affine Hecke algebras of type A. The highest weights of irreducible modules are given by the so-called good words, and the highest weights of the ‘cuspidal modules’ are given by the good Lyndon words. In a sense, this has been predicted by Leclerc.     

Regularity properties of viscosity solutions of integro-partial differential equations of Hamilton–Jacobi–Bellman type

We study the regularity properties of integro-partial differential equations of Hamilton–Jacobi–Bellman type with the terminal condition, which can be interpreted through a stochastic control system, composed of a forward and a backward stochastic differential equation, both driven by a Brownian motion and a compensated Poisson random measure. More precisely, we prove that, under appropriate assumptions, the viscosity solution of such equations is jointly Lipschitz and jointly semiconcave in (t,x)∈Δ×R^d$(t,x)\in \Delta \times {\mathbb{R}}^d$, for all compact time intervals Δ$\Delta$ excluding the terminal time. Our approach is based on the time change for the Brownian motion and on Kulik’s transformation for the Poisson random measure.     

Inversion of the Cauchy–Bunyakovskii–Schwarz inequality

In the present paper, the inequality inverse to the Cauchy–Bunyakovskii–Schwarz inequality and generalizing other well-known inversions of this inequality is proved.     

Cellularity of cyclotomic Birman–Wenzl–Murakami algebras

We show that cyclotomic BMW algebras are cellular algebras.     

Analyticity of the Cox–Ingersoll–Ross semigroup

Positivity - We study the analyticity of the Cox–Ingersoll–Ross semigroup generated by $$\begin{aligned} A_r u=\nu ^2 xu''+\gamma u'+\beta x u'-rx u, \end{aligned}$$ in...     

Algebras of Quotients of Jordan–Lie Algebras

In this article, we introduce the notion of algebra of quotients of a Jordan–Lie algebra. Properties such as semiprimeness or primeness can be lifted from a Jordan–Lie algebra to its algebras of quotients. Finally, we construct a maximal algebra of quotients for every semiprime Jordan–Lie algebra.     

Cohen–Macaulayness of Rees Algebras of Modules

Abstract

The notion of quasi-polynomials is very important in the theory of functional identities. For example, results on quasi-polynomials were tools in the solution of long-standing Herstein's Lie map conjectures. In this paper, we show that functional identities involving quasi-polynomial of degree one have only standard solutions on d-free sets.     

Blow-up of Compressible Navier–Stokes–Korteweg Equations

Based on the results of Xin (Commun. Pure Appl. Math. 51(3):229–240, 1998), Zhang and Tan (Acta Math. Sin. Engl. Ser. 28(3):645–652, 2012), we show the blow-up phenomena of smooth solutions to the non-isothermal compressible Navier–Stokes–Korteweg equations in arbitrary dimensions, under the assumption that the initial density has compact support. Here the coefficients are generalized to a more general case which depends on density and temperature. Our work extends the previous corresponding results.     

Probabilistic interpretation of a coupled system of Hamilton–Jacobi–Bellman equations

In this paper, we give a probabilistic interpretation for a coupled system of Hamilton–Jacobi–Bellman equations using the value function of a stochastic control problem. First we introduce this stochastic control problem. Then we prove that the value function of this problem is deterministic and satisfies a (strong) dynamic programming principle. And finally, the value function is shown to be the unique viscosity solution of the coupled system of Hamilton–Jacobi–Bellman equations.