Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

A very special nonexistence theorem for abelian difference sets

It is wellknown that the technique of character sums together with the tools of algebraic number theory is the adequate method for the study of difference sets in abelian groups, compare for instance Ott [5] or Turyn [6]. In this paper we use this method to prove a new non-existence theorem for certain difference sets in abelian groups of order rp^a rp^a , where r 1 2 r \neq 2 and p are distinct primes.     

Optimal volume-corrected laplace-metropolis method

The article provides a refinement for the volume-corrected Laplace-Metropolis estimator of the marginal likelihood of DiCiccioet al. The correction volume of probability α in DiCiccioet al. is fixed and suggested to take the value α=0.05. In this article α is selected based on an asymptotic analysis to minimize the mean square relative error (MSRE). This optimal choice of α is shown to be invariant under linear transformations. The invariance property leads to easy implementation for multivariate problems. An implementation procedure is provided for practical use. A simulation study and a real data example are presented.     

Enhanced Binding in Non-Relativistic QED

 We consider a spinless particle coupled to a photon field and prove that even if the Schr?dinger operator p ² +V does not have eigenvalues the system can have a ground state. We describe the coupling by means of the Pauli-Fierz Hamiltonian and our result holds in the case where the coupling constant α is small. Received: 7 January 2002 / Accepted: 8 November 2002 Published online: 13 January 2003     

The focusing problem for the Eikonal equation

We study the focusing problem for the eikonal equation¶¶ ?_tu=| ?u| ², \partial _{t}u=\left| \nabla u\right| ^{2}, ¶¶i.e., the initial value problem in which the support of the initial datum is outside some compact set in R^d \mathbf{R}^{d} . The hole in the support will be filled in finite time and we are interested in the asymptotics of the hole as it closes. We show that in the radially symmetric case there are self-similar asymptotics, while in the absence of radial symmetry essentially any convex final shape is possible. However in R² \mathbf{R}^2 , for generic initial data the asymptotic shape will be either a vanishing triangle or the region between two parabolas moving in opposite directions (a closing eye). We compare these results with the known results for the porous medium pressure equation which approaches the eikonal equation in the limit as m? 1 m\rightarrow 1 .     

Rückbezüge des Mathematikunterrichts und der Methodik des Mathematikunterrichts in der DDR auf historische Vorausentwicklungen

The author discusses at some examples exemplarily, how the pedagogy of mathematics education in the GDR from curricular and educational/psychological knowledge from the time before 1945 has developed scientifically.     

Security Applications of Optical Face Recognition System: Access Control in E-Learning

The educational system has gradually shifted from a face-to-face to an e-learning system, which has become prevalent in advanced countries with the advance of information technology, and connection of global networks. Accordingly, a growing demand is emerging for more reliable individual certification with technical precision in order to measure and record learning achievements and credentials of participants. The present system has a limit in terms of registration capacity, therefore, its accuracy has often been questioned. Against this background, an individual certification system is proposed particularly for access control in e-learning. Under our proposed system, a compact optical correlator for facial recognition is employed. This correlator was previously tested for of biometrics authentication accuracy and proved highly reliable, having recorded remarkably low error rates (below 1%). The recorded error rate is sufficiently robust that the system itself can be regarded as a valid and practical viable attestation system.     

The Dual Properties of Lk-UR and k-SS Space

In this paper, we get some properties in the dual space of Lk-UR and k-SS Banach space.AMS Subject Classification: 46B09