We analyze cosmological equations in the brane world scenario with one extra space-like dimension. We demonstrate that the cosmological equations can be reduced to the usual 4D Friedmann type if the bulk energy-momentum tensor is different from zero. We then generalize these equations to the case of a brane of finite thickness. We also demonstrate that when the bulk energy-momentum tensor is di...

The built up layer thickness in secondary deformation zone is one of the important parameters in metal cutting process. The built up layer (BUL) is formed in second deformation zone near the tool-chip interface in the back of the chip. This parameter influences the tool life and machined surface quality. This BUL should not be confused with the built up edge (BUE). The deformation of the BUL in...

We consider the spectrum of the Fibonacci Hamiltonian for small values of the coupling constant. It is known that this set is a Cantor set of zero Lebesgue measure. Here we study the limit, as the value of the coupling constant approaches zero, of its thickness and its Hausdorff dimension. We announce the following results and explain some key ideas that go into their proofs. The thickness tend...

Abstract. The recently introduced perfectly matched layer (PML) method is an efficient method to reduce the exterior wave propagation problem which is defined in the unbounded domain to the problem in the bounded domain. Under the assumption that the exterior solution is composed of outgoing waves only, the basic idea of the PML technique is to surround the computational domain by a layer of fi...

Abstract: In this paper, the forming process of a central hub by radial-forward extrusion is analyzed by using the finite element software, ABAQUS. Radial-forward extrusion is used to produce hollow parts that generally feature a central hub with radial protrusions. Effective design factors such as mandrel diameter, die corner radius, die fillet radius, mandrel corner radius, tube wall thick...

Introduction. Borocoppering is one of the methods thermochemical treatment (TCT) aimed at forming diffusion layers with high physical and mechanical properties on surface carbon alloy steels. The thickness layer most important characteristic TCT, which determines depth hardening. Consequently, intensity main characteristics TCT (layer thickness, alloying element concentration profile) depend pr...

Finite element methods for the Reissner–Mindlin plate theory are discussed. Methods in which both the tranverse displacement and the rotation are approximated by finite elements of low degree mostly suffer from locking. However a number of related methods have been devised recently which avoid locking effects. Although the finite element spaces for both the rotation and transverse displacement ...