On Overspill Principles and Axiom Schemes for Bounded Formulas

We study the theories I?_n, L?_n and overspill principles for ?_n formulas. We show that IE_n ? L?_n ? I?_n, but we do not know if I?_n L?_n. We introduce a new scheme, the growth scheme Crγ, and we prove that L?_n ? Cr?_n? I?_n. Also, we analyse the utility of bounded collection axioms for the study of the above theories. Mathematics Subject Classification: 03F30, 03H15.     

Existence and stability of bounded solutions for a system of parabolic equations

In this paper we study the existence and the stability of bounded solutions of the following non-linear system of parabolic equations with homogeneous Dirichlet boundary conditions:

     

Intransitive Permutation Group with Bounded Movement

Let G be a intransitive permutation group on a set with no fixed point in ; let m, n be a positive integer and let |^g – | m, for every and g G. When G has t orbits and degree n close to [2mp/(p – 1)] + t – 1, this paper constructs such a group with m close to [n(p – 1)/2p].AMS Subject Classification: 20BXX.     

On a rational differential quadrature method in irregular domains for problems with boundary layers

A rational differential quadrature method in irregular domains (RDQMID) is investigated to deal with a kind of singularly perturbed problems with boundary layers. Through a transformation, the boundary layer, which may be not straight, is transformed into a segment of a line parallel to one of the Cartesian axes. The rational differential quadrature method (RDQM) is applied to discretize the governing equation. Finally, a direct expansion method of the boundary conditions (DEMBC) is raised to deal with the boundary conditions. Numerical experiments show that RDQMID is of high accuracy, efficiency and easy to programme.     

Bounded holomorphic functions and maps with some boundary behavior

Let Ω be a domain of . As a study of boundary behavior of functions and maps in Ω, we consider “the linear cluster set,” which is the cluster set along segment terminating at a boundary point of Ω. We prove that there exist bounded holomorphic functions and maps defined in Ω which have the linear cluster sets of positive measure at every point of a discrete subset of the boundary of Ω under some conditions.     

Bounded edge-connectivity and edge-persistence of Cartesian product of graphs

The bounded edge-connectivity λ_k(G) of a connected graph G with respect to is the minimum number of edges in G whose deletion from G results in a subgraph with diameter larger than k and the edge-persistence D⁺(G) is defined as λ_d(G)(G), where d(G) is the diameter of G. This paper considers the Cartesian product G₁×G₂, shows λ_k1+k2(G₁×G₂)≥λ_k1(G₁)+λ_k2(G₂) for k₁≥2 and k₂≥2, and determines the exact values of D⁺(G) for G=C_n×P_m, C_n×C_m, Q_n×P_m and Q_n×C_m.     

Numerical methods for portfolio selection with bounded constraints

This work develops an approximation procedure for portfolio selection with bounded constraints. Based on the Markov chain approximation techniques, numerical procedures are constructed for the utility optimization task. Under simple conditions, the convergence of the approximation sequences to the wealth process and the optimal utility function is established. Numerical examples are provided to illustrate the performance of the algorithms.     

Another generalization of weighted Ostrowski type inequality for mappings of bounded variation

A new generalization of weighted Ostrowski type inequality for mappings of bounded variation with a unified sharp bound is established.     

Markov-type Inequalities for Surface Gradients of Multivariate Polynomials

Let K ^d be a compact set with a smooth boundary and consider a polynomial p of total degree n such that p_C(K)1. Then we show that D_Tp(x)=o(n²) for any x Bd K and T a tangential direction at x. Moreover, the o(n²) term is given in terms of the modulus of smoothness of Bd K.     

Photoinduced alignment of polymer liquid crystals containing azobenzene moieties in the side group VII. On He-Ne laser beam irradiation

Photoinduced alignment in a polymer liquid crystal prepared from 6-{1-[4-(2-cyano-4-nitrophenylazo)phenyl]piperazino}hexyl acrylate and 4'-[6-(methacryloyloxy)hexyloxy]-4-cyanobiphenyl was investigated for the first time on irradiation with a polarized He-Ne laser beam at 633 nm. The azobenzene moieties as well as the inert cyanobiphenyl mesogenic units were aligned with the molecular long axis perpendicular to the polarization direction of the irradiation light. Alignment induced on short irradiation was reversible, while that induced under prolonged irradiation was irreversible due to the occurrence of crosslinking which might be caused by photoinduced decomposition of the azobenzene moieties during the photoirradiation process.