基于[λ，μ]-截段的一般分解定理和截段矩阵

推广了λ-截集的定义,提出并证明了一般分解定理,在此基础上定义了截段矩阵并讨论了它的一些性质以及[λ,μ]-截段.     

The nonexistence of ternary [105,6,68] and [230,6,152] codes

Let [n,k,d]_q-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). In this paper, the nonexistence of [105,6,68]₃ and [230,6,152]₃ codes is proved.     

Addendum to “On Attractors of Multivalued Semiflows and Differential Inclusions” [Set-Valued Anal., 6 (1998), 83–111]

In this note we extend a previous result concerning the existence of global compact attractors for multivalued semiflows in metric spaces.      

Lightning modeling and protection zone of conducting rod using Monte Carlo technique

Lightning strike is a harmful process and protection from lightning using conducting rods has been a subject of discussion for decades. In particular, there have been a lot of researches regarding the protection zone of a single conducting rod. This is important for the purpose of installing them to protect complex building structures. In the present article, the protection zone of a conducting rod has been obtained by Monte Carlo simulation method. The lightning process has been modeled for computer simulation. The authors have presented a new Monte Carlo modeling of lightning path. The origin of the downward stepped leader and the magnitude of peak current of the return stroke have appropriate random distributions. The obtained results are compared with already available experimental results present in various literatures. It is shown that this technique is reliable and in fair agreement with the established theories for finding protection zone of conducting rods.     

Modelling and resonance of a flexible rod using a floating reference frame

A direct variational approach with a floating frame is presented to derive the ordinary differential equations of motion of a flexible rod, constant crank speed slider-crank mechanism. Potential energy terms contained in the derivation include beam-bending energy and energy in foreshortening of the rod tip (which were selected because of the importance of these terms in a pinned-pinned rod parametric resonance). A symbolic manipulator code is used to reduce the constrained equations of motion to unconstrained nonlinear equations. A linearized version of these equations is used to explore parametric resonance stability-instability zones by a monodromy matrix technique.     

On the bases of the spaces L1[0, 1] and C[0, 1]

New and simple proofs are given for the non-existence of unconditional bases in the spaces L₁[0, 1] and C[0, 1].Translated from Matematicheskie Zametki, Vol. 11, No. 3, pp. 241–249, March, 1972.The author wishes to thank P. L. Ul'yanov for his interest in the problem under consideration.     

The Versatility of MMAP[K] and the MMAP[K]/G[K]/1 Queue

This paper studies a single server queueing system with multiple types of customers. The first part of the paper discusses some modeling issues associated with the Markov arrival processes with marked arrivals (MMAP[K], where K is an integer representing the number of types of customers). The usefulness of MMAP[K] in modeling point processes is shown by a number of interesting examples. The second part of the paper studies a single server queueing system with an MMAP[K] as its input process. The busy period, virtual waiting time, and actual waiting times are studied. The focus is on the actual waiting times of individual types of customers. Explicit formulas are obtained for the Laplace–Stieltjes transforms of these actual waiting times.     

Toughness of Graphs and [2,b]-Factors

A sharp bound of the toughness of a graph for the existence of a [2,b]-factor is given in this paper, whereb > 2.     

Coverings of [MO n ] and minimal orthomodular lattices

If T is an orthomodular lattice (OML), we denote by [T] the equational class generated by T. In this paper we characterize the finite OMLs T such that [T] covers some [MO _n ]. These OMLs T are the non-modular OMLs such that all proper sub-OMLs of T are modular. An OML satisfying that last property is called minimal. There exist infinitely many minimal OMLs provided by quadratic spaces over finite fields. We describe them and give a new way to represent their Greechie diagrams in two separate parts. Other methods to obtain finite minimal OMLs are given. Received May 14, 2005; accepted in final form May 30, 2007.     

On a Property of the Franklin System in C[0, 1] and L1[0, 1]

Mathematical Notes - A problem posed by J. R. Holub is solved. In particular, it is proved that if $$\left\{ {{{\tilde f}_n}} \right\}$$ is the normalized Franklin system in L1[0, 1], {an} is a...     

On residual coordinates and stable coordinates of R [3]

Let R be a polynomial ring over ${\mathbb{C}}$ . In this paper we show that a polynomial in R ^[3] is a residual coordinate if and only if it is a stable coordinate.     

R_0-代数[0,1]的子代数与广义重言式

本文是对修正的Kleene系统中广义重言式理论的推广,讨论了R_0-代数[0,1]的各类无限子R_0-代数中的广义重言式,证明了在子R_0-代数E_2中,中存在着可数多个不同的广义重言式。     

Electrodeposition of copper on copper single crystal (100), (110) and (111) planes in presence of Thiosemicarbazide

Thiosemicarbazide (TSC), present in small quantities in acid copper sulphate bath, modifies the growth habits of copper on copper single crystal planes and reduces cathodic polarization. On (100) plane a transition from layer type of growth to ridge type and from ridges to pyramidal type and finally to polycrystalline type was noticed. On (110) plane ridges change to platelet type then finally to polycrystalline type. On (111) plane at low current densities triangular pyramids formed in pure solution transforms to hexagonal pyramids and to polycrystalline type. At high current densities hexagonal pyramids change to layer type, which transforms to nonsymmetrical pyramids and polycrystalline deposit at critical concentration of the addition agent. The transitions noticed depend on the concentrations of TSC and current density. These changes in morphology are attributed to the adsorption of TSC on the substrate.     

Conjugacy Classes and Invariant Subrings of R-Automorphisms of R[x]

We consider the group G of R-automorphisms of the polynomial ring R[x] in the case where the ring R has nonzero nilpotent elements. Little is known about G in this case, and because of the importance of G in understanding questions involving the polynomial ring R[x], we initiate here several lines of investigation. We do this by examining in detail examples involving the ring of integers modulo n. If R is a local ring with maximal ideal m such that R/m = ?₂ and m ² = (0), we describe more explicitly the structure of G and determine all rings of invariants of R[x] with respect to subgroups of G.     

Coordinates of R[x,y]: Constructions and Classifications

Let R be a PID. We construct and classify all coordinates of R[x, y] of the form p ₂ y + Q ₂(p ₁ x + Q ₁(y)) with p ₁, p ₂ ∈ qt(R) and Q ₁, Q ₂ ∈ qt(R)[y]. From this construction (with R = K[z]) we obtain nontame automorphisms σ of K[x, y, z] (where K is a field of characteristic 0) such that the subgroup generated by σ and the affine automorphisms contains all tame automorphisms.     

The convolution equation of Choquet and Deny on [IN]-groups

Let be a probability measure on a locally compact groupG. A real Borel functionf onG is called -harmonic if it satisfies the convolution equation *f=f. Given that isnonsingular with its translates, we show that the bounded -harmonic functions are constant on a class of groups including the almost connected [IN]-groups. If is nondegenerate and absolutely continuous, we solve the more general equation *= for positive measure on those groups which are metrizable and separable.Supported by Hong Kong RGC Earmarked Grant and CUHK Direct Grant     

K[X]~m中模的生成基及其应用

本文研究了多项式环上的素模中的生成基理论和方法．通过建立新的约化准则,得到了模中生成基的结构和机械化计算方法．对于低维情形给出了素模中生成基的充分必要条件．文中的方法本质地简化了传统的模中Ｇｒｏｂｎｅｒ基方法．文中同时介绍了该方法在样条理论研究中的应用,并给出了一些计算例子．