Some Properties of a Class Self—homomorphism of BCI—algebras

ＢｙａＢＣＩ－ａｌｇｅｂｒａｗｅｍｅａｎａｎａｌｇｅｂｒａ（Ｘ；，０）ｏｆｔｙｐｅ（２，０）ｓａｔｉｓｆｙｉｎｇｔｈｅａｘｉｏｍｓ：（１）（（ｘｙ）（ｘｚ））（ｚｙ）＝０；（２）（ｘ（ｘｙ））ｙ＝０；（３）ｘｘ＝０；（４）ｘｙ＝ｙｘ＝０ｘ＝ｙｆｏｒａｎｙｘ，ｙａｎｄｚｉｎＸ．ＦｏｒａｎｙＢＣＩ－ａｌｇｅｂｒａＸ，ｔｈｅｒｅｌａｔｉｏｎ≤ｄｅｆｉｎｅｄｂｙｘ≤ｙｉｆａｎｄｏｎｌｙｉｆｘｙ＝０ｉｓａｐａｒｔｉａｌｏｒｄｅｒｏｎＸ［１］．ＩｎａｎｙＢＣＩ－ａｌｇｅｂｒａＸ，…     

Integrals of psi—function

To the author's knowledge, among the so—called special functions, the gamma function is a unique one which is defined by a linear difference equation and is a hyper—transcendental function. There exists an another well—known hyper—transcendental function called the psi function, which is merely the logarithmic derivative of the gamma function. In this paper the author consider an extension of the gamma function and then obtain a series of integrals of the psi function.     

Long-time Convergence of Fully Discrete Nonlinear Galerkin Method——Case of Finite-elements

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＴｈｅｎｏｎｌｉｎｅａｒＧａｌｅｒｋｉｎｍｅｔｈｏｄｉｓａｎｅｆｆｅｃｔｉｖｅｎｕｍｅｒｉｃａｌｍｅｔｈｏｄｆｏｒｓｏｌｖｉｎｇａｄｉｓｓｉｐａｔｉｖｅｅｖｏｌｕｔｉｏｎｅｑｕａｔｉｏｎ ,ｗｈｉｃｈｃａｎｂｅｒｅｇａｒｄｅｄａｓａｐｒｏｊｅｃｔｉｏｎｏｆｔｈａｔｅｑｕａｔｉｏｎｏｎｔｏａｎｏｎｌｉｎｅａｒａｐｐｒｏｘｉｍａｔｅｉｎｅｒｔｉａｌｍａｎｉｆｏｌｄ (ＡＩＭ )ｃｌｏｓｅｄｔｏｔｈｅａｔｔｒａｃｔｏｒ .ＴｈｅｒｅｆｏｒｅｔｈｅｎｏｎｌｉｎｅａｒＧａｌｅｒｋｉ…     

Existence Criteria of Blending Surfaces of Three Quadric Surfaces——Wu Wen-tsun''''s Formulae

Smoothly blending several implicit quadric surfaces with surfaces of the lowest degree is very useful in engineering technology.     

Continuity of integrated density of states — independent randomness

In this paper we discuss the continuity properties of the integrated density of states for random models based on that of the single site distribution. Our results are valid for models with independent randomness with arbitrary free parts. In particular in the case of the Anderson type models (with stationary, growing, decaying randomness) on the ν dimensional lattice, with or without periodic and almost periodic backgrounds, we show that if the single site distribution is uniformly α-Hölder continuous, 0 < α ≤ 1, then the density of states is also uniformly α-Hölder continuous.     

Numerical Mathematics——A Journal of Chinese Universities

Aims and Scope： Numerical Mathematics： A Journal of Chinese Universities （English Series） published quarterly. It is an international journal covering numerical methods, analysis and applications. The journal publishes original research papers in all branches of modern computational mathematics such as numerical linear algebra, numerical optimization, numerical differential equations and computational statistics. Papers containing new ideas, creative approaches and/or innovative applications as well as invited reviews are expected to appear regularly in the journal.     

On absolute convergence of Haar—Fourier series of superpositions of functions

В работе решены некот орые задачи, поставле нные П. Л. Ульяновым [5]. ПустьA _χ обозначает мн ожество тех функций?∈L(0, l), ряды Фурье которых вс юду абсолютно сходятся. Если? — вещественная функция на интервале [a, b], то для того, чтобы для каж дой?∈A _χ удовлетворяющей ус ловиюa≦?(t)≦b, 0≦t≦1, выполнялось включен ие?○?∈A _χ , необходимо и достато чно, чтобы? была лине йной функцией, т.е.?(x)=cx+d,x∈[a,b], гдеc иd — вещественны е постоянные. То же самое утвержден ие остается в силе, есл и заменить классA _? наA _χ ?C[0, 1]. Пусть далее? непреры вно дифференцируема я функция на [a,b]. Если некоторый мо дуль непрерывностиω и мод уль непрерывностиω(δ;?′) удовлетворяют услов ию \(\sum\limits_{n = 0}^\infty {\omega (\omega (2^{ - n} } ;\varphi '))\omega (2^{ - n} )< \infty ,\) , то?○?∈A _χ для каждой функци и?∈A _χ ∩H ^ω , гдеa≦?(t)≦b, 0≦t≦1.     

Graphlike Manifolds with the Type of the 1—skeleton of a 4—simplex

ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓｗｉｔｈｔｈｅＴｙｐｅｏｆｔｈｅ１－ｓｋｅｌｅｔｏｎｏｆａ４－ｓｉｍｐｌｅｘＧｕｏＴｕｏｙｉｎｇ（ＨｕａｚｈｏｎｇＮａｒｍａｌＵｎｉｖｅｒｓｄｙ，Ｗｕｈａｎ，Ｃｈｉｎａ）（郭驼英）ｈＴｈｅｃｏｎｃｅｐｔｏｆｇｒａｐ...     

A Generalization of C—semigroup

§ 1.ＴｈｅＧｅｎｅｒａｌＣ ｓｅｍｉｇｒｏｕｐ　Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅｌｅｔＸｂｅａＢａｎａｃｈｓｐａｃｅ,ａｎｄＢ(Ｘ)ｔｈｅｓｐａｃｅｏｆａｌｌｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｆｒｏｍＸｉｎｔｏＸ .　Ｄｅｆｉｎｉｔｉｏｎ 1 .1　ＳｕｐｐｏｓｅＣｉｓａｂｏｕｎｄｅｄｉｎｊｅｃｔｉｖｅｏｐｅｒａｔｏｒｆｒｏｍＸｉｎｔｏＸ .Ｔｈｅｆａｍｉｌｙｏｆｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓ (Ｓ(ｔ) ) ｔ≥ 0 ｉｓａｇｅｎｅｒａｌＣ ｓｅｍｉｇｒｏｕｐｉｆｉｔｈａｓｔｈｅｆｏｌｌｏｗｉｎｇ…     

Maintenance of light-standards—a case-study

This paper discusses several strategies for the maintenance of light-standards, where each light-standard consists of n independent and identical lamps screwed on a lamp assembly. The lamps are subject to stochastic failures, and must be correctly replaced if the number of failed lamps reaches a prespecified number m, a norm that is set by the local management to guarantee a minimum luminance. As lamps have an increasing hazard rate and there is a fixed cost of hoisting the assembly, we propose various variants of the m-failure group replacement rule which have in particular an age-criterion to indicate which of the non-failed lamps must be preventively replaced at the time that the assembly is lowered for a corrective lamp replacement. We show how the optimal threshold age can be determined. It appears that this modification reduces the long run average maintenance cost of the Europe Combined Terminals by approximately 8.3%.     

Global Asymptotics of Krawtchouk Polynomials——a Riemann-Hilbert Approach

In this paper, we study the asymptotics of the Krawtchouk polynomials KnN(z;p,q) as the degree n becomes large. Asymptotic expansions are obtained when the ratio of the parameters n/N tends to a limit c∈(0,1) as n→∞. The results are globally valid in one or two regions in the complex z-plane depending on the values of c and p; in particular, they are valid in regions containing the interval on which these polynomials are orthogonal. Our method is based on the Riemann-Hilbert approach introduced by Deift and Zhou.     

The Infinite—dimensional σ—widths of Besov Classes

Let (X(Rd),|.|X) be a normed space of real functions on Rd.Let >0 and Pα be the operator in X(Rd) defined by Pα f(x)=χα(x) f(x) (where χα(x) is thecharacteristic function of the cube Idα=［-α,α］d). Let L be asubspace of X(Rd). Set PαL=Pα f:f∈L. Suppose L islocally-finite dimensional, I.e., dim(Pα L,X)<+∞ for every >0.Then the following quantity is said to be the average dimension of L in X(in the sense of LED)(see ［1］).     

On the Stabilizer of the Automorphism Group of a 4—valent Vertex—transitive Graph with Odd—prime—power Order

Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p^κ（κ≥1） and let A be the full automorphism group of X.In this paper,we prove that the stabilizer Av of a vertex v in A is a 2-group if p≠5,or a {2,3}-group if p=5.Furthermore,if p=5|Av| is not divisible by 3^2.As a result ,we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p^κ(κ≥1） is at most 1-arc-transitive for p≠5 and 2-arc-transitive for p=5.     

RESEARCH ANNOUNCEMENTS——Structure of Solvable Quadratic Lie Algebras

Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics^[10，12，13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras. In this paper, we study solvable quadratic Lie algebras. In Section 1, we study quadratic solvable Lie algebras whose Cartan subalgebras consist of semi-simple elements. In Section 2,we present a procedure to construct a class of quadratic Lie algebras, and we can exhaust all solvable quadratic Lie algebras in such a way. All Lie algebras mentioned in this paper are finite dimensional Lie algebras over a field F of characteristic 0.     

Asymptotic behavior of the Landau—Lifshitz model of ferromagnetism

According to the classical theory of Weiss, Landau, and Lifshitz, on a microscopic scale a ferromagnetic body is magnetically saturated (i.e., |M| =: constant) and consists of regions in which the magnetization is uniform, separated by thin transition layers. Any stationary configuration corresponds to a minimum point of an energy functional in which a small parameter is present. The asymptotic behavior as 0 is studied here. It is easy to see that any sequence of minimizers contains a subsequenceM _j that converges to a fieldM. By means of a -limit procedure it is shown that this fieldM is a minimizer of a new functional containing a term proportional to the area of the surfaces separating different domains of uniform magnetization. TheC ^1, -regularity of these surfaces, for < 1/2, is also proved under suitable assumptions for the external magnetic field.     

Generators of Rings of Differential Operators on a Class of k—algebras

51.IlltroductionSmithL4JproPoseaso1vingprocedure,whichcIcternllnesl1olyno[nialresolutlonofI3:lrt1itldifferentialequationcorrespondingbysomecoordinateringsofirreduciblel7l;lnecurves.-I'l1lsprogrameventual1ydependsontl1edeterminationofgeneratorsofringsofdif…     

RESEARCH ANNOUGCEMENTS—Kolmogorov Width of Classes of Smooth Functions on the Sphere s^d—1

Let Rd be the d-dimensional Euclidean space and Sd-1 = {(x1,…,xd): x21 + … + x2d = 1} be the unit sphere of Rd equipped with the normal Lebesgue measure dσ(x).For r ＞ 0,denotc by Brp := Brp(Sd-1) (1 ≤ p ≤∞) the class of functions f on the sphere Sd-1 representable in the form