优化练习设计 增强教学效果

优化练习设计增强教学效果席亚仑教师备课，要重视习题的设计，从内容到形式，都应仔细推敲，使每一道习题都能发挥较好的作用．为提高练习的教学效果，在练习中要处理对以下关系．一、量与质的关系练习要有一定的量，但要避免过量与机械重复，遍免增加学生不必要的负担。...

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The calculation for C-G coefficients

The eigenfunction method put forward by Chen Jin-quan is illustrated. We apply this theory to the space group D1_ 6h. The selection rules of this space are worked out in the points of higher symmetry A,K,H in the first Brillion Zone. The C-G coefficients are calculated for K.HA.

The C-G coefficients for the space group D_6~1h

In this paper, the eigenfunction method established by Chen Jin-quan is used to compute the C-G coefficients in regard to the coupling between symmetry points and lines in the first Brillouin zone of the structure D6h^1, space group. Therewith, the wave vector selection rule and the C-G series, are also given as the middle result of computing the C-G coefficients.

New Pseudorandom Number Generator Artin-Sc hreier Tower for p = 5

The standard method to construct a finite field requires a primitive irreducible polynomial of a given degree. Therefore, it is difficult to apply for the construction of huge finite fields. To avoid this problem, we propose a new method to construct huge finite fields with the characteristic p = 5 by using an Artin-Schreier tower. Utilizing the recursive basis of the Artin-Schreier tower, we define a nmltiplication algorithm The algorithm can explicitly calculate the multiplication of two elements on the top finite field of this tower, without any primitive element. We also define a linear recurrence equation as an application, which produces a sequence of numbers, and call the new pseudorandom number generator Abstract Syntax Tree （AST） for p = 5. The experircental results show that our new pseudorandom number generator can produce a sequence of numbers with a long period.

Symmetry Reductions of Two-Dimensional Variable Coefficient Burgers Equation

By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial differential equation and three types of symmetry reducing VCBurgers to ordinary differential equation are obtained.

Representation of Simple(n+1)-Dimensional n-Lie Algebras

This paper gives the sufficient and necessary conditions when an irreducible L（A）- module is an A-module, and gets the classification of finite dimensional irreducible representations of simple （n ＋1）-dimensional n-Lie algebras.

The Irreducibility and Isomorphism of Piecewise Algebraic Sets

In this paper , we define the piecewise algebraic sets by using multivariatespline functions and discuss their irreducibility and isomorphism problem. We presenttwo equivalent conditions for the irreducibility of piecewise algebraic sets, and turn theisomorphism and classifying problem of piecewise algebraic sets into the isonorphismand classifying problem of commutative algebras.

DECOMPOSITIONS OF BOSONIC MODULES OF LIE ALGEBRAS W_(1+∞) AND W_(1+∞)(gl_N)

A bosonic construction (with central charge c = 2) of Lie algebras W1+∞ and W1+∞ (glN), as well as the decompositions into irreducible modules are described. And for W1+∞, when restricted to its Virasoro subalgebra Vir, a bosonic construction and the same decomposition for Vir are obtained.

CONSTRUCTION OF INDECOMPOSABLEDEFINITE HERMITIAN FORMS

This Paper gives a method to construct indecomposable positive definite integral Hermitianforman imnginary quadratic field Q with gin discriminant and g。n rank.It is shown that for ally natural numbers n and a, there are n-ary Indecomposable positivedefinite intopal Herlllltian lattices over Q(resp. Q)with discriminant a, exceptfor four(resp. one) exceptions. In these exceptional cases there are no lattices with the desiredproperties.

Similarity invariants of operators on a class of Gowers-Maurey spaces

This paper studies the similarity invariants of operators on a class of Gowers-Maurey spaces, ∑dc spaces, where an infinite dimensional Banach space X is called a ∑dc space if for every bounded linear operator on X the spectrum is disconnected unless it is a singleton. It shows that two strongly irreducible operators T1 and T2 on a ∑dc space are similar if and only if theK0-group of the commutant algebra of the direct sum T1 GT2 is isomorphic to the group of integers Z. On a ∑dc space X, it uses the semigroups of the commutant algebras of operators to give a condition that an operator is similar to some operator in （∑SI）（X）, it further gives a necessary and sufficient condition that two operators in （∑SI）（X） are similar by using the ordered K0-groups. It also proves that every operator in （∑SI）（X） has a unique （SI） decomposition up to similarity on a ∑dc space X, where （∑SI）（X） denotes the class of operators which can be written as a direct sum of finitely many strongly irreducible operators.

Indecomposable modules of the intermediate series over W(a,b)

For any complex parameters a and b,W(a,b)is the Lie algebra with basis{Li,Wi|i∈Z}and relations[Li,Lj]=(j i)Li+j,[Li,Wj]=(a+j+bi)Wi+j,[Wi,Wj]=0.In this paper,indecomposable modules of the intermediate series over W(a,b)are classified.It is also proved that an irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight module or a uniformly bounded module.Furthermore,if a∈/Q,an irreducible weight W(a,b)-module is simply a Vir-module with trivial actions of Wk’s.

Regularity of vertex operator superalgebras

We prove that the regularity of a vertex operator superalgebra can be reduced to the semisimplicity of the category of its weak modules.Moreover,the rationality can be replaced by requiring that each 1/2Z+-graded module is a direct sum of irreducible weak modules.

Graphs of nonsolvable groups with four degree-vertices

Let G be a finite group. The degree(vertex) graph Γ(G) attached to G is a character degree graph.Its vertices are the degrees of the nonlinear irreducible complex characters of G, and different vertices m, n are adjacent if the greatest common divisor(m, n) > 1. In this paper, we classify all graphs with four vertices that occur as Γ(G) for nonsolvable groups G.

L-Factor of Irreducible χ_1×χ_2■σ

The L-factor of irreducible x1 × x2 ×｜ σdefined by Piatetski-Shapiro is computed by using non-split Bessel functional.

On tempered and square integrable representations of classical p-adic groups

This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturMly the classification of irreducible square integrable representations modulo cuspidal data obtained by Mceglin and the author of this article （2002）. The second aim of the paper is to give a description of an invariant （partially defined function） of irreducible square integrable representation of a classical p-adic group （defined by Mceglin using embeddings） in terms of subquotients of Jacquet modules. As an application, we describe behavior of partially defined function in one construction of square integrable representations of a bigger group from such representations of a smaller group （which is related to deformation of Jordan blocks of representations）.

A class of irreducible modules for the extended affne Lie algebra ■

We construct a class of modules for extended affine Lie algebra gl l（Cq） by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.

Fractional Moments of Automorphic L-Functions on GL(m)

Let πr be an irreducible unitary cuspidal representation of GL,^（AQ）, m ≥ 2. Assume that π is self-contragredient. The author gets upper and lower bounds of the same order for fractional moments of automorphic L-function L（s, π） on the critical line under Generalized Ramanujan Conjecture; the upper bound being conditionally subject to the truth of Generalized Riemann Hypothesis.

Investigation of Conformable Fractional Schr¨odinger Equation in Presence of Killingbeck and Hyperbolic Potentials

In this article, conformable fractional form of Schrodinger equation has been presented. Then in this formalism two different and well-known potential have been come in. Wave function of these potential are obtained in terms of Heun function and energy eigen values of each case is determined as well.

A CRITERION FOR TESTING WHETHER A DIFFERENCE IDEAL IS PRIME

This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension field.Using this criterion and the characteristic set method,the authors give a criterion fortesting whether certain difference ascending chains are strong irreducible,and as a consequence,whetherthe saturation ideals of these ascending chains are prime ideals.