关于Y.H.Kim两篇论文的注记

指出并改正了Y.H.Kim两篇论文中关于某些不等式的错误和疏忽.     

Engel Subalgebras of n-Lie Algebras

Engel subalgebras of finite-dimensional n-Lie algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that an n-Lie algebra, all of whose maximal subalgebras are ideals, is nilpotent. A primitive 2-soluble n-Lie algebra is shown to split over its minimal ideal, and all the complements to its minimal ideal are conjugate. A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel, provided that the field has sufficiently many elements. Cartan subalgebras are shown to have a property analogous to intravariance.     

关于立方幂补数倒数的性质

Let n be any positive integer,and S(n) be the cubic complements of n.The main purpose of this paper is to study the asymptotic of sum from (n≤x) (n/(S(n)))~k (k≥1).And by using the elementary methods,it intends to give two sharper asymptotic formulas,and thus extends the related conclusious.     

关于半局部群环

Let R be an associative ring with identity.R is said to be semilocal if R/J(R)is(semisimple)Artinian,where J(R)denotes the Jacobson radical of R.In this paper,we give necessary and sufficient conditions for the group ring RG to be semilocal,where G is a locally finite nilpotent group.     

拓扑分子格C.T.Yang定理与K.Fan定理的推广

C_1 T. Yang's theorem concerning derived sets and K. Fan's theorem concerning connectivity in general topology have been extended to fuzzy topological spaces and to the theory of topological molecular lattices and generalized topological molecular lattices. In this paper, they will be further extended to the more general theory of POINTWISE TOPOLOGY ON COMPLETELY DISTRIBUTIVB LATTICES.     

ON THE INVERTIBILITY OF HILBERT SPACE IDEMPOTENTS

This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.     

On A. Lino, W. Demelo and C. C. Pugh''''s Conjecture (Part 1)

For Lienard's equation or its equivalent system (?)=y-F(x),(?)=-x,(F(x)=integral from n=0 to x (f(ξ)dξ)). (*) there were quite a few papers studied (*) to have some limit cycles. Although there were few papers studied (*) to have at most m limit cycles, but good results were given already. A. Lino, W. Demelo and C. C. Pugh conjectured following fact: when f(x)=sum from N (a_ix~i) (N=2n+1,2n+2),system (*) has at most n limit cycles.     

Modular Lie Superalgebras of H-type

In this article the Z-graded transitive modular Lie superalgebra О i≥-1 Li, whose representation of Lo in L-1 is isomorphic to the natural representation of osp(L-1), is determined.     

本刊英文版Vol.27(2011),No.6论文摘要

<正>New Algebraic Approaches to Classical Boundary Layer Problems Xiao Ping XU Abstract Classical non-steady boundary layer equations are fundamental nonlinear partial differential equations in the boundary layer theory of fluid dynamics.In this paper,we introduce various schemes with multiple parameter functions to solve these equations and obtain many families of new explicit exact solutions with multiple parameter functions.Moreover,symmetry transformations are used to simplify our arguments.The technique of moving frame is applied in the three-dimensional case in order to capture the rotational properties of the fluid.In     

Evaluations of Parameters for the Optimization of S.S.O.R. and A.D.I. Preconditioning

The main goal of this paper is to give two ways to estimate the needed parameters in order to obtain the condition number of S.S.O.R. preconditioned matrices, namely, the algebraic matricial formulation of convexity Riesz theorem and the tridiagonal Fourier analysis. The improvement with respect to Axelsson's approach is explicitly given. Estimations of the condition number in the case of A.D.I. preconditioning is also considered.     

Two-point b.v.p. for multivalued equations with weakly regular r.h.s.

A two-point boundary value problem associated to a semilinear multivalued evolution equation is investigated, in reflexive and separable Banach spaces. To this aim, an original method is proposed based on the use of weak topologies and on a suitable continuation principle in Fréchet spaces. Lyapunov-like functions are introduced, for proving the required transversality condition. The linear part can also depend on the state variable x and the discussion comprises the cases of a nonlinearity with sublinear growth in x or of a noncompact valued one. Some applications are given, to the study of periodic and Floquet boundary value problems of partial integro-differential equations and inclusions appearing in dispersal population models. Comparisons are included, with recent related achievements.     

Optimization of the Relaxation Parameter for S.S.O.R. and A.D.I. Preconditioning

We present and compare several approaches for the optimization of the relaxation parameter both for A.D.I. and S.S.O.R. basic iteration and preconditioning conjugate gradient method. For each kind of preconditioning a detailed link between estimates of the spectral radius of the iteration matrix and of the condition number resulting from preconditioning is proposed. It allows to choose the best approach in order to obtain the optimal relaxation parameter and the corresponding optimal estimates either of the spectral radius of the iteration matrix and of the resulting condition mumber of the S.S.O.R. and A.D.I. preconditioning.     

The E.E.C. and the development of O.R.

The growth of the E.E.C. has brought about a change in the scale of many organizational problems and a change in the ways that they can be tackled. Accordingly it is plausible that the techniques of O.R. should develop in response to these changes. This paper examines some desirable developments and suggests ways in which they might be achieved by adapting methods devised in other fields for similar problems.     

Lettera del prof. G. A. Miller al prof. Luigi Bianchi

P. S. — In view of the delay in writing I would say that you have my permission to publish the above letter in order to avoid the spreading of these errors.G. A. Miller     

S.A.G.B.I. bases for rings of formal modular seminvariants

We use the theory of S.A.G.B.I. bases to construct a generating set for the ring of invariants for the four and five dimensional indecomposable modular representations of a cyclic group of prime order. We observe that for the four dimensional representation the ring of invariants is generated in degrees less than or equal to 2p–3, and for the five dimensional representation the ring of invariants is generated in degrees less than or equal to 2p–2. Received: January 22, 1997     

p.p. rings and generalized p.p. rings

This paper concerns two conditions, called right p.p. and generalized right p.p., which are generalizations of Baer rings and von Neumann regular rings. We study the subrings and extensions of them, adding proper examples and counterexamples to some situations and questions that occur naturally in the process of this paper.     

Mathematics in the time of the pharaohs: By Richard J. Gillings. Cambridge,Mass. (M.I.T. Press), 1972. 297 p. US $25

The author's treatment of many problems and some of his hypotheses are original and elegant. He does not limit himself to describing the content of his sources but tries to reveal the paths followed by the Egyptians as well as their ideas and methods. This leads him to interesting and on the whole covinncing reconstructions and results. For example, the author concludes that there must have existed extensive addition tables that have not survived.Although the materials available today seem insufficient to explain how the Egyptians happened to use the qlumsy binary method mu multiplication and division, Gillings' discussion throws light on the problem and poses questions for further research. Careful analysis of special tables and solutions of problems and the comparison of sources enable the author in large measure to reveal the methods and ideas of Egyptian mathematicians. How the Egyptians constructed their tables still remains an unsolved problem. Because divisions sometimes began by dividing by 3, Gillings concludes that tables for 3 must have existed and his reconstruction of such a table has great interstt. His Rule G for sums and differences of fractions is original and ingenious. He strsses the importance of EMLR. He argues that the Egyptians used the concepts of arithmetic and harmonic means. He gives an interesting explanation for the origin of the Egyptian formulas for squaring the circle, though its simplicity is clear only after the result is known.Although answers are not given to all questions, the book leads the reader to search for answers, to formulate new reconstructions, and to make new hypotheses. This is its greatest merit.     

O.R. and U.K. natural gas depletion strategy

This paper describes two models using operational research techniques to explore alternative strategies for the depletion of U.K. natural gas reserves. The first is a linear programming formulation of the problem of matching annual supply and demand for gas over the indefinite future. The second evaluates the financial implications of the matches produced by the first. The key variables which affect results from the model are discussed as are some of the ways in which results are used. These results have an influence on decisions ranging from detailed peak shaving policy to considerations of national fuel policy and the balance of energy supplies in the U.K. in the longer term.     

Uncountable constructions for B.A. e.c. groups and banach spaces

This paper has two aims: to aid a non-logician to construct uncountable examples by reducing the problems to finitary problems, and also to present some construction solving open problems. We assume the diamond forℵ ₁ and solve problems in Boolean algebras, existentially closed groups and Banach spaces. In particular, we show that for a given countable e.c. groupM there is no uncountable group embeddable in everyG -equivalent toM; and that there is a non-separable Banach space with noℵ ₁ elements, no one being the closure of the convex hull of the others. Both had been well-known questions. We also deal generally with inevitable models (§4). The author would like to thank the NSF for partially supporting this research by grants H144-H747 and MCS-76-08479, and the United States-Israel Binational Science Foundation for partially supporting this research.