On the classification of fuzzy projective planes of fuzzy 3-dimensional projective space

In this work, the classifications of fuzzy 3-dimensional vector spaces of fuzzy 4-dimensional vector space and fuzzy projective planes of fuzzy 3-dimensional projective space from fuzzy 4-dimensional vector space are given.     

Nonclassical 4-Dimensional Minkowski Planes Obtained as Brothers of Semiclassical 4-Dimensional Laguerre Planes

We describe the first nonclassical 4-dimensional Minkowski planes and show that they have 6-dimensional automorphism groups. These planes are obtained by a construction of Schroth [18] from generalized quadrangles associated with the semiclassical 4-dimensional Laguerre planes. All 4-dimensional Minkowski planess that can be obtained in this way from the semiclassical 4-dimensional Laguerre planes are determined.     

Decomposition of a 2 + 1-dimensional Volterra type lattice and its quasi-periodic solutions

A 2 + 1-dimensional Volttera type lattice is proposed. Resorting to the nonlinearization of Lax pair, the 2 + 1-dimensional Volttera type lattice is decomposed into the known 1+1-dimensional differential-difference equations. The relation between a new 2 + 1-dimensional differential-difference equation, certain 1+1-dimensional continuous evolution equations and the known 1+1-dimensional differential-difference equations is discussed. Based on finite-order expansion of the Lax matrix, we introduce elliptic coordinates, from which the two 2 + 1-dimensional differential-difference equations are separated into solvable ordinary differential equations. The evolution of various flows is explicitly given through the Abel–Jacobi coordinates. Quasi-periodic solutions for the two 2 + 1-dimensional differential-difference equations are obtained.     

新(2+1)-维超可积系统的生成

本文利用二项式残数表示方法生成(2+1)-维超可积系统. 由这些系统得到了一个新的(2+1)-维超孤子族,它能约化为(2+1)-维超非线性Schrodinger方程. 特别地,我们得到两个具有重要物理应用的结果,一个是(2+1)-维超可积耦合方程,另一个是(2+1)-维的扩散方程. 最后借助超迹恒等式给出了新(2+1)-维超可积系统的Hamilton结构.     

Are critical exponents multivalued or unique?

The scaling law theories of the critical point phenomena, together with possible stability conditions at the critical point, allow a whole range of critical exponents in a 2-dimensional system but only two sets of exponents in a 3-dimensional system. In the 3-dimensional case the two sets explain the differences between the critical exponents in magnetic and ferroelectric transitions. It also seems possible to correlate the small differences between the exponents of liquid/gas and magnetic transitions. No set of exponents is allowed in a 1-dimensional case, corresponding to the absence of phase transitions in a 1-dimensional system with short range interactions.     

Dirac equation in a 5-dimensional Kaluza-Klein theory

Dirac equation is discussed in 5-dimensional space time having topology M ⁴ ×T ¹, whereM ⁴ and T ¹ both are curved. It is shown that 4-dimensional fermion can be obtained from 5-dimensional fermion, as a result of compactification of extra dimension. It is found that the realistic 4-dimensional fermions are possible in higher modes earlier than those in lower modes during the course of expansion of 4-dimensional universe. 4-dimensional Dirac equation, obtained from 5-dimensional Dirac equation after compactification, is solved for an arbitrary mode for superheavy as well as light (realistic) fermions. Time-dependence of polarization vector and magnetization density, as a result of Gordon-decomposition of the current vector for 4-dimensional spin-½ field (with arbitrary mode), is exhibited.     

关于m-HPK(n1,n2,n3,n4)-残差图

本文研究了3-维超平面完备残差图以及m 重3-维超平面完备残差图. 利用容斥原理以及集合的运算性质等方法, 分别获得了3-维超平面完备残差图和m 重3-维超平面完备残差图的最下阶以及二者的唯一极图, 将文献[1] 中定义的残差图从平面推广到超平面上.     

Weakly Regular Subdivisions

It is shown that 2-dimensional subdivisions can be made regular by moving their vertices within parallel 1-dimensional spaces. As a consequence, any 2-dimensional subdivision is projected from the boundary complex of a 4-polytope.     

Seiberg-Witten theory as a complex version of Abelian Higgs model

The adiabatic limit procedure associates with every solution of Abelian Higgs model in (2 + 1) dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg-Witten equations on 4-dimensional symplectic manifolds introduced by Taubes may be considered as a complex (2+2)-dimensional version of the (2 + 1)-dimensional picture. More precisely, the adiabatic limit procedure in the 4-dimensional case associates with a solution of Seiberg-Witten equations a pseudoholomorphic divisor which may be treated as a complex version of a geodesic in (2+1)-dimensional case.     

实用下料的数学模型

考虑到整数规划模型的下料方式数量难以穷尽的问题,本文以原材料最少为目标,采用启发式多级序列线性优化的方法建立一维下料模型.对于二维下料问题,采用降维启发式的方法即通过形成“板条”把二维下料问题化为一维下料问题.     

4-Dimensionale projektive Ebenen mit grosser abelscher Kollineationsgruppe

We show that a 4-dimensional connected abelian group can act in exactly five different ways as a collineation group of a compact 4-dimensional projective plane. Furthermore the complex projective plane is characterized as the only compact 4-dimensional projective plane which admits two different 4-dimensional abelian collineation groups.

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Herrn Professor Dr. Eelmut Karzel zum 60. Geburtstag     

Note on Weakly n-Dimensional Spaces

 Weakly n-dimensional spaces were first distinguished by Karl Menger. In this note we shall discuss three topics concerning this class of spaces: universal spaces, products, and the sum theorem. We prove that there is a universal space for the class of all weakly n-dimensional spaces, present a simpler proof of Tomaszewski’s result about the dimension of a product of weakly n-dimensional spaces, and show that there is an n-dimensional space which admits a pairwise disjoint countable closed cover by weakly n-dimensional subspaces but is not weakly n-dimensional itself. (Received 17 August 2000)     

Note on Weakly n -Dimensional Spaces

 Weakly n-dimensional spaces were first distinguished by Karl Menger. In this note we shall discuss three topics concerning this class of spaces: universal spaces, products, and the sum theorem. We prove that there is a universal space for the class of all weakly n-dimensional spaces, present a simpler proof of Tomaszewski’s result about the dimension of a product of weakly n-dimensional spaces, and show that there is an n-dimensional space which admits a pairwise disjoint countable closed cover by weakly n-dimensional subspaces but is not weakly n-dimensional itself.     

用二维游动描述DNA系列

在文献中,DNA序列曾被描述为一维游动和三维游动.对前者,一个游动对应于多个DNA序列;对后者,游动和DNA序列一一对应.我们发现在三维游动(xn,yn,zn)中,由xn,yn和zn中任意有序的两个给出的二维游动已经与DNA序列一一对应,且余下的一维游动由该二维游动完全决定.因此,二维游动似乎是描述DNA序列最合适的模型.4个碱基A,C,G和T共有4 !=24个排序.每一个排序都给出DNA序列用二维游动的一种描述.两个游动(x'n,y'n)和(x"n,y"n)被看作是等价的,如果(x'n,y'n)=(εx"n,δy"n)或(εy"n,δx"n),这里ε=±1,且δ=±1.于是这24个类型的游动被分成三个等价类;它们的代表分别是(xn,yn),(yn,zn),和(xn,zn),这里(xn,yn,zn)正好是张和张的三维游动.     

On 2-dimensional Laguerre planes of shift type

We construct 2-dimensional Laguerre planes of shift type and determine the automorphism groups and isomorphism classes of these planes. Laguerre planes of shift type occur in the classification of 2-dimensional Laguerre planes with 4-dimensional automorphism groups that fix precisely one parallel class.     

Anosov Lie algebras and algebraic units in number fields

We study nilmanifolds admitting Anosov automorphisms by applying elementary properties of algebraic units in number fields to the associated Anosov Lie algebras. We identify obstructions to the existence of Anosov Lie algebras. The case of 13-dimensional Anosov Lie algebras is worked out as an illustration of the technique. Also, we recapture the following known results: (1) Every 7-dimensional Anosov nilmanifold is toral, and (2) every 8-dimensional Anosov Lie algebra with 3 or 5-dimensional derived algebra contains an abelian factor.     

The classification of n-dimensional anticommutative algebras with (n − 3)-dimensional annihilator

We give the classification of all n-dimensional anticommutative complex algebras with (n???3)-dimensional annihilator. Namely, we describe all central extensions of all 3-dimensional anticommutative complex algebras.     

The classification of N-dimensional non-associative Jordan algebras with (N − 3)-dimensional annihilator

The paper is devoted to give a complete classification of all n-dimensional non-associative Jordan algebras with (n?3)-dimensional annihilator over an algebraically closed field of characteristic ≠2. We also give a complete classification of all n-dimensional Jordan algebras with (n?1)- and (n?2)-dimensional annihilator.     

Determination of 7-Dimensional Indecomposable Nilpotent Complex Lie Algebras by Adjoining a Derivation to 6-Dimensional Lie Algebras

For any complex 6-dimensional nilpotent Lie algebra \mathfrakg,\mathfrak{g}, we compute the strain of all indecomposable 7-dimensional nilpotent Lie algebras which contain \mathfrakg\mathfrak{g} by the adjoining a derivation method. We get a new determination of all 7-dimensional complex nilpotent Lie algebras, allowing to check earlier results (some contain errors), along with a cross table intertwining nilpotent 6- and 7-dimensional Lie algebras.     

4-Dimensional point-transitive groups of automorphisms of 2-dimensional laguerre planes

It is shown that a 2-dimensional Laguerre plane that admits a closed connected 4-dimensional point-transitive group of automorphisms must be classical. Further, up to conjugacy in the automorphism group of the classical real Laguerre plane, all closed connected 4-dimensional point-transitive subgroups are determined.