Jordan Canonical Form of a Matrix over the Quaternion Field

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Representation of Binary Quadratic Forms by a Quaternary Form

The paper presents formulas for finding the number of representations r(A; Q) of a form A with odd square-free level by the form Q defined by the identity matrix of order 4. The case where the difference of the dimensions n — m is even (the codimension is even), which was not considered previously, is analyzed. Bibliography: 8 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 302, 2003, pp. 68–80.     

一类具复杂偏差变元的微分方程的周期解存在性

应用重合度理论研究了一类具复杂偏差变元的二阶Liénard微分方程的周期解存在性问题,改进和推广了以往文献的相关结果.     

On the Representation of Integers by the Lorentzian Quadratic Form

In this paper, we establish an asymptotic formula, for large radiusr, for the number of representations of a nonzero integerkby the Lorentzian quadratic formx²₁+x²₂+…+x²_n−x²_n+1that are contained in the ball of radiusrcentered at the origin in Euclidean (n+1)-space.     

可变幅角复系数的解析函数族

研究了在单位开圆盘内单叶解析且规范化的复系数函数族gφ1,φ2,φ3,φ4（m1,m2,m3,m4;λ）的一些性质,给出了其子族gφ1,φ2,φ3,φ4（m1,m2,m3,m4;λ）在内闭一致收敛拓扑下的极值点和支撑点,并讨论解决了gφ1,φ2,φ3,φ4（m1,m2,m3,m4;λ）与凸函数相关的一些半径问题,推广了近来的一些研究结果．     

Relaxed linear spaces and a generalization of the Cayley-Dickson process

In this paper first we introduce a new generalization of vector spaces and linear nonassociative algebras, and then we apply these new concepts to produce new structures related to the classical real division algebras but with dimensions other than 1, 2, 4 and 8.     

A Fractal Representation of the Complex Clifford Algebra Equivalent to the Fock Representation

We construct a representation of the infinite dimensional complex Clifford algebra on the Hilbert space of square-integrable complex-valued functions on the Cantor set, which we show to be equivalent to the classical Fock representation.     

Linear Groups of Degree 4 Over a Quaternion Division Ring that Contain the Special Unitary Group of a Skew-Hermitian Form with Maximal Witt Index

The paper describes subgroups of the general linear group GL ₄(D) over a quaternion division ring D that contain the special unitary group of degree 4 over a non-central subfield of D. The connections between these subgroups and the spinor groups of appropriate symmetric bilinear forms are established.     

An A Priori Estimate for the Modulus of Continuity of a Generalized Solution of a Parabolic Equation of Divergent Form with Degeneracy

We study parabolic equations of divergent form with degeneracy (x) with respect to the space variable. We establish an a priori estimate of the Hölder norm of generalized solutions. The problem is considered in parabolic cylinders having a special time dimension induced by the degeneracy (x).     

Bestvina's Normal Form Complex and the Homology of Garside Groups

A Garside group is a group admitting a finite lattice generating set . Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice , and there is a simple sufficient condition that implies G is a duality group. The universal covers of these K(π, 1)s enjoy Bestvina's weak nonpositive curvature condition. Under a certain tameness condition, this implies that every solvable subgroup of G is virtually Abelian.     

Impulsive Integral Inequalities with a Deviation of the Argument

In the present work are proved linear generalizations of the classical Gronwall-Bellman's integral inequality on partially continuous functions with a constant deviation.     

复向量空间的分解与复线性变换的Jordan标准形*

本文引入表征复线性变换结构的新对象。这些新对象给出复向量空间关于复线性变换分解的新结果且给出构造Jordan标准形的所有Jordan基。因而,它们能够直接导致着名的Jordan定理及空间的第三分解定理,且能给出对Jordan形精致微妙结构的新的深刻洞察。后者表明,复线性变换的Jordan标准形是一种在双重任意选择下具有不变性的结构。     

Peristaltic Wave Locomotion and Shape Morphing with a Millipede Inspired System

We present the mechanical model of a bio-inspired deformable system, modeled as a Timoshenko beam, which is coupled to a substrate by a system of distributed elements. The locomotion action is inspired by the coordinated motion of coupling elements that mimic the legs of millipedes and centipedes, whose leg-to-ground contact can be described as a peristaltic displacement wave. The multi-legged structure is crucial in providing redundancy and robustness in the interaction with unstructured environments and terrains. A Lagrangian approach is used to derive the governing equations of the system that couple locomotion and shape morphing. Features and limitations of the model are illustrated with numerical simulations.     

Representation of a quiver with relations

Representations of a quiver that is a chain of commutative squares are studied. It is proved that the problem of classification of representations of such a quiver is a tame problem, and a structure of representations is given. This result is a generalization of several known results concerning some important matrix problems. Bibliography:3 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 140–151.     

Invariant Form of the Generators of Semisimple Lie and Quantum Algebras in Their Arbitrary Finite-Dimensional Representation

An explicit form of the generators of quantum and ordinary semisimple algebras for an arbitrary finite-dimensional representation is found. The generators corresponding to the simple roots are obtained in terms of a solution of a system of matrix equations. The result is presented in the form of N _l×N _l matrices, where N _l is the dimension of the corresponding representation determined by the invariant Weyl formula.