Lectures on Algebraic topology

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Lectures on Algebraic topology de Marvin Greenberg, W. A. Benjamin, N. Y. 1967. US$5.95

     

Algebraic properties of Riordan subgroups

Journal of Algebraic Combinatorics - We present properties of the group structure of Riordan arrays. We examine similar properties among known Riordan subgroups, and from this, we define...     

长方矩阵常见广义逆的代数扰动

本文详细讨论了长方矩阵常见广义逆的代数扰动理论,并给出了他们代数扰动的表达式,改进了文献3,4的相应结论.     

Algebraic Geometry Over Completely Simple Semigroups

Algebraic geometry over completely simple semigroups is considered. We prove theorems that define coordinate semigroups and irreducible coordinate semigroups in several classes of completely simple semigroups.     

Algebraic invariants of weighted oriented graphs

Journal of Algebraic Combinatorics - Let $$\mathcal {D}$$ be a weighted oriented graph and let $$I(\mathcal {D})$$ be its edge ideal in a polynomial ring R. We give the formula of...     

Algebraic aspects of two-dimensional chiral fields

Algebraic (in the broad sense of the word) methods of the theory of solitons — the theory of differential equations related to the Korteweg-de Vries equation — are described for the example of two-dimensional, principal, chiral fields.     

Algebraic manipulation detection codes

Algebraic manipulation detection codes are a cryptographic primitive that was introduced by Cramer et al. (Eurocrypt 2008). It encompasses several methods that were previously used in cheater detection in secret sharing. Since its introduction, a number of additional applications have been found. This paper contains a detailed exposition of the known results about algebraic manipulation detection codes as well as some new results.     

Quantitative Morse–Sard Theorem via Algebraic Lemma

We give a short proof of the so-called Quantitative Morse–Sard Theorem as an application of Gromov?s Algebraic Lemma.     

Algebraic theory of difference equations and Mahler functions

Algebraic independence of certain Mahler functions constructed from Rudin–Schapiro sequences and Baum–Sweet sequences is proved, using difference Riccati equations and the notion of difference field extension of valuation ring type.     

Categorical Abstract Algebraic Logic: Partially Ordered Algebraic Systems

An extension of parts of the theory of partially ordered varieties and quasivarieties, as presented by Pałasińska and Pigozzi in the framework of abstract algebraic logic, is developed in the more abstract framework of categorical abstract algebraic logic. Algebraic systems, as introduced in previous work by the author, play in this more abstract framework the role that universal algebras play in the more traditional treatment. The aim here is to build the generalized framework and to formulate and prove abstract versions of the ordered homomorphism theorems in this framework. To Don Pigozzi and Kate Pałasińska.     

Algebraic Counterparts for Some Properties of Superintuitionistic Predicate Logics

Algebraic counterparts are found for the Beth, projective Beth, interpolation, disjunction, and existential properties of superintuitionistic first-order logics.     

R~n上扩散过程的代数式收敛

本文研究n维欧氏空间上的扩散过程在L2意义下的代数式收敛的情况,给出了判定代数式收敛的方法,并对两种特殊情形扩散算子进行了讨论.将所得判敛法应用于两个例子可得到精确的结果.     

Algebraic and homological properties of generalized mixed product ideals

Archiv der Mathematik - Algebraic and homological invariants of generalized mixed product ideals induced by a monomial ideal are studied. We characterize the Cohen–Macaulay generalized mixed...     

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Algebraic convergence in-sense is studied for the reflecting
diffusion processes on noncompact manifold with non-convex boundary. A series of sufficient
and necessary conditions for the algebraic convergence are presented.     

Algebraic Independence of Reciprocal Sums of Binary Recurrences II

 Algebraic independence of the numbers for various d and l, where is a periodic sequence of algebraic numbers and is a sequence of integers satisfying a binary linear recurrence relation, is studied by Mahler’s method.     

Algebraic aspects of two-dimensional chiral fields. II

Algebraic methods, in the broad sense of the word, of the theory of solitons (the theory of nonlinear differential equations related to the Korteweg-de Vries equation) are described for the example of relativistically invariant, two-dimensional, principal chiral fields.Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 18, pp. 73–150, 1981.     

树的变形与代数连通度

本文利用瓶颈矩阵的Perron值和代数连通度的二次型形式,系统地研究了当迁移或改变分支(边、点)和变动一些边的权重时无向赋权树的代数连通度的变化规律,认为代数连通度可用来描述树的边及其权重的某种中心趋势性.引入广义树和广义特征点概念,将II型树转换成具有相同代数连通度的I型树,使得树的代数连通度的讨论只须限于I型树的研究即可.     

Differential Algebraic Birkhoff Decomposition and the renormalization of multiple zeta values

In the Hopf algebra approach of Connes and Kreimer on renormalization of quantum field theory, the renormalization process is viewed as a special case of the Algebraic Birkhoff Decomposition. We give a differential algebra variation of this decomposition and apply this to the study of multiple zeta values.     

Software Engineering and complexity in effective Algebraic Geometry

One may represent polynomials not only by their coefficients but also by arithmetic circuits which evaluate them. This idea allowed in the past fifteen years considerable complexity progress in effective polynomial equation solving. We present a circuit based computation model which captures all known symbolic elimination algorithms in effective Algebraic Geometry and exhibit a class of simple elimination problems which require exponential size circuits to be solved in this model. This implies that the known, circuit based elimination algorithms are already optimal.     

Rosenbrock methods for Differential Algebraic Equations

Summary This paper deals with the numerical solution of Differential/Algebraic Equations (DAE) of index one. It begins with the development of a general theory on the Taylor expansion for the exact solutions of these problems, which extends the well-known theory of Butcher for first order ordinary differential equations to DAE's of index one. As an application, we obtain Butcher-type results for Rosenbrock methods applied to DAE's of index one, we characterize numerical methods as applications of certain sets of trees. We derive convergent embedded methods of order 4(3) which require 4 or 5 evaluations of the functions, 1 evaluation of the Jacobian and 1 LU factorization per step.