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61.
We consider two analogues of associativity for ternary algebras: total and partial associativity. Using the corresponding ternary associators, we define ternary analogues of alternative and assosymmetric algebras. On any ternary algebra the alternating sum [a, b, c] = abc − acb − bac + bca + cab − cba (the ternary analogue of the Lie bracket) defines a structure of an anticommutative ternary algebra. We determine the polynomial identities of degree ?7 satisfied by this operation in totally and partially associative, alternative, and assosymmetric ternary algebras. These identities define varieties of ternary algebras which can be regarded as ternary analogues of Lie and Malcev algebras. Our methods involve computational linear algebra based on the representation theory of the symmetric group. 相似文献
62.
Josep M. Brunat 《Discrete Mathematics》2006,306(4):401-412
Let Φ(x,y) be a bivariate polynomial with complex coefficients. The zeroes of Φ(x,y) are given a combinatorial structure by considering them as arcs of a directed graph G(Φ). This paper studies some relationship between the polynomial Φ(x,y) and the structure of G(Φ). 相似文献
63.
Pinar Heggernes 《Discrete Mathematics》2006,306(24):3267-3280
Broadcast domination was introduced by Erwin in 2002, and it is a variant of the standard dominating set problem, such that different vertices can be assigned different domination powers. Broadcast domination assigns an integer power f(v)?0 to each vertex v of a given graph, such that every vertex of the graph is within distance f(v) from some vertex v having f(v)?1. The optimal broadcast domination problem seeks to minimize the sum of the powers assigned to the vertices of the graph. Since the presentation of this problem its computational complexity has been open, and the general belief has been that it might be NP-hard. In this paper, we show that optimal broadcast domination is actually in P, and we give a polynomial time algorithm for solving the problem on arbitrary graphs, using a non-standard approach. 相似文献
64.
Some possible modifications of the governing equations of the linear theory of elasticity are considered. The stress–strain relation is specified by an integral equality instead of the local Hooke’s law. The modified integrodifferential boundary value problem is reduced to the minimization of a nonnegative functional under differential constraints. A numerical algorithm based on polynomial approximations of unknown functions (stresses and displacements) is developed and applied to linear elasticity problems. The bilateral estimation criteria of solution errors are proposed in order to analyze the algorithm convergence rate. The numerical results obtained by applying the integrodifferential relation method and the conventional variational method are compared and discussed. 相似文献
65.
A new accurate high-order numerical method is presented for the coupled transport of a passive scalar (concentration) by advection and diffusion. Following the method of characteristics, the pure advection problem is first investigated. Interpolation of the concentration and its first derivative at the foot of the characteristic is carried out with a fifth-degree polynomial. The latter is constructed by using as information the concentration and its first and second derivatives at computational points on current time level t in Eulerian co-ordinates. The first derivative involved in the polynomial is transported by advection along the characteristic towards time level t + Δt in the same way as is the concentration itself. Second derivatives are obtained at the new time level t + Δt by solving a system of linear equations defined only by the concentrations and their derivatives at grid nodes, with the assumption that the third-order derivatives are continuous. The approximation of the method is of sixth order. The results are extended to coupled transport by advection and diffusion. Diffusion of the concentration takes place in parallel with advection along the characteristic. The applicability and precision of the method are demonstrated for the case of a Gaussian initial distribution of concentrations as well as for the case of a steep advancing concentration front. The results of the simulations are compared with analytical solutions and some existing methods. 相似文献
66.
平坦的多项式剩余类环 总被引:1,自引:0,他引:1
本文证明了如果多项式的剩余类环 A=R[T]/fR[T]作为 R-模是平坦模,且R是约化环,则f是正规多项式.特别地,若R还是连通的,则f的首项系数是单位.也证明了弱整体有限的凝聚环是约化环,以及弱整体为有限的凝聚连通环是整环. 相似文献
67.
本文首先给出了Riemann引理及其三种证法;然后通过直接方法、变量替换方法和多项式逼近的方法分别进行了证明.最后给出了Riemann引理的推广及其证明。 相似文献
68.
We present a new axiomatization of the non-associative Lambek calculus. We prove that it takes polynomial time to reduce any non-associative Lambek categorial grammar to an equivalent context-free grammar. Since it is possible to recognize a sentence generated by a context-free grammar in polynomial time, this proves that a sentence generated by any non-associative Lambek categorial grammar can be recognized in polynomial time. 相似文献
69.
In this paper, the authors proved that finding all solutions of a given multivariate polynomial system is equivalent to solving a relative joint eigenvalue problem(Theorem 1) and in some cases one can find all solutions of the given system from the eigenvalues and vectors of one matrix or matrix pencil (Theorem 2). Especially the situation that the ideal generated by the given system is 0-dimensional is discussed. 相似文献
70.
Let f∈C[0,1],and Bn(f,x) be the a-th Bernstein polynomial associated with function f.ln 1967,the limit of iterates for B.(f,x) was given by Kelisky and Rivlin.After this,Many mathematicians studied and generalized this result.But anyway,all these discussions are only for univariate case ,In this paper,the main contrlbution is that the limit of lterates for Bernstein polynomial defined on a triangle is given completely. 相似文献