共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider images of primitive elements of free color Lie (p-)su per algebras under endomorphisms of these algebras Web prove that endomorphisms preserving primitivity of elements are automorphisms (Theorem 4). Note that for free groups this problem was discussed in [10], Problem 2a. At the same time we show that it is not true if we consider only images of linear combinations of elements from free generatig set (see Example, Theorem 5). We formulate some open questions. In Section 1 we give necessary definitions and collect preliminary results. In Section 2 we prove main theorems. The results of this article were presented at algebraic seminars of Moscow State University. 相似文献
2.
Every semisimple Lie algebra defines a root system on the dual space of a Cartan subalgebra and a Cartan matrix, which expresses the dual of the Killing form on a root base. Serre’s Theorem [J.-P. Serre, Complex Semisimple Lie Algebras (G.A. Jones, Trans.), Springer-Verlag, New York, 1987] gives then a representation of the given Lie algebra in generators and relations in terms of the Cartan matrix.In this work, we generalize Serre’s Theorem to give an explicit representation in generators and relations for any simply laced semisimple Lie algebra in terms of a positive quasi-Cartan matrix. Such a quasi-Cartan matrix expresses the dual of the Killing form for a Z-base of roots. Here, by a Z-base of roots, we mean a set of linearly independent roots which generate all roots as linear combinations with integral coefficients. 相似文献
3.
B. Tromborg 《Linear algebra and its applications》1978,20(3):189-195
It was shown by A. Horn that the diagonal elements of a unitary n×n matrix satisfy a set of linear inequalities (Theorem I). We give a simple proof of this result, and we show that the diagonal elements satisfy additional linear inequalities (Theorem II) if the matrix is also symmetric. 相似文献
4.
The aim of this note is twofold. First, we prove an analogue of the well-known Robinson–Ursescu Theorem on the relative openness with a linear rate (restrictive metric regularity) of a multivalued mapping. Second, we prove a generalization of Graves Open Mapping Theorem for a class of mappings which can be approximated at a reference point by a bunch of linear mappings. The approximated non-linear mapping is restricted to a closed convex subset of a Banach space. 相似文献
5.
《Linear and Multilinear Algebra》2007,55(4):327-353
We briefly consider several formulations of Farkas' Lemma first. Then we assume the setting of two vector spaces, one of them being linearly ordered, over a linearly ordered field till the end of this article. In this setting, we state a generalized version of Farkas' Lemma and prove it in a purely linear-algebraic way. Afterwards, we present Theorems of Motzkin, Tucker, Carver, Dax, and some other theorems of the alternative that characterize consistency of a finite system of linear inequalities. We also mention the Key Theorem, which is a related result. Finally, we use Farkas' Lemma to prove the Duality Theorem for linear programming (with a finite number of linear constraints). The Duality Theorem that is proved here covers, among others, linear programming in a real vector space of finite or infinite dimension and lexicographic linear programming. 相似文献
6.
In this paper, we give several results of learning errors for linear programming support vector regression. The corresponding theorems are proved in the reproducing kernel Hilbert space. With the covering number, the approximation property and the capacity of the reproducing kernel Hilbert space are measured. The obtained result (Theorem 2.1) shows that the learning error can be controlled by the sample error and regularization error. The mentioned sample error is summarized by the errors of learning regression function and regularizing function in the reproducing kernel Hilbert space. After estimating the generalization error of learning regression function (Theorem 2.2), the upper bound (Theorem 2.3) of the regularized learning algorithm associated with linear programming support vector regression is estimated. 相似文献
7.
《Optimization》2012,61(1-2):155-166
A topological version of Passy–Prisman’s minimax Theorem is proved. We introduce to pological cones and we prove our results under connectedness assumptions. We give examples of cones in spaces without any linear structure. Even when interpreted in a linear framework our results are new and improve Passy–Prisman’s minimax Theorem, and consequently Sion’s minimax Theorem 相似文献
8.
Borg定理是判定周期系数二阶线性微分方程稳定的一个重要定理,这个定理在一定意义下是不可改进的.本文利用判别式的一个新形式,在弱的限制下,得到判定周期系数二阶线性微分方程稳定的定理,所得结论改进了Borg定理的判定结果. 相似文献
9.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(10):3808-3819
This paper is concerned with Theorem 2 in Matignon and d’André-Novel (1997) [1], which was sufficient and necessary criterion on a state observer for a class of linear fractional differential systems. Based on the stability theory, the dual principle and the pole assignment theory of the fractional differential system, we have proved the validity of sufficiency of Theorem 2 in details. A counterexample is provided to show that the condition of Theorem 2 is not necessary. 相似文献
10.
Consideration of correlation inequalities for Ising ferromagnets with arbitrary spins has led to the discovery of a class of positive definite functions on sets. These functions are linear combinations of the functions which enter into Muirhead's Theorem. We prove these functions to be positive definite and also show how they can be applied to the Ising problem to prove Griffiths second inequality for arbitrary spins. 相似文献
11.
《Operations Research Letters》1988,7(1):27-31
In this paper, we establish two characterization theorems for the linear and non-linear complementarity problems. Theorem 1 concerns the local uniqueness of a solution to a linear complementarity problem. Theorem 2 provides a necessary and sufficient condition for the differentiability of a solution to a parametric non-linear complementarity problem. 相似文献
12.
13.
14.
Manfred Möller 《manuscripta mathematica》1987,58(3):283-294
Let T be a continuous linear operator in LF-spaces. In [3], Theorem (2.6) we gave sufficient conditions for normal solvability of the adjoint T. Here we will prove that the conditions stated under B in this theorem are also necessary if N(T) is orthogonal in X. 相似文献
15.
We will give formulas to compute the regularity index of s fat points in general position on a linear r-space, s≤r+3 (Theorem 3.1). Then we will show formulas to compute the regularity index of s equimultiple fat points not on a linear (r?1)-space, s≤r+3 (Theorem 4.6). Our results show that the Segre’s bound is attained in these cases. 相似文献
16.
Caiming Lei 《Applied mathematics and computation》2009,215(8):2855-2857
In this remark, we shall show that the Lemma 1 and parts of the proof of Theorem 1 in the paper “Oscillation criteria for second-order linear difference equations” (Applied Mathematics and Computation 145 (2003) 591-601) are incorrect. 相似文献
17.
M. Beiglbck V. Bergelson T. Downarowicz A. Fish 《Topology and its Applications》2009,156(16):2565-2571
Rado's Theorem characterizes the systems of homogeneous linear equations having the property that for any finite partition of the positive integers one cell contains a solution to these equations. Furstenberg and Weiss proved that solutions to those systems can in fact be found in every central set. (Since one cell of any finite partition is central, this generalizes Rado's Theorem.) We show that the same holds true for the larger class of D-sets. Moreover we will see that the conclusion of Furstenberg's Central Sets Theorem is true for all sets in this class. 相似文献
18.
Constantinos Kardaras Eckhard Platen 《Stochastic Processes and their Applications》2011,121(11):2678-2691
A financial market model where agents trade using realistic combinations of simple (i.e., finite combinations of buy-and-hold) no-short-sales strategies is considered. Minimal assumptions are made on the discounted asset-price process — in particular, the semimartingale property is not assumed. Via a natural market viability assumption, namely, absence of arbitrage of the first kind, we establish that discounted asset-prices have to be semimartingales. Our main result can also be regarded as reminiscent of the Fundamental Theorem of Asset Pricing. 相似文献
19.
To prove existence and uniqueness (or just existence) of a bounded solution to nonlinear differential equations of higher order, we employ the contraction mapping principle and the Tikhonov Fixed Point Theorem. A quantitative estimate of a nonlinear perturbation preserving basic features of behavior of the corresponding linear equation (asymptotic stability or exponential dichotomy) is important when we pass to a nonlinear equation. 相似文献
20.
《Applied Mathematics Letters》2000,13(2):105-109
In this letter, we examine conservation laws for the vibrating membrane which arise from Noether's Theorem. We show that for linear membranes Noether's Theorem gives conservation laws which appear to contradict the basic assumptions on the model. We then show that the appropriate interpretation of these laws must follow from the nonlinear theory. 相似文献