共查询到20条相似文献,搜索用时 15 毫秒
1.
We show how functions F(z) which satisfy an identity of the form F(α z) = g(F(z)) for some complex number α and some function g(z) give rise to infinite product formulas that generalize Viète's product formula for π. Specifically, using elliptic and trigonometric
functions we derive closed form expressions for some of these infinite products. By evaluating the expressions at certain
points we obtain formulas expressing infinite products involving nested radicals in terms of well-known constants. In particular,
simple infinite products for π and the lemniscate constant are obtained.
2000 Mathematics Subject Classification: Primary—40A20; Secondary—33E05 相似文献
2.
In this article we study the problem when a left distributive algebra over a field determines an atom of the lattice of all radicals of rings. We show that this problem is strictly connected with the problem of describing extensions of left chain algebras and give a characterization of left chain algebras determining atoms. 相似文献
3.
T. Binder L. Blank W. Dahmen W. Marquardt 《Journal of Optimization Theory and Applications》2001,111(3):501-527
The objective of the present investigation is to explore the potential of multiscale refinement schemes for the numerical solution of dynamic optimization problems arising in connection with chemical process systems monitoring. State estimation is accomplished by the solution of an appropriately posed least-squares problem. To offer at any instant of time an approximate solution, a hierarchy of successively refined problems is designed using a wavelet-based Galerkin discretization. In order to fully exploit at any stage the approximate solution obtained also for an efficient treatment of the arising linear algebra tasks, we employ iterative solvers. In particular, we will apply a nested iteration scheme to the hierarchy of arising equation systems and adapt the Uzawa algorithm to the present context. Moreover, we show that, using wavelets for the formulation of the problem hierarchy, the largest eigenvalues of the resulting linear systems can be controlled effectively with scaled diagonal preconditioning. Finally, we deduce appropriate stopping criteria and illustrate the characteristics of the solver with a numerical example. 相似文献
4.
Antonio J. Calderón Martín 《Proceedings Mathematical Sciences》2009,119(2):165-177
We begin the study of arbitrary split Lie triple systems by focussing on those with a coherent 0-root space. We show that
any such triple systems T with a symmetric root system is of the form T = + Μ
j
I
j
with a subspace of the 0-root space T
0 and any I
j
a well described ideal of T, satisfying [I
j
, T, I
k
] = 0 if j ≠ k. Under certain conditions, it is shown that T is the direct sum of the family of its minimal ideals, each one being a simple split Lie triple system, and the simplicity
of T is characterized. The key tool in this job is the notion of connection of roots in the framework of split Lie triple systems. 相似文献
5.
We study the structure of arbitrary split Leibniz triple systems with a coherent 0-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of T being of maximal length, the simplicity of the Leibniz triple systems is characterized. 相似文献
6.
图的spread定义为图的邻接矩阵的最大特征值与最小特征值的差.本文确定了n(n≥84)顶点四圈图中spread最大的唯一的图. 相似文献
7.
8.
Bahman Kalantari 《Journal of Complexity》2013,29(3-4):302-322
9.
《代数通讯》2013,41(5):1357-1368
Abstract The paper generalizes some of our previous results on quasi-hereditary Koszul algebras to graded standardly stratified Koszul algebras. The main result states that the class of standardly stratified algebras for which the left standard modules as well as the right proper standard modules possess a linear projective resolution – the so called linearly stratified algebras – is closed under forming their Yoneda extension algebras. This is proved using the technique of Hilbert and Poincaré series of the corresponding modules. 相似文献
10.
ABSTRACT The role played by fields in relation to Galois Rings corresponds to semifields if the associativity is dropped, that is, if we consider Generalized Galois Rings instead of (associative) Galois rings. If S is a Galois ring and pS is the set of zero divisors in S, S* = S pS is known to be a finite {multiplicative} Abelian group that is cyclic if, and only if, S is a finite field, or S = ?/n? with n = 4 or n = p r for some odd prime p. Without associativity, S* is not a group, but a loop. The question of when this loop can be generated by a single element is addressed in this article. 相似文献
11.
A. P. Pojidaev 《代数通讯》2013,41(10):3593-3608
Derivations of the simple ternary Malcev algebra M 8 and its algebra of multiplications are described. 相似文献
12.
H是 Hopf代数,A是左 H-模代数,本文给出了当 A是 QF代数时,AH也是 QF代数的一个条件. 相似文献
13.
V. T. Filippov 《Mathematical Notes》1999,65(4):506-509
It is proved that ifS is a simple finite-dimensional anticommutative algebra over a field ϕ of characteristic zero satisfying the identityJ(x, y, z)t=J(t, z, xy)+J(t, y, zx)+J(t, x,yz), whereJ(x, y, z)=(xy)z+(zx)y+(yz)x, thenS is a Lie algebra.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 607–611, April, 1999. 相似文献
14.
The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. 𝒦2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a 𝒦2 algebra would be another 𝒦2 algebra. We show that this is not necessarily the case by constructing a monomial 𝒦2 algebra for which the corresponding Yoneda algebra is not 𝒦2. 相似文献
15.
16.
Qi Xia 《高校应用数学学报(英文版)》2010,25(1):117-126
In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras and K p algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of K p algebras admit non-pure resolutions. We provide necessary and sufficient conditions for a notherian semiperfect algebra either to be a quasi-δ-Koszul algebra or to be a quasi-K p algebra. 相似文献
17.
WEN Dao-wei 《高校应用数学学报(英文版)》2014,29(1):119-126
In this article, we consider endomorphism algebras of direct sums of some local left ideals over a local algebra and give a construction of quasi-hereditary algebras. 相似文献
18.
Antonio J. Calderón Martín 《代数通讯》2017,45(2):866-877
The class of extended Lie-type algebras contains the ones of associative algebras, Lie algebras, Leibniz algebras, dual Leibniz algebras, pre-Lie algebras, and Lie-type algebras, etc. We focus on the class of extended Lie-type algebras graded by an Abelian group G and study its structure, by stating, under certain conditions, a second Wedderburn-type theorem for this class of algebras. 相似文献
19.
The obvious necessary conditions for the existence of a nested Steiner triple system of order v containing a nested subsystem of order w are v ≥ 3w + 4 and v ≡ w ≡ 1 (mod 6). We show that these conditions are also sufficient. © 2004 Wiley Periodicals, Inc. 相似文献
20.
We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted tensor products, regular central extensions and Ore extensions. We explore the monomial algebras in this class and we include some well-known examples of algebras that fall into this class. 相似文献