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151.
E. I. Timoshenko 《Algebra and Logic》2006,45(1):67-74
For a factor group with respect to periodic part of a group of the form F/[R′, F], an embedding in the matrix group is defined.
The criteria for a matrix to belong to an image of this group and for elements to be conjugate are specified. Some statements
having a direct bearing on groups of the form in question are proved. Application of the results obtained allows us to refine
the answer in [7] to a question by O. Chapuis concerning the universal classification of ∀-free soluble groups with two generators.
Supported by RFBR grant No. 02-01-00293 and by FP “Universities of Russia” grant No. UR.04.01.227.
__________
Translated from Algebra i Logika, Vol. 45, No. 1, pp. 114–125, January–February, 2006. 相似文献
152.
In this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two
new applications of this transform. One concerns the construction of symmetries of the massless field equations from mathematical
physics. The other concerns obstructions to the embedding of CR structures on the three-sphere.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
153.
Mourad E. H. Ismail 《The Ramanujan Journal》2006,11(3):349-353
We give short elementary proofs of a formula of Ramanujan as interpreted by Bradley, and a companion formula originally proved
by W. Chu. We also give an elementary proof of a generalization of an identity originally proved using modular functions and
used to study a generating function for the number of partitions with specified crank.
Research partially supported by NSF grant DMS 99-70865.
2000 Mathematics Subject Classification Primary—39A70, 11P83; Secondary—33C20 相似文献
154.
Quantum Bayesian computation is an emerging field that levers the computational gains available from quantum computers. They promise to provide an exponential speed-up in Bayesian computation. Our article adds to the literature in three ways. First, we describe how quantum von Neumann measurement provides quantum versions of popular machine learning algorithms such as Markov chain Monte Carlo and deep learning that are fundamental to Bayesian learning. Second, we describe quantum data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Third, we show how quantum algorithms naturally calculate Bayesian quantities of interest such as posterior distributions and marginal likelihoods. Our goal then is to show how quantum algorithms solve statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes and stochastic gradient descent. On the empirical side, we apply a quantum FFT algorithm to Chicago house price data. Finally, we conclude with directions for future research. 相似文献
155.
丁协平 《应用数学和力学(英文版)》2005,26(12):1547-1555
A new notion of finite continuous topological space (in short, FC-space) with out convexity structure was introduced. A new continuous selection theorem was established in FC-spaces. By applying the continuous selection theorem, some new coincidence theorems for two families of set-valued mappings defined on product space of noncompact FC-spaces are proved under much weak assumptions. These results generalize many known results in recent literature. Some applications will be given in a follow-up paper. 相似文献
156.
微分达布定理表明区间内的导函数具有介值性,这使得我们在考虑一些数学分析问题时,往往可以不需要最高阶导函数的连续性.而在微分方程理论中,比较定理的思想对于解的估计非常重要.本文利用比较定理的思想将中值定理类问题转化为微分方程解的估计问题,对于在数学分析的学习中提高学生的认识和兴趣很有意义. 相似文献
157.
Henning Sulzbach 《Random Structures and Algorithms》2017,50(3):493-508
For a martingale (Xn) converging almost surely to a random variable X, the sequence (Xn– X) is called martingale tail sum. Recently, Neininger (Random Structures Algorithms 46 (2015), 346–361) proved a central limit theorem for the martingale tail sum of Régnier's martingale for the path length in random binary search trees. Grübel and Kabluchko (in press) gave an alternative proof also conjecturing a corresponding law of the iterated logarithm. We prove the central limit theorem with convergence of higher moments and the law of the iterated logarithm for a family of trees containing binary search trees, recursive trees and plane‐oriented recursive trees. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 493–508, 2017 相似文献
158.
At some point, after publication, we realized that Proposition 4.1(2) and Theorem 4.4 in [2] hold under the assumption (not explicitly declared) that B = f(A)+J. Furthermore, we provide here the exact value for the embedding dimension of A?fJ, also when B≠f(A)+J, under the hypothesis that J is finitely generated as an ideal of the ring f(A)+J. 相似文献
159.
160.
V. I. Kushch 《International Applied Mechanics》2004,40(8):893-899
An elastic-equilibrium problem is rigorously solved for a transversely isotropic body containing a finite number of arbitrarily arranged and oriented transversely isotropic spherical inclusions or an infinite periodic array of such inclusions. The solution is found based on the superposition principle for general solutions of single-particle problems and the addition theorems for partial vector solutions of the elastic equilibrium equations. The numerical results presented allow assessing the influence of matrix anisotropy on the stress concentration between inclusions 相似文献