Equations of the Gel'fand-Levitan type in a multidimensional inverse problem for the wave equation

An approach to the solution of inverse problems using the ideas and results of the theory of boundary-value control (J. L. Lions and D. L. Russell) is developed in the paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 165, pp. 15–20, 1987.I am grateful to participants of A. S. Blagoveshchenskii's seminar for valuable advice and discussions. I wish to thank S. A. Avdonin for consultation on the TBVC.     

具最小二乘谱约束的结构矩阵逼近问题及其扰动分析

从两个方面讨论具有最小二乘谱约束的对称斜哈密尔顿矩阵的逼近问题:(Ⅰ)研究使AX-XA的Frobenius范数最小的n阶实对称斜哈密尔顿矩阵A的集合C,其中X,A分别是特征向量和特征值矩阵, (Ⅱ)求(A)∈c使得‖C-(A)‖=min ‖C-A‖,这里‖·‖是Frobenius范数.给出了C的元素的一般表达式和(A)的显示表达式,分析了该最佳逼近矩阵A的扰动理论,并给出了数值实验.     

An estimate of the Hecke L-functions on the critical line

One obtains, under certain restrictions, an estimate for the Hecke L -functions on the critical line, similar to the estimate for the Riemann zeta-function.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 91, pp. 40–51, 1979.In conclusion, I would like to express my gratitude to A. I. Vinogradov for his constant interest and help in the writing of this paper.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

On a class of Newton-like methods for solving nonlinear equations

We provide a semilocal convergence analysis for a certain class of Newton-like methods considered also in [I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004) 374–397; I.K. Argyros, Computational theory of iterative methods, in: C.K. Chui, L. Wuytack (Eds.), Series: Studies in Computational Mathematics, vol. 15, Elsevier Publ. Co, New York, USA, 2007; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971], in order to approximate a locally unique solution of an equation in a Banach space.     

The existence of maximal invariant subalgebras in simple Cartan-type Lie algebras

It is proved that a Cartan-type Lie algebra contains a maximal subalgebra, invariant with respect to the group of automorphisms of .Translated from Matematicheskie Zametki, Vol. 9, No. 2, pp. 211–222, February, 1971.The author wishes to express his gratitude to A. I. Kostrikin for the interest he has shown in this work.     

Solvable subgroups of finite simple groups

This article is the author's abstract of his dissertation for the degree Doctor of Physico-mathematical Sciences. The dissertation was defended on September 17, 1973, at the session of the Academic Council on the conferring of academic degrees in the mathematical sciences of the Uralian Order of the Red Banner of Labor of the A. M. Gor'kii State University. The official opponents were: Professor A. I. Shirshov, Corresponding Member of the Academy of Sciences of the USSR and Doctor of Physicomathematical Sciences; Professor A. I. Kostrikin, Doctor of Physicomathematical Sciences; Professor A. I. Starostin, Doctor of Physicomathematical Sciences; Professor L. A. Shemetkov, Doctor of Physico-mathematical Sciences. The chief institution was the Institute of Mathematics, Academy of Sciences of the Ukrainian SSR.Translated from Matematicheskie Zametki, Vol. 16, No. 5, pp. 833–842, November, 1974.     

Properties of asymptotic expansions

The distribution function of a normalized sum of identically distributed independent random vectors is considered and some properties of its asymptotic expansions are studied. With the help of the results obtained here a theorem due to I. A. Ibragimov is strengthened.Translated from Matematicheskie Zametki, Vol. 22, No. 6, pp. 907–914, December, 1977.The author thanks V. V. Petrov and L. V. Osipov for taking interest in this article.     

Representation of square matrices by the product of diagonal,orthogonal, triangular,and integral unimodular matrices (in connection with the inhomogeneous Minkowski conjecture)

It is shown that for all sufficiently large numbers n nonsingular square matrices of order n are found for which the representation indicated in the title is impossible.Translated by L. Guy and J. P. Jones.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 67, pp. 86–94, 1977.In closing, I express deep gratitude to B. F. Skubenko for posing the problem and his attention to the work, and also to L. V. Kuz'min and A. V. Malysev for remarks and assistance in the final formulation of this paper.     

On the semilocal convergence of inexact Newton methods in Banach spaces

We provide two types of semilocal convergence theorems for approximating a solution of an equation in a Banach space setting using an inexact Newton method [I.K. Argyros, Relation between forcing sequences and inexact Newton iterates in Banach spaces, Computing 63 (2) (1999) 134–144; I.K. Argyros, A new convergence theorem for the inexact Newton method based on assumptions involving the second Fréchet-derivative, Comput. Appl. Math. 37 (7) (1999) 109–115; I.K. Argyros, Forcing sequences and inexact Newton iterates in Banach space, Appl. Math. Lett. 13 (1) (2000) 77–80; I.K. Argyros, Local convergence of inexact Newton-like iterative methods and applications, Comput. Math. Appl. 39 (2000) 69–75; I.K. Argyros, Computational Theory of Iterative Methods, in: C.K. Chui, L. Wuytack (Eds.), in: Studies in Computational Mathematics, vol. 15, Elsevier Publ. Co., New York, USA, 2007; X. Guo, On semilocal convergence of inexact Newton methods, J. Comput. Math. 25 (2) (2007) 231–242]. By using more precise majorizing sequences than before [X. Guo, On semilocal convergence of inexact Newton methods, J. Comput. Math. 25 (2) (2007) 231–242; Z.D. Huang, On the convergence of inexact Newton method, J. Zheijiang University, Nat. Sci. Ed. 30 (4) (2003) 393–396; L.V. Kantorovich, G.P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982; X.H. Wang, Convergence on the iteration of Halley family in weak condition, Chinese Sci. Bull. 42 (7) (1997) 552–555; T.J. Ypma, Local convergence of inexact Newton methods, SIAM J. Numer. Anal. 21 (3) (1984) 583–590], we provide (under the same computational cost) under the same or weaker hypotheses: finer error bounds on the distances involved; an at least as precise information on the location of the solution. Moreover if the splitting method is used, we show that a smaller number of inner/outer iterations can be obtained.     

A counter-example to a conjecture of Friedland

In 1982, S. Friedland proved that a bounded linear operator A on a Hilbert space is normal if and only if (αI + A + A*)² ≧ AA* − A*A ≧ −(αI + A + A*)² for all real α. And he conjectured the inequality (αI + A + A*)² ≧ AA* − A*A for all real α will imply that A*A − AA* ≧ 0, i.e., A is hyponormal. But his conjecture is incorrect. In this note I’ll give a counter-example for his conjecture.     

On the identric and logarithmic means

Summary Leta, b > 0 be positive real numbers. The identric meanI(a, b) of a andb is defined byI = I(a, b) = (1/e)(b ^b /a ^a ) ^1/(b–a) , fora b, I(a, a) = a; while the logarithmic meanL(a, b) ofa andb isL = L(a, b) = (b – a)/(logb – loga), fora b, L(a, a) = a. Let us denote the arithmetic mean ofa andb byA = A(a, b) = (a + b)/2 and the geometric mean byG =G(a, b) = . In this paper we obtain some improvements of known results and new inequalities containing the identric and logarithmic means. The material is divided into six parts. Section 1 contains a review of the most important results which are known for the above means. In Section 2 we prove an inequality which leads to some improvements of known inequalities. Section 3 gives an application of monotonic functions having a logarithmically convex (or concave) inverse function. Section 4 works with the logarithm ofI(a, b), while Section 5 is based on the integral representation of means and related integral inequalities. Finally, Section 6 suggests a new mean and certain generalizations of the identric and logarithmic means.     

Rules for the partial multiplicities of the product of holomorphic matrix functions

In [4] I. Gohberg and M.A. Kaashoek formulated the question how the partial multiplicities of the product AB of two holomorphic matrix (or operator) functions are related to those of the factors A and B. E.I. Sigal presented a set of necessary relations in [7], and recently L. Rodman and M. Schaps ([6]) obtained another set of relations which must hold. Here we prove a generalization of Sigal's rules which form a proper superset of the rules obtained by Sigal, Rodman and Schaps. Unlike Rodman and Schaps we formulate all results for matrix functions of fixed nxn-size; this leads to another set of relations which are derived for fixed n at first; however, we prove that such rules must hold independently of n, once they are derived for fixed n. Finally we show that this new set of relations completely determines the case of 3×3-matrices.     

Formulae for formfactors in the quantum sh-Gordon model

In this paper we get formulae for the formfactors in the quantum sh-Gordon model.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 54–66, 1987.The author thanks L. D. Faddeev, N. Yu. Reshetikhin, I. M. Khamitov, and F. A. Smirnov for numerous helpful discussions of the questions touched on in the paper.     

Topological K-groups of two-dimensional local fields

A complete two-dimensional local field K of mixed characteristic with finite second residue field is considered. The existence of a completely ramified extension L of K such that L is a standard field is assumed. It is proved that the rank of the quotient U(1)K ₂ ^top K/T_K, where T_K is the closure of the torsion subgroup, is equal to the degree of the constant subfield of K over ℚ_p. I. B. Zhukov constructed a set of generators of this quotient in the case where K is a standard field. In this paper, two natural generalizations of this set are considered, and it is proved that one of them generates the entire group and the other generates its subgroup of finite index. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 343, 2007, pp. 206–221.     

关于半格的一个定理

文中给出了如下定理：设（Ｌ，∨，∧，Π，Σ），ＡＬ，则（Ａ，∨，∧，Σ）＝（Ａ，∨，∧，Π，Σ）ｉｆｆ（Ｌ，∧）上的内部算子Ｉ，使得Ａ＝｛ｘ：Ｉ（ｘ）＝ｘ｝＝ｒａｎｇｅ（Ｉ）＆ＢＡ，Ｉ∧ｂ∈Ｂｂ＝∧ｂ∈ＢＩ（ｂ）．另外，还给出［１］中定理１的一个改进证明．     

Generalized Liouville differentiation and the method of multiplicators in imbedding theory for function classes

Author's review of his dissertation for the degree of doctor of the physico-mathematical sciences. Dissertation defended May 23, 1968, at the Mathematical Institute of the Academy of Sciences of the USSR.Official opponents: Doctor of Phys.-Math Sciences V. P. Il'in, Doctor of Phys.-Math Sciences I. A. Kipriyanov, and Doctor of Phys.-Math Sciences L. N. Slobodetskii.Translated from Matematicheskie Zametki, Vol. 4, No. 4, pp. 467–482, October, 1968.     

Factorization in finite-codimensional ideals of group algebras

Let G be a -compact, locally compact group and I be a closed2-sided ideal with finite codimension in L¹(G). It is shownthat there are a closed left ideal L having a right boundedapproximate identity and a closed right ideal R having a leftbounded approximate identity such that I = L + R. The proofuses ideas from the theory of boundaries of random walks ongroups. 2000 Mathematics Subject Classification: primary 43A20;secondary 42A85, 43A07, 46H10, 46H40, 60B11.     

AF C*-代数中的Lie理想

本文描述了AF C*-代数中闭Lie理想,证明了如果AF C*-代数A中的线性流形L 是A的闭Lie理想,则存在A的闭结合理想I和A的典型masa D中的闭子代数EI使得[A,I](?)L(?)I EI,并且A中每一个这种形式的闭子空间都是A的闭Lie理想.     

Characterization of elliptic distributions

We characterize elliptic distributions in ^d by an extremal property for a class of probability distances. A generalization to the case of Hilbert spaces is given. Bibliography: 2 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 19–28.Translated by Ya. I. Belopolskaya, L. B. Klebanov, and V. E. Volkovich.