Piercing Families of Convex Sets with the <Emphasis Type="Italic">d</Emphasis>-Intersection Property in ℝ<Superscript><Emphasis Type="Italic">d</Emphasis></Superscript>

In this paper, we consider finite families of convex sets in ℝ ^d such that every d or fewer sets of the family have a common point. For some families of this type, we give upper bounds on the size of a finite set intersecting all sets of the family. This research was supported by the Russian Foundation for the Basic Research Grants No. 03-01-00801 and 06-01-00648, and by the President of the Russian Federation Grant No. MK-5724.2006.1.     

On Automorphic Tuples of Elements in Computable Models

A criterion is obtained for existence of two isomorphic but not hyperarithmetically isomorphic tuples in a hyperarithmetical model. This criterion is used to show that such a situation occurs in the models of well-known classes.Original Russian Text Copyright © 2005 Goncharov S. S., Harizanov V. S., Knight J. F., Morozov A. S., Romina A. V.The first four authors are supported by the Binational Grant NSF DMS-0075899; the first and fourth authors are partially supported by the Russian Foundation for Basic Research (Grant 02-01-00953) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2112.03.1).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 523–532, May–June, 2005.     

Some natural equivalence relations in the Solovay model

We obtain some non-reducibility results concerning some natural equivalence relations on reals in the Solovay model. The proofs use the existence of reals x which are minimal with respect to the cardinals in L[x], in a certain sense. S.-D. Friedman research was supported by Grant P 19375-N18 of the Austrian Science Fund (FWF). V. Kanovei research was supported by Grants 06-01-00608 and 07-01-00445 of the Russian Foundation for Basic Research (RFBR).     

Asymptotic Behavior of Generalized Risk Processes

In this paper, the asymptotic behavior of generalized risk processes without any moment assumptions on the controlling process is described.     

Root Decomposition of the Ternary Malcev Algebra <Emphasis Type="Italic">M</Emphasis><Subscript>8</Subscript>

A root decomposition is constructed of the simple eight-dimensional ternary Malcev algebra M ₈. In result, M ₈ is equipped with a structure of a Z ₃-graded ternary algebra.Original Russian Text Copyright © 2005 Pozhidaev A. P.The author was supported by the Russian Science Support Foundation and partially by the Russian Foundation for Basic Research (Grant 05-01-00230).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 901–906, July–August, 2005.     

Weight of faces in plane maps

Precise upper bounds are obtained for the minimum weight of minor faces in normal plane maps and 3-polytopes with specified maximum vertex degree. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 648–657, November, 1998. The research of the first named author was supported in part by the Visiting Fellowship Research Grant GR/K00561 from the Engineering and Physical Sciences Research Council and by the Russian Foundation for Basic Research under grant No. 96-01-01614 and No. 97-01-01075.     

Differential equations with almost periodic or conditionally periodic coefficients: Recurrence and reducibility

Recurrence of an individual trajectory of a linear nonautonomous differential equation on a compact Lie group for the case of an almost periodic or conditionally periodic dependence of the right-hand side on time is proved. The relation between recurrence and reducibility is examined.Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 229–237, August, 1998.This research was supported by the Russian Foundation for Basic Research under grants No. 96-01-00378 and No. 96-15-96072.     

Inverse nodal problems for the Sturm-Liouville differential operators on a star-type graph

We study inverse nodal problems for the second order differential operators on a star-type graph satisfying the standard matching conditions at the interior vertex. We prove uniqueness theorems and obtain a constructive solution to the inverse problems of this class. Original Russian Text Copyright ? 2009 Yurko V. A. The author was supported by the Russian Foundation for Basic Research (Grant 07-01-00003) and the National Science Council of Taiwan (Grant 07-01-92000-NSC-a). __________ Saratov. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 2, pp. 469–475, March–April, 2009.     

Inequalities for derivatives of functions analytical in a strip

This work was supported by the Russian Foundation for Fundamental Research, Grant No. 93-01-00237, and by the International Scientific Foundation, Grant No. MP 1000.     

Recurrence of the integral of a smooth conditionally periodic function

We prove that the integral of a smooth multifrequency conditionally periodic function with zero mean oscillates. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 737–748, May, 1998. The author wishes to express his deep gratitude to S. V. Konyagin for fruitful discussions, verification of the results, and the correction of some misprints. This research was supported by the Russian Foundation for Basic Research under grants No. 96-01-00378 and No. 96-15-96072 and by the EFAKOD Foundation.     

The number of periodic solutions of polynomial differential equations

We estimate the number of periodic solutions for special classes ofnth-order ordinary differential equations with variable coefficients. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 720–727, November, 1998. The author thanks Yu. S. Il'yashenko for setting the problems, permanent advice, and overall support. The author is also thankful to D. A. Panov for numerous discussions. This research was supported by the CRDF Foundation under grant MR1-220, by the INTAS Foundation under grant No. 93-05-07, and by the Russian Foundation for Basic Research under grant No. 95-01-01258.     

Justification of Dipole Approximation in the Problem of Nonlinear Wave Generation by a Submerged Sphere

Some nonlinear dipole approximation is constructed for the nonstationary problem of a solid sphere motion under a free surface. The approximation is justified in the class of analytic functions decaying at infinity.Original Russian Text Copyright © 2005 Pyatkina E. V.The author was supported by the State Maintenance Program for the Leading Scientific Schools (Grant NSh-440.2003.1) and the Russian Foundation for Basic Research (Grant 05-01-00250).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 907–927, July–August, 2005.     

Extremum problems for functions with small support

In this paper we consider an extremum problem for even periodic functions having small intervals as their supports and subject to restrictions on the sum of the absolute values of their Fourier coefficients. Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 323–332, September, 1996. We wish to express our gratitude to S. B. Stechkin for his interest in our work. This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00378, and the work of the first and second authors also by the International Science Foundation under grant No. MC5300.     

Lower bound for the maximum of a stochastic process

The first author's participation in the preparation of this paper was supported by the Russian Foundation for Basic Research (Grant No. 93-01-00240).     

Analytic properties of quasiconformal mappings on Carnot groups

The research was supported by the Russian Foundation for Fundamental Research (Grant 94-01-00378) and the International Science Foundation (Grant RAT000).     

Approximately differentiable transformations and change of variables on nilpotent groups

The research was financially supported by the Russian Foundation for Basic Research (Grant 94-01-00378) and the International Science Foundation (Grant RAT000).     

Gaining efficiency via weighted estimators for multivariate failure time data

Multivariate failure time data arise frequently in survival analysis. A commonly used technique is the working independence estimator for marginal hazard models. Two natural questions are how to improve the efficiency of the working independence estimator and how to identify the situations under which such an estimator has high statistical efficiency. In this paper, three weighted estimators are proposed based on three different optimal criteria in terms of the asymptotic covariance of weighted estimators. Simplified close-form solutions are found, which always outperform the working independence estimator. We also prove that the working independence estimator has high statistical efficiency, when asymptotic covariance of derivatives of partial log-likelihood functions is nearly exchangeable or diagonal. Simulations are conducted to compare the performance of the weighted estimator and working independence estimator. A data set from Busselton population health surveys is analyzed using the proposed estimators. This work was supported by National Natural Science Foundation of China (Grant No. 10628104), Fan was also supported by National Institutes of Health (Grant No. R01-GM072611) and Natural Science Foundation (Grant No. DMS-0714554), Zhou was supported by National Natural Science Funds for Distinguisheel Young Scholar (Grant No. 70825004), National Natural Science Foundation of China (Grant Nos. 10731010, 10628104), the National Basic Research Program (Grant No. 2007CB814902), Creative Research Groups of China (Grant No. 10721101) and Leading Academic Disipline Program, the 10 ^th five year plan of 211 Project for Shanghai University of Finance and Economics (the 3 ^rd phase), Cai was supported by National Institutes of Health (Grant No. R01-HL57444)     

An Estimate for the <Emphasis Type="Italic">n</Emphasis>th Minimal Error of Linear Algorithms for One Problem in a Normed Vector Space

We find an estimate for the nth minimal error of linear algorithms for some problem defined in a finite-dimensional space with values in an arbitrary normed vector space.Original Russian Text Copyright © 2005 Sidorov S. P.The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00060), the State Maintenance Programs for the Leading Scientific Schools of the Russian Federation (Grant 1295.2003.1), and the Program Universities of Russia (Grant 04.01.374).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 673–678, May–June, 2005.     

Dynamics of elementary maps of dendrites

The notion of elementary map of a dendrite into itself is introduced. Arithmetical relations between the periods of periodic points are given; the structure ofω-limit sets, sets of periodic and nonwandering points is described; the topological entropy of elementary maps is shown to be equal to 0. Examples are given illustrating the differences in the entropic properties of continuous maps of dendrites with a countable set of branch points and continuous maps of their retracts which are finite trees. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 183–195, February, 1998. This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01755.     

On Recognition by Spectrum of Finite Simple Linear Groups over Fields of Characteristic 2

A finite group G is said to be recognizable by spectrum, i.e., by the set of element orders, if every finite group H having the same spectrum as G is isomorphic to G. We prove that the simple linear groups L _n (2^k) are recognizable by spectrum for n = 2^m ≥ 32.Original Russian Text Copyright © 2005 Vasil’ev A. V. and Grechkoseeva M. A.The authors were supported by the Russian Foundation for Basic Research (Grant 05-01-00797), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2069.2003.1), the Program “ Development of the Scientific Potential of Higher School” of the Ministry for Education of the Russian Federation (Grant 8294), the Program “Universities of Russia” (Grant UR.04.01.202), and a grant of the Presidium of the Siberian Branch of the Russian Academy of Sciences (No. 86-197).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 749–758, July–August, 2005.