Affine umbilical surfaces inR 4

Summary A surface in ℝ⁴ is called affine umbilical if for each vector belonging to the affine normal plane the corresponding shape operator is a multiple of the identity. We will classify affine umbilical definite surfaces which either have constant curvature or which satisfy ∇^⊥ g ^⊥. Furthermore, it will be shown that for an affine umbilical definite surface, the affine mean curvature vector can not have constant non-zero length. The last author is a Senior Research Assistant of the National Fund for Scientific Research (Belgium) This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991.     

Links of surface singularities and CR space forms

We classify 3-dimensional compact locally homogeneous non-degenerate CR-manifolds (“CR space-forms”). Most of them are links of normal complex surface singularities, and we classify these singularities. In memory of Peter Scherk Research partially supported by the NSF.     

A degenerate extreme point strategy for the classification of linear constraints as redundant or necessary

This paper presents a degenerate extreme point strategy for active set algorithms which classify linear constraints as either redundant or necessary. The strategy makes use of an efficient method for classifying constraints active at degenerate extreme points. Numerical results indicate that significant savings in the computational effort required to classify the constraints can be achieved.This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grants A8807 and A4625 and by an Undergraduate Summer Research Award.     

Elimination theory and Newton polytopes

We study elimination theory in the context of Newton polytopes and develop its convex-geometry counterpart. Research of A. Esterov was supported in part by the grants RFBR-JSPS-06-01-91063, RFBR-07-01-00593, and INTAS-05-7805. Research of A. Khovanskii was supported in part by the grant OGP 0156833 (Canada).     

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.     

Robust convex quadratically constrained programs

In this paper we study robust convex quadratically constrained programs, a subset of the class of robust convex programs introduced by Ben-Tal and Nemirovski [4]. In contrast to [4], where it is shown that such robust problems can be formulated as semidefinite programs, our focus in this paper is to identify uncertainty sets that allow this class of problems to be formulated as second-order cone programs (SOCP). We propose three classes of uncertainty sets for which the robust problem can be reformulated as an explicit SOCP and present examples where these classes of uncertainty sets are natural. Research partially supported by DOE grant GE-FG01-92ER-25126, NSF grants DMS-94-14438, CDA-97-26385, DMS-01-04282 and ONR grant N000140310514.Research partially supported by NSF grants CCR-00-09972, DMS-01-04282 and ONR grant N000140310514.     

Singularities and bifurcations of 3-dimensional Poisson structures

We give a normal form for families of 3-dimensional Poisson structures. This allows us to classify singularities with nonzero 1-jet and typical bifurcations. The Appendix contains corollaries on classification of families of integrable 1-forms on ℝ³. Zhitomirskii’s research was supported by the Fund for the Promotion of Research at the Technion.     

Diffraction of whispering gallery waves by a conjunction line

A nonhomogeneous elastic body with stress-free boundary is considered. The boundary consists of two smooth cylindrical surfaces with continuous tangent plane. The curvature of the boundary is assumed to have a discontinuity on the conjunction line. The behavior of two kinds of transversal surface whispering gallery waves passing through the conjunction line is studied. For a wave of the first kind, corresponding to the Dirichlet boundary condition, the displacement vector is normal to the boundary. For a wave of the second kind, corresponding to the Neumann boundary condition, the displacement vector is tangent to the boundary and normal to the ray, which is similar to the case of Love waves.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 95–109.This work was supported by the Russian Foundation for Basic Research under grant No. 96-01-00666.     

On Controllability of an Elastic Ring

We study the exact controllability problem for a ring under stretching tension that varies in time. We are looking for a couple of forces, which drive the state solution to rest. We show that applying two forces is necessary for controllability and the ring is controllable in the time interval greater than the optical length of the string. We also explain why one force would not be enough to control the ring. We use the method of moments to reduce the controllability problem to a moment problem for the controlling forces. The solution of that problem is based on an auxiliary basis property result. Both method of moments and proof of the basis property are developed for the model with time-dependent parameters. S.A.’s research was supported in part by the NSF, grant ARC–0724860. B.B.’s research was supported in part by University of Tennessee at Chattanooga Faculty Research Grant. S.I.’s research was supported in part by the Russian Foundation for Basic Research, grants 08-01-00595a and 08-01-00676a.     

Pseudocomplementation in (Normal) Subgroup Lattices

The goal of this article is to study finite groups admitting a pseudocomplemented subgroup lattice (PK-groups) or a pseudocomplemented normal subgroup lattice (PKN-groups). In particular, we obtain a complete classification of finite PK-groups and of finite nilpotent PKN-groups. We also study groups with a Stone normal subgroup lattice, and we classify finite groups for which every subgroup has a Stone normal subgroup lattice. Finally, we obtain a complete classification of finite groups for which every subgroup is monolithic.     

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.     

Decay rates at low and high frequencies for a plate equation with feedback concentrated in interior curves

In this paper we study the stabilization of plate vibrations by means of piezoelectric actuators. In this situation the geometric control condition of Bardos, Lebeau and Rauch [6] is not satisfied. We prove that we have exponential stability for the low frequencies but not for the high frequencies. We give an explicit decay rate for regular initial data at high frequencies while clarifying the behavior of the constant which intervenes in this estimation there function of the frequency of cut n. The method used is based on some trace regularity which reduces stability to some observability inequalities for the corresponding undamped problem. Moreover, we show numerically at low frequencies, that the optimal location of the actuator is the center of the domain Ω. Research supported by the RIP program of Oberwolfach Institut and by the Tunisian Ministry for Scientific Research and Technology (MRST) under Grant 02/UR/15-01. Research supported by the RIP program of Oberwolfach Institut. (Received: September 17, 2003; revised: February 26, 2004)     

Empirical likelihood for partial linear models

In this paper the empirical likelihood method due to Owen (1988,Biometrika,75, 237–249) is applied to partial linear random models. A nonparametric version of Wilks' theorem is derived. The theorem is then used to construct confidence regions of the parameter vector in the partial linear models, which has correct asymptotic coverage. A simulation study is conducted to compare the empirical likelihood and normal approximation based method. Research supported by NNSF of China and a grant to the first author for his excellent Ph.D. dissertation work in China. Research supported by Hong Kong RGC CERG No. HKUST6162/97P.     

An estimate of stability of the reconstruction of the normal multiplicative type

An estimate of the characterization stability of the normal distribution type is obtained for the case of the multiplicative type. Under some conditions, the estimate has the orderɛ ^1/3 L(ɛ), where L(∈) is a slowly varying function. Supported by the Russian Founation for Basic Research (grant Nos. 97-01-00273, 98-01-00621, and 98-01-00926) and by INTAS-RFBR (grant No. IR-97-0537). Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part II.     

Conformal type and isoperimetric dimension of Riemannian manifolds

The notion of conformal isoperimetric dimension is introduced. For Riemannian manifolds, connections between its conformal isoperimetric dimension and its conformal type are established. Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 379–385, March, 1998. The authors are greatly indebted to N. A. Zorich for her help in preparing the computer version of this paper. This research was partially supported by the Russian Foundation for Basic Research under grants No. 96-01-01218 and No. 96-01-00901.     

Affine surfaces with constant affine curvatures

In this paper, we study affine non-degenerate Blaschke immersions from a surface M in ³. We will assume that M has constant affine curvature and constant affine mean curvature, i.e. both the determinant and the trace of the shape operator are constant. Clearly, affine spheres satisfy both these conditions. In this paper, we completely classify the affine surfaces with constant affine curvature and constant affine mean curvature, which are not affine spheres.Research Assistant of the National Fund for Scientific Research (Belgium).     

Classification of surfaces with planar normal sections

A surface in E^m is said to have planar normal sections if normal sections of M are planar curves. In this paper we completely classify surfaces in E^m with planar normal sections. Consequently, a new characterization of the Veronese surface is obtained.     

Centroaffine surfaces in -geodesics

For (positive) definite surfaces in there is a canonical choice of a centroaffine normal plane bundle, which induces a centroaffine invariant Ricci-symmetric connection . We classify all surfaces in with planar -geodesics. It turns out that the resulting class of surfaces is umbilical with projectively flat induced connection and flat normal plane bundle.

     

Subadditivity Inequalities in von Neumann Algebras and Characterization of Tracial Functionals

We examine under which assumptions on a positive normal functional φ on a von Neumann algebra, and a Borel measurable function f: R ⁺ → R with f(0) = 0 the subadditivity inequality φ (f(A+B)) ≤ φ(f(A))+φ (f (B)) holds true for all positive operators A, B in . A corresponding characterization of tracial functionals among positive normal functionals on a von Neumann algebra is presented. O.E. Tikhonov - Supported by the Russian Foundation for Basic Research (grant no. 01-01-00129) and the scientific program Universities of Russia – Basic Research (grant no. UR.04.01.061).