A criterion for coarse iterability

The main result of this paper is the following theorem: Let M be a premouse with a top extender, F. Suppose that (a) M is linearly coarsely iterable via hitting F and its images, and (b) if M ^* is a linear iterate of M as in (a), then M ^* is coarsely iterable with respect to iteration trees which do not use the top extender of M ^* and its images. Then M is coarsely iterable.     

Some <Emphasis Type="Italic">I</Emphasis>-convergent sequence spaces defined by Orlicz functions

In this article we introduce the sequence spaces cI(M),c0I(M),mI(M) and m0I(M) using the Orlicz function M.We study some of the properties like solid,symmetric,sequence algebra,etc and prove some inclusion relations.     

Effect of the initial estimator on the asymptotic behavior of one-step M-estimator

For a general (real) parameter, let M _nbe the M-estimator and M _n ⁽¹⁾ be its one-step version (based on a suitable initial estimator M _n ⁽⁰⁾). It is known that, under certain regularity conditions, n(M _n ⁽¹⁾-M _n)=O _p(1). The asymptotic distribution of n(M _n ⁽¹⁾-M _n) is studied; it is typically non-normal and it reveals the role of the initial estimator M _n ⁽⁰⁾.Work of this author was partially supported by the Office of Naval Research, Contract No. N00014-83-K-0387     

The torsion of a submanifold of a Riemannian manifold

For a submanifoldM ⁿ of a Riemannian manifoldM ^q, the concept of a torsion bivector at the point x M ⁿ for given one- and two-dimensional directions fromT _x M ⁿ is introduced using only the first and second fundamental forms ofM ⁿ. Its relation to the concept of Gaussian torsion is then established. It is proved that: 1) equality to zero of the torsion bivector is necessary and, whenM ⁿ is a nondevelopable surface of a space of constant curvature with nonzero second fundamental form, is also sufficient for the "flattening" ofM ⁿ into some totally geodesicM ⁿ⁺¹ inM ^q; 2) when n = 2, the independence of the nonzero torsion bivector of direction characterizes a minimalM ² inM ^q.Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 39–42, 1991.     

Some dimension-free features of vector-valued martingales

Summary Given any local maringaleM inR ^d orl ², there exists a local martingaleN inR ², such that |M|=|N|, [M]=[N], and «M»=«N». It follows in particular that any inequality for martingales inR ² which involves only the processes |M|, [M] and «M» remains true in arbitrary dimension. WhenM is continuous, the processes |M|² and |M| satisfy certain SDE's which are independent of dimension and yield information about the growth rate ofM. This leads in particular to tail estimates of the same order as in one dimension. The paper concludes with some new maximal inequalities in continuous time.Research supported by NSF grant DMS-9002732 and by AFOSR Contract F49620 85C 0144     

The canonical spectral sequences for poisson manifolds

For a compact symplectic manifoldM of dimension 2n, Brylinski proved that the canonical homology groupH _k ^can (M) is isomorphic to the de Rham cohomology groupH ^2n-k (M), and the first spectral sequence {E ^r (M)} degenerates atE ¹(M). In this paper, we show that these isomorphisms do not exist for an arbitrary Poisson manifold. More precisely, we exhibit an example of a five-dimensional compact Poisson manifoldM ⁵ for whichH ₁ ^can (M ⁵) is not isomorphic toH ⁴(M ⁵), andE ¹(M ⁵) is not isomorphic toE ²(M ⁵). This work has been partially supported through grants DGICYT (Spain), Projects PB91-0142 and PB89-0571, PB94-0633-C02-02; and through grants UPV, Project 127.310-EA 191/94, 127.310-EC248/96.     

On the canonical extension of a differentiable manifold

In this paper, the differential geometry of second canonical extension² M of a differentiable manifoldM is studied. Some vector fields tangent to² M inTTM are determined. In addition we obtain that the second canonical extensions ofM and a totally geodesic submanifold inM are totally geodesic submanifolds inTTM and² M respectively.     

Simple-direct-modules

A right R-module M is called simple-direct-injective if, whenever, A and B are simple submodules of M with A?B, and B?^⊕M, then A?^⊕M. Dually, M is called simple-direct-projective if, whenever, A and B are submodules of M with M∕A?B?^⊕M and B simple, then A?^⊕M. In this paper, we continue our investigation of these classes of modules strengthening many of the established results on the subject. For example, we show that a ring R is uniserial (artinian serial) with J²(R) = 0 iff every simple-direct-projective right R-module is an SSP-module (SIP-module) iff every simple-direct-injective right R-module is an SIP-module (SSP-module).     

Circularm-functions

Circularm-functions are introduced on smooth manifolds with boundary. We study the distribution of their critical circles and construct an example of a four-dimensional manifoldM ⁴ with boundary ∂M ⁴ that satisfies the condition ξ(∂M ⁴)=ξ(M ⁴,∂M ⁴)=0 but does not contain any circularm-function. We prove that a manifold with boundaryM ⁿ (n≥5) such that ξ(∂M ⁿ , ∂M ⁿ )=0 always contains a circularm-function without critical points in the interior manifold. Sukhumi Branch of the Tbilisi University, Sukhumi. Translated from Ukrainskii Matermaticheskii Zhurnal, Vol. 46, No. 6, pp. 776–781, June, 1994.     

Properties of Hadamard product of inverse M‐matrices

This paper concerns with the properties of Hadamard product of inverse M‐matrices. Structures of tridiagonal inverse M‐matrices and Hessenberg inverse M‐matrices are analysed. It is proved that the product A ○ A^T satisfies Willoughby's necessary conditions for being an inverse M‐matrix when A is an irreducible inverse M‐matrix. It is also proved that when A is either a Hessenberg inverse M‐matrix or a tridiagonal inverse M‐matrix then A ○ A^T is an inverse M‐matrix. Based on these results, the conjecture that A ○ A^T is an inverse M‐matrix when A is an inverse M‐matrix is made. Unfortunately, the conjecture is not true. Copyright © 2004 John Wiley Sons, Ltd.     

Geometry of the Normal Bundle of a Submanifold*

 We study the geometric behavior of the normal bundle T ^⊥ M of a submanifold M of a Riemannian manifold . We compute explicitely the second fundamental form of T ^⊥ M and look at the relation between the minimality of T ^⊥ M and M. Finally we show that the Maslov forms with respect to a suitable connection of the pair (T ^⊥ M, are null. Received March 14, 2001; in revised form February 11, 2002     

Analytic Discs and Extension of CR Functions

Let M be a manifold of X = C ⁿ , A a small analytic disc attached to M, z ^o a point of A where A is tangent to M, z ¹ another point of A where M extends to a germ of manifold M ₁ with boundary M. We prove that CR functions on M which extend to M ₁ at z ¹ also extend at z ^o to a new manifold M ₂. The directions M ₁ and M ₂ point to, are related by a sort of connection associated to A which is dual to the connection obtained by attaching 'partial analytic lifts' of A to the co-normal bundle to M in X.     

Heegaard Genus Formula for Haken Manifolds

Suppose M is a compact orientable 3-manifold and a properly embedded orientable boundary incompressible essential surface. Denote the completions of the components of M – Q with respect to the path metric by M ¹, ...,M ^k . Denote the smallest possible genus of a Heegaard splitting of M, or M ^j respectively, for which ∂M, or ∂M ^j respectively, is contained in one compression body by g(M, ∂M), or g(M ^j , ∂M ^j ) respectively. Denote the maximal number of non-parallel essential annuli that can be simultaneously embedded in M ^j by n _j . Then

On a class of finite rings

In [7], Corbas determined all finite rings in which the product of any two zero-divisors is zero, and showed that they are of two types, one of characteristic p ²and the other of characteristic p².

The purpose of this paper is to address the problem of the classification of finite rings such that.

(i)the set of all zero-divisors form an ideal M.

(ii)M ³=(0); and.

(iii)M ³≠(0).

Because of (i), these rings are called completely primary and we shall call a finite completely primary ring R which satisfies conditions (i), (ii) and (iii), a ring with property(T). These rings are of three types, namely, of characteristic p p ² and p ³. The characteristic p ² case is subdivided into cases in which p?M ² p?ann(M)?M ² and p?M ?ann(M), where ann(M) denotes the two-sided annihilator of where M in R.     

Splines (with optimal knots) are better

Let S^M _k be the Polynominal splines of degree n-1, and with K segments. If f∈ C ⁿ [a,b],then the distance in the L^p-norm form(0< p ≦ ∞)of from S ^M _k is boundedby M/K ⁿ , with a much smaller M than in similar estimates for other processes of approximation.     

On the first pontrjagin class of homotopy complex projective spaces

Let M ²ⁿ be a closed smooth manifold homotopy equivalent to the complex projective space ℂP(n). It is known that the first Pontrjagin class p ₁(M) of M ²ⁿ has the form (n+1+24α(M))u ² for some integer α(M) where u is a generator of H ²(M; ℤ). We prove that α(M) is even when n is even but not divisible by 64.     

Analysis of the M X /G/1 Queue Under D-Policy

Abstract

We study the queue length of the M ^X /G/1 queue under D-policy. We derive the queue length PGF at an arbitrary point of time. Then, we derive the mean queue length. As special cases, M/G/1, M ^X /M/1, and M/M/1 queue under D-policy are investigated. Finally, the effects of employing D-policy are discussed.     

Complete hypersurfaces with constant mean curvature and finite L p norm curvature in Euclidean spaces

In this paper, we consider complete hypersurfaces in R ⁿ⁺¹ with constant mean curvature H and prove that M ⁿ is a hyperplane if the L ² norm curvature of M ⁿ satisfies some growth condition and M ⁿ is stable. It is an improvement of a theorem proved by H. Alencar and M. do Carmo in 1994. In addition, we obtain that M ⁿ is a hyperplane (or a round sphere) under the condition that M ⁿ is strongly stable (or weakly stable) and has some finite L ^p norm curvature. Received: 14 July 2007     

Über Die Assoziierten Primideale des Bidualen

Let (R, 𝔪) be a commutative, noetherian, local ring, E the injective hull of the residue field R/𝔪, and M ^○○ = Hom _R (Hom _R (M, E), E) the bidual of an R-module M. We investigate the elements of Ass(M ^○○) as well as those of Coatt(M) = {𝔭 ∈ Spec(R)|𝔭 = Ann _R (Ann _M (𝔭))} and provide criteria for equality in one of the two inclusions Ass(M) ? Ass(M ^○○) ? Coatt(M). If R is a Nagata ring and M a minimax module, i.e., an extension of a finitely generated R-module by an artinian R-module, we show that Ass(M ^○○) = Ass(M) ∪ {𝔭 ∈ Coatt(M)| R/𝔭 is incomplete}.     

A Hadamard product involving N-matrices

We show that for any pair M,N of n by n M-matrices, the Hadamard (entry-wise) product M°N _-1 is again an M-matrix. For a single M-matrix M, the matrix M°M ^-1 is also considered.