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Yu. E. Hohlov, D. V. ProkhorovOn geometrical properties of free boundaries in the Hele-Shaw flows moving boundary problemVolume_1/1_1.htmlIn the article we discuss the geometrical properties of the moving boundary for two basic cases in the plain problem of the Hele-Shaw flows: for the inner problem for the flows in a bounded simply connected domain; and for the exterior problem for dynamics of an aerofoil connected with the flows in the exterior part of a bounded simply connected domain. We prove the invariance of the properties of starlikeness in case of the inner problem of pumping; of convexity in case of the exterior problem of tightening of an aerofoil. We also adduce some examples for the problem of tightening where the corresponding properties of starlikeness, convexity and close-to-convexity are not inherited by the moving boundary. Yu. F. KorobeinikAbsolutely convergent dirichlet series and analytic continuation of its sumVolume_1/1_2.htmlThe paper contains some results on analytic continuation of the sum of Dirichlet series obtained with the help of the wellknown Ploya theorem. A special attention is paid to an effective determination of the domain into which the sum of series can be continued analytically. Some methods of the effective continuation of the sum of Dirichlet series are considered including, in particular, the analytic continuation by means of initial series. In this part of paper the author employs the results of Leont'ev and other russian mathematicians including his own. A many dimensional analogue of Polya theorem is also obtained as well as some results on analytic continuation of its sum. Finally, the characterization of the exact domain of absolute convergence of many-dimensional Dirichlet series is given under comparatively mild restriction. Igor V. KonnovCombined Relaxation Methods for Variational Inequality Problems over Product SetsVolume_2/2_1.htmlA general framework based on combining, modifying and generalizing various relaxation methods is proposed for solving variational inequality problems. This framework involves a decomposition scheme for certain structured problems. Convergence of the corresponding methods is proved under rather mild assumptions. M.A. MalakhaltsevThe Lie derivative and cohomology of G-structuresVolume_3/3_10.htmlIn [Pommaret], J.F. Pommaret constructed the so-called Spencer P-complex for a differential operator. Applying this construction to the Lie derivative associated with a general pseudogroup structure on a smooth manifold, he defined the deformation cohomology of a pseudogroup structure. The aim of this paper is to specify this complex for a particular case of pseudogroup structure, namely, for a first-order G-structure, and to express this complex in differential geometric form, i. e., in terms of tensor fields and the covariant derivative. We show that the Pommaret construction provides a powerful tool for associating a differential complex to a G-structure. In a unified way one can obtain the Dolbeaut complex for the complex structure, the Vaisman complex for the foliation structure [Vaisman], and the Vaisman-Molino cohomology for the structure of manifold over an algebra [Shurygin]. Kentaro MikamiNambu-Poisson structures and their foliationsVolume_3/3_11.htmlNambu-Poisson bracket is a natural generalization of Poisson bracket. A very distinguished property is its decomposability. This is investigated from the second order term of the fundamental identity (see [Gauth:LMP] or [nakanisi:nambu]). In this paper, we shall study the first order term of the fundamental identity and get a relation with the Schouten-Nijenhuis bracket. And also we shall show that for a given Poisson structure, the top power of it gives a Nambu-Poisson structure. We shall characterize the Godbillon-Vey class of the foliation defined from a regular Nambu-Poisson tensor. R. MiyaokaHypersurface geometry and Hamiltonian systems of hydrodynamic typeVolume_3/3_12.html V. F. MolchanovRepresentations of pseudo-unitary groups associated with a coneVolume_3/3_13.htmlWe study representations of the pseudo-unitary group SU(p,q), p,q≥ 2, associated with an isotropic cone. Y. AgaokaOn the variety of 3-dimensional Lie algebrasVolume_3/3_1.htmlIt is known that a 3-dimensional Lie algebra is unimodular or solvable as a result of the classification. We give a simple proof of this fact, based on a fundamental identity for 3-dimensional Lie algebras, which was first appeared in [21]. We also give a representation theoretic meaning of the invariant of 3-dimensional Lie algebras introduced in [15], [22], by calculating the GL(V)-irreducible decomposition of polynomials on the space Λ2 V⊗ V up to degree 3. Typical four covariants naturally appear in this decomposition, and we show that the isomorphism classes of 3-dimensional Lie algebras are completely determined by the GL(V)-invariant concepts in Λ2 V⊗ V defined by these four covariants. We also exhibit an explicit algorithm to distinguish them. B. Doubrov and B. KomrakovClassification of homogeneous submanifolds in homogeneous spacesVolume_3/3_2.htmlWe develop algebraic methods for study of homogeneous submanifolds in homogeneous spaces. This includes the description of stationary subgroups of k-jets of homogeneous submanifolds, algebraic version of Cartan's method of the moving frame, description of subalgebras corresponding to symmetry groups of homogeneous submanifolds. We also develop several algebraic techniques for classification of homogeneous submanifolds. As application we present the results of such classifications in low-dimensional affine and projective geometries. B. Doubrov, B. Komrakov, and T. MorimotoEquivalence of holonomic differential equationsVolume_3/3_3.html A. Fujioka, J. InoguchiOn some generalisations of constant mean curvature surfacesVolume_3/3_4.htmlIn this paper we shall study relations between three generalisations of CMC surfaces - Bonnet surfaces, H-surfaces and HIMC surfaces. We introduce the notion of HIMC surfaces in space forms and show that HIMC surfaces have similar properties to CMC surfaces. Furthermore we shall introduce a special one-parameter family of framings for H- surfaces in the space forms. Through these framings we reveal relationship between the associated family of H-surfaces and the extended solutions for harmonic maps into SO(3). M. GraevIntermediate inversion formulas in integral geometryVolume_3/3_5.htmlWe solve the following ``intermediate'' problem of integral geometry: to reconstruct integrals of a function over p-dimensional planes in Rn starting from its integrals over k-planes, where p. Some generalizations are also presented. G. IshikawaDevelopable hypersurfaces and homogeneous spaces in a real projective spaceVolume_3/3_6.htmlWe present new examples of non-singular developable hypersurfaces, which are algebraic and homogeneous, in real projective spaces. Moreover we give a characterization of compact homogeneous developable hypersurfaces, using the theory of isoparametric hypersurfaces. I.S. Krasil'shchikCohomological approach to Poisson structures on nonlinear evolution equationsVolume_3/3_7.htmlLet E be a differential equation, and let F=F(E) be the function algebra on the infinite prolongation E. Consider the algebra A= Λ(F) of differential forms on F endowed with the horizontal differential dh: A→A. A Poisson structure P on E is understood as the homotopy equivalence class (with respect to dh) of a skew symmetric super bidifferential operator P in A satisfying the condition [[P,P]]s=0, [[•,•]]s being the super Schouten bracket.

A description of Poisson structures for an evolution equation with an arbitrary number of space variables is given. It is shown that the computations, in essence, reduce to solving the operator equation PºlE+ lE º P=0. We demonstrate that known structures for some evolution equations (e.g., the KdV equation) are special cases of those considered here.
Olga KuzmichGraded nilpotent Lie algebras in low dimensionsVolume_3/3_8.htmlWe classify all graded nilpotent Lie algebras up to dimension 7 and compute their universal prolongations. Y. Machida, T. MorimotoOn decomposable Monge-Ampère equationsVolume_3/3_9.html D.P. ZhelobenkoOn formal series and infinite products over Lie algebrasVolume_4/4_10.htmlA brief survey of new methods for the study of nonstandard associative envelopes of Lie algebras is presented. Various extensions of the universal enveloping algebra U( g) are considered, where g is a symmetrizable Kac-Moody algebra. An elementary proof is given for describing the ``extremal projector'' over g as an infinite product over U ( g). Certain applications to the theory of g-modules are discussed. N. NakanishiA Survey of Nambu-Poisson GeometryVolume_4/4_1.htmlWe survey geometry of Nambu-Poisson manifolds. First we recall Nambu's work which is the origin of Nambu-Poisson geometry. Next adopting Takhtajan's geometric formulation and applying the local structure theorem of Nambu-Poisson tensors, we study the projectability of left invariant Nambu-Poisson tensors on Lie groups to certain homogeneous spaces. H. OmoriIntroduction to noncommutative differential geometryVolume_4/4_2.htmlIt is getting a major understanding that the function ring of the underlying space of the quantum world is not a commutative ring, and the underlying space itself is not even a point set.

In spite of this, the underlying space of the quantum world should be a continuum, on which one can make a calculus. We hope we can see such mathematics in the coming century.

This article is a survey of such effort or trial to make such calculus. However, this article does not give a bird-eye-view of the noncommutative world but this gives several toys which come from the noncommutative world.
A.L. OnishchikOn classification of complex analytic supermanifoldsVolume_4/4_3.htmlWe consider the problem of classification of complex analytic supermanifolds with a given reduction M. As is well known, any such supermanifold is a deformation of its retract, i.e., of a supermanifold M whose structure sheaf is the Grassmann algebra over the sheaf of holomorphic sections of a holomorphic vector bundle E→ M. Thus, the problem is reduced to the following two classification problems: of holomorphic vector bundles over M and of supermanifolds with a given retract M. We are dealing here with the second problem. By a well-known theorem of Green [9], it can be reduced to the calculation of the 1-cohomology set of a certain sheaf of automorphisms of O. We construct a non-linear resolution of this sheaf giving rise to a non-linear cochain complex whose 1-cohomology is the desired one. For a compact manifold M, we apply Hodge theory to construct a finite-dimensional affine algebraic variety which can serve as a moduli variety for our classification problem it is analogous to the Kuranishi family of complex structures on a compact manifold (see [6, 7]). Y. SakaneHomogeneous Einstein metrics on flag manifoldsVolume_4/4_4.htmlIt is known that a flag manifold admits a Kähler-Einstein metric. We investigate K-invariant Einstein metrics on a flag manifold M = K/T which is not Kähler-Einstein. This problem has been studied by Alekseevsky and Arvanitoyeorgos in case of generalized flag manifolds. We give an explicit expression of Ricci tensor of a flag manifold K/T for the case of a classical simple Lie group and we present more new K-invariant Einstein metrics on a flag manifold K/T. We compute a Gröbner basis for a system of polynomials of multi-variables and show the existence of positive solutions for a system of algebraic equations to prove the existence of K-invariant Einstein metrics. H. SatoSchwarzian derivatives of contact diffeomorphismsVolume_4/4_5.html Akira Mizuhara, Hirohiko ShimaInvariant projectively flat connections and its applicationsVolume_4/4_6.htmlIn this paper we study invariant projectively flat affine connections and invariant dualistic structures of constant curvature. We first relate the existence of invariant projectively flat affine connections to that of certain affine representation of Lie algebras (Theorem 1). Using such affine representations we give a correspondence between semi-simple symmetric spaces with invariant projectively flat affine connections and central-simple Jordan algebras (Theorem 2). As an application we prove that invariant dualistic structures of constant curvature come from certain invariant Hessian structures (Theorem 3). O.P. TchijContact geometry of hyperbolic Monge--Ampère equationsVolume_4/4_7.htmlThis paper is devoted to the geometry of hyperbolic Monge-Ampère equations with large symmetry algebras. We classify all hyperbolic Monge-Ampére equations whose Lie algebra of contact symmetries is transitive. We also give the explicit construction for Cartan connections associated with generic hyperbolic Monge-Ampére equations and find those equations which correspond to connections with vanishing curvature tensor. D.V. TunitskyOn contact equivalence of holomorphic Monge-Ampère equations.Volume_4/4_8.htmlThis paper deals with holomorphic Monge-Ampère equations on 5-dimensional complex contact manifolds, i.e., Monge-Ampère equations with two complex independent variables. If a Monge-Ampère equation is in general position,then a complex affine connection can be put in correspondence to this equation in natural manner. This correspondence allows to formulate and prove a number of results on contact equivalence of Monge-Ampère equations using suitable properties of affine connections. A. YoshiokaWeyl manifold and Quantized connectionVolume_4/4_9.htmlThis paper is two folds. First we give a brief review of Weyl manifold and Deformation quantization. Poincare-Cartan class is introduced and complete classification of Weyl manifolds is given. Second, Quantized connection or twisted exterior derivative is discussed. Degree operator field is introduced and plays an important role. Classical coordinate is constructed by means of the degree operator field. Quantized connection is then defined on Weyl manifold. In terms of classical coordinates the quantized connection is shown to be the same as Fedosov connection. Finally, we show the Poincare-Cartan class is equal to the deRham cohomology class of the curvature of Fedosov connection. B. MarzoukiAlmost periodic solutions for some multivalued differential equations in Banach spacesVolume_5/5_1.htmlIt is known that in the frame of ordinary differential equationsx'=f(t,x) in Banach space with f almost-periodic in tuniformly for x and strongly dissipative with respect to x, theexistence of a bounded solution is equivalent to the existence ofan almost-periodic one ( see [H1],[H2]). In this note we wantto generalize the result in the frame of a multivalueddifferential equation x'∈F(t,x). S.Z. NemethGeodesic monotone vector fieldsVolume_5/5_2.htmlHaving in mind the Minty-Browder monotonicity notion, we shall generalize it for vector fields on Riemannian manifolds, defining the geodesic monotone vector fields. The gradients of geodesic convex functions, important in optimization, linear and nonlinear programming on Riemannian manifolds, are geodesic monotone vector fields. The geodesic monotonicity will be related with the first variation of the length of a geodesic. The connection between the existence of closed geodesics and monotone vector fields will also be analyzed. We give a class of strictly monotone vector fields on a simply connected, complete Riemannian manifold with nonpositive sectional curvature, which generalize the notion of position vector fields. The notion of geodesic scalar derivative will be introduced for characterization of geodesic monotone vector fields on such manifolds. The constant sectional curvature case will be analized separately, since it has important peculiarities. Vadim V. ShuryginThe structure of smooth mappings over Weil algebras and the category of manifolds over algebrasVolume_5/5_3.htmlAs is known, the bundle TAMn of infinitely near points of A-type defined for any local Weil algebra A and smooth real manifold Mn is one of basic examples of smooth manifolds over A. In the present paper we give a description of the local structure of smooth mappings in the category of smooth manifolds over local algebras and consider various examples of such manifolds. Next we study the homotopy and holonomy groupoids of a smooth manifold MAn over a local algebra A associated with canonical foliations corresponding to ideals of A. In particular, it is proved that a complete manifold MAn has neither homotopy nor holonomy vanishing cycles. Donald YauCohomology of unitary and sympletic groupsVolume_5/5_4.htmlWe compute the cohomology rings of U(n) and Sp(n) and of their Stiefel varieties by using the Serre spectral sequence. This approach is much simpler than the usual method, that of using the cell structures. The argument here also shows that the cohomology of U(n) is built from those of U(n - 1) and S2n - 1 through a fiber bundle a similar result holds for Sp(n). A.Addou, S.LahrechSufficient Conditions for elliptic problem of optimal control in R2Volume_6/6_1.htmlIt is known that when we look for sufficient conditions of local extremum for Gateaux functionals (G.f) associated to Dirichlet problem of second order in R2, the (G.f) is not necesseraly Frechet differentiable. In this note, using a recent extension of Frechet Differentiability, we obtain that the (G.f) is differentiable with respect to the new notion. Thus we can give sufficient conditions for obtaining local minimum. A.Addou, S.LahrechSufficient Conditions for elliptic problem of optimal control in Rn in Orlicz Sobolev spaceVolume_6/6_2.htmlWe consider here a problem for which we seek the local minimum in Orlicz Sobolev spaces (W10LM(\Omega),\|.\|M) for the Gateaux functional J(f)\equiv ≡\Omega v(x,u,f)dx,where u is the solution of Dirichlet problem with Laplacian operator associated to f and \|.\|M is the Orlicz norm. Note that, under the rapid growth conditions on v, the (G.f) J is not necesseraly Frechet differentiable in (W10LM(\Omega),\|.\|M). In this note, using a recent extension of Frechet Differentiability, we prove that, under the rapid growth conditons on v the (G.f) is differentiable for the new notion. Thus we can give sufficient conditions for local minimum. B. T. BatikyanPoint derivations on algebraic extension of Banach algebraVolume_6/6_3.htmlIt is shown that a point y0 in the carrier space of algebraic extension B of commutative Banach algebra A is a branch point if and only if there exists a local point derivation on B at y0, whose kernel contains A. S. A. Grigorian, R. N. Gumerov, A. V. KazantsevGroup structure in finite coverings of compact solenoidal groupsVolume_6/6_4.htmlLet p:X → G be an n - fold covering of a compact solenoidal group G by a connected topological space X. We prove that there exists a group structure in X turning p into a homomorphism between compact abelian groups O. E. TikhonovPartial measuresVolume_6/6_5.htmlWe study σ-additive set functions defined on a hereditary subclass of a σ-algebra and taken values in the extended real line. Analogs of the Jordan decomposition theorem and the Radon-Nikodym theorem are obtained. A. I. FedotovOn convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equationsVolume_7/7_1.htmlWe prove the convergence of polynomial collocation method for periodic singular integral, pseudodifferential and the systems of pseudodifferential equations in Sobolev spaces Hs via the equivalence between the collocation and modified Galerkin methods. The boundness of the Lagrange interpolation operator in this spaces when s>1/2 allows to obtain the optimal error estimate for the approximate solution i.e. it has the same rate as the best approximation of the exact solution by the polynomials. B.A. KatsThe Cauchy integral along Φ-rectifiable curvesVolume_7/7_2.htmlThe paper treats existence and boundary properties of the Cauchy integral over certain classes of non-rectifiable curves. These classes contain, in particular, known fractal curves: von Koch snowflakes, Weierstrass curves, lacunary wavelet trajectories and so on. Branko SaricA functional expression for the curvature of hyper-dimensional Riemannian spacesVolume_7/7_3.htmlAnalogously to a notion of curvature of a curve and a surface, in the differential geometry, in the main part of this paper the notion of curvature of hyper-dimensional vector spaces of Riemannian metric is generally defined. The defined notion of curvature of Riemannian spaces of higher dimensions M: M≥ 2, in the further text of the paper, is functional related to the fundamental parameters of internal geometry of a space, more exactly, to components of Riemann-Christoffel's curvature tensor. At the end, analogously to a notion of lines of a curvature in the differential geometry, the notion of sub-spaces of curvature of Riemannian hyper-dimensional vector spaces is also generally defined. E.N.SosovOn existence and uniqueness of Chebyshev center of bounded set in a special geodesic spaceVolume_7/7_4.htmlIn this paper we obtain sufficient conditions for existence and uniqueness of Chebyshev center of nonempty bounded set in a special geodesic space. Analogous conditions for Banach space are well known [1] M.A.BousaidiOn the Eta Invariant, Stable Positive Scalar, Curvature, and Higher A-GeneraVolume_8/8_1.htmlWe show that the eta invariant provides obstructions to the existence, and stable existence, of positive scalar curvature metrics on odd dimensional closed connected spin smooth manifolds. We also prove, using the eta invariant, that the "stable existence" of a positive scalar curvature metric implies the vanishing of some higher A-genera. A.BuckiSome properties of almost r-paracontact manifoldsVolume_8/8_2.htmlFor an almost r-paracontact manifold M with a structure Σ, almost r-paracontact connections, D-connections, and pairs of connections compatible with Σ have been defined and discussed in [2]. In this paper, which is a continuation of [2], some properties of almost r-paracontact manifolds have been studied by means of the curvature and torsion tensor fields of these connections. B. Komrakov, Jnr.Einstein--Maxwell equation on four-dimensional homogeneous spacesVolume_8/8_3.htmlThis paper presents the solutions of the Einstein-Maxwell equation on all local four-dimensional pseudo-Riemannian homogeneous spaces and the complete local classification of four-dimensional Einstein-Maxwell homogeneous spaces with an invariant pseudo-Riemannian metric of arbitrary signature. E. Laitinen, A.V. Lapin, J.PieskäLarge Splitting iterative methods and parallel solution of variational inequalitiesVolume_8/8_4.htmlSplitting iterative methods for the sum of maximal monotone and single-valued monotone operators in a finite-dimensional space are studied: convergence, rate of convergence and optimal iterative parameters are derived. A two-stage iterative method with inner iterations is analysed in the case when both operators are linear, self-adjoint and positive definite. The results are applied for the mesh variational inequalities which are solved using a non-overlapping domain decomposition method and the splitting iterative procedure. Parallel solution of a mesh scheme for continuous casting problem is presented and the dependence of the calculation time on the number of processors is discussed. E.N.SosovOn Hausdorff intrinsic metricVolume_8/8_5.htmlIn this paper we prove that in the set of all nonempty bounded closed subsets of a metric space (X,ρ ) the Hausdorff metric is the Hausdorff intrinsic metric if and only if the metric ρ is an intrinsic metric. In a space with an intrinsic metric we obtain the upper bound for the Hausdorff distance between generalized balls. F.G. Avhadiev, R.G.SalahutdinovBilateral Isoperimetric Inequalities for Boundary Moments of Plane DomainsVolume_9/9_1.htmlIn this paper we prove some analogs of the St Venant conjecture on the torsional rigidity. One of them is connected with Leavitt and Ungar's inequality (Leavitt, J. Ungar, P., Comment. Pure Appl. Math., 15 (1962), 35-37). V.R. BairashevaAtoms in the structure of degrees of automata transformations and their monadic theoriesVolume_9/9_2.htmlThe existence of atoms of automaton reducibility degrees structure with essential different properties is proved. In the proof the priority method from the theory of recursive funtions was used. Eduardo Brandani da Silva, Dicesar L. FernandezInterpolation Spaces with Function Parameter and Measures of Non-CompactnessVolume_9/9_3.htmlThe behaviour of the measure of non-compactness of an operator acting on interpolation spaces, with function parameter and having one-sided hypothesis is studied. We obtain as corollaries a theorem of Cwikel type and a result to the radius of the essential spectrum of the interpolated operator. S. Grigoryan, T. TonevLinear multiplicative functionals of algebras of S-analytic functions on groupsVolume_9/9_4.htmlLet S be a subsemigroup of a semigroup Σ that generates a group G. We find conditions that assure extendability of linear multiplicative functionals of the algebra AS of S-analytic functions on G with spectra in S to linear multiplicative functionals of the corresponding algebra AΣ. Conditions for existence of dense homeomorphic embeddings of the upper half plane in the maximal ideal space of the algebra of almost periodic functions on R with spectrum in S, and of the open unit disc in the maximal ideal space of certain subalgebras of H are obtained as corollaries. A. V. KazantsevOn a problem of Polya and SzegoVolume_9/9_5.htmlWe give a new proof of a theorem, which is originally due to Gehring and Pommerenke on the triviality of the extrema set Mf of the inner mapping radius f'(ζ)( 1 - |ζ|2) over the unit disk in the plane, where the Riemann mapping function f satisfies the well-known Nehari univalence criterion. Our main tool is the local bifurcation research of Mf for the level set parametrization fr(ζ) = f(rζ), r>0. D. H. MushtariSome remarks on measures on orthogonal rational projections and the rational sphereVolume_9/9_6.htmlWe examine measures on the quantum logic of all projections with rational n× n-matrices and on its sublogic generated by all projections onto one-dimensional subspaces in Qn passing through elements of the unit sphere in Qn. Vadim V. Shurygin, Larisa B. SmolyakovaAn analog of the Vaisman-Molino cohomology for manifolds modelled on some types of modules over Weil algebras and its applicationVolume_9/9_7.htmlAn epimorphism μ: A → B of local Weil algebras induces the functor Tμ from the category of fibered manifolds to itself which assigns to a fibered manifold p:M → N the fibered product pμ:T AT BNT BM→ T AN. In this paper we show that the manifold T AT BNT BM can be naturally endowed with a structure of an A-smooth manifold modelled on the A-module L=An ⊕ Bm, where n=dim N, n+m=dim M. We extend the functor Tμ to the category of foliated manifolds (M, F). Then we study A-smooth manifolds ML whose foliated structure is locally equivalent to that of T AT BNT BM. For such manifolds ML we construct bigraduated cohomology groups which are similar to the bigraduated cohomology groups of foliated manifolds and generalize the bigraduated cohomology groups of A-smooth manifolds modelled on A-modules of the type An. As an application, we express the obstructions for existence of an A-smooth linear connection on ML in terms of the introduced cohomology groups. B. Aqzzouz, M. KadiriInfinite dimensional extension of A.P. CalderÒn's theorem on positive semidefinite biquadraric formsVolume_10/10_1.htmlWe extend to the infinite dimensional separable real Hilbert spaces a theorem of A. P. Calderòn which says that, if m=2 or n=2, then every positive semidefinite biquadratic form on Rm× Rn is a sum of squares of bilinear forms. S. A. Grigorian, R. N. GumerovOn a covering group theorem and its applicationsVolume_10/10_2.htmlLet p:X→ G be an n-fold covering of a compact group G by a connected topological space X. Then there exists a group structure in X turning p into a homomorphism between compact groups. As an application, we describe all n-fold coverings of a compact connected abelian group. Also, a criterion of triviality for n-fold coverings in terms of the dual group and the one-dimensional Cech cohomology group is obtained. M. O. Cabrera, T.-C. Hu, S. H. Sung, A.I. VolodinComplete convergence of weighted sums in Banach spaces and the bootstrap meanVolume_10/10_3.htmlLet {Xni, 1 ≤ i ≤ kn, n ≥ 1} be an array of rowwise independent random elements taking values in a real separable Banach space, and {ani, 1 ≤ i ≤ kn, n ≥ 1} an array of constants. Under some conditions of Chung [7] and Hu and Taylor [10] types for the arrays, and using a theorem of Hu et al. [9], the equivalence amongst various kinds of convergence of i=1knani Xni to zero is obtained. It leads to an unified vision of recent results in the literature. The authors use the main result in the paper in order to obtain the strong consistency of the bootstrapped mean of random elements in a Banach space from its weak consistency. A.Lapin, J.PieskäOn the parallel domain decomposition algorithms for time-dependent problemsVolume_10/10_4.htmlSeveral new finite-difference schemes for a nonlinear convection-diffusion problem are constructed and numerically studied. These schemes are constructed on the basis of non-overlapping domain decomposition and predictor-corrector approach. Our study was motivated by the article [rivera], where so-called EPIC (explicit predictor-implicit corrector) method have been proposed for a linear one-dimensional problem and founded to be stable and scalable when solving on big number of processors. We construct the predictor-corrector schemes for a nonlinear problem, which serves as a mathematical model for the continuous casting problem (see [Chen1], [Chen2], [lait2], [lalapi], where implicit and characteristic grid approximations of the continuous casting problem have been theoretically and experimentally studied). We use different non-overlapping decomposition of a domain, with cross-points and angles, schemes with grid refinement in time in some subdomains. All proposed algorithms are extensively numerically tested and are founded stable and accurate under natural assumptions for time and space grid steps. Also, the parallel algorithms scales well as the number of processors increases. M. Arslanov, Niovi KehayopuluA note on minimal and maximal ideals of ordered semigroupsVolume_11/11_1.htmlConsidering the question under what conditions an ordered semigroup (or semigroup) contains at most one maximal ideal we prove that in an ordered groupoid S without zero there is at most one minimal ideal which is the intersection of all ideals of S. In an ordered semigroup, for which there exists an element a ∈S such that the ideal of S generated by a is S, there is at most one maximal ideal which is the union of all proper ideals of S. In ordered semigroups containing unit, there is at most one maximal ideal which is the union of all proper ideals of S. Farit G. Avkhadievi, K.-J. WirthsOn the coefficient multipliers theorem of Hardy and LittlewoodVolume_11/11_2.htmlLet an(f) be the Taylor coefficients of a holomorphic function f which belongs to the Hardy space Hp, 0 < p < 1. We prove the estimate C(p) ≤ π ep/r[(p(1-p)r]) in the Hardy-Littlewood inequality Σn=0 |an(f)|p (n+1)p-2 ≤ C(p)(||f||p)p. We also give explicit estimates for sums Σ | an(f) λn |s in the mixed norm space H(1,s,β). In this way we obtain a new version of some results by Blasco and by Jevtič and Pavlovič. J. S. Eivazloo, M. MoniriPathological Functions on Puiseux Series Ordered Fields and OthersVolume_11/11_3.htmlWe show that over closed bounded intervals in certain Archimedean ordered fields as well as in all non-Archimedean ones of countable cofinality, there are uniformly continuous 1-1 functions not mapping interior to interior. For the latter kind of fields, there are also uniformly continuous 1-1 functions mapping all interior points to interior points of the image which are, nevertheless, not open. In particular the ordered Laurent and Puiseux series fields with coefficients in any ordered field accommodate both kinds of such strange functions. Niovi Kehayopulu, M. TsingelisA note on pseudocongruences in semigroupsVolume_11/11_4.htmlIn this short note we introduce the concept of pseudocongruence in semigroups and we prove that each pseudocongruence on a semigroup S induces a congruence σ on S such that S/σ is an ordered semigroup. L. PushkinSmall digitwise perturbations of a number make it normal to unrelated basesVolume_11/11_5.htmlLet r, g ≥ 2 be integers such that logg/logr is irrational. We show that under r-digitwise random perturbations of an expanded to base r real number x, which are small enough to preserve r-digit asymptotic frequency spectrum of x, the g-adic digits of x tend to have the most chaotic behaviour. E. SokolovOn the cyclic subgroup separability of free products of two groups with amalgamated subgroupVolume_11/11_6.htmlLet G be a free product of two groups with amalgamated subgroup, π be either the set of all prime numbers or the one-element set {π} for some prime number . Denote by Σ the family of all cyclic subgroups of group G, which are separable in the class of all finite π-groups. Obviously, cyclic subgroups of the free factors, which aren't separable in these factors by the family of all normal subgroups of finite π-index of group G, the subgroups conjugated with them and all subgroups, which aren't π'-isolated, don't belong to Σ. Some sufficient conditions are obtained for Σ to coincide with the family of all other π'-isolated cyclic subgroups of group G. It is proved, in particular, that the residual p-finiteness of a free product with cyclic amalgamation implies the p-separability of all p'-isolated cyclic subgroups if the free factors are free or finitely generated residually p-finite nilpotent groups. S. S. Bhatia, Kulwinder Kaur, Babu RamL1-convergence of modified complex trigonometric sumsVolume_12/12_1.htmlIn this paper we study L1-convergence of modified complex trigonometric sums introduced by Ram and Kumari and obtain a necessary and sufficient condition for L1-convergence of Fourier series under a new class K of coefficients. A. N. Chuprunov, O. V. RusakovConvergence for step line processes under summation of random indicators and models of market pricingVolume_12/12_2.htmlFunctional limit theorems for random step lines and random broken lines defined by sums of iid random variables with replacements are obtained and discussed. Also we obtained functional limit theorems for integrals of such random processes. We use our results to study a number of models of the financial market. Konstantin B. IgudesmanLacunary self-similar fractal sets and intersection of Cantor setsVolume_12/12_3.htmlThe problem on intersection of Cantor sets was examined in many papers. To solve this problem, we introduce the notion of lacunary self-similar set. The main difference to the standard (Hutchinson) notion of self-similarity is that the set of similarities used in the construction may vary from step to step in a certain way. We find the Hausdorff dimension of a lacunary self-similar set. Miroslav Kure š, Wodzimierz M. MikulskiLiftings of linear vector fields to product preserving gauge bundle functors on vector bundlesVolume_12/12_4.htmlAll natural operators lifting linear vector fields to product preserving gauge bundle functors on vector bundles are classified. Some relevant properties of Weil modules are studied, too. L. LanzheBoundedness for commutators of Littlewood-Paley operators on some Hardy spacesVolume_12/12_5.htmlIn the present paper the ( (Hpb,Lp)-type and (Hp,∞b,Lp,∞)-type boundedness for the commutators associated with the Littlewood-Paley operators and b ∈BMO(Rn) are obtained, where Hpb and Hp,∞ are, respectively, variants of the standard Hardy spaces and weak Hardy spaces, and n/(n+ε) < p ≤ 1. Yi ZhangConstructing a maximal cofinitary groupVolume_12/12_6.htmlAssuming continuum hypothesis (CH), we construct a maximal cofinitary group step by step. We also outline a way of constructing maximal cofinitary group by assuming the negation of CH and Martin's Axiom (MA). R. Dautov, R. Kadyrov, E. Laitinen, A. Lapin, J. Pieskä, V. ToivonenOn 3D dynamic control of secondary cooling in continuous casting processVolume_13/13_1.htmlIn this paper a 3D-model for simulation and dynamic control of the continuous casting process is presented. The diffusion convection equation with multiphase transition is used as a simulation model. The developed model is discretized by finite element method and the algebraic equations are solved using pointwise relaxation method. Two different type of methods are used to control the secondary cooling, namely PID and optimal control method. The numerical results are presented and analyzed. M. A. Ignatieva, A. V. LapinMixed hybrid finite element scheme for Stefan problem with prescribed convectionVolume_13/13_2.htmlWe construct a mixed hybrid finite element scheme of lowest order for the Stefan problem with prescribed convection and suggest and investigate an iterative method for its solution. In the iterative method we use a preconditioner constructed by using "standard" finite element approximation of Laplace operator on a finer grid. The proposed approach develops the results of [igkuz], where a spectrally equivalent preconditioner for the condensed matrix in mixed hybrid finite element approximation for linear elliptic equation was constructed. R. F. Kadyrov, E. Laitinen, A. V. LapinUsing explicit schemes for control problems in continuous casting processVolume_13/13_3.htmlIn this article, we solve an optimal control problem of the cooling process in the steel continuous casting, which mathematical formulation is a coefficient identification problem for Stefan problem with prescribed convection. To minimize a cost function we use a gradient method, state and adjoint state problem being approximated by explicit mesh schemes with variable time steps. Presented numerical results show an advantage in calculations time of this approach in comparison with using implicit mesh schemes. Kulwinder KaurTauberian conditions for L1-convergence of modified complex trigonometric sumsVolume_13/13_4.htmlAn L1-convergence property of the complex form gn(c,t)=Sn(c,t)- [ cnEn(t)+c-nE-n(t) ] of the modified sums introduced by Garrett and Stanojevic [3] is established and a necessary and sufficient condition for L1-convergence of Fourier series is obtained. Niovi Kehayopulu, Michael TsingelisThe embedding of an ordered semigroup into an le-semigroupVolume_13/13_5.htmlIn this paper we prove the following: If S is an ordered semigroup, then the set P (S) of all subsets of S with the multiplication "º" on P(S) defined by "Aº B: = (AB] if A, B∈ P(S), A≠ ∅, B≠ ∅ and Aº B: =∅ if A = ∅ or B=∅ is an le-semigroup having a zero element and S is embedded in P(S). Niovi Kehayopulu, Michael TsingelisA note on semi-pseudoorders in semigroupsVolume_13/13_6.htmlAn important problem for studying the structure of an ordered semigroup S is to know conditions under which for a given congruence ρ on S the set S/ρ is an ordered semigroup. In [1] we introduced the concept of pseudoorder in ordered semigroups and we proved that each pseudoorder on an ordered semigroup S induces a congruence σ on S such that S/ σ is an ordered semigroup. In [3] we introduced the concept of semi-pseudoorder (also called pseudocongruence) in semigroups and we proved that each semi-pseudoorder on a semigroup S induces a congruence σ on S such that S/ σ is an ordered semigroup. In this note we prove that the converse of the last statement also holds. That is each congruence σ on a semigroup (S, .) such that S/ σ is an ordered semigroup induces a semi-pseudoorder on S. Igor V. Konnov, Olga V. PinyaginaD-gap functions and descent methods for a class of monotone equilibrium problemsVolume_13/13_7.htmlWe consider a general class of monotone equilibrium problems, which involve nonsmooth convex functions, in a real Banach space. We combine the D-gap function approach and regularization techniques and suggest a descent type algorithm to find solutions to the initial problem. E. Laitinen, A. V. Lapin, J. PieskäNumerical experiments with with multilevel subdomain decomposition methodVolume_13/13_8.htmlIn this paper we present a new numerical approach to solve the continuous casting problem. The main tool is to use so-called IPEC method and DDM similar to [lapi] with multilevel domain decomposition. On the subdomains we use the multidecomposition of the subdomains. The IPEC is used both in the whole calculation domain and inside the subdomains. Calculation algorithm is presented and numerically tested. Several conclusions are made and discussed. Koji Matsumoto, Adela Mihai, Dorotea NaitzaSubmanifolds of an even-dimensional manifold structured by a T-parallel connectionVolume_13/13_9.htmlEven-dimensional manifolds N structured by a T-parallel connection have been defined and studied in [DR], [MRV]. In the present paper, we assume that N carries a (1,1)-tensor field J of square -1 and we consider an immersion x:M→ N. It is proved that any such M is a CR-product [B] and one may decompose M as M=MD× MD, where MD is an invariant submanifold of M and MD is an antiinvariant submanifold of M. Some other properties regarding the immersion x:M→ N are discussed. Abdulla AljouieeOn the Brauer Monoid of S3Volume_14/14_1.htmlIn [HLS], the authors showed that the Brauer monoid of a finite Galois group can be written as a disjoint union of smaller pieces (groups). Each group can be computed following Stimets by defining a chain complex and checking its exactness. However, this method is not so encouraging because of the difficulty of dealing with such computations even with small groups. Unfortunately, this is the only known method so far. This paper is to apply Stimets' method to some idempotent weak 2-cocycles defined on S3. In particular, the idempotent 2-cocycles whose associated graphs have two generators. Some nice results appear in the theory of noncommutative polynomials. A. M. BikchentaevThe continuity of multiplication for two topologies associated with a semifinite trace on von Neumann algebraVolume_14/14_2.html A. I. FedotovLebesgue constant estimation in multidimensional Sobolev spaceVolume_14/14_3.htmlThe norm estimation of the Lagrange interpolation operator is obtained. It is shown that the rate of convergence of the interpolative polynomials depends on the choice of the sequence of multiindices and, for some sequences, is equal to the rate of the best approximation of the interpolated function. Ghulam MustafaA Double-Sequence Random Iteration Process for Random Fixed Points of Contractive Type Random OperatorsVolume_14/14_4.htmlIn this paper, we introduce the concept of a Mann-type double-sequence random iteration scheme and show that if it is strongly convergent then it converges to a random fixed point of continuous contractive type random operators. The iteration is a random version of double-sequence iteration introduced by Moore (Comput. Math. Appl. 43(2002), 1585-1589). Pyotr N. IvanshinStructure of function algebras on foliated manifoldsVolume_14/14_5.htmlWe consider a manifold M with a foliation F given by a locally free action of a commutative Lie group H. Also we assume that there exists an integrable Ehresmann connection on (M, F) invariant with respect to the action of the group H. We get the structure of the restriction of the algebra C0(M) to the leaves in three partial cases. Also we consider a classification of the quasiinvariant measures and means on the leaves of F. Kai Lieska, Visa-Matti Jokela, Erkki LaitinenA simulation of traffic equilibration multi-path routing in ad hoc networksVolume_14/14_6.htmlLimited battery life is a known problem with mobile computers. In multi-hop ad hoc networks mobile nodes' excessive energy consumption leads to extinction of nodes and network partition. As communication is the main cause for energy consumption, we need to develop routing methods that prevent overloading of nodes. For this we propose the use of network equilibration. By distributing traffic to several routes according to traffic equilibrium we achieve longer network lifetime and maintain better connectivity. On the other hand, this kind of multi-path routing, carried out here by the use of load balancing cost functions, is a form of congestion control. Network congestion control decreases packet collisions and eventually leads to better throughput [gli]. This paper reports a study of ad hoc routing covering equilibrated routing, simulation and performance evaluation in terms of energy consumption and network lifetime. Alexander Lapin, Serguei LapinIdentification of nonlinear coefficient in a transport equationVolume_14/14_7.htmlConsidered a problem of identification a nonlinear coefficient in a first order PDE via final observation. The problem is stated as an optimal control problem and solved numerically. Implicit finite difference scheme is used for the approximation of the state equation. A space of control variables is approximated by a sequence of finite-dimensional spaces with increaing dimensions. Finite dimensional problems are solved by a gradient method and numerical results are presented. Serge SkryabinDegree one cohomology for the Lie algebras of derivationsVolume_14/14_8.htmlLet R be a commutative ring and W a Lie algebra of its derivations which is an R-submodule in the full derivation algebra \Der R. We consider a class of W-modules generalizing the natural representations of the Lie algebras of vector fields in tensor fields of arbitrary type. The main result consists in the determination of the cohomology of those modules in degree 1. Its applications include a description of derivations and the universal central extension for the Lie algebra W. Liu ChangchunSome Properties of Solutions of the Pseudo-parabolic EquationVolume_15/15_1.htmlIn this paper we discuss properties of solutions for a class of pseudo-parabolic equation. Some results on the asymptotic behavior and monotonicity of support are established. Frantisek KatrnoskaLogics that are generated by idempotentsVolume_15/15_2.htmlThe main result of this paper is the generalization of the theorem which represents one of the generally accepted cases concerning the characterization of the logic of idempotents. If R is a ring then the R-circulant matrices are introduced and some consequences for the logics of idempotents of the corresponding rings. Some convenient examples are added as well. Certain results of this paper may find applications in the foundation of quantum theory. Andrei I. Volodin, R. Giuliano Antonini, T.-C. HuA note on the rate of complete convergence for weighted sums of arrays of Banach space valued random elementsVolume_15/15_3.htmlWe obtain complete convergence results for arrays of rowwise independent Banach space valued random elements. In the main result no assumptions are made concerning the geometry of the underlying Banach space. As corollaries we obtain results on complete convergence in stable type p Banach spaces. Bin WuAlgebraic Properties of Refinable SetsVolume_15/15_4.htmlIn this paper we study the algebraic properties of finite refinable sets which was introduced for the fast solution of integral equations. Furthermore, the family of refinable sets is classified according to the algebraic characteristics. Some open problems are raised for the future study. Andrey BovykinOrder-types of models of arithmetic and a connection with arithmetic saturationVolume_16/16_1.htmlFirst, we study a question we encountered while exploring order-types of models of arithmetic. We prove that if M \ PA is resplendent and the lower cofinality of M \ IN is uncountable then (M,<) is expandable to a model of any consistent theory T ⊇ \PA whose set of Gödel numbers is arithmetic. This leads to the following characterization of Scott sets closed under jump: a Scott set X is closed under jump if and only if X is the set of all sets of natural numbers definable in some recursively saturated model M \ PA with lcf(M \ N)>ω. The paper concludes with a generalization of theorems of Kossak, Kotlarski and Kaye on automorphisms moving all nondefinable points: a countable model M \ PA is arithmetically saturated if and only if there is an automorphism h : M→ M moving every nondefinable point and such that for all x ∈M, N < x < cl ∅ N, we have h(x)>x. Per K. Jakobsen, Valentin V. LychaginOperator valued probability theoryVolume_16/16_2.htmlWe outline an extention of probability theory based on positive operator valued measures. We generalize the main notions from probability theory such as random variables, conditional expectations, densities and mappings. We introduce a product of extended probability spaces and mappings, and show that the resulting structure is a monoidal category, just as in the classical theory. Alexander KuznetsovOn a problem of AvhadievVolume_16/16_3.htmlIn this paper we consider a lower estimate for the ratio I(Ω) of the conformal moment of a simple connected domain Ω in the complex plane to the moment of inertia of this domain about its boundary. Related functionals depending on a simple connected domain Ω and two points w1,w2\inΩ with fixed hyperbolical distance between them are estimated. As a consequence a nontrivial lower estimate for I(Ω) is obtained. Fumikazu NagasatoEfficient formula of the colored Kauffman bracketsVolume_16/16_4.htmlIn this paper, we introduce a formula for the homogeneous linear recursive relations of the colored Kauffman brackets, which is more efficient than the formula in [rg2]. Abdur RashidThe Pseudospectral Method for Thermotropic Primitive Equation and its Error EstimationVolume_16/16_5.htmlIn this paper, a pseudospectral method is proposed for solving the periodic problem of thermotropic primitive equation. The strict error estimation is proved. Oleg ZubelevichOn regularity of stationary solutions to the Navier-Stokes equation in 3-D torusVolume_17/17_10.htmlWe consider the Navier-Stokes equation in 3-D torus in the stationary setup and prove that any weak solution of this problem is actually smooth provided the stationary external force is also smooth. F.G. Avkhadiev, K.-J. WirthsConcave schlicht functions with bounded opening angle at infinityVolume_17/17_1.htmlLet D denote the open unit disc. In this article we consider functions f(z)=z + Σn=2an(f)zn that map D conformally onto a domain whose complement with respect to C is convex and that satisfy the normalization f(1)=∞. Furthermore, we impose on these functions the condition that the opening angle of f(D) at infinity is less than or equal to π A, A∈(1,2]. We will denote these families of functions by CO(A). Generalizing the results of [AW1], [APW2], and [W1], where the case A=2 has been considered, we get representation formulas for the functions in CO(A). They enable us to derive the exact domains of variability of a2(f) and a3(f), f∈CO(A). It turns out that the boundaries of these domains in both cases are described by the coefficients of the conformal maps of D onto angular domains with opening angle π A. Md. Azizul BatenOn the smoothness of solutions of linear-quadratic regulator for degenerate diffusionsVolume_17/17_2.htmlThe paper studies the smoothness of solutions of the degenerate Hamilton-Jacobi-Bellman (HJB) equation associated with a linear-quadratic regulator control problem. We establish the existence of a classical solution of the degenerate HJB equation associated with this problem by the technique of viscosity solutions, and hence derive an optimal control from the optimality conditions in the HJB equation. Mohammed BenaliliOn a class of non linear differential operators of first order with singular pointVolume_17/17_3.htmlWe consider the problem of the existence and uniqueness of solutions for partial differential operator of the form Lu=DXu-B(x,u) where X is a vector field. The solvability of L may be of some interest since by the Nash-Moser inverse function theorem the equivalence problem in differential geometry can be solved via Lie derivative operator and the later is locally a particular case of L. An application to the equivalence of dynamic systems is given. R. N. GumerovOn the existence of means on solenoidsVolume_17/17_4.htmlA mean on a topological space is a continuous idempotent and symmetric operation on it. A proof of a criterion for the existence of means on solenoids is given. Konstantin B. IgudesmanDynamics of finite-multivalued transformationsVolume_17/17_5.htmlWe consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such a transformation an m-transformation. In this case the orbit of any point looks like a tree. In the study of m-transformations we are interested in the properties of the trees. An m-transformation generates a stochastic kernel and a new measure. Using these objects, we introduce analogies of some main concept of ergodic theory: ergodicity, Koopman and Frobenius-Perron operators etc. We prove ergodic theorems and consider examples. We also indicate possible applications to fractal geometry and give a generalization of our construction. Per K. Jakobsen, Valentin V. LychaginQuantizations in a category of relationsVolume_17/17_6.htmlIn this paper we develops a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to be symmetric monoidal categories in their own right and are found to be isomorphic to certain categories of A-A bicomodules. Properties of relations are defined in terms of the symmetric monoidal structure. Equivalence relations are shown to be commutative monoids in the category of relations. Quantization in our view is a property of functors between monoidal categories. This notion of quantization induce a deformation of all algebraic structures in the category, in particular the ones defining properties of relations like transitivity and symmetry. Cathrine V. JensenLinear ODEs and D-modules, solving and decomposing equations using symmetry methods.Volume_17/17_7.htmlThis text investigates homogeneous systems of linear ODEs with smooth coefficients. Associating to an equation a differential module proves that these equations form a monoidal category with respect to the tensor product of modules, and objects in this category include homomorphisms, symmetric and exterior powers as well as dual equations. Viewing symmetries as endomorphisms of the D-modules enables direct application of results from the theory of representations of Lie algebras. In particular we find decomposition and solution methods of equations with semisimple symmetry algebras, as well as solvable symmetry algebras. Sufficient conditions for equations to be solved by algebraic manipulations and quadrature are given, and unlike most previous results, there is no requirement on the symmetry algebras of having dimension equal to the order of the equations, in some cases even a single symmetry is sufficient to solve an equation. V. RechnoiExistence Theorems for Commutative DiagramsVolume_17/17_8.htmlGiven a relation f ⊂ A× B, there exist two symmetric relations (see [Bourbaki], Chapter 2) f-1f ⊂ A2, ff-1 ⊂ B2. These relations make it possible to formalize definitions and proofs of existence theorems. For example, the equation h=gf, where h and g (or h and f) are given maps, admits a solution f (g, respectively.) if and only if hh-1⊂ gg-1 (h-1h ⊂ f-1f). Well-known ,,homomorphism theorems'' get more general interpretation. Namely, any map can be represented up to bijection as a composition of surjection and injection, and any morphism of diagrams can be represented up to isomorphism as a composition of epimorphism and monomorphism. In this paper we further develop the scheme from [MR1] and consider it as an application in category of vector spaces and linear maps. Vadim V. Shurygin, juniorPoisson structures on Weil bundlesVolume_17/17_9.htmlIn the present paper, we construct complete lifts of covariant and contravariant tensor fields from the smooth manifold M to its Weil bundle TA M for the case of a Frobenius Weil algebra A. For a Poisson manifold (M,w) we show that the complete lift wC of a Poisson tensor w is again a Poisson tensor on TA M and that wC is a linear combination of some "basic" Poisson structures on TA M induced by w. Finally, we introduce the notion of a weakly symmetric Frobenius Weil algebra A and we compute the modular class of (TA M, wC) for such algebras. S. Ejaz Ahmed, Deli Li, Andrew Rosalsky, Andrei VolodinOn the Asymptotic Probability for the Deviations of Dependent Bootstrap Means from the Sample MeanVolume_18/18_1.htmlIn this paper, the asymptotic probability for the deviations of dependent bootstrap means from the sample mean is obtained without imposing any conditions on the joint distributions associated with the original sequence of random variables from which the dependent bootstrap sample is selected. The mild condition of stochastic domination by a random variable is imposed on the marginal distributions of the random variables in this sequence. A. L. Barrenechea, C. C. PenaOn innerness of derivations on S(H)Volume_18/18_2.htmlWe consider general bounded derivations on the Banach algebra of Hilbert-Schmidt operators on an underlying complex infinite dimensional separable Hilbert space H. Their structure is described by means of unique infinite matrices. Certain classes of derivations are identified together in such a way that they correspond to a unique matrix derivation. In particular, Hadamard derivations, the action of general derivations on Hilbert-Schmidt and nuclear operators and questions about innerness are considered. Mohammed Benalili, Azzedine LansariSpectral properties of the adjoint operator and applicationsVolume_18/18_3.htmlWe present some spectral properties of the adjoint operator corresponding to an admissible dilatation vector field and its perturbations. Next, we apply these results via the Nash-Moser function inverse theorem to show that the group G of diffeomorphisms on the Euclidean space Rn which are 1-time flat, close to the identity and of small support acts transitively on the affine space of appropriate perturbations of the dilation vector field Xo. G. N. Bushueva, V. V. ShuryginOn the higher order geometry of Weil bundles over smooth manifolds and over parameter-dependent manifoldsVolume_18/18_4.htmlThe Weil bundle TA Mn of an n-dimensional smooth manifold Mn determined by a local algebra A in the sense of A. Weil carries a natural structure of an n-dimensional A-smooth manifold. This allows ones to associate with TA Mn the series Br(A)TA Mn, r=1,...,∞, of A-smooth r-frame bundles. As a set, Br(A)TA Mn consists of r-jets of A-smooth germs of diffeomorphisms (An,0)→ TA Mn. We study the structure of A-smooth r-frame bundles. In particular, we introduce the structure form of Br(A)TA Mn and study its properties. Next we consider some categories of m-parameter-dependent manifolds whose objects are trivial bundles Mn × Rm → Rm, define (generalized) Weil bundles and higher order frame bundles of m-parameter-dependent manifolds and study the structure of these bundles. We also show that product preserving bundle functors on the introduced categories of m-parameter-dependent manifolds are equivalent to generalized Weil functors. Per K. Jakobsen, V.V. LychaginUniversal semigroupsVolume_18/18_5.htmlIn this paper we introduce the notion of a universal semigroup and its dual, the universal cosemigroup. We show that the class of universal semigroups include the class of monoids and is included in the class of semigroups with a product that is an epimorphism. Both inclusions are proper. Semigroups in the category of Banach spaces are Banach algebras and we show that all Banach algebras with an approximate unit are universal and construct a finite dimensional Banach algebra that has no unit but is universal. The property of being universal is thus a generalized unit property. M. I. KarahanyanOn the abstract theorem of PicardVolume_18/18_6.htmlLet A be a complex Banach algebra with unit. It was shown by Williams [W] that elements a, b ∈A commute if and only if supλ ∈ C | exp (λ b) a exp (-λ b) | <∞. This result allows us to obtain an analog of the von Neumann-Fuglede-Putnam theorem in case of normal elements in a complex Banach algebra. In the present paper the results by Williams [W] and Khasbardar et Thakare [Kh] are refined by using [G,Ka,Ka2]. An abstract version of Picard theorem is obtained in this context. Niovi Kehayopulu, Michael TsingelisOn ordered left groupsVolume_18/18_7.htmlOur purpose is to give some similarities and some differences concerning the left groups between semigroups and ordered semigroups. Unlike in semigroups (without order) if an ordered semigroup is left simple and right cancellative, then it is not isomorphic to a direct product of a zero ordered semigroup and an ordered group, in general. Unlike in semigroups (without order) if an ordered semigroup S is regular and has the property a S ⊆ (Sa] for all a∈S, then the N-classes of S are not left simple and right cancellative, in general. The converse of the above two statements hold both in semigroups and in ordered semigroups. Exactly as in semigroups (without order), an ordered semigroup is a left group if and only if it is regular and right cancellative. Ghulam Mustafa, Nusrat Anjum Noshi, Abdur RashidSome Random Coincidence and Random Fixed Point Theorems for Hybrid ContractionsVolume_18/18_8.htmlSome new random coincidence point and random fixed point theorems for multifunctions in separable complete metrically convex metric spaces are proved. Our results are stochastic generalizations of classical coincidence and fixed point theorems. Ye. A. UtkinaOn a Partial Differential Equation in 4-dimensional Euclidean SpaceVolume_18/18_9.htmlThe objective of this article is to construct in a hyper-rectangular region of the 4-dimensional Euclidean space a solution of the Goursat problem for the following equation: E. BallicoQuivers, vector bundles and coverings of smooth curvesVolume_19/19_1.htmlFix a finite quiver Q and consider quiver-bundles on smooth and connected projective curves. Let f: X → Y be a degree m morphism between such curves and E a quiver bundle on Y. We prove that E is semistable (resp. polystable) if and only if f (E) is semistable. Then we construct many stable quiver-bundles on bielliptic curves. Boris Kruglikov, Olga LychaginaFinite Dimensional Dynamics for Kolmogorov-Petrovsky-Piskunov EquationVolume_19/19_2.htmlWe construct new finite-dimensional submanifolds in the solution space of Kolmogorov-Petrovsky-Piskunov equation. We describe the corresponding evolutionary dynamics and exact solutions. Xiang-Yun Xie, Feng YanFuzzy Ideals Extenstions of Ordered SemigroupsVolume_19/19_3.htmlIn this paper, we introduce the concepts of the extension of fuzzy ideals , prime, semiprime and 3-prime fuzzy ideals in an ordered semigroup S, respectively. We discuss properties of fuzzy ideals extensions and the relationships between prime fuzzy ideals and 3-prime fuzzy ideals of S in terms of the extension of fuzzy ideals of S, we give an example to show that 3-prime fuzzy ideal is not necessarily prime. Moreover, for commutative ordered semigroups, we obtain some properties of the extension of fuzzy ideals in commutative ordered semigroup. Zhi-Gang WangA New Subclass of Quasi-convex Functions with Respect to k-Symmetric PointsVolume_19/19_4.htmlIn the present paper, we introduce a new subclass Cs(k)(α,β) of quasi-convex functions with respect to k-symmetric points. The integral representation and several coefficient inequalities of functions belonging to this class are obtained. V. Alferiev, E. KuznetsovThe best argument for the parametric continuation of solutions of differential-algebraic equationsVolume_20/20_1.htmlNew algorithms for numerical continuation of Cauchy problem solution for different forms of DAEs, and results of their implementations are presented. M. V. BulatovApplication of matrix polynomials to investigation of singular equationsVolume_20/20_2.htmlA class of matrix polynomials having some dominant properties is described, and some characteristic properties of such polynomials have been found. Reduction of integral and integro-differential equations having singular matrices at the main part to systems with nonsingular ones is proposed. For systems of nonlinear finite-dimensional equations with singular Jacobi matrix, the definition for multiplicity of a solution is introduced. Reduction methods of such systems to the systems with isolated solutions, which can be numerically solved by well-known methods, are suggested. M. V. Falaleev, N. A. SidorovContinuous and Generalized Solutions of Singular Partial Differential EquationsVolume_20/20_3.htmlThe paper discusses continuous and generalized solutions of equations with partial derivatives having the operator coefficients which operate in Banach spaces. The operator with the elder derivative with respect to time is Fredholm. We apply Lyapunov-Schmidt's ideas and the generalized Jordan sets techniques to reduce partial differential-operator equations with the Fredholm operator in the main part to regular problems. In addition this technique has been exploited to prove the theorem of existence and uniqueness for a singular initial-value problem, as well as to construct the left and right regularizators of singular operators in Banach spaces and to construct fundamental operators in the theory of generalized solutions of singular equations. M. V. Falaleev, N. A. Sidorov, D. N. SidorovGeneralized Solutions of Volterra Integral Equations of the First KindVolume_20/20_4.htmlIn this paper we derived the explicit structure of generalized solutions of the Volterra integral equations of the first kind. The solution contains singular and regular components. These components can be constructed separately. On the first stage we construct the singular component of the solution by solving the special linear algebraic system. On the second stage the regular component of generalized solution can be constructed. V. Gorbunov, A. Gorobetz, V. SviridovThe method of normal splines for linear implicit differential equations of second orderVolume_20/20_5.htmlThe method of normal splines is specified for the initial and boundary-value problems for systems of linear ordinary differential equations of second order, possible being stiff or unresolved with respect to derivatives (differential-algebraic equations), without their reduction to first order ones. The algorithm of nonuniform collocation grid creation for stiff problems is described. Results of numerical solution to test problems, including linear mathematical physics boundary-value problem of the second order are given. Numerical schemes for the last case are based on the method of lines. B. Karas ö zen, I. V. Konopleva, B. V. LoginovDifferential-algebraic equations in the theory of invariant manifolds for singular equationsVolume_20/20_6.htmlAnalogs of Grobman-Hartman theorem on stable and unstable manifolds solutions for differential equations in Banach spaces with degenerate Fredholm operator at the derivative are proved. Jordan chains tools and the implicit operator theorem are used. In contrast to the usual evolution equation here the central manifold appears even for the case of spectrum absence on the imaginary axis. If on the imaginary axis there is only a finite number of spectrum points, then the original nonlinear equation is reduced to two differential-algebraic systems on the center manifold. B. V. Loginov, O. V. MakeevSolutions with subgroup symmetry for singular equations in bifurcation theoryVolume_20/20_7.htmlIn the article, on the base of abstract theory (B. V. Loginov, 1979) the nonlinear eigenvalue problems for nonlinearly perturbed Helmholtz equations having application to low temperature plasma theory and to some problems of differential geometry are considered. Other possible often technically more difficult applications (for instance, periodical solutions in heat convection theory) are completely determined by the group symmetry of original equations and do not depend on their concrete essence. In the general case of finite group symmetry with known composition law, a computer program for determination of all subgroups is given, in particular, for dihedral and also planar and spatial crystallographic groups. F. G. AvkhadievHardy type inequalities in higher dimensions with explicit estimate of constantsVolume_21/21_1.htmlLet Ω be an open set in Rn such that Ω ≠ Rn. For 1 ≤ p < ∞, 1 < s < ∞ and δ = dist(x, ∂Ω) we estimate the Hardy constant cp(s, Ω)= sup {||f/ δs/p||Lp(Ω): f ∈ C0(Ω), ||(∇ f)/δs/p - 1||Lp(Ω)=1} and some related quantities. For open sets Ω ⊂ R2 we prove the following bilateral estimates min {2, p} M0(Ω) ≤ cp (2, Ω) ≤ 2 p (π M0 (Ω) + a0)2, a0=4.38, where M0(Ω) is the geometrical parameter defined as the maximum modulus of ring domains in Ω with center on ∂Ω. Since the condition M0 (Ω) < ∞ means the uniformly perfectness of ∂Ω, these estimates give a direct proof of the following Ancona-Pommerenke theorem: c2(2, ∂Ω) is finite if and only if the boundary set ∂Ω is uniformly perfect. Moreover, we obtain the following direct extension of the one-dimensional Hardy inequality to the case n ≥ 2: if s > n, then for arbitrary open sets Ω ⊂ Rn (Ω ≠ Rn) and any p ∈ [1, ∞) the sharp inequality cp (s, Ω) ≤ p/(s-n) is valid. This gives a solution of a known problem due to J.L.Lewis and A.Wannebo. Estimates of constants in certain other Hardy and Rellich type inequalities are also considered. In particular, we obtain an improved version of a Hardy type inequality by H.Brezis and M.Marcus for convex domains and give its generalizations. A. Benbrik, A. Mbarki, S. Lahrech, A. OuahabEkeland's Principle for Vector-Valued Maps based On the Characterization of Uniform Spaces via Families of generalized quasi-metricsVolume_21/21_2.htmlUsing a new characterization of uniform spaces via Families of generalized quasi-metrics, we present a variant of Ekeland's variational principle for vector-valued maps being a consequence of minimal point theorem. Pingyan Chen, Tien-Chung Hu, Andrei VolodinA note on the rate of complete convergence for maximus of partial sums for moving average processes in Rademacher type Banach spacesVolume_21/21_3.htmlWe obtain the complete convergence rates for maximums of partial sums of Banach space valued random elements consisting of a moving average process. The corresponding almost sure convergence results for partial sums are derived, too. Ying GeOn closed inverse images of base-paracompact spacesVolume_21/21_4.htmlIn this paper, we prove that every base-paracompact mapping f:X → Y inversely preserves base-paracompactness if w(X)≥ w(Y), where w(X) and w(Y) denote the weight of X and the weight of Y respectively. As an application of this result, we prove that every closed Lindelof mapping f:X → Y inversely preserves base-paracompactness if X is a regular space and w(X) is a regular cardinality, where ``X is a regular space'' cannot be relaxed to ``X is a Hausdorff space'', which give some answers for a question on inverse images of base-paracompact spaces posed by L.Wu. Niovi Kehayopulu, Michael TsingelisFuzzy interior ideals in ordered semigroupsVolume_21/21_5.htmlIn regular and in intra-regular ordered semigroups the ideals and the interior ideals coincide. In regular and in intra-regular poe-semigroups the ideal elements and the interior ideal elements coincide. In an attempt to show the similarity between the theory of ordered semigroups and the theory of fuzzy ordered semigroups, we prove here that in regular and in intra-regular ordered semigroups the fuzzy ideals and the fuzzy interior ideals coincide. We also prove that A is an interior ideal of an ordered semigroup S if and only if the characteristic function fA is a fuzzy interior ideal of S. We finally introduce the concept of a fuzzy simple ordered semigroup, we prove that an ordered semigroup is simple if and only if it is fuzzy simple, and we characterize the simple ordered semigroups in terms of fuzzy interior ideals. Zhi-Gang WangCertain Subclasses of Close-to-Convex and Quasi-Convex Functions with respect to k-symmetric pointsVolume_21/21_6.htmlIn the present paper, the author introduce two new subclasses C(k)(α,β,γ) of close-to-convex functions and QC(k)(α,β,γ) of quasi-convex functions with respect to k-symmetric points. The sufficient conditions and integral representations for functions belonging to these classes are provided, the inclusion relationships and convolution conditions for these classes are also provided. V. K. BhatA note on Krull dimension of skew polynomial ringsVolume_22/22_1.htmlLet A be a commutative Noetherian ring such that Krull dimension of A is α. Let M be a finitely generated critical module over A[x,σ], (where σ is an automorphism of A) and Krull dimension of M is α + 1. Then M has a prime annihilator. Changhong Wu, Lanzhe LiuBoundedness for Multilinear Commutator of Littlewood-Paley Operator on Hardy and Herz-Hardy SpacesVolume_22/22_2.htmlIn this paper, the (Hpb,Lp) and (H Kα,pq,b,Kqα,p) type boundedness for the multilinear commutator associated with the Littlewood-Paley operator are obtained. Maslina Darus, K .Al ShaqsiOn harmonic univalent functions defined by a generalized Ruscheweyh derivatives operatorVolume_22/22_3.htmlLet SH denote the class of functions f=h+ g which are harmonic univalent and sense preserving in the unit disk U. Al-Shaqsi and Darus introduced a generalized Ruscheweyh derivatives operator denoted by Dnλ where Dnλ f(z)= z+ Σk = 2 [1+λ(k-1)]C(n,k)akzk. The authors, using this operators, introduce the class Hnλ of functions which are harmonic in U . Coefficient bounds, distortion bounds and extreme points are obtained. Niovi Kehayopulu, Michael TsingelisDecomposition of commutative ordered semigroups into archimedean componentsVolume_22/22_4.htmlThe decomposition of a commutative semigroup (without order) into its archimedean components, by means of the division relation, has been studied by Clifford and Preston. Exactly as in semigroups, the complete semilattice congruence `` N'' defined on ordered semigroups by means of filters, plays an important role in the structure of ordered semigroups. In the present paper we introduce the relation "η" by means of the division relation (defined in an appropriate way for ordered case), and we prove that, for commutative ordered semigroups, we have η = N. As a consequence, for commutative ordered semigroups, one can also use that relation η which has been also proved to be useful for studying the structure of such semigroups. We first prove that in commutative ordered semigroups, the relation η is a complete semilattice congruence on S. Then, since N is the least complete semilattice congruence on S, we have η = N. Using the relation η, we prove that the commutative ordered semigroups are, uniquely, complete semilattices of archimedean semigroups which means that they are decomposable, in a unique way, into their archimedean components. A. V. Lapteva, E. I. YakovlevIndex Vector-Function and Minimal CyclesVolume_22/22_5.htmlLet P be a closed triangulated manifold, dim P = n. We consider the group of simplicial 1-chains C1(P)= C1(P,Z2) and the homology group H1(P)= H1(P,Z2). We also use some nonnegative weighting function L:C1(P)→R. For any homological class [x] ∈ H1(P) the method proposed in article builds a cycle z ∈ [x] with minimal weight L(z). The main idea is in using a simplicial scheme of space of the regular covering p:P → P with automorphism group G ≅ H1(P). We construct this covering applying the index vector-function J:C1(P)→Z2r relative to any basis of group Hn-1(P), r= rank H n-1(P). Mehmet Zeki Sarikaya, Huseyin YildirimOn Hardy Type Inequality with Non-isotropic KernelsVolume_22/22_6.htmlIn the present paper we establish a Stein-Weiss type generalization of the Hardy type inequality with non-isotropic kernels depending on λ -distance for the spaces Lp(.)(Ω ) with variable exponent p(x) in the case of bounded domains Ω in Rn. H. L. HuruAssociativity constraints, braidings and quantizations of modules with grading and actionVolume_23/23_1.htmlWe study quantizations, associativity constraints and braidings in the monoidal category of monoid graded modules over a commutative ring. All of them can be described in terms of the cohomology of the underlying (finite) monoid. The Fourier transform of finite groups gives a corresponding description in the monoidal category of modules with action by a group. Per K. Jakobsen, V.V. LychaginMaximum Entropy Wave functionsVolume_23/23_2.htmlIn this paper we use the classical Maximum Entropy principle to define maximum entropy wave functions. These are wave functions that maximize the entropy among all wave functions satisfying a finite set of constraints in the form of expectation values.This lead to a nonlinear equation for the wave function that reduce to the usual stationary Schrö dinger equation if the energy is the only constraint and the value of the constraint is an eigenvalue. We discuss the extension of the thermodynamical formalism to this case and apply our general formalism to several simple quantum systems, the two-level atom,the particle in a box, the free particle and the Harmonic Oscillator and compare with the results obtained by applying the usual von Neumann quantum statistical method to the same systems. Boris KruglikovNote on two compatibility criteria: Jacobi-Mayer bracket vs. differential Gröbner basisVolume_23/23_3.htmlWe compare two compatibility criteria for overdetermined PDEs: one via geometric theory of differential equations and another via differential algebra approach. Whenever both are applicable, we show that the former is more effective, though in some very special cases they are equivalent. D. KrupkaThe total divergence equationVolume_23/23_4.htmlIn this paper, the total divergence equation is investigated by means of the methods used in the theory of finite order variational sequences. Integrability conditions for this equation are found, and all solutions are described. The correspondence of the solutions with some differential forms on jet spaces is established. O. Krupkova, P. VolnyDifferential equations with constraints in jet bundles: Lagrangian and Hamiltonian systemsVolume_23/23_5.htmlThe paper is a survey of the theory of Lagrangian systems with non-holonomic constraints in jet bundles. The subject of the paper are systems of second-order ordinary and partial differential equations that arise as extremals of variational functionals in fibered manifolds. A geometric setting for Euler-Lagrange and Hamilton equations, based on the concept of Lepage class is presented. A constraint is modeled in the underlying fibered manifold as a fibered submanifold endowed with a distribution (the canonical distribution). A constrained system is defined by means of a Lepage class on the constraint submanifold. Constrained Euler-Lagrange equations and constrained Hamilton equations, and properties of the corresponding exterior differential systems, such as regularity, canonical form, or existence of a constraint Legendre transformation, are presented. The case of mechanics (ODE's) and field theory (PDE's) are investigated separately, however, stress is put on a unified exposition, so that a direct comparison of results and formulas is at hand. Alexei KushnerAlmost product structures and Monge-Ampere EquationsVolume_23/23_6.htmlTensor invariants of an almost product structure are constructed. We apply them to solving the problem of contact equivalence and the problem of contact linearization for Monge-Ampère equations. Mikhail A. MalakhaltsevDifferential complex associated to closed differential forms of nonconstant rankVolume_23/23_7.htmlIn the present paper we construct a complex of sheaves associated to a closed differential form ω. We study this complex in case ω is a) a closed 1-form vanishing at an embedded submanifold, b) a symplectic structure with Martinet singularities. In particular, we prove that, under additional conditions on ω, this complex gives a fine resolution for the sheaf of infinitesimal automorphisms of ω. H. AzanchilerExtension of Line-splitting Operation from Graphs to Binary MatroidsVolume_24/24_1.htmlIn this paper, we characterize the n-line splitting operation of graphs in terms of cycles of respective graphs and then extend this operation to binary matroids. In matroids, we call this operation an element-set splitting. The resulting matroid is called the es-splitting matroid. We characterize circuits of an es-splitting matroid. We also characterize the es-splitting matroid in terms of matrices. Also, we show that if M is a connected binary matroid then the es-splitting matroid MeX is also connected. H. L. HuruQuantizations of braided derivations. 1. Monoidal categoriesVolume_24/24_2.htmlFor monoidal categories we describe braidings and quantizations. We use them to find quantizations of braided symmetric algebras and modules, braided derivations, braided connections, curvatures and differential operators. Ying-Jun Jiang, Jin-Ping ZengL-error estimate for a discrete two-sided obstacle problem and multilevel projective algorithmVolume_24/24_3.htmlWe are interested in the approximation in the L-norm of variational inequalities with two-sided obstacle. We show that the order of convergence will be the same as that of variational inequalities with one obstacle. We also give multilevel projective algorithm and discuss its convergence. S. Lahrech, A. Jaddar, A. Ouahab, A. MbarkiSome remarks about strictly pseudoconvex functions with respect to the Clarke-Rockafellar subdifferentialVolume_24/24_4.htmlUsing the notion of radially Clarke-Rockafellar subdifferentiable functions (RCRS-functions), we characterize strictly pseudoconvex functions with respect to the Clarke-Rockafellar subdifferential in two different ways, and we study a maximization problem involving RCRS-strictly pseudoconvex functions over a convex set. Changchun LiuSelf-similar solutions for a nonlinear degenerate parabolic equationVolume_24/24_5.htmlIn this paper, the author investigates the initial boundary value problem for a nonlinear degenerate parabolic equation, which comes from a compressible fluid flowing in a homogeneous isotropic rigid porous medium. We establish the existence of nonnegative self-similar solutions. Eldar StraumeA geometric study of many body systemsVolume_24/24_6.htmlAn n-body system is a labelled collection of n point masses in a Euclidean space, and their congruence and internal symmetry properties involve a rich mathematical structure which is investigated in the framework of equivariant Riemannian geometry. Some basic concepts are n-configuration, configuration space, internal space, shape space, Jacobi transformation and weighted root system. The latter is a generalization of the root system of SU(n), which provides a bookkeeping for expressing the mutual distances of the point masses in terms of the Jacobi vectors. Moreover, its application to the study of collinear central n-configurations yields a simple proof of Moulton's enumeration formula. A major topic is the study of matrix spaces representing the shape space of n-body configurations in Euclidean k-space, the structure of the m-universal shape space and its O(m)-equivariant linear model. This also leads to those left orbital fibrations where SO(m) or O(m) act on a sphere with a sphere as orbit space. A few of these examples are encountered in the literature, e.g. the special case S5/O(2) ⊬ S4 was analyzed independently by Arnold, Kuiper and Massey in the 1970's. W. S. Zhou, S. F. CaiPositive Solutions for a Singular Second Order Ordinary Differential EquationVolume_24/24_7.htmlThis paper is concerned with the positive solutions for a singular second order ordinary differential equation. Under appropriate conditions, by the classical method of elliptic regularization, we prove the existence of position solutions. F. G. Avkhadiev, A. N. ChuprunovThe probability of a successful allocation of ball groups by boxesVolume_25/25_1.htmlLet p=pNn be the probability of a successful allocation of n groups of distinguishable balls in N boxes in equiprobable scheme for group allocation of balls with the following assumption: each group contains m balls and each box contains not more than q balls from a same group. If q=1, then we easily calculate p and observe that p → ea0(m-1)/2 α as n, N→∞ such that α = n/N → α0<∞. In the case 2≤ q we also find an explicit formula for the probability and prove that p→ 1 as n, N→∞ such that α = n/N ≤ α'<∞. Wu-Yi Hsiang, Eldar StraumeKinematic geometry of triangles and the study of the three-body problemVolume_25/25_2.html H. L. HuruQuantizations of braided derivations. 2. Graded modulesVolume_25/25_3.htmlFor the monoidal category of graded modules we find braidings and quantizations. We use them to find quantizations of braided symmetric algebras and modules, braided derivations, braided connections, curvatures and differential operators. H. L. HuruQuantizations of braided derivations. 3. Modules with action by a group.Volume_25/25_4.htmlFor the monoidal category of modules with action by a group we find braidings and quantizations. We use them to find quantizations of braided symmetric algebras and modules, braided derivations, braided connections, curvatures and differential operators. Miroslav Kures, David SehnalThe order of algebras with nontrivial fixed point subalgebrasVolume_25/25_5.htmlThe paper represents an advancement of research the fundamental problem of which is a classification of algebras A (Weil algebras primarily) having a nontrivial fixed point subalgebra (with respect to all algebra automorphisms). The main result is the determination of the algebra order allowing a nontrivial fixed point subalgebra. Moreover, an autonomous importance of some results about socle elements of A and the unipotency of algebra automorphisms is highlighted. M. S. Martirosyan, S.V. Samarchyanq-Bounded Systems: Common Approach to Fisher-Micchelli's and Bernstein-Walsh's Type ProblemsVolume_25/25_6.htmlWe have developed a new common method to investigate geometrically fast approximation problems. Fisher-Micchelli's, Bernstein-Walsh's and Batirov-Varga's well known results are obtained as applications. R.RajaRajeswari, M.Lellis Thivagar, S.Athisaya PonmaniCharacterization of ultra separation axioms via (1,2)α-kernelVolume_25/25_7.htmlIn this paper, we introduce the concept of weakly-ultra-separation of two sets in a bitopological space using (1,2)α-open sets. The (1,2)α-closure and the (1,2)α-kernel are defined in terms of this weakly-ultra-separation. We also investigate the properties of some weak separation axioms like ultra-T0, ultra-T1, and ultra-R0. Matvejchuk M. S., Ionova A. M.Positive projections as generators of J-projections of type (B)Volume_26/26_10.htmlLet A be a von Neumann J-algebra of type (B) acting in an indefinite metric space. The aim of the paper is to study J-projections from A. Vadim V. Shurygin, jr.Product preserving bundle functors on multifibered and multifoliate manifoldsVolume_26/26_11.htmlWe show that the set of the equivalence classes of multifoliate structures is in one-to-one correspondence with the set of equivalence classes of finite complete projective systems of vector space epimorphisms. After that we give the complete description of all product preserving bundle functors on the categories of multifibered and multifoliate manifolds. Zhi-Gang Wang, Da-Zhao ChenOn Subclasses of Close-to-Convex and Quasi-Convex Functions with Respect to 2k-Symmetric Conjugate PointsVolume_26/26_12.htmlIn the present paper, the authors introduce two new subclasses Ssc(k)(λ,α) of close-to-convex functions and Csc(k)(λ,α) of quasi-convex functions with respect to 2k-symmetric conjugate points. The integral representations and convolution conditions for these classes are provided. Some coefficient inequalities for functions belonging to these classes and their subclasses with negative coefficients are also provided. H. L. HuruErrata: Addendum to ``Quantizations of braided derivations. 1. Monoidal catagories'', LJM, vol.XXXIV, and ``Quantizations of braided derivations. 2.~Graded modules, 3.~Modules with action by a group'', LJM, vol.XXXVVolume_26/26_13.html In memory of Boris Nikitovich Shapukov (15.02.1937 - 13.02.2007)Volume_26/26_1.html H. AzanchilerA Characterization of the Bases of Line-splitting MatroidsVolume_26/26_2.htmlIn [1] the author extended n-line splitting from graphs to binary matroids and characterized the circuits of the result matroid, i.e. line-splitting matroid (es-splitting). In this paper, we characterize dependent, independent and base sets in line-splitting matroid MeX. Moreover, we determine rank function of MeX. Kamon Budsaba, Pingyan Chen, Andrei VolodinLimiting Behaviour of Moving Average Processes Based on a Sequence of ρ- Mixing and Negatively Associated Random VariablesVolume_26/26_3.htmlLet Yi, -∞<i∞< be a doubly infinite sequence of identically distributed ρ--mixing or negatively associated random variables, ai, -∞< i<∞ a sequence of real numbers. In this paper, we prove the rate of convergence and strong law of large numbers for the partial sums of moving average processes Σi=-∞aiYi+n,n≥1 under some moment conditions. K. Fukuyama, R. KondoOn recurrence property of Riesz-Raikov sumsVolume_26/26_4.htmlThe Riesz-Raikov sums Σ f(θk x) are recurrent in most cases. Xun GeSpaces with a locally countable sn-networkVolume_26/26_5.htmlIn this paper, we discuss a class of spaces with a locally countable sn-network. We give some characterizations of this class and investigate variance and inverse invariance of this class under certain mappings. Ghulam Mustafa, Sadiq Hashmi, K. P. AkhtarEstimating error bounds of Bajaj's solid models and their control hexahedral meshesVolume_26/26_6.htmlIn this article, we estimate error bounds between the surface boundary patch of Bajaj et al's solid models (The Visual Computer 18, 343-356, 2002) and their boundary of control hexahedral meshes after k-fold subdivision. Our bounds are express in terms of the maximal differences of the initial control point sequences and constants. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. From this error bound one can predict the subdivision depth within a user specified error tolerance. Dinh Trung Hoa, Tikhonov O. E.Weighted trace inequalities of monotonicityVolume_26/26_7.htmlWe study the inequality Tr (w(A)f(A)) ≤ Tr(w(A)f(B)), where w : R → R+ is a ``weight function'' and A,B are Hermitian matrices with A ≤ B, and find corresponding characterizations of the trace. Wei JiaqunA Note On Generalized Gorenstein DimensionVolume_26/26_8.htmlWe prove that two categories Gω and Xω, introduced for the faithfully balanced selforthogonal module ω by Auslander and Reiten in [AR1] and [AR2] respectively, coincide with each other. As an application we give a generalization of a main theorem in [H1]. Z. Q. Ling, Z. J. WangUniqueness of Solutions to A Class of Strongly Degenerate Parabolic EquationVolume_26/26_9.htmlIn this paper, by virtue of Holmgren's approach, we show the uniqueness of the bounded solutions to a class of parabolic equation with two kinds degeneracies at the same time under some necessary conditions on the growth of the convection and sources. K. K. Baishya, S. Eyasmin, A. A. ShaikhOn Φ-recurrent generalized (k, μ)-contact metric manifoldsVolume_27/27_1.htmlThe aim of the present paper is to introduce a type of contact metric manifolds called φ-recurrent generalized (k, μ)-contact metric manifolds and to study their geometric properties. The existence of such manifolds is ensured by a non-trivial example. D. Foroutannia, R. LashkaripourLower bounds for summability matrices on weighted sequence spacesVolume_27/27_2.htmlThe purpose of this paper is finding a lower bound for summability matrix operators on sequence spaces lp(w) and Lorentz sequence spaces d(w,p) and also the sequence space e(w,∞). Also, this study is an extension of some works of Bennett. Niovi KehayopuluWeakly prime and prime fuzzy ideals in ordered semigroupsVolume_27/27_3.htmlIntra-regular ordered semigroups play an important role in studying the structure, especially the decomposition of ordered semigroups. In this paper we prove that the fuzzy ideals of an ordered semigroup S are weakly prime if and only if they are idempotent and they form a chain, and that they are prime if and only if S is intra-regular and the fuzzy ideals of S form a chain. Moreover we show that a fuzzy ideal of an ordered semigroup is prime if and only if it is both semiprime and weakly prime and that in commutative ordered semigroups the prime and weakly prime fuzzy ideals coincide. Our results extend the corresponding results on semigroups (without order) given by G. Szasz in [11] in case of ordered semigroups using fuzzy sets. J. Kurek, W.M. MikulskiRiemannian structures on higher order frame bundles over Riemannian manifoldsVolume_27/27_4.htmlWe describe all M fm-natural operators A: Riemr Riem Pr transforming Riemannian structures g on m-dimensional manifolds M into Riemannian structures A(g) on the r-th order frame bundle PrM=invJr0(Rm, M) over M.

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