
Lobachevskii Journal of Mathematics
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Yu. E. Hohlov, D. V. ProkhorovOn geometrical properties of free boundaries in the HeleShaw 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 HeleShaw 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 closetoconvexity 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 manydimensional 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 GstructuresVolume_3/3_10.htmlIn [Pommaret], J.F. Pommaret constructed the socalled Spencer Pcomplex 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 firstorder Gstructure, 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 Gstructure. In a unified way one can obtain the Dolbeaut complex for the complex structure, the Vaisman complex for the foliation structure [Vaisman], and the VaismanMolino cohomology for the structure of manifold over an algebra [Shurygin].
Kentaro MikamiNambuPoisson structures and their foliationsVolume_3/3_11.htmlNambuPoisson 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 SchoutenNijenhuis bracket. And also we shall show that for a given Poisson structure, the top power of it gives a NambuPoisson structure. We shall characterize the GodbillonVey class of the foliation defined from a regular NambuPoisson tensor.
R. MiyaokaHypersurface geometry and Hamiltonian systems of hydrodynamic typeVolume_3/3_12.html
V. F. MolchanovRepresentations of pseudounitary groups associated with a coneVolume_3/3_13.htmlWe study representations of the pseudounitary group SU(p,q), p,q≥ 2, associated with an isotropic cone.
Y. AgaokaOn the variety of 3dimensional Lie algebrasVolume_3/3_1.htmlIt is known that a 3dimensional 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 3dimensional Lie algebras, which was first appeared in [21]. We also give a representation theoretic meaning of the invariant of 3dimensional Lie algebras introduced in [15], [22], by calculating the GL(V)irreducible decomposition of polynomials on the space Λ^{2} V^{∗}⊗ V up to degree 3. Typical four covariants naturally appear in this decomposition, and we show that the isomorphism classes of 3dimensional Lie algebras are completely determined by the GL(V)invariant concepts in Λ^{2} 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 kjets 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 lowdimensional 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, Hsurfaces 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 oneparameter family of framings for H surfaces in the space forms. Through these framings we reveal relationship between the associated family of Hsurfaces 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 pdimensional planes in R^{n} starting from its integrals over kplanes, 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 nonsingular 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 d_{h}: A→A. A Poisson structure P on E is understood as the homotopy equivalence class (with respect to d_{h}) 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 Pºl_{E}+ l_{E} 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 MongeAmpère 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 KacMoody 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 gmodules are discussed.
N. NakanishiA Survey of NambuPoisson GeometryVolume_4/4_1.htmlWe survey geometry of NambuPoisson manifolds. First we recall Nambu's work which is the origin of NambuPoisson geometry. Next adopting Takhtajan's geometric formulation and applying the local structure theorem of NambuPoisson tensors, we study the projectability of left invariant NambuPoisson 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 birdeyeview 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 wellknown theorem of Green [9], it can be reduced to the calculation of the 1cohomology set of a certain sheaf of automorphisms of O. We construct a nonlinear resolution of this sheaf giving rise to a nonlinear cochain complex whose 1cohomology is the desired one. For a compact manifold M, we apply Hodge theory to construct a finitedimensional 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 KählerEinstein metric. We investigate Kinvariant Einstein metrics on a flag manifold M = K/T which is not KählerEinstein. 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 Kinvariant Einstein metrics on a flag manifold K/T. We compute a Gröbner basis for a system of polynomials of multivariables and show the existence of positive solutions for a system of algebraic equations to prove the existence of Kinvariant 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 semisimple symmetric spaces with invariant projectively flat affine connections and centralsimple 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 MongeAmpère equationsVolume_4/4_7.htmlThis paper is devoted to the geometry of hyperbolic MongeAmpère equations with large symmetry algebras. We classify all hyperbolic MongeAmpére equations whose Lie algebra of contact symmetries is transitive. We also give the explicit construction for Cartan connections associated with generic hyperbolic MongeAmpére equations and find those equations which correspond to connections with vanishing curvature tensor.
D.V. TunitskyOn contact equivalence of holomorphic MongeAmpère equations.Volume_4/4_8.htmlThis paper deals with holomorphic MongeAmpère equations on 5dimensional complex contact manifolds, i.e., MongeAmpère equations with two complex independent variables. If a MongeAmpère 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 MongeAmpère 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. PoincareCartan 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 PoincareCartan 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 almostperiodic in tuniformly for x and strongly dissipative with respect to x, theexistence of a bounded solution is equivalent to the existence ofan almostperiodic 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 MintyBrowder 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 T^{A}M_{n} of infinitely near points of Atype defined for any local Weil algebra A and smooth real manifold M_{n} 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 M^{A}_{n} over a local algebra A associated with canonical foliations corresponding to ideals of A. In particular, it is proved that a complete manifold M^{A}_{n} 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 S^{2n  1} through a fiber bundle a similar result holds for Sp(n).
A.Addou, S.LahrechSufficient Conditions for elliptic problem of optimal control in R^{2}Volume_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 R^{2}, 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 R^{n} in Orlicz Sobolev spaceVolume_6/6_2.htmlWe consider here a problem for which we seek the local minimum in Orlicz Sobolev spaces (W^{1}_{0}L_{M}^{∗}(\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 (W^{1}_{0}L_{M}^{∗}(\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 y_{0} 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 y_{0}, 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 σadditive set functions defined on a hereditary subclass of a σalgebra and taken values in the extended real line. Analogs of the Jordan decomposition theorem and the RadonNikodym 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 H^{s} 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 Φrectifiable curvesVolume_7/7_2.htmlThe paper treats existence and boundary properties of the Cauchy integral over certain classes of nonrectifiable 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 hyperdimensional 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 hyperdimensional 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 RiemannChristoffel's curvature tensor. At the end, analogously to a notion of lines of a curvature in the differential geometry, the notion of subspaces of curvature of Riemannian hyperdimensional 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 AGeneraVolume_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 Agenera.
A.BuckiSome properties of almost rparacontact manifoldsVolume_8/8_2.htmlFor an almost rparacontact manifold M with a structure Σ, almost rparacontact connections, Dconnections, 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 rparacontact manifolds have been studied by means of the curvature and torsion tensor fields of these connections.
B. Komrakov, Jnr.EinsteinMaxwell equation on fourdimensional homogeneous spacesVolume_8/8_3.htmlThis paper presents the solutions of the EinsteinMaxwell equation on all local fourdimensional pseudoRiemannian homogeneous spaces and the complete local classification of fourdimensional EinsteinMaxwell homogeneous spaces with an invariant pseudoRiemannian 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 singlevalued monotone operators in a finitedimensional space are studied: convergence, rate of convergence and optimal iterative parameters are derived. A twostage iterative method with inner iterations is analysed in the case when both operators are linear, selfadjoint and positive definite. The results are applied for the mesh variational inequalities which are solved using a nonoverlapping 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), 3537).
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 NonCompactnessVolume_9/9_3.htmlThe behaviour of the measure of noncompactness of an operator acting on interpolation spaces, with function parameter and having onesided 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 Sanalytic 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 A_{S} of Sanalytic functions on G with spectra in S to linear multiplicative functionals of the corresponding algebra A_{Σ}. 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 M_{f} 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 wellknown Nehari univalence criterion. Our main tool is the local bifurcation research of M_{f} for the level set parametrization f_{r}(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× nmatrices and on its sublogic generated by all projections onto onedimensional subspaces in Q^{n} passing through elements of the unit sphere in Q^{n}.
Vadim V. Shurygin, Larisa B. SmolyakovaAn analog of the VaismanMolino 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 T^{μ} from the category of fibered manifolds to itself which assigns to a fibered manifold p:M → N the fibered product p^{μ}:T^{ A}N×_{T BN}T^{ B}M→ T^{ A}N. In this paper we show that the manifold T^{ A}N×_{T BN}T^{ B}M can be naturally endowed with a structure of an Asmooth manifold modelled on the Amodule L=A^{n} ⊕ B^{m}, where n=dim N, n+m=dim M. We extend the functor T^{μ} to the category of foliated manifolds (M, F). Then we study Asmooth manifolds M^{L} whose foliated structure is locally equivalent to that of T^{ A}N×_{T BN}T^{ B}M. For such manifolds M^{L} we construct bigraduated cohomology groups which are similar to the bigraduated cohomology groups of foliated manifolds and generalize the bigraduated cohomology groups of Asmooth manifolds modelled on Amodules of the type A^{n}. As an application, we express the obstructions for existence of an Asmooth linear connection on M^{L} 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 R^{m}× R^{n} 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 nfold 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 nfold coverings of a compact connected abelian group. Also, a criterion of triviality for nfold coverings in terms of the dual group and the onedimensional 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 {X_{ni}, 1 ≤ i ≤ k_{n}, n ≥ 1} be an array of rowwise independent random elements taking values in a real separable Banach space, and {a_{ni}, 1 ≤ i ≤ k_{n}, 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=1}^{kn}a_{ni} X_{ni} 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 timedependent problemsVolume_10/10_4.htmlSeveral new finitedifference schemes for a nonlinear convectiondiffusion problem are constructed and numerically studied. These schemes are constructed on the basis of nonoverlapping domain decomposition and predictorcorrector approach. Our study was motivated by the article [rivera], where socalled EPIC (explicit predictorimplicit corrector) method have been proposed for a linear onedimensional problem and founded to be stable and scalable when solving on big number of processors. We construct the predictorcorrector 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 nonoverlapping decomposition of a domain, with crosspoints 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 a_{n}(f) be the Taylor coefficients of a holomorphic function f which belongs to the Hardy space H^{p}, 0 < p < 1. We prove the estimate C(p) ≤ π e^{p}/r[(p(1p)r]) in the HardyLittlewood inequality Σ^{∞}_{n=0} a_{n}(f)^{p} (n+1)^{p2} ≤ C(p)(f_{p})^{p}. We also give explicit estimates for sums Σ  a_{n}(f) λ_{n} ^{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 nonArchimedean ones of countable cofinality, there are uniformly continuous 11 functions not mapping interior to interior. For the latter kind of fields, there are also uniformly continuous 11 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 rdigitwise random perturbations of an expanded to base r real number x, which are small enough to preserve rdigit asymptotic frequency spectrum of x, the gadic 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 oneelement 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 πgroups. Obviously, cyclic subgroups of the free factors, which aren't separable in these factors by the family of all normal subgroups of finite πindex 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 pfiniteness of a free product with cyclic amalgamation implies the pseparability of all p'isolated cyclic subgroups if the free factors are free or finitely generated residually pfinite nilpotent groups.
S. S. Bhatia, Kulwinder Kaur, Babu RamL^{1}convergence of modified complex trigonometric sumsVolume_12/12_1.htmlIn this paper we study L^{1}convergence of modified complex trigonometric sums introduced by Ram and Kumari and obtain a necessary and sufficient condition for L^{1}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 selfsimilar 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 selfsimilar set. The main difference to the standard (Hutchinson) notion of selfsimilarity 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 selfsimilar 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 LittlewoodPaley operators on some Hardy spacesVolume_12/12_5.htmlIn the present paper the ( (H^{p}_{b},L^{p})type and (H^{p,∞}_{b},L^{p,∞})type boundedness for the commutators associated with the LittlewoodPaley operators and b ∈BMO(R^{n}) are obtained, where H^{p}_{b} and H^{p,∞} 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 3Dmodel 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 L_{1}convergence of modified complex trigonometric sumsVolume_13/13_4.htmlAn L^{1}convergence property of the complex form g_{n}(c,t)=S_{n}(c,t) [ c_{n}E_{n}(t)+c_{n}E_{n}(t) ] of the modified sums introduced by Garrett and Stanojevic [3] is established and a necessary and sufficient condition for L^{1}convergence of Fourier series is obtained.
Niovi Kehayopulu, Michael TsingelisThe embedding of an ordered semigroup into an lesemigroupVolume_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 lesemigroup having a zero element and S is embedded in P(S).
Niovi Kehayopulu, Michael TsingelisA note on semipseudoorders 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 semipseudoorder (also called pseudocongruence) in semigroups and we proved that each semipseudoorder 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 semipseudoorder on S.
Igor V. Konnov, Olga V. PinyaginaDgap 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 Dgap 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 socalled 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 evendimensional manifold structured by a Tparallel connectionVolume_13/13_9.htmlEvendimensional manifolds N structured by a Tparallel 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 CRproduct [B] and one may decompose M as M=M_{D}× M_{D⊥ }, where M_{D} is an invariant submanifold of M and M_{D⊥ } is an antiinvariant submanifold of M. Some other properties regarding the immersion x:M→ N are discussed.
Abdulla AljouieeOn the Brauer Monoid of S_{3}Volume_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 2cocycles defined on S_{3}. In particular, the idempotent 2cocycles 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 DoubleSequence Random Iteration Process for Random Fixed Points of Contractive Type Random OperatorsVolume_14/14_4.htmlIn this paper, we introduce the concept of a Manntype doublesequence 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 doublesequence iteration introduced by Moore (Comput. Math. Appl. 43(2002), 15851589).
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 C_{0}(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, VisaMatti Jokela, Erkki LaitinenA simulation of traffic equilibration multipath routing in ad hoc networksVolume_14/14_6.htmlLimited battery life is a known problem with mobile computers. In multihop 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 multipath 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 finitedimensional 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 Rsubmodule in the full derivation algebra \Der R. We consider a class of Wmodules 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 Pseudoparabolic EquationVolume_15/15_1.htmlIn this paper we discuss properties of solutions for a class of pseudoparabolic 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 Rcirculant 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 BovykinOrdertypes of models of arithmetic and a connection with arithmetic saturationVolume_16/16_1.htmlFirst, we study a question we encountered while exploring ordertypes 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 w_{1},w_{2}\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 NavierStokes equation in 3D torusVolume_17/17_10.htmlWe consider the NavierStokes equation in 3D 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 + Σ_{n=2}^{∞}a_{n}(f)z^{n} 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 a_{2}(f) and a_{3}(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 linearquadratic regulator for degenerate diffusionsVolume_17/17_2.htmlThe paper studies the smoothness of solutions of the degenerate HamiltonJacobiBellman (HJB) equation associated with a linearquadratic 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=D_{X}uB(x,u) where X is a vector field. The solvability of L may be of some interest since by the NashMoser 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 finitemultivalued 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 mtransformation. In this case the orbit of any point looks like a tree. In the study of mtransformations we are interested in the properties of the trees. An mtransformation generates a stochastic kernel and a new measure. Using these objects, we introduce analogies of some main concept of ergodic theory: ergodicity, Koopman and FrobeniusPerron 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 AA 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 Dmodules, 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 Dmodules 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^{1}f ⊂ A^{2}, ff^{1} ⊂ B^{2}. 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^{1}h ⊂ f^{1}f). Wellknown ,,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 T^{A} M for the case of a Frobenius Weil algebra A. For a Poisson manifold (M,w) we show that the complete lift w^{C} of a Poisson tensor w is again a Poisson tensor on T^{A} M and that w^{C} is a linear combination of some "basic" Poisson structures on T^{A} M induced by w. Finally, we introduce the notion of a weakly symmetric Frobenius Weil algebra A and we compute the modular class of (T^{A} M, w^{C}) 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 HilbertSchmidt 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 HilbertSchmidt 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 NashMoser function inverse theorem to show that the group G of diffeomorphisms on the Euclidean space R^{n} which are 1time flat, close to the identity and of small support acts transitively on the affine space of appropriate perturbations of the dilation vector field X_{o}.
G. N. Bushueva, V. V. ShuryginOn the higher order geometry of Weil bundles over smooth manifolds and over parameterdependent manifoldsVolume_18/18_4.htmlThe Weil bundle T^{A} M_{n} of an ndimensional smooth manifold M_{n} determined by a local algebra A in the sense of A. Weil carries a natural structure of an ndimensional Asmooth manifold. This allows ones to associate with T^{A} M_{n} the series B^{r}(A)T^{A} M_{n}, r=1,...,∞, of Asmooth rframe bundles. As a set, B^{r}(A)T^{A} M_{n} consists of rjets of Asmooth germs of diffeomorphisms (A^{n},0)→ T^{A} M_{n}. We study the structure of Asmooth rframe bundles. In particular, we introduce the structure form of B^{r}(A)T^{A} M_{n} and study its properties. Next we consider some categories of mparameterdependent manifolds whose objects are trivial bundles M_{n} × R^{m} → R^{m}, define (generalized) Weil bundles and higher order frame bundles of mparameterdependent manifolds and study the structure of these bundles. We also show that product preserving bundle functors on the introduced categories of mparameterdependent 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 sup_{λ ∈ C}  exp (λ b) a exp (λ b)  <∞. This result allows us to obtain an analog of the von NeumannFugledePutnam 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 Nclasses 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 4dimensional Euclidean SpaceVolume_18/18_9.htmlThe objective of this article is to construct in a hyperrectangular region of the 4dimensional 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 quiverbundles 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 quiverbundles on bielliptic curves.
Boris Kruglikov, Olga LychaginaFinite Dimensional Dynamics for KolmogorovPetrovskyPiskunov EquationVolume_19/19_2.htmlWe construct new finitedimensional submanifolds in the solution space of KolmogorovPetrovskyPiskunov equation. We describe the corresponding evolutionary dynamics and exact solutions.
XiangYun 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 3prime fuzzy ideals in an ordered semigroup S, respectively. We discuss properties of fuzzy ideals extensions and the relationships between prime fuzzy ideals and 3prime fuzzy ideals of S in terms of the extension of fuzzy ideals of S, we give an example to show that 3prime 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.
ZhiGang WangA New Subclass of Quasiconvex Functions with Respect to kSymmetric PointsVolume_19/19_4.htmlIn the present paper, we introduce a new subclass C_{s}^{(k)}(α,β) of quasiconvex functions with respect to ksymmetric 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 differentialalgebraic 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 integrodifferential equations having singular matrices at the main part to systems with nonsingular ones is proposed. For systems of nonlinear finitedimensional 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 wellknown 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 LyapunovSchmidt's ideas and the generalized Jordan sets techniques to reduce partial differentialoperator 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 initialvalue 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 boundaryvalue problems for systems of linear ordinary differential equations of second order, possible being stiff or unresolved with respect to derivatives (differentialalgebraic 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 boundaryvalue 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. LoginovDifferentialalgebraic equations in the theory of invariant manifolds for singular equationsVolume_20/20_6.htmlAnalogs of GrobmanHartman 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 differentialalgebraic 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 R^{n} such that Ω ≠ R^{n}. For 1 ≤ p < ∞, 1 < s < ∞ and δ = dist(x, ∂Ω) we estimate the Hardy constant c_{p}(s, Ω)= sup {f/ δ^{s/p}_{Lp(Ω)}: f ∈ C_{0}^{∞}(Ω), (∇ f)/δ^{s/p  1}_{Lp(Ω)}=1} and some related quantities. For open sets Ω ⊂ R^{2} we prove the following bilateral estimates min {2, p} M_{0}(Ω) ≤ c_{p} (2, Ω) ≤ 2 p (π M_{0} (Ω) + a_{0})^{2}, a_{0}=4.38, where M_{0}(Ω) is the geometrical parameter defined as the maximum modulus of ring domains in Ω with center on ∂Ω. Since the condition M_{0} (Ω) < ∞ means the uniformly perfectness of ∂Ω, these estimates give a direct proof of the following AnconaPommerenke theorem: c_{2}(2, ∂Ω) is finite if and only if the boundary set ∂Ω is uniformly perfect. Moreover, we obtain the following direct extension of the onedimensional Hardy inequality to the case n ≥ 2: if s > n, then for arbitrary open sets Ω ⊂ R^{n} (Ω ≠ R^{n}) and any p ∈ [1, ∞) the sharp inequality c_{p} (s, Ω) ≤ p/(sn) 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 VectorValued Maps based On the Characterization of Uniform Spaces via Families of generalized quasimetricsVolume_21/21_2.htmlUsing a new characterization of uniform spaces via Families of generalized quasimetrics, we present a variant of Ekeland's variational principle for vectorvalued maps being a consequence of minimal point theorem.
Pingyan Chen, TienChung 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 baseparacompact spacesVolume_21/21_4.htmlIn this paper, we prove that every baseparacompact mapping f:X → Y inversely preserves baseparacompactness 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 baseparacompactness 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 baseparacompact spaces posed by L.Wu.
Niovi Kehayopulu, Michael TsingelisFuzzy interior ideals in ordered semigroupsVolume_21/21_5.htmlIn regular and in intraregular ordered semigroups the ideals and the interior ideals coincide. In regular and in intraregular poesemigroups 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 intraregular 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 f_{A} 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.
ZhiGang WangCertain Subclasses of ClosetoConvex and QuasiConvex Functions with respect to ksymmetric pointsVolume_21/21_6.htmlIn the present paper, the author introduce two new subclasses C^{(k)}(α,β,γ) of closetoconvex functions and QC^{(k)}(α,β,γ) of quasiconvex functions with respect to ksymmetric 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 LittlewoodPaley Operator on Hardy and HerzHardy SpacesVolume_22/22_2.htmlIn this paper, the (H^{p}_{b},L^{p}) and (H K^{α,p}_{q,b},K_{q}^{α,p}) type boundedness for the multilinear commutator associated with the LittlewoodPaley operator are obtained.
Maslina Darus, K .Al ShaqsiOn harmonic univalent functions defined by a generalized Ruscheweyh derivatives operatorVolume_22/22_3.htmlLet S_{H} denote the class of functions f=h+ g which are harmonic univalent and sense preserving in the unit disk U. AlShaqsi and Darus introduced a generalized Ruscheweyh derivatives operator denoted by D^{n}_{λ} where D^{n}_{λ} f(z)= z+ Σ_{k = 2}^{∞} [1+λ(k1)]C(n,k)a_{k}z^{k}. The authors, using this operators, introduce the class H^{n}_{λ} 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 VectorFunction and Minimal CyclesVolume_22/22_5.htmlLet P be a closed triangulated manifold, dim P = n. We consider the group of simplicial 1chains C_{1}(P)= C_{1}(P,Z_{2}) and the homology group H_{1}(P)= H_{1}(P,Z_{2}). We also use some nonnegative weighting function L:C_{1}(P)→R. For any homological class [x] ∈ H_{1}(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 ≅ H_{1}(P). We construct this covering applying the index vectorfunction J:C_{1}(P)→Z_{2}^{r} relative to any basis of group H_{n1}(P), r= rank H _{n1}(P).
Mehmet Zeki Sarikaya, Huseyin YildirimOn Hardy Type Inequality with Nonisotropic KernelsVolume_22/22_6.htmlIn the present paper we establish a SteinWeiss type generalization of the Hardy type inequality with nonisotropic kernels depending on λ distance for the spaces L_{p(.)}(Ω ) with variable exponent p(x) in the case of bounded domains Ω in R^{n}.
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 twolevel 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: JacobiMayer 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 nonholonomic constraints in jet bundles. The subject of the paper are systems of secondorder ordinary and partial differential equations that arise as extremals of variational functionals in fibered manifolds. A geometric setting for EulerLagrange 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 EulerLagrange 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 MongeAmpere 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 MongeAmpère 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 1form 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 Linesplitting Operation from Graphs to Binary MatroidsVolume_24/24_1.htmlIn this paper, we characterize the nline 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 elementset splitting. The resulting matroid is called the essplitting matroid. We characterize circuits of an essplitting matroid. We also characterize the essplitting matroid in terms of matrices. Also, we show that if M is a connected binary matroid then the essplitting matroid M^{e}_{X} 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.
YingJun Jiang, JinPing ZengL^{∞}error estimate for a discrete twosided obstacle problem and multilevel projective algorithmVolume_24/24_3.htmlWe are interested in the approximation in the L^{∞}norm of variational inequalities with twosided 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 ClarkeRockafellar subdifferentialVolume_24/24_4.htmlUsing the notion of radially ClarkeRockafellar subdifferentiable functions (RCRSfunctions), we characterize strictly pseudoconvex functions with respect to the ClarkeRockafellar subdifferential in two different ways, and we study a maximization problem involving RCRSstrictly pseudoconvex functions over a convex set.
Changchun LiuSelfsimilar 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 selfsimilar solutions.
Eldar StraumeA geometric study of many body systemsVolume_24/24_6.htmlAn nbody 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 nconfiguration, 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 nconfigurations yields a simple proof of Moulton's enumeration formula. A major topic is the study of matrix spaces representing the shape space of nbody configurations in Euclidean kspace, the structure of the muniversal 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 S^{5}/O(2) ⊬ S^{4} 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=p_{Nn} 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 → e^{a0(m1)/2 α } as n, N→∞ such that α = n/N → α_{0}<∞. 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'<∞.
WuYi Hsiang, Eldar StraumeKinematic geometry of triangles and the study of the threebody 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. SamarchyanqBounded Systems: Common Approach to FisherMicchelli's and BernsteinWalsh's Type ProblemsVolume_25/25_6.htmlWe have developed a new common method to investigate geometrically fast approximation problems. FisherMicchelli's, BernsteinWalsh's and BatirovVarga's well known results are obtained as applications.
R.RajaRajeswari, M.Lellis Thivagar, S.Athisaya PonmaniCharacterization of ultra separation axioms via (1,2)αkernelVolume_25/25_7.htmlIn this paper, we introduce the concept of weaklyultraseparation of two sets in a bitopological space using (1,2)αopen sets. The (1,2)αclosure and the (1,2)αkernel are defined in terms of this weaklyultraseparation. We also investigate the properties of some weak separation axioms like ultraT_{0}, ultraT_{1}, and ultraR_{0}.
Matvejchuk M. S., Ionova A. M.Positive projections as generators of Jprojections of type (B)Volume_26/26_10.htmlLet A be a von Neumann Jalgebra of type (B) acting in an indefinite metric space. The aim of the paper is to study Jprojections 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 onetoone 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.
ZhiGang Wang, DaZhao ChenOn Subclasses of ClosetoConvex and QuasiConvex Functions with Respect to 2kSymmetric Conjugate PointsVolume_26/26_12.htmlIn the present paper, the authors introduce two new subclasses S_{sc}^{(k)}(λ,α) of closetoconvex functions and C_{sc}^{(k)}(λ,α) of quasiconvex functions with respect to 2ksymmetric 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 Linesplitting MatroidsVolume_26/26_2.htmlIn [1] the author extended nline splitting from graphs to binary matroids and characterized the circuits of the result matroid, i.e. linesplitting matroid (essplitting). In this paper, we characterize dependent, independent and base sets in linesplitting matroid M^{e}_{X}. Moreover, we determine rank function of M^{e}_{X}.
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 Y_{i}, ∞<i∞< be a doubly infinite sequence of identically distributed ρ^{}mixing or negatively associated random variables, a_{i}, ∞< 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 Σ^{∞}_{i=∞}a_{i}Y_{i+n},n≥1 under some moment conditions.
K. Fukuyama, R. KondoOn recurrence property of RieszRaikov sumsVolume_26/26_4.htmlThe RieszRaikov sums Σ f(θ^{k} x) are recurrent in most cases.
Xun GeSpaces with a locally countable snnetworkVolume_26/26_5.htmlIn this paper, we discuss a class of spaces with a locally countable snnetwork. 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, 343356, 2002) and their boundary of control hexahedral meshes after kfold 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 G_{ω} and X_{ω}, 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 Φrecurrent 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 φrecurrent generalized (k, μ)contact metric manifolds and to study their geometric properties. The existence of such manifolds is ensured by a nontrivial 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 l_{p}(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.htmlIntraregular 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 intraregular 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 f_{m}natural operators A: Riemr Riem P^{r} transforming Riemannian structures g on mdimensional manifolds M into Riemannian structures A(g) on the rth order frame bundle P^{r}M=invJ^{r}_{0}(R^{m}, M) over M.
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