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We show geometrical properties of a submanifold of a (LCS)n-manifold. The properties of the induced structures on such a submanifold are also studied. [ABSTRACT FROM AUTHOR]

Bianchi-type transformations are constructed for two-dimensional surfaces with constant negative intrinsic curvature in the space S × ℝ. [ABSTRACT FROM AUTHOR]

Abstract: Let be a four-dimensional complete noncompact Bach-flat Riemannian manifold with positive Yamabe constant. In this paper, we show that has a constant curvature if it has a nonnegative constant scalar curvature and sufficiently small -norm of trace-free Riemannian curvature tensor. Moreover, we get a gap theorem for with positive scalar curvature. [Copyright &y& Elsevier]

In this paper, we introduce and discuss minimal γ-open sets in topological spaces. We establish some basic properties of minimal γ-open sets and provide an example to illustrate that minimal γ-open sets are independent of minimal open sets introduced and discussed in [3]. We obtain some properties of pre γ-open sets using properties of minimal γ-open sets. As an application of a theory of minimal γ-open sets, we obtain a sufficient condition for a γ-locally finite space to be a pre γ-T2 space. [ABSTRACT FROM AUTHOR]

In this paper we prove a realizability theorem for Quinn's mapping cylinder obstructions for stratified spaces. We prove a continuously controlled version of the s-cobordism theorem which we further use to prove the relation between the torsion of an h-cobordism and the mapping cylinder obstructions. This states that the image of the torsion of an h-cobordism is the mapping cylinder obstruction of the lower stratum of one end of the h-cobordism in the top filtration. These results are further used to prove a theorem about the realizability of end obstructions. [ABSTRACT FROM AUTHOR]

We establish two-sided bounds for the complexity of two infinite series of closed orientable three-dimensional hyperbolic manifolds, the Löbell manifolds and the Fibonacci manifolds. The manifolds of the two series are indexed by an integer n and the corresponding complexity estimates are both linear in n. [ABSTRACT FROM AUTHOR]

We construct $mathcal {F}$-structures on a Bott manifold and on some other manifolds obtained by Kummer-type constructions. We also prove that if $M=E# X$, where $E$ is a fiber bundle with structure group $G$ and a fiber admitting a $G$-invariant metric of non-negative sectional curvature and $X$ admits an $mathcal {F}$-structure with one trivial covering, then one can construct on $M$ a sequence of metrics with sectional curvature uniformly bounded from below and volume tending to zero (i.e. $operatorname {Vol}_K(M)=0$). As a corollary we prove that all the elements in the Spin cobordism ring can be represented by manifolds $M$ with $operatorname {Vol}_K (M)=0$. [ABSTRACT FROM AUTHOR]

Abstract: By means of the orbit method we show that, for a compact Lie group, the Blattner–Kostant–Sternberg pairing map, with the constants being appropriately fixed, is unitary. Along the way we establish a holomorphic Peter–Weyl theorem for the complexification of a compact Lie group. Among our crucial tools is Kirillov’s character formula. The basic observation is that the Weyl vector is lurking behind the Kirillov character formula, as well as behind the requisite half-form correction on which the Blatter–Kostant–Sternberg-pairing for the compact Lie group relies, and thus produces the appropriate shift which, in turn, controls the unitarity of the BKS-pairing map. Our methods are independent of heat kernel harmonic analysis, which is used by B. C. Hall to obtain a number of these results [B.C. Hall, The Segal–Bargmann Coherent State Transform for compact Lie groups, J. Funct. Anal. 122 (1994) 103–151; B.C. Hall, Geometric quantization and the generalized Segal–Bargmann transform for Lie groups of compact type, Comm. Math. Phys. 226 (2002) 233–268, quant.ph/0012015]. [Copyright &y& Elsevier]

Abstract: In this paper, we carry a detailed study of mechanical systems with configuration space for which the base variables are being controlled. The overall system’s motion is considered to be induced from the base one due to the presence of general non-holonomic constraints. It is shown that the solution can be factorized into dynamical and geometrical parts. Moreover, under favorable kinematical circumstances, the dynamical part admits a further factorization since it can be reconstructed from an intermediate (body) momentum solution, yielding a reconstruction phase formula. Finally, we apply this results to the study of concrete mechanical systems. [Copyright &y& Elsevier]

Abstract: Let be a norm on . Averaging over all the choices of , we obtain an expression which is an unconditional norm on . Bourgain, Lindenstrauss and Milman [J. Bourgain, J. Lindenstrauss, V.D. Milman, Minkowski sums and symmetrizations, in: Geometric Aspects of Functional Analysis (1986/1987), Lecture Notes in Math., vol. 1317, Springer, Berlin, 1988, pp. 44–66] showed that, for a certain (large) constant , one may average over ηn (random) choices of and obtain a norm that is isomorphic to . We show that this is the case for any . [Copyright &y& Elsevier]

The article presents information on a simplified mathematical approach which is used to measure differentiation in mathematics. This approach uses a local maximal function developed and employed by researchers to deal with limit theorems in various mathematics setting. The principal device of this approach is to differentiate a local maximal function defined in terms of a finite Borel measure and Lebesgue measure. This approach has cut almost half the time spent by researchers in covering mathematical topics.

Abstract: In this paper we develop several algebraic structures on the simplicial cochains of a triangulated manifold and prove they converge to their differential-geometric analogues as the triangulation becomes small. The first such result is for a cochain cup product converging to the wedge product on differential forms. Moreover, we show any extension of this product to a -algebra also converges to the wedge product of forms. For cochains equipped with an inner product, we define a combinatorial star operator and show that for a certain cochain inner product this operator converges to the smooth Hodge star operator. [Copyright &y& Elsevier]

Abstract: We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial interpretation of these formulas in terms of certain abelian subalgebras of simple Lie algebras. [Copyright &y& Elsevier]

Abstract: We present a universal formula for the dimension of the Cartan powers of the adjoint representation of a complex simple Lie algebra (i.e., a universal formula for the Hilbert functions of homogeneous complex contact manifolds), as well as several other universal formulas. These formulas generalize formulas of Vogel and Deligne and are given in terms of rational functions where both the numerator and denominator decompose into products of linear factors with integer coefficients. We discuss consequences of the formulas including a relation with Scorza varieties. [Copyright &y& Elsevier]

Abstract: We obtain formulas for the first and second cohomology groups of a general current Lie algebra with coefficients in the “current” module, and apply them to compute structure functions for manifolds of loops with values in compact Hermitian symmetric spaces. [Copyright &y& Elsevier]

Using the Jordan algebras methods, specially the properties of Peirce decomposition and the Frobenius transformation, we compute the coefficients of the zeta functional equation, in the case of Jordan algebras of type II. As particular cases of our result, we can cite the case of V=M(n,R) studied by Gelbart [Mem. Amer. Math. Soc. 108 (1971)] and Godement and Jacquet [Zeta functions of simple algebras, Lecture Notes in Math., vol. 260, Springer-Verlag, Berlin, 1972], and the case of V=Herm(3,Os) studied by Muro [Adv. Stud. Pure Math. 15 (1989) 429]. Let us also mention, that recently, Bopp and Rubenthaler have obtained a more general result on the zeta functional equation by using methods based on the algebraic properties of regular graded algebras which are in one-to-one correspondence with simple Jordan algebras [Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces, IRMA, Strasbourg, 2003]. The method used in this paper is a direct application of specific properties of Jordan algebras of type II. [Copyright &y& Elsevier]

A four-dimensional integrable rigid-body system is considered and it is shown that it represents two twisted three-dimensional Lagrange tops. A polynomial Lax representation, which doesn't fit neither in Dubrovin's nor in Adler-van Moerbeke's picture is presented. The algebro-geometric integration procedure is based on deep facts from the geometry of the Prym varieties of double coverings of hyperelliptic curves: Mumford's relation and Mumford-Dalalyan theory. The correspondence between all such coverings with Prym varieties splitted as a sum of two varieties of the same dimension and the integrable hierarchy associated to the initial system is established. [ABSTRACT FROM AUTHOR]

We analyze the integral points on varieties defined by one equation of the form f1 … fr = g, where the fi , g are polynomials in n variables with algebraic coefficients, and g has "small" degree; we shall use a method that we recently introduced in the context of Siegel's Theorem for integral points on curves. Classical, very particular, instances of our equations arise, e.g., in a well-known corollary of Roth's Theorem (the case n = 2, fi linear forms, deg g < r - 2) and with the norm-form equations, treated by W. M. Schmidt. Here we shall prove (Thm. 1) that the integral points are not Zariski-dense, provided &Sum; deg fi > n · max ( degfi) + deg g and provided the fi, g, satisfy certain (mild) assumptions which are "generically" verified. Our conclusions also cover certain complete- intersection subvarieties of our hypersurface (Thm. 2). Finally, we shall prove (mm. 3) an analogue of the Schmidt's Subspace Theorem for arbitrary polynomials in place of linear forms. [ABSTRACT FROM AUTHOR]

Abstract: Periodicity questions of differential systems on infinite-dimensional Hilbert spaces arestudied via a new methodology which is based on Fan-Knaster-Kuratowski-Mazurkiewicz theorem. We obtain in this way an alternative, to the classical fixed point theory, approach to the study of such type of problems with various applications on issues of mathematical analysis and differential geometry. Two examples of such applications are included. [Copyright &y& Elsevier]

We study a longitudinal constant-speed impact against the end of a linearly elastic semi-infinite thread following the curvature of a fixed solid. The analytical solution found takes into account waves multiply reflected from the contact surface and the impact point. [ABSTRACT FROM AUTHOR]

The article offers an annotation to the mathematical congruence (mdnd) ≡ (mn) (modq). Mathematical problems that involve binomial coefficients modulo a prime power have been the focus of many great mathematicians of the 19th century. These mathematicians have derived different theorems that could be easily proved. One of these theorems is the congruence (mdnd) ≡ (mn) (modq). The author presented a partial converse theorem based on this established equation and observed that the same products of binomial coefficients are established on the right of Lucas's theorem.

The article presents the mathematical analysis of q-analogue of wolstenholme's harmonic series congruence. It is stated that congruence is considered over the ring of the polynomials in the variable q with integral coefficients.

Presents a mathematical proof that the difference between the lengths of two curves, which are not convex, at a fixed distance apart is constant. Establishment of the parameters of the curve; Simplification of the expression for the arclength of the outer curve; Use of Green's theorem in determining the distance between the curves.