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Approach of q-Derivative Operators to Terminating q-Series Formulae

Abstract

The q-derivative operator approach is illustrated by reviewing several typical summation formulae of terminating basic hypergeometric series.

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Geometry of Mus-Sasaki metric

Abstract

In this paper, we introduce the Mus-Sasaki metric on the tangent bundle T M as a new natural metric non-rigid on T M. First we investigate the geometry of the Mus-Sasakian metrics and we characterize the sectional curvature and the scalar curvature.

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A new class of almost complex structures on tangent bundle of a Riemannian manifold

Abstract

In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced (0, 2)-tensor on the tangent bundle using these structures and Liouville 1-form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

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New stability results for spheres and Wulff shapes

Abstract

We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the Lp-sense is W 2 ,p-close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [10] and [11].

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On some extremal problems in Bergman spaces in weakly pseudoconvex domains

Abstract

We consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂn based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces Aαp in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.

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A sequence adapted from the movement of the center of mass of two planets in solar system

Abstract

In this paper we derive a sequence from a movement of center of mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.

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A Study on ϕ-recurrence τ-curvature tensor in (k, µ)-contact metric manifolds

Abstract

In this paper we study ϕ-recurrence τ -curvature tensor in (k, µ)-contact metric manifolds.

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Area Nevanlinna Type Classes of Analytic Functions in the Unit Disk and Related Spaces

Abstract

The survey collects many recent advances on area Nevanlinna type classes and related spaces of analytic functions in the unit disk concern- ing zero sets and factorization representations of these classes and discusses approaches, used in proofs of these results.

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Nonlinear *-Lie Higher Derivations of Standard Operator Algebras

Abstract

Let ℌ be an in finite-dimensional complex Hilbert space and A be a standard operator algebra on ℌ which is closed under the adjoint operation. It is shown that every nonlinear *-Lie higher derivation D = {δn}gn∈N of A is automatically an additive higher derivation on A. Moreover, D = {δn}gn∈N is an inner *-higher derivation.

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On Self-Similar Subgroups in the Sense of IFS

Abstract

In this paper, we first give several properties with respect to subgroups of self-similar groups in the sense of iterate function system (IFS). We then prove that some subgroups of p-adic numbers ℚp are strong self-similar in the sense of IFS.

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