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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.

###### 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.

###### 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.

###### 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 *L ^{p}*-sense is

*W*

^{2}

*-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].*

^{,p}###### 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 ℂ* ^{n}* based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces

###### 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.

######
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.

###### 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.

###### 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 = {δ_{n}}gn∈N of A is automatically an additive higher derivation on A. Moreover, D = {δ_{n}}gn∈N is an inner *-higher derivation.

###### 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 ℚ_{p} are strong self-similar in the sense of IFS.