<abstract xmlns="http://www.w3.org/1999/xhtml">

 In this paper a remarkable simple proof of the Gauss’s generalization of the Wilson’s theorem is given. The proof is based on properties of a subgroup generated by element of order 2 of a finite abelian group. Some conditions equivalent to the cyclicity of (Φ(n), ·n), where n > 2 is an integer are presented, in particular, a condition for the existence of the unique element of order 2 in such a group. 
</abstract>

Simple proofs of some generalizations of the Wilson’s theorem

<abstract xmlns="http://www.w3.org/1999/xhtml">

It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.
</abstract>

Perturbation of Toeplitz operators and reflexivity

<abstract xmlns="http://www.w3.org/1999/xhtml">

For every two-dimensional manifold M with locally symmetric linear connection ∇, endowed also with ∇-parallel volume element, we construct a flat connection on some principal fibre bundle P(M,G). Associated with - satisfying some particular conditions - local basis of TM local connection form of such a connection is an R(G)-valued 1-form build from the dual basis ω1, ω2 and from the local connection form ω of ▽. The structural equations of (M,∇) are equivalent to the condition dΩ-Ω∧Ω=0. 
This work was intended as an attempt to describe in a unified way the construction of similar 1-forms known for constant Gauss curvature surfaces, in particular of that given by R. Sasaki for pseudospherical surfaces. 
</abstract>

On some flat connection associated with locally symmetric surface

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper we study approximation properties of partial modified Szasz-Mirakyan operators for functions from exponential weight spaces. We present some direct theorems giving the degree of approximation for these operators. The considered version of Szász-Mirakyan operators is more useful from the computational point of view.
</abstract>

A note on the convergence of partial Szász-Mirakyan type operators

<abstract xmlns="http://www.w3.org/1999/xhtml">

 Recently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| &lt; 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities for the function ƒ ∈ T Sξ(α, β,γ). 
</abstract>

Starlike functions of complex order involving q-hypergeometric functions with fixed point

<abstract xmlns="http://www.w3.org/1999/xhtml">

 In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) (X, δX) and (Y, δY ) with nonempty intersection and we wonder whether there is a natural way to glue them so that the new glued diversity (or metric space) remains being hyperconvex. We provide positive and negative answers in both situations. 
</abstract>

On the gluing of hyperconvex metrics and diversities

<abstract xmlns="http://www.w3.org/1999/xhtml">

The purpose of the present paper is to study generalized M-projectively recurrent manifolds. Some geometric properties of generalized M projectively recurrent manifolds have been studied under certain curvature conditions. An application of such a manifold in the theory of relativity has also been shown. Finally, we give an example of a generalized M-projectively recurrent manifold.
</abstract>

Department of Pure Mathematics University of Calcutta 35, Ballygaunge Circular Road Kolkata 700019 West Bengal India

Chakdaha Co-operative Colony Vidyayatan (H.S) P.O.- Chakdaha Dist- Nadia West Bengal India

On generalized M-projectively recurrent manifolds

<abstract xmlns="http://www.w3.org/1999/xhtml">

We give an elementary and self-contained proof of the theorem which says that for a semiprime ring commutativity, Lie-nilpotency, and nilpotency of the Lie ring of inner derivations are equivalent conditions
</abstract>

Semiprime rings with nilpotent Lie ring of inner derivations

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.
</abstract>

First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

<abstract xmlns="http://www.w3.org/1999/xhtml">

A new proof of the Ficken criterion is given together with a comment concerning the known proofs and related results
</abstract>

À la recherche de la preuve perdue: a simple proof of the Ficken theorem

Conference on Ulam’s Type Stability Rytro, Poland, June 2-6, 2014

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