In this paper we describe the proof of ’Riesz Theorems’ in 2inner product spaces. The main result holds only for a b-linear functional but not for a bilinear functional. AMS Mathematics Subject Classification (2010): 41A65, 41A15

The classification of the invariant subspaces of an endomorphism has been an open problem for a long time, and it is a ”wild” problem in the general case. Here we obtain a full classification for the monogenic ones. Some applications are derived: in particular, canonical forms for uniparametric linear control systems, non necessarily controllable, with regard to linear changes of state variable...

Let Zt be a one-dimensional symmetric stable process of order α with α ∈ (0, 2) and consider the stochastic differential equation dXt = φ(Xt−)dZt. For β < 1 α ∧ 1, we show there exists a function φ that is bounded above and below by positive constants and which is Hölder continuous of order β but for which pathwise uniqueness of the stochastic differential equation does not hold. This result is...

In this paper, a Gröbner-Shirshov basis for the Chinese monoid is obtained and an algorithm for the normal form of the Chinese monoid is given. AMS Mathematics Subject Classification (2000): 16S15, 16S35, 20M25.

We review some aspects of the geometry of length spaces and metric spaces, in particular Alexandrov spaces with curvature bounded below and/or above. We then point out some possible directions of research to explore connections between the synthetic approach to Riemannian geometry and some aspects of the approach to non-smooth differential geometry through generalised functions. AMS Mathematics...

This paper presents criteria for the existence and uniqueness of solutions to five-point boundary value problems associated with third order differential equations by using matching technique. ’Liapunov-like’ functions are used as a tool to establish existence and uniqueness of solutions by matching two three-point boundary value problems. AMS Mathematics Subject Classification (2000): 34B10, 3...

In this paper, we investigate the generalized Hyers-Ulam stability of a bi-reciiprocal functional equation in quasi-β-normed spaces. AMS Mathematics Subject Classification (2010): 39B82, 39B72

The purpose of the present paper is to investigate some interesting properties on generalized convolutions of functions for the classes HP ∗(α),HS(α) andHC(α). Further, an application of the convolution on certain integral operator are mentioned. AMS 2010 Mathematics Subject Classification : 30C45, 26D15.

In this paper, we consider the problem of the farthest poinst for bounded sets in a real 2-normed spaces. We investigate some properties of farthest points in the setting of 2-normalised spaces and present various characterizations of b-farthest point of elements by bounded sets in terms of b-linear functional. We also provide some applications of farthest points in the setting of 2inner produc...

We introduce the concept of "uniformly primary submodules" of a module over a commutative ring R, which generalizes the concept of "uniformly primary ideals" of R, a concept that imposes a certain boundedness condition on the usual notion of "primary ideal". Several results on uniformly primary submodules are proved. Also, we characterize uniformly primary submodules of a multiplication module....