G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first generalize the concept of g-frames to Hilbert modules over pro-C*-algebras. Then, we introduce the g-frame operators in such spaces and show that they sha...

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions, for which a dual extremal function exists in terms of the existence of a maximizing vector of the corresponding Hankel operator and in terms of certain spec...

Closed-form reliability functions for the wellknown dual homing configuration for the Fiber Distributed Data Interface (FDDI) are derived. The new reliability functions are then compared to that of the dual ring configuration, which again show that the dual homing network is often more reliable than the dual ring network; however, the model analysis also shows that dual homing is recommended on...

A highly efficient and simple method for the preparation of α,α´-bis(arylidene)cycloalkanones under solvent-free conditions has been developed. The crossed-aldol condensation of cycloalkanones (1 eq.) with arylaldehydes (2 eq.) in the presence of 2.5 mol% of ionic liquid 1,3-disulfonic acid imidazolium hydrogen sulfate {[Dsim]HSO4} afforded the title compounds in high yields and short reaction ...

we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...