In this dissertation, we first focus on the generalized Laplace transform on time scales. We prove several properties of the generalized exponential function which will allow us to explore some of the fundamental properties of the Laplace transform. We then give a description of the region in the complex plane for which the improper integral in the definition of the Laplace transform converges,...

Let $A$ be a $C^*$-algebra and $E$ be a left Hilbert $A$-module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$  is Arens regular. We also study the relationship between derivations of $A$ and $E$.

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

I discuss recent progress in developing and exploiting connections between SAT algorithms and circuit lower bounds. The centrepiece of the article is Williams’ proof that NEXP * ACC0, which proceeds via a new algorithm for ACC0-SAT beating brute-force search. His result exploits a formal connection from non-trivial SAT algorithms to circuit lower bounds. I also discuss various connections in th...

Introduction: The aim was to assess the effects on lifestyle and lipid profile while fasting during holy month of Ramadan. Material and Methods: An interventional cohort study designed with 160 subjects who were fasting during Ramadan recruited from different mosques in Kermanshah. Data were collected in three stages at the beginning and at the end of Ramadan as well as one month following Rama...

Background & Aim: Policosanol is a component from main alcohol groups with long-chain that extracted from cane sugar. In the present research, the effect of policosanol was investigated on decrease of lipid metabolite levels in blood of hypercholesterolemia rats. Experimental: A number of 32 male Wistar rats race with average weight of 250 g was divided into four groups including negative cont...

Regio and stereoselective addition of a phosphine-borane to alkynyl vinyl gold(i) complexes.