The weighted semigroup algebra Mb (S, w) is studied via its identification with Mb (S) together with a weighted algebra product *w so that (Mb (S, w), *) is isometrically isomorphic to (Mb (S), *w). This identification enables us to study the relation between regularity and amenability of Mb (S, w) and Mb (S), and improve some old results from discrete to general case.

Let G be a locally compact Hausdorff topological group and H be a compact subgroup of G. Then, the homogeneous space G/H possesses a specific Radon measure, which is called a relatively invariant measure. We show that the concepts of Convolution and involution can be extended to the integrable functions defined on this homogeneous space. We study the properties of Convolution and prove that the space of integrable functions is an involutive Banach algebra with an approximate identity. We also find a necessary and sufficient condition on a closed subspace of this Banach algebra to make it a left ideal.

We show that the second-order Hochschild cohomology groups of measure algebra M(G) and group algebra L-1(G) with coefficients in C-phi are Banach spaces where G is a locally compact group and phi is the augmentation character. 

Let G be a locally compact group or a discrete group and let w be a weight function on G. We define a new Convolution on the Beurling algebra L1(G, w) and show that it is also a Banach algebra with this new Convolution. We show that there is a one to one correspondence between the unitary representations of G and the non-degenerate ?-representations of L1(G, w). We show that L1(G, w) is amenable if and only if G is amenable. This improves earlier results which require w to be diagonally bounded.

In this paper, seepage analysis in isotropic environment is presented by discrete singular Convolution (DSC) method. This method has been used for solving numerical problems since 1999. The theoretical basis of the method is distribution and wavelet theory. DSC exhibits accuracy for integration of global methods and flexibility for handling complex geometries and boundary conditions of local methods. At first, a simple case governed by Laplace equation and regularized Shannon’s kernel is considered to show the accuracy and efficiency of DSC method through L? and L2 errors. Seepage under concrete dam with or without sheet-pile is then solved through two different case studies. The results of this method against finite difference results are considered. The results show that this method is more accurate than finite difference method with reception of more operation value and optimization of R parameter.

Background: This study measured socioeconomic inequalities in different types of disabilities in Iran. We also examined the prevalence of disabilities across different socio-demographic groups in Iran in 2011. Methods: This was cross-sectional study using secondary data analysis on all Iranian. Data related to disability prevalence and socioeconomic status (SES) of each province was extracted from the 2011 National Census of Population and Housing (NCPH) and the 2011 Households Income and Expenditure Survey (HIES), con-ducted by Statistical Center of Iran (SCI). The concentration index and concentration curve were used to measure and illustrate socioeconomic inequalities in different types of disabilities. Chi-squared test was also used to examine the relationship between the socio-demographic variables (age-groups, sex, education level, employment status) and disability. Results: The results suggested the existence of socioeconomic inequalities in blindness, deafness, vocal disor-ders and hand disorders in Iran. The concentration index for these four disabilities were-0. 0527 (95% confi-dence interval [CI]:-0. 0881,-0. 0173),-0. 0451 (CI:-0. 0747,-0. 0156),-0. 0663 (CI:-0. 1043,-0. 0282) and-0. 0545 (CI:-0. 0940,-0. 0151), respectively. There were also significant associations between the demographic variables such as age-groups, sex, education level, employment status and disability (P<0. 05). Conclusion: There were significant socioeconomic inequalities in different types of disabilities in Iran with poorer provinces having higher prevalence of disabilities in blindness, deafness, vocal disorders and hand dis-orders. Strategies to address the higher prevalence of different types of disabilities among poorer provinces should be considered a priority in Iran.

In this paper, we introduce a Convolution-type product for  strongly integrable Hilbert $C^*$-module valued maps on locally compact groups. We investigate various properties of this product related to uniform continuity, boundless, etc. For instance, we prove a Convolution theorem. Also, we study the boundless of the  related Convolution operator in various settings.