this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

Introduction: Single isocentre half-beam block (HBB) technique permits the avoidance of hot and cold spots. This technique is very useful in sparing the underlying ipsilateral lung and heart, if the left breast is treated. The major advantage of this technique is that it facilitates the complete sparing of both contralateral breast and lung. Regarding this, the present study aimed to analyse th...

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.

In this paper, for the first time, a comprehensive experimental study is performed on hydroforming process of metallic bellows. For this purpose, the effects of the main process parameters and their interactions on the characteristics of hydroformed metallic bellows are investigated using Response Surface Methodology (RSM). The selected parameters as input variables are internal pressure, die s...

In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions  for a weighted Lebesgue space  $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$.  Among the other things, we also show that if $K$ is a locally compact hyper...

We define a Fourier transform and a convolution product for functions and distributions on Heisenberg–Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for the left regular representation. We generalize various classical theorems, including the Paley–Wiener–Schwartz theorem, and define a convolution Banach algebra.

BACKGROUND AND PURPOSE Prefrontal cortex, known to be a crucial region for the function of attention, is generally thought to be largely associated with the pathogenesis of attention-deficit hyperactivity disorder (ADHD). Most previous structural imaging studies of ADHD reported abnormality of grey matter volume in prefrontal region. However, volume measure is affected by the size of the interr...

introduction radiotherapy with small fields is used widely in newly developed techniques. additionally, dose calculation accuracy of treatment planning systems in small fields plays a crucial role in treatment outcome. in the present study, dose calculation accuracy of two commercial treatment planning systems was evaluated against monte carlo method. materials and methods siemens once or linea...

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.