‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

The endometrium is a highly dynamic tissue empowered with the capacity to undergo cyclic dramatic changes in response to ovarian steroid hormones, ultimately aiming to create a window of receptivity for blastocyst implantation. Intensive research has been performed to understand and establish morphological and molecular correlates of embryo implantation. However, it still remains a biological m...

Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...

We consider a generalization of heterogeneous meta-programs by (1) introducing an extra level of abstraction within the meta-program structure, and (2) meta-program transformations. We define basic terms, formalize transformation tasks, consider properties of meta-program transformations and rules to manage complexity through the following transformation processes: (1) reverse transformation, w...

Background: Surgery and accurate removal of the brain tumor in the operating room and after opening the scalp is one of the major challenges for neurosurgeons due to the removal of skull pressure and displacement and deformation of the brain tissue. This displacement of the brain changes the location of the tumor relative to the MR image taken preoperatively. Methods: This study, which is done...

This question has always been put forward in the mind of curious people why some countries have developed termed in spite of very few natural resources and facilities while other countries have not developed in spite of having more suitable resources and facilities. Various factors such as economy, culture, geography, etc. are perhaps a background to answer this question, but there is a more im...

for a graph $g$ with edge set $e(g)$, the multiplicative sum zagreb index of $g$ is defined as$pi^*(g)=pi_{uvin e(g)}[d_g(u)+d_g(v)]$, where $d_g(v)$ is the degree of vertex $v$ in $g$.in this paper, we first introduce some graph transformations that decreasethis index. in application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum zagreb ...

Model-to-model transformation is a key technology for the OMG’s Model Driven Architecture. The need for standardization in this area lead to the MOF 2.0 Query/Views/Transformations Request for Proposals (RFP) from the OMG. The RFP elicited eight separate submissions. This paper makes the following contributions: Terminology for queries, views, and transformations is introduced that is based on ...