It has been suggested that primary afferent C-fibres that respond to innocuous tactile stimuli are important in the sensation of pleasurable touch. Although it is known that C-tactile fibres terminate in the substantia gelatinosa (lamina II) of the spinal cord, virtually all of the neurons in this region are interneurons, and currently it is not known how impulses in C-mechanoreceptors are tran...

Graded ditopological texture spaces have been presented and discussed in categorical aspects by Lawrence M. Brown and Alexander {v S}ostak in cite{BS}. In this paper, the authors generalize the structure of diuniformity in ditopological texture spaces defined in cite{OB} to the graded ditopological texture spaces and investigate graded ditopologies generated by graded diuniformities. The autors...

A direct algorithm for evaluating hypersingular integrals arising in a three-dimensional Galerkin boundary integral analysis is presented. The singular integrals are defined as limits to the boundary, and by integrating two of the four dimensions analytically, the coincident integral is shown to be divergent. However, the divergent terms can be explicitly calculated and shown to cancel with cor...

Hidden-variable resultant methods are a class of algorithms for solving multidimensional polynomial rootfinding problems. In two dimensions, when significant care is taken, they are competitive practical rootfinders. However, in higher dimensions they are known to miss zeros, calculate roots to low precision, and introduce spurious solutions. We show that the hidden-variable resultant method ba...

Recently a new algorithm for reverse engineering of biochemical networks was developed by Laubenbacher and Stigler. It is based on methods from computational algebra and finds most parsimonious models for a given data set. We derive mathematically rigorous estimates for the expected amount of data needed by this algorithm to find the correct model. In particular, we demonstrate that for one typ...

This article evolves an analytical theory of nonuniform PN-junctions by employing the transverse averaging technique (TAT) to reduce the three-dimensional semiconductor equations to the quasione-dimensional (quasi-1D) form involving all physical quantities as averaged over the longitudinallyvarying cross section S(z). Solution of the quasi-1D Poisson’s equation shows that, besides the usual dep...

In order to study the effects of recycled aggregate with different particle gradations and contents on mechanical properties cement soil modified by nano-MgO, unconfined compressive strength scanning electron microscope (SEM) tests were carried out. The content was fixed at 15% nano-MgO 1.5%. two ages, three contents, considered. test results show that natural graded (RA), coarse (SRA), fine (T...

for an $n$-gon with vertices at points $1,2,cdots,n$, the betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. in this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and betti numbers of the $s$-module $s/i$ where  $s=k[x_{1},cdots, x_{n}]$ and $i$ is the associated ideal to ...

Let $G$ be an abelian group with identity $e$. $R$ a $G$-graded commutative ring identity, $M$ graded $R$-module and $S\subseteq h(R)$ multiplicatively closed subset of $R$. In this paper, we introduce the concept $S$-prime submodules modules over rings. We investigate some properties class their homogeneous components. $N$ submodule such that $(N:_{R}M)\cap S=\emptyset $. say is \textit{a }$S$...