In this paper we pose the $\infty$-Laplace Equation as a Dirichlet Problem in class of Grushin-type spaces whose vector fields are form \begin{equation*} X_k(p):=\sigma_k(p)\frac{\partial}{\partial x_k} \end{equation*} and $\sigma_k$ is not polynomial for indices $m+1 \leq k n$. Solutions to $\infty$-Laplacian viscosity sense have been shown exist be unique [3], when polynomial; extend these re...

The objective of our paper is to start the theoretical investigation of the most commonly used mathematical model for natural convection in a horizontal annulus. First, one shows existence of solutions for the unsteady problem. Then, for any Prandtl number and inverse relative gap width, existence and stability of a steady solution is proved, provided that the Rayleigh number is sufficiently sm...

We prove the existence of many different symmetry types of relative equilibria for systems of identical point vortices on a non-rotating sphere. The proofs use the rotational symmetry group SO(3) and the resulting conservation laws, the time-reversing reflectional symmetries in O(3), and the finite symmetry group of permutations of identical vortices. Results include both global existence theor...

Recognizing the link between “Cognition" and "Architectural Creation” indicates that there is a relation between subject and object. Correct understanding of this relationship helps artistic creativity, especially in the architecture, to take steps towards proving truth that have caused works to be continued over the past times. Knowledge and cognitions in architecture are categories that today...

Strong difference families are an interesting class of discrete structures which can be used to derive relative difference families. Relative difference families are closely related to 2-designs, and have applications in constructions for many significant codes, such as optical orthogonal codes and optical orthogonal signature pattern codes. In this paper, with a careful use of cyclotomic condi...

the objective of this study was to compare an indirect elisa, based on a purified 60 kda envelope glycoprotein (gp51su), with a pourquire indirect elisa for the detection of antibodies to the bovine leukemia virus. for conducting this research, 340 serum samples were collected from two different breeds of cows (sarabi and holestin) in different herds. commercial elisa revealed positive results ...