This paper is devoted to present a numerical methods for a model of incompressible and miscible flow in porous media. We analyze a numerical scheme combining a mixed finite element method (MFE) and finite volume scheme (FV) for solving a coupled system includes an elliptic equation (pressure and velocity) and a linear convection-diffusion equation (concentration). The (FV) scheme considered is "vertex centered" type semi implicit. We show that this scheme is $L^{\infty}$, BV stable under a CFL condition and satisfies a discrete maximum principle. We prove also the convergence of the approximate solution obtained by the combined scheme (MFE)-(FV) to the solution of the coupled system. Finally the numerical results are presented for two spaces dimensions problem in a homogenous isotropic medium.

We study the Cauchy problem for the damped Kirchhoff equation in the phase space $\, H^{r}\times H^{r-1}$, with $r\ge{3/ 2}$. We prove global solvability and decay of solutions when the initial data belong to an open, dense subset $B$ of the phase space such that $B+B= H^{r} \times H^{r-1}$.

We investigate the initial value problem for a semi-linear Schrödinger equation with exponential-growth nonlinearity. We establish global well-posedness and scattering in the energy space.

It is shown that the commutative binary Knuth semifield planes of order $2^{n}$, for $n=5k~$\ or $7k$ and $k$ odd, their transposes and transpose-duals admit subplanes of order $2^{2}$. In addition, many of the Kantor commutative semifield planes of order $2^{5k}$ or $2^{7k}$ also admit subplanes of order $4$. Furthermore, a large number of maximal partial spreads of order $p^{k}$ and deficiency at least $p^{k}-p^{k-1}$ or translation planes of order $p^{k}$ are constructed using direct sums of matrix spreads sets of different dimensions. Given any translation plane $\pi_{0}$ of order $p^{d}$, there is either a proper maximal partial spread of order $p^{c+d}$ whose associated translation net contains a subplane of order $p^{d}$ isomorphic to $\pi_{0}$ or there is a translation plane of order $p^{c+d}$ admitting a subplane of order $p^{d}$. Other than the semifield planes mentioned above and a few sporadic planes of even order, there are no other known translation planes of order $p^{c+d}$ admitting a subplane of order $p^{d}$, where $d$ does not divide $c$.

In this paper we construct a formula $\varphi(x,a)$ on the language of set theory $\mathcal{L}\mathbin{:}(\in,=)$ such that $\{x\ | \ \varphi(x,a)\}$ is a proper class for each element $a$ and such that if $a\neq a'$, the classes $\{x\ | \ \varphi(x,a)\}$ and $\{x\ | \ \varphi(x,a')\}$ are different. This formula works for any structure with the exception of 2 structures with two elements each. This formula ``maps'' elements to proper classes injectively.

In this note we consider homomorphisms between differentiable Lipschitz algebras $Lip^n(X,\alpha)$ ($0<\alpha \leq 1$) and $lip^n(X,\alpha)$ ($0<\alpha <1$), where $X$ is a perfect compact plane set. We give sufficient conditions implying the compactness and power compactness of these homomorphisms. Moreover, we investigate under what conditions a quasicompact homomorphism between these algebras is power compact. We also give a necessary condition for a homomorphism between these algebras to be quasicompact and in certain cases to be power compact. Finally, using these results, by giving an example we show that there exists a quasicompact homomorphism between these algebras which is not power compact.

On an odd dimensional manifold, we define a structure which generalizes several known structures on almost contact manifolds, namely Sasakian, trans-Sasakian, quasi-Sasakian, Kenmotsu and cosymplectic structures. This structure, hereinafter called a G.Q.S. manifold, is defined on an almost contact metric manifold and satisfies an additional condition (1.5). We then consider a codimension-one distribution on a G.Q.S. manifold. Necessary and sufficient conditions for the normality of the complemented framed structure on the distribution defined on a G.Q.S manifold are studied (Th. 3.2). The existence of the foliation on G.Q.S. manifolds and of bundle-like metrics are also proven. It is shown that under certain circumstances a new foliation arises and its properties are investigated. Some examples illustrating these results are given in the final part of this paper.

In this paper we study analytic sets extending the graph of proper holomorphic mappings. As applications, we present some results on the local holomorphic extension of proper holomorphic mappings between certain algebraic domains in ${\mathbb C}^n$, not necessarily bounded. Further supplementary results are obtained.

In this article we prove existence and approximation results for convolution equations on the spaces of $\left( s;\left( r,q\right) \right) $-quasi-nuclear mappings of a given type and order on a Banach space $E$. As special case this yields results for partial differential equations with constant coefficients for entire functions on finite-dimensional complex Banach spaces. We also prove division theorems for $\left( s;m\left( r,q\right) \right) $-summing functions of a given type and order, that are essential to prove the existence and approximation results.

We show that there exists an uncountably generated algebra every non-zero element of which is an everywhere surjective function on $\mathbb{C}$, that is, a function $f : \mathbb{C} \rightarrow \mathbb{C}$ such that, for every non void open set $U \subset \mathbb{C}$, $f(U) = \mathbb{C}$.