In this paper, we deal with the existence of subharmonic solutions for the $p(t)$-Laplacian Hamiltonian system. Some new existence theorems are obtained by using minimax methods in critical point theory, and our results generalize and improve some existence theorems.

Soient $G$ un groupe de Lie connexe et $ \pi$ une représentation unitaire de $G$ dans un espace de Hilbert ${\mathcal H}_{\pi}$ non séparable. Pour chaque ensemble infini $I$, on définit la représentation unitaire $\hat{\pi}_I=(\# I) \pi$ de $G$ dans l'espace ${\mathcal H}_{\hat{\pi}_I}=(\# I){\mathcal H}_{\pi}$. Alors, on montre que l'ensemble moment généralisé de $\hat{\pi}_I$ caractérise $\pi$ à quasi-équivalence près.

Let $G$ be a connected Lie group and $\pi$ a unitary representation of $G$ on a non separable Hilbert space ${\mathcal H}_\pi$. For any infinite set $I$, we define the representation $\hat{\pi}_I=(\# I) \pi$ of $G$ on ${\mathcal H}_{\hat{\pi}_I}=(\# I){\mathcal H}_{\pi}$. Then, we show that the generalized moment set of $\hat{\pi}_I$ characterize $\pi$ up to quasi-equivalence.

In this paper we deal with four generalized notions of amenability which are called approximate, approximate weak, approximate cyclic and approximate $n$-weak amenability. The first two were introduced and studied by Ghahramani and Loy in [9]. We introduce the third and fourth ones and we show by means of some examples, their distinction with their classic analogs. Our main result is that under some mild conditions on a given Banach algebra $\mathcal{A}$, if its second dual $\mathcal{A}^{**}$ is $(2n-1)$-weakly [respectively approximately/ approximately weakly/ approximately $n$-weakly] amenable, then so is $\mathcal{A}$. Also if $\mathcal{A}$ is approximately $(n+2)$-weakly amenable, then it is approximately $n$-weakly amenable. Moreover we show the relationship between approximate trace extension property and approximate weak [respectively cyclic] amenability. This answers question 9.1 of [9] for approximate weak and cyclic amenability.

In this paper, we introduce the notion of manifolds with isotropic cubic tensor. We give a complete classification of the Lagrangian submanifolds in 3-dimensional complex space forms with isotropic cubic tensor.

We give an existence result of the obstacle parabolic degenerate or singular problem associated to the equation, $\displaystyle\frac{\partial u}{\partial t} + A(u) = f$ in $Q_T,$ where $A$ is a classical Leray-Lions operator acting from the weighted Sobolev space $L^p(0,T,W_0^{1,p}(\Omega,w))$ into its dual $L^{p'}(0,T,W^{-1,p'}(\Omega,w^*))$, while the datum $f$ is assumed to lie in $L^1(Q_T)$. The proof is based on the penalization methods.

In this paper, we obtain the analytical solution for a strongly coupled reaction-diffusion system with initial condition by the Homotopy Analysis Method (HAM). The HAM allows for the solution of the strongly coupled reaction-diffusion system to be calculated in the form of an infinite series with components which can be easily calculated. The obtained results are presented and only a few terms are required to obtain an approximate solution that is accurate and efficient.

In this paper, easily verifiable conditions for the existence and global attraction of periodic solutions of n-dimension nonautonomous discrete-time neural networks with time-varying delays are established by using the well--known Gaines--Mawhin theorem and some analysis techniques. These results obtained are more generalizable than the previously known results. Moreover, an example is provided to illustrate the validity of our results.

Let $X$ be a simply connected CW complex with finite rational cohomology. For the finite quotient set of rationalized orbit spaces of $X$ obtained by almost free toral actions, ${\mathcal T}_0(X) =\{[Y_i] \}$, induced by an equivalence relation based on rational toral ranks, we order as $[Y_i]<[Y_j]$ if there is a rationalized Borel fibration $Y_i\to Y_j\to BT^n_{\Q}$ for some $n>0$. It presents a variation of almost free toral actions on $X$. We consider about the Hasse diagram ${\mathcal H}(X)$ of the poset ${\mathcal T}_0(X)$, which makes a based graph $G{\mathcal H}(X)$, with some examples. Finally we will try to regard $G{\mathcal H}(X)$ as the 1-skeleton of a finite CW complex ${\mathcal T}(X)$ with base point $X_{\Q}$.

The standard Clifford torus is characterized as the only connected compact orientable affine Lagrangian surface in $\mathbb C ^2$ whose second fundamental tensor is parallel.

The paper deals with infinite weakly coupled systems of quasilinear parabolic differential functional equations. Initial boundary conditions of the Robin type are considered. We construct an explicit Euler type approximation method based on an infinite system of difference functional equations. Next we apply the truncation method to obtain a finite difference scheme corresponding to the original differential problem. We present a complete convergence analysis for the methods. The results are based on a comparison technique with nonlinear estimates of the Perron type for given functions.

In this paper, under an appropriated restriction on the Gauss map, we obtain an extension of the Xin-Aiyama theorem concerning to complete spacelike hypersurfaces immersed with bounded mean curvature in the Minkowski space.

We prove that continuous linear decomposition operators exist on the space $A(J)$ of real analytic germs and on the space $A(I)$ of real analytic functions where $J$ is a compact interval (and $I$ is an open interval). We then characterize when $A(J)$ and $A(I)$ contain the space $A_{per}(\mathbb{R})$ of $2\pi-$periodic real analytic functions as a complemented subspace. As a further application we present new formulas for continuous linear right inverses for convolution operators on real analytic functions.

We study the behaviors of one turn pushdown automata using the notions of fairness defined by L. Priese et al. in [10], as conditions of acceptance. We show in particular that these notions are simulable by the modes of acceptance of J. R. Buchi and D. Muller.

On s'intéresse dans ce papier au comportements des automates à pic en utilisant les notions d'équités définies par L. Priese et al. dans [10] . On montre en particulier que ces notions d'équités sont simulables par les conditions d'acceptance de J. R. Buchi et D. Muller sur les systèmes à pic. Pour l'équité définie sur les grammaires algébriques par N. Francez et al. dans [3], on montre que cette notion d'équité ne peut être équivalente à ces conditions d'acceptations.

The \emph{rank of apparition} of a prime $q$ in a given Lehmer sequence is the index of the first term in which $q$ occurs as a divisor. Furthermore, $q$ is said to have \emph{maximal rank of apparition} in an underlying Lehmer sequence provided that its rank of apparition is $q \pm 1$. Letting $p$ be a prime, in this paper we identify all primes of the form $2^{\alpha}p \pm 1$ that have maximal rank of apparition in the noted sequences.