In the present paper, we obtain an interesting subordination relation for a family of analytic functions of complex order by using subordination theorem.

It is well-known that the concept of Hyers-Ulam-Rassias stability originated by Th. M. Rassias (Proc. Amer. Math. Soc. 72(1978), 297-300) and the concept of Ulam-Gavruta-Rassias stability by J. M. Rassias (J. Funct. Anal. U.S.A. 46(1982), 126-130; Bull. Sc. Math. 108 (1984), 445-446; J. Approx. Th. 57 (1989), 268-273) and P. Gavruta (``An answer to a question of John M. Rassias concerning the stability of Cauchy equation", in: Advances in Equations and Inequalities, in: Hadronic Math. Ser. (1999), 67-71). In this paper we give results concerning these two stabilities.

The main purpose of this note is to present an alternative, more transparent treatment of the results obtained in [4], which link the epistasis of a function to its Walsh coefficients and its order.

We estimate the number of homotopy types of the gauge groups of $Sp(2)$ and $SU(3)$.

The aim of this paper is to develop an improved version of the Multi-Stage (MUSTA) approach to the construction of upwind fluxes that avoid the solution of the Riemann Problem (RP) in the conventional manner. We propose to use the second order TVD flux as a building block in the MUSTA scheme instead of the first order flux used in the original MUSTA. The numerical solution is advanced by TVD Runge-Kutta method. The new MUSTA scheme improves upon the original MUSTA and TVD schemes in terms of better convergence, higher overall accuracy, better resolution of discontinuities and find its justification when solving very complex systems for which the solution of the RP is costly or unknown. A way to extend this scheme to two dimensional systems of hyperbolic conservation laws is presented. In this paper we also extend the scheme in the framework of high order WENO methods. Numerical results suggest that our scheme is superior to the original schemes. This is specially so for long time evolution problems containing both smooth and non-smooth features.

New constructions of Sperner spaces using `generalized extended André spreads' are used to construct a wide variety of new subgeometry partitions of finite projective spaces.

D. K. Biss (Topology and its Applications 124 (2002) 355-371) introduced the topological fundamental group and presented some interesting basic properties of the notion. In this article we intend to extend the above notion to homotopy groups and try to prove some similar basic properties of the topological homotopy groups. We also study more on the topology of the topological homotopy groups in order to find necessary and sufficient conditions for which the topology is discrete. Moreover, we show that studying topological homotopy groups may be more useful than topological fundamental groups.

We construct metrizable simplices $X_1$ and $X_2$ and a homeomorphism $\varphi:\overline{ext X_1}\to\overline{ext X_2}$ such that $\varphi(ext X_1)=ext X_2$, the space $\mathfrak{A}(X_1)$ of all affine continuous functions on $X_1$ is complemented in $\mathcal C(X_1)$ and $\mathfrak{A}(X_2)$ is not complemented in any $\mathcal C(K)$ space. This shows that complementability of the space $\mathfrak{A}(X)$ cannot be determined by topological properties of the couple $(ext X,\overline{ext X})$.

In this note we study the geometry of drops in Banach spaces, and we use it to characterize two well known geometrical properties: rotundity and smoothness.

La stabilisation des systèmes couplés soumis à un seul feedback (stabilisation indirecte) a suscité l'intérêt de nombreux auteurs ces dernières années. Les résultats les plus récents dans cette direction sont ceux obtenus par F. Alabau-Boussouira [1] et F. Alabau-Boussouira, P. Cannarsa et V. Komornik [2] où des estimations polynomiales (dépendant de la régularité des solutions) ont été démontrées pour quelques systèmes hyperboliques linéaires faiblement couplés. L'objectif de ce papier est d'étendre ces résultats au cas de systèmes {\it non linéaires} ou {\it non dissipatifs} et de donner des applications à la stabilisation indirecte de certains systèmes couplés non dissipatifs.

Stabilization of coupled systems with only one feedback (indirect stabilization) was considered by many authors the last years. The most recent results in this direction were obtained by F. Alabau-Boussouira [1] and F. Alabau-Boussouira, P. Cannarsa et V. Komornik [2] where polynomial estimates (depending on the regularity of solutions) were proved for some weakly coupled linear hyperbolic systems. The main goal of this paper is to extend these results to the case of {\it nonlinear} or {\it non dissipative} systems and give applications to indirect stabilization of some nondissipative coupled systems.

We study the blow-up for the solution of a system of quasilinear hyperbolic equations involving the $p$-laplacian. We derive a differential inequality for a function involving some norms of the solution which yields the finite time blow-up.

We study a property of extension of partial isometries in a Banach space. This property is formulated in game-theoretic language. It is weaker than transitivity, self-dual for reflexive spaces and it is related to a well-known open problem in functional analysis and to model-theoretic notions from mathematical logic.

Fix a poset $\mathcal P$ and a natural number $n$. For various commutative local rings $\Lambda$, each of Loewy length $n$, consider the category $\textrm{sub}_\Lambda\mathcal P$ of $\Lambda$-linear submodule representations of $\mathcal P$. We give a criterion for when the underlying translation quiver of a connected component of the Auslander-Reiten quiver of $\sub_\Lambda\mathcal P$ is independent of the choice of the base ring $\Lambda$. If $\mathcal P$ is the one-point poset and $\Lambda=\mathbb Z/p^n$, then $\textrm{sub}_\Lambda\mathcal P$ consists of all pairs $(B;A)$ where $B$ is a finite abelian $p^n$-bounded group and $A\subset B$ a subgroup. We can respond to a remark by M.~C.~R. Butler concerning the first occurence of parametrized families of such subgroup embeddings.

The aim of this paper is to study the canonical partial metric associated to the norm of a normed space, whose related non-translation-invariant topology can be used to characterize the convexity properties of the original space. In order to do this, we define and characterize a new intermediate geometric property that we call continuous convexity, which appears in a natural way in the context of the canonical partial metric topology.

We show that the Generalized Hermite linear form $\mathcal{H}(\mu)$, which is symmetric $D$-semiclassical of class one, is the unique $\mathcal{D}_{\theta}$-Appell classical where $\mathcal{D}_{\theta}$ is the Dunkl operator.