The convergence properties of extended negatively dependent sequences under some conditions of uniform integrability are studied. Some sufficient conditions of the weak law of large numbers, the $p$-mean convergence and the complete convergence for extended negatively dependent sequences are obtained, which extend and enrich the known results in the literature.

A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we classify tetravalent symmetric graphs of order $9p$ for each prime $p$.

We study some anisotropic boundary value problems involving variable exponent growth conditions and we establish the existence and multiplicity of weak solutions by using as main argument critical point theory.

Let $p$ be an odd prime number and let F be a finite field with $p^m$ elements. We study representations and strict representations of polynomials $M{\in}F$[T] by sums of ($p^r$ + 1)-th powers. A representation $$M=M_1^k+{\cdots}+M_s^k$$ of $M{\in}F$[T] as a sum of $k$-th powers of polynomials is strict if $k$ deg $M_i<k$ + degM.

This paper examines a temperature dependent Stokes flow in a semi-infinite cylinder. Under appropriate initial and boundary conditions the author establishes exponential decay of solutions in energy norm with distance from the finite end of the cylinder.

A class of autonomous control systems with fixed unknown parameters is considered to be stabilized with respect to only a part of the variables. A certain type of such systems can be recursively adaptively partially stabilized. The bifurcation analysis reveals the nature of the closed loop system.

The classes of $G_C$ homological modules over commutative ring, where C is a semidualizing module, extend Holm and J${\varnothing}$gensen's notions of C-Gorenstein homological modules to the non-Noetherian setting and generalize the classical classes of homological modules and the classes of Gorenstein homological modules within this setting. On the other hand, transfer of homological properties along ring homomorphisms is already a classical field of study. Motivated by the ideas mentioned above, in this article we will investigate the transfer properties of C and $G_C$ homological dimension.

The membership of the generalized local cohomology modules $H_a^i$(M,N) of two R-modules M and N with respect to an ideal a in certain Serre subcategories of the category of modules is studied from below ($i<t$). Furthermore, the behaviour of the $n$th graded component $H_a^i(M,N)_n$ of the generalized local cohomology modules with respect to an ideal containing the irrelevant ideal as $n{\rightarrow}-{\infty}$ is investigated by using the above result, in certain graded situations.

We study the relation between an R-Cartan structure ${\alpha}$ an an (I, J, K)-generalized Finsler structure ${\omega}$ on a 3-manifold ${\Sigma}$ showing the difficulty in finding a general transformation that maps ${\alpha}$ to ${\omega}$. In some particular cases, the mapping can be uniquely determined by geometrical conditions. Moreover, we are led in this way to a negative answer to our conjecture in [12].

We consider a tournament T = (V,A). For each subset X of V is associated the subtournament T(X) = (X,$A{\cap}(X{\times}X)$) of T induced by X. We say that a tournament T' embeds into a tournament T when T' is isomorphic to a subtournament of T. Otherwise, we say that T omits T'. A subset X of V is a clan of T provided that for a, $b{\in}X$ and $x{\in}V{\backslash}X$, $(a,x){\in}A$ if and only if $(b,x){\in}A$. For example, ${\emptyset}$, $\{x\}(x{\in}V)$ and V are clans of T, called trivial clans. A tournament is indecomposable if all its clans are trivial. In 2003, B. J. Latka characterized the class ${\tau}$ of indecomposable tournaments omitting a certain tournament $W_5$ on 5 vertices. In the case of an indecomposable tournament T, we will study the set $W_5$(T) of vertices $x{\in}V$ for which there exists a subset X of V such that $x{\in}X$ and T(X) is isomorphic to $W_5$. We prove the following: for any indecomposable tournament T, if $T{\notin}{\tau}$, then ${\mid}W_5(T){\mid}{\geq}{\mid}V{\mid}$ -2 and ${\mid}W_5(T){\mid}{\geq}{\mid}V{\mid}$ -1 if ${\mid}V{\mid}$ is even. By giving examples, we also verify that this statement is optimal.

We prove the global regularity of weak solutions to a conormal derivative boundary value problem for quasilinear elliptic equations in divergence form on Lipschitz domains under the controlled growth conditions on the low order terms. The leading coefficients are in the class of BMO functions with small mean oscillations.

In this paper we study the unique solvability of backward stochastic Volterra integral equations (BSVIEs in short), in terms of both the adapted M-solutions introduced in [19] and the adapted solutions via a new method. A general existence and uniqueness of adapted M-solutions is proved under non-Lipschitz conditions by virtue of a briefer argument than the ones in [13] and [19], which modifies and extends the results in [13] and [19] respectively. For the adapted solutions, the unique solvability of BSVIEs under more general stochastic non-Lipschitz conditions is shown, which improves and generalizes the results in [7], [14] and [15].