Issue 3, Volume 38, September 2013

2013

1. On a conjecture by Pierre Cartier about a group of associators V. Hoang Ngoc Minh PDF

   ▸ Abstract

   In Cartier (Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents. Sém. BOURBAKI, 53ème 2000–2001, no. 885), Pierre Cartier conjectured that for any non-commutative formal power series $\Phi$ on $X=\{x_0,x_1\}$ with coefficients in a $\mathbb Q$-extension, $A$, subjected to some suitable conditions, there exists a unique algebra homomorphism $\varphi$ from the $\mathbb Q$-algebra generated by the convergent polyzetas to $A$ such that $\Phi$ is computed from the $\Phi_{KZ}$ Drinfel’d associator by applying $\varphi$ to each coefficient. We prove that $\varphi$ exists and that it is a free Lie exponential map over $X$. Moreover, we give a complete description of the kernel of $\zeta$ and draw some consequences about the arithmetical nature of the Euler constant and about an algebraic structure of the polyzetas.

   339-398
2. On initial and boundary value problems for implicit dynamic equations on time scales Nguyen Chi Liem PDF

   ▸ Abstract

   This paper is concerned with the index concept, the unique solvability of the initial value problem, the two point boundary-value problem and Green’s function for a class of linear implicit dynamic equations with index-1 on time scales. The results are a generalization of the previous ones for differential and difference-algebraic equations.

   399-412
3. Existence and finite time approximation of strong solutions to 2D $g$-Navier–Stokes equations Cung The Anh , Dao Trong Quyet , Dao Thanh Tinh PDF

   ▸ Abstract

   onsidered here is the first initial boundary value problem for the two-dimensional g-Navier–Stokes equations in bounded domains. We first prove the existence and uniqueness of strong solutions to the problem by using the Faedo–Galerkin method. Then we study the finite time numerical approximation of the strong solutions by discretization schemes.

   413-428
4. Reverses of the Jensen inequality in terms of first derivative and applications S. S. Dragomir PDF

   ▸ Abstract

   Two new reverses of the celebrated Jensen integral inequality for convex functions with applications for means, the Hölder inequality and $f$-divergence measures in information theory are given.

   429-446
5. On the existence of solutions to Pareto quasivariational inclusion problems of type I Bui The Hung PDF

   ▸ Abstract

   In this paper, we apply a version of Kakutani’s fixed point theorem to study Pareto quasivariational inclusion problems. Some sufficient conditions on the existence of solutions to Pareto quasivariational inclusion problems with multivalued mappings are given. As special cases, we obtain several results on the existence of solutions to Pareto quasi-equilibrium problems.

   447-459
6. Positive periodic solutions of discrete Lotka–Volterra cooperative systems with delays Trinh Tuan Anh PDF

   ▸ Abstract

   The existence of positive periodic solutions of discrete nonautonomous Lotka–Volterra cooperative systems with delays is studied by applying the continuation theorem of coincidence degree theory.

   461-470
7. Lacunary statistical convergence of double sequences and some inclusion results in $n$-normed spaces Bipan Hazarika , Ekrem Savas PDF

   ▸ Abstract

   In this paper, we introduce the concept of lacunary statistical convergence of double sequences in $n$-normed spaces. Some inclusion relations between the sets of statistically convergent and lacunary statistically convergent cases of double sequences are established. In addition, we also define lacunary statistical Cauchy double sequences and prove that this notion is equivalent to the lacunary statistical convergence of double sequences.

   471-485