After studying in a previous work the smoothness of the space U_{\Gamma _0 } = \{ u \in W^{1,p( \cdot )} (\Omega );u = 0on\Gamma _0 \subset \Gamma = \partial \Omega \} , where dΓ − measΓ0 > 0, with p(·) ∈ \mathcal{C}(\bar \Omega ) and p(x) > 1 for all x ∈ \bar \Omega , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space. The results obtained in this direction are used for proving existence results for operator equations having the form J φ u = N, where J φ is a duality mapping on U_{\Gamma _0 } corresponding to the gauge function φ, and N f is the Nemytskij operator generated by a Carathéodory function f satisfying an appropriate growth condition ensuring that N f may be viewed as acting from U_{\Gamma _0 } into its dual.
The authors introduce a new Large Eddy Simulation model in a channel, based on the projection on finite element spaces as filtering operation in its variational form, for a given triangulation {T h} h>0. The eddy viscosity is expressed in terms of the friction velocity in the boundary layer due to the wall, and is of a standard sub grid-model form outside the boundary layer. The mixing length scale is locally equal to the grid size. The computational domain is the channel without the linear sub-layer of the boundary layer. The no-slip boundary condition (or BC for short) is replaced by a Navier (BC) at the computational wall. Considering the steady state case, the authors show that the variational finite element model they have introduced, has a solution (v h, p h) h>0 that converges to a solution of the steady state Navier-Stokes equation with Navier BC.
The authors give an upper bound of the essential norms of composition operators between Hardy spaces of the unit ball in terms of the counting function in the higher dimensional value distribution theory defined by Professor S. S. Chern. The sufficient condition for such operators to be bounded or compact is also given.
The existence of classical solutions to a stationary simplified quantum energy-transport model for semiconductor devices in 1-dimensional space is proved. The model consists of a nonlinear elliptic third-order equation for the electron density, including a temperature derivative, an elliptic nonlinear heat equation for the electron temperature, and the Poisson equation for the electric potential. The proof is based on an exponential variable transformation and the Leray-Schauder fixed-point theorem.
In this paper the author gives a method of constructing characteristic matrices, and uses it to determine the Buchstaber invariants of all simple convex 3-polytopes, which imply that each simple convex 3-polytope admits a characteristic function. As a further application of the method, the author also gives a simple new proof of five-color theorem.
Let l be a given nonzero integer. The authors give an explicit characterization of the positive integer k that makes the Diophantine equation x 2 − kxy + y 2 +lx = 0 have infinitely many positive integer solutions (x, y).
The authors prove some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space P N(ℂ) with two families of moving targets, and the results obtained improve some earlier work.
This paper is concerned with the mixed H 2/H ∞ control for stochastic systems with random coefficients, which is actually a control combining the H 2 optimization with the H ∞ robust performance as the name of H 2/H ∞ reveals. Based on the classical theory of linear-quadratic (LQ, for short) optimal control, the sufficient and necessary conditions for the existence and uniqueness of the solution to the indefinite backward stochastic Riccati equation (BSRE, for short) associated with H ∞ robustness are derived. Then the sufficient and necessary conditions for the existence of the H 2/H ∞ control are given utilizing a pair of coupled stochastic Riccati equations.
A class of curvature estimates of spacelike admissible hypersurfaces related to translating solitons of the higher order mean curvature flow in the Minkowski space is obtained, which may offer an idea to study an open question of the existence of hypersurfaces with the prescribed higher mean curvature in the Minkowski space.
A 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V (G) | D has at least two neighbors in D. A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) | D is independent. The 2-domination (total outer-independent domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (total outer-independent dominating, respectively) set of G. We investigate the ratio between 2-domination and total outer-independent domination numbers of trees.
The degree pattern of a finite group G associated with its prime graph has been introduced by Moghaddamfar in 2005 and it is proved that the following simple groups are uniquely determined by their order and degree patterns: All sporadic simple groups, the alternating groups A p (p ≥ 5 is a twin prime) and some simple groups of the Lie type. In this paper, the authors continue this investigation. In particular, the authors show that the symmetric groups S p+3, where p + 2 is a composite number and p + 4 is a prime and 97 < p ∈ π(1000!), are 3-fold OD-characterizable. The authors also show that the alternating groups A116 and A134 are OD-characterizable. It is worth mentioning that the latter not only generalizes the results by Hoseini in 2010 but also gives a positive answer to a conjecture by Moghaddamfar in 2009.
The main purpose of the present paper is to give some properties of the Jacobson radical, the Frattini subsystem and c-ideals of a Lie triple system. Some further results concerning the Frattini subsystems of nilpotent and solvable Lie triple systems are obtained. Moreover, we develop initially c-ideals for a Lie triple system and make use of them to give some characterizations of a solvable Lie triple system.