Natural examples of Valdivia compact spaces

We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L¹ spaces, Banach lattices and noncommutative L¹ spaces.     

An upper bound for the restrained domination number of a graph with minimum degree at least two in terms of order and minimum degree

Let G=(V,E) be a graph. A set S⊆V is a restrained dominating set if every vertex in V−S is adjacent to a vertex in S and to a vertex in V−S. The restrained domination number of G, denoted γ_r(G), is the smallest cardinality of a restrained dominating set of G. We will show that if G is a connected graph of order n and minimum degree δ and not isomorphic to one of nine exceptional graphs, then .     

Some properties of the class of positive Dunford-Pettis operators

We characterize Banach lattices for which each positive Dunford-Pettis operator is M-weakly compact (resp. L-weakly compact) and we give some consequences.     

The Order Completion Method for Systems of Nonlinear PDEs Revisited

In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion as presented in Oberguggenberger and Rosinger (Solution of continuous nonlinear PDEs through order completion, North-Holland, Amsterdam, 1994). In particular, spaces of generalized functions are constructed that contain generalized solutions to a large class of systems of continuous, nonlinear PDEs. In terms of the existence and uniqueness results previously obtained for such systems of equations (van der Walt, Acta Appl. Math. 103:1–17, 2008), one may interpret the existence of generalized solutions presented here as a regularity result. Furthermore, it is indicated how the methods developed in this paper may be adapted to solve initial and/or boundary value problems. In particular, we consider the Navier-Stokes equations in three spacial dimensions, subject to an initial condition on the velocity. In this regard, we obtain the existence of a generalized solution to a large class of such initial value problems.      

Critical and multicritical behavior in the Ising–Heisenberg universality class

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang–Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N = 1, 2, 3 and in all of them find a first-order transition. For the N = 1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.     

Study of Heat Transfer Control with Magnetic Field Using Higher Order Finite Difference Scheme

The control of convective heat transfer from a heated circular cylinder immersed in an electrically conducting fluid is achieved using an externally imposed magnetic field. A Higher Order Compact Scheme (HOCS) is used to solve the governing energy equation in cylindrical polar coordinates. The HOCS gives fourth order accurate results for the temperature field. The behavior of local Nusselt number, mean Nusselt number and temperature field due to variation in the aligned magnetic field is evaluated for the parameters 5≤$Re$≤40, 0≤$N$≤20 and 0.065≤$Pr$≤7. It is found that the convective heat transfer is suppressed by increasing the strength of the imposed magnetic field until a critical value of $N$, the interaction parameter, beyond which the heat transfer increases with further increase in $N$. The results are found to be in good agreement with recent experimental studies.     

复平面上无限级Dirichlet级数和随机Dirichlet级数的下级

研究了复平面上无限级Dirichlet级数和随机Dirichlet级数下级的增长性,得到了关于它们下级增长性的两个定理.     

About the fastest growth of the Order Parameter in models of percolation

The growth of the average size 〈_smax〉$〈s_{max}〉$ of the largest component at the percolation threshold _pc(N)$p_c\left(N\right)$ on a graph of size N$N$ has been defined as 〈_smax(_pc(N),N)〉∼N^χ$〈s_{max}(p_c\left(N\right),N)〉\sim N^{\chi }$. Here we argue that the precise value of the ‘growth exponent’ χ$\chi$ indicates the nature of percolation transition; χ<1$\chi <1$ or χ=1$\chi =1$ determines if the transition is continuous or discontinuous. We show that a related exponent η=1−χ$\eta =1-\chi$ which describes how the average maximal jump sizes in the Order Parameter decays on increasing the system size, is the single exponent that describes the finite-size scaling of a number of distributions related to the fastest growth of the Order Parameter in these problems. Excellent quality scaling analysis are presented for the two single peak distributions corresponding to the Order Parameters at the two ends of the maximal jump, the bimodal distribution constructed by the weighted average of these distributions and for the distribution of the maximal jump in the Order Parameter.     

Order-convexity in order topologies

In this survey the role of order-convexity in topologies compatible with a preference (i.e a negatively transitive partial order) is considered. Two main issues are highlighted:the (topoiogical) subspaces of preference ordered topological spaces, and the orderability of a topological space