MHD mixed convection of a viscous dissipating fluid about a permeable vertical flat plate

The problem of steady laminar magnetohydrodynamic (MHD) mixed convection heat transfer about a vertical plate is studied numerically, taking into account the effects of Ohmic heating and viscous dissipation. A uniform magnetic field is applied perpendicular to the plate. The resulting governing equations are transformed into the non-similar boundary layer equations and solved using the Keller box method. Both the aiding-buoyancy mode and the opposing-buoyancy mode of the mixed convection are examined. The velocity and temperature profiles as well as the local skin friction and local heat transfer parameters are determined for different values of the governing parameters, mainly the magnetic parameter, the Richardson number, the Eckert number and the suction/injection parameter, f_w. For some specific values of the governing parameters, the results agree very well with those available in the literature. Generally, it is determined that the local skin friction coefficient and the local heat transfer coefficient increase owing to suction of fluid, increasing the Richardson number, Ri (i.e. the mixed convection parameter) or decreasing the Eckert number. This trend reverses for blowing of fluid and decreasing the Richardson number or decreasing the Eckert number. It is disclosed that the value of Ri determines the effect of the magnetic parameter on the momentum and heat transfer.     

The identity is isolated among composition operators

Let be the Banach algebra of bounded holomorphic functions on the open unit ball of a Banach space. We show that the identity operator is an isolated point in the space of composition operators on . This answers a conjecture of Aron, Galindo and Lindström.

     

关于图的直径和平均距离

图的直径和平均距离是度量网络有效性的两个重要参数．Ore通过图的顶点数和直径给出无向图的最大边数．Entringer，Jakson，Slater和Ng，Teh通过图的顶点数和边数分别给出无向图和有向图平均距离的下界．该文提供这两个结果的简单证明，给出有向图类似Ore的结果，并通过图的直径改进Entringer等人的结果到更一般的情形．结合本文和Ore的结果，可以得到一个无向图和有向图平均距离的下界，它比Plesnik得到的下界更好．     

Structural properties and tractability results for linear synteny

The syntenic distance between two species is the minimum number of fusions, fissions, and translocations required to transform one genome into the other. The linear syntenic distance, a restricted form of this model, has been shown to be close to the syntenic distance. Both models are computationally difficult to compute and have resisted efficient approximation algorithms with non-trivial performance guarantees. In this paper, we prove that many useful properties of syntenic distance carry over to linear syntenic distance. We also give a reduction from the general linear synteny problem to the question of whether a given instance can be solved using the maximum possible number of translocations. Our main contribution is an algorithm exactly computing linear syntenic distance in nested instances of the problem. This is the first polynomial time algorithm exactly solving linear synteny for a non-trivial class of instances. It is based on a novel connection between the syntenic distance and a scheduling problem that has been studied in the operations research literature.     

Randomized incremental construction of simple abstract Voronoi diagrams in 3-space

We introduce the simple abstract Voronoi diagram in 3-space as an abstraction of the usual Voronoi diagram. We show that the 3-dimensional simple abstract Voronoi diagram of n sites can be computed in O(n²) expected time using O(n²) expected space by a randomized algorithm. The algorithm is based on the randomized incremental construction technique of Clarkson and Shor (1989). We apply the algorithm to some concrete types of such diagrams: power diagrams, diagrams under ellipsoid convex distance functions, and diagrams under the Hausdorff distance for sites that are parallel segments all having the same length.     

3-D vertical ray shooting and 2-D point enclosure, range searching, and arc shooting amidst convex fat objects

We present a new data structure for a set of n convex simply-shaped fat objects in the plane, and use it to obtain efficient and rather simple solutions to several problems including (i) vertical ray shooting—preprocess a set of n non-intersecting convex simply-shaped flat objects in 3-space, whose xy-projections are fat, for efficient vertical ray shooting queries, (ii) point enclosure—preprocess a set C of n convex simply-shaped fat objects in the plane, so that the k objects containing a query point p can be reported efficiently, (iii) bounded-size range searching— preprocess a set C of n convex fat polygons, so that the k objects intersecting a “not-too-large” query polygon can be reported efficiently, and (iv) bounded-size segment shooting—preprocess a set C as in (iii), so that the first object (if exists) hit by a “not-too-long” oriented query segment can be found efficiently. For the first three problems we construct data structures of size O(λ_s(n)log³n), where s is the maximum number of intersections between the boundaries of the (xy-projections) of any pair of objects, and λ_s(n) is the maximum length of (n, s) Davenport-Schinzel sequences. The data structure for the fourth problem is of size O(λ_s(n)log²n). The query time in the first problem is O(log⁴n), the query time in the second and third problems is O(log³n + klog²n), and the query time in the fourth problem is O(log³n).

We also present a simple algorithm for computing a depth order for a set as in (i), that is based on the solution to the vertical ray shooting problem. (A depth order for , if exists, is a linear order of , such that, if K₁, K₂ and K₁ lies vertically above K₂, then K₁ precedes K₂.) Unlike the algorithm of Agarwal et al. (1995) that might output a false order when a depth order does not exist, the new algorithm is able to determine whether such an order exists, and it is often more efficient in practical situations than the former algorithm.     

Gaussian Version of a Theorem of Milman and Schechtman

Using Gordon's inequalities, we give a short proof of the existence of an embedding T:l2k to ln such that ||T||||T-1|| c k/ln(1+n/k). In the same way, we give a new proof of a theorem of Milman and Schechtman (1995).     

球面型空间有限点集的两个不等式

运用距离几何的理论与方法，给出了涉及球面型空间有限点集的两个不等式．     

Discrepancies between metric dimension and partition dimension of a connected graph

Let and be graphs where the set of vertices is the set of points of the integer lattice and the set of edges consists of all pairs of vertices whose city block and chessboard distances, respectively, are 1.In this paper it is shown that the partition dimensions of these graphs are 3 and 4, respectively, while their metric dimensions are not finite. Also, for every n3 there exists an induced subgraph of of order 3n-1 with metric dimension n and partition dimension 3. These examples will answer a question raised by Chartrand, Salehi and Zhang. Furthermore, graphs of order n9 having partition dimension n-2 are characterized, thus completing the characterization of graphs of order n having partition dimension 2, n, or n-1 given by Chartrand, Salehi and Zhang. The list of these graphs includes 23 members.     

Distribution dependent SDEs for Landau type equations

The distribution dependent stochastic differential equations (DDSDEs) describe stochastic systems whose evolution is determined by both the microcosmic site and the macrocosmic distribution of the particle. The density function associated with a DDSDE solves a nonlinear PDE. Due to the distribution dependence, some standard techniques developed for SDEs do not apply. By iterating in distributions, a strong solution is constructed using SDEs with control. By proving the uniqueness, the distribution of solutions is identified with a nonlinear semigroup $P_t^1$ on the space of probability measures. The exponential contraction as well as Harnack inequalities and applications are investigated for the nonlinear semigroup $P_t^1$ using coupling by change of measures. The main results are illustrated by homogeneous Landau equations.