The general Riemann problem for the linearized system of two-dimensional isentropic flow in gas dynamics

In this paper, we give the explicit solution to the general Riemann problem for the linearized system of two-dimensional isentropic flow in gas dynamics.     

Hitting time of a half-line by two-dimensional random walk

We consider the probability that a two-dimensional random walk starting from the origin never returns to the half-line {(x₁,x₂)|x₁0,x₂=0} before time n. It is proved that for aperiodic random walk with mean zero and finite 2+(>2)-th absolute moment, this probability times n^1/4 converges to some positive constant c^* as . We show that c^* is expressed by using the characteristic function of the increment of the random walk. For the simple random walk, this expression gives Mathematics Subject Classification (2000):60G50, 60E10     

Feature extraction using two-dimensional local graph embedding based on maximum margin criterion

In this paper, we propose a novel method for image feature extraction, namely the two-dimensional local graph embedding, which is based on maximum margin criterion and thus not necessary to convert the image matrix into high-dimensional image vector and directly avoid computing the inverse matrix in the discriminant criterion. This method directly learns the optimal projective vectors from 2D image matrices by simultaneously considering local graph embedding and maximum margin criterion. The proposed method avoids huge feature matrix problem in Eigenfaces, Fisherfaces, Laplacianfaces, maximum margin criterion (MMC) and inverse matrix in 2D Fisherfaces, 2D Laplacianfaces and 2D Local Graph Embedding Discriminant Analysis (2DLGEDA) so that computational time would be saved for feature extraction. Experimental results on the Yale and the USPS databases show the effectiveness of the proposed method under various experimental conditions.     

Simplest optimal cutting patterns for equal rectangles

This paper presents branch-and-bound algorithms that can guarantee the simplest optimal cutting patterns of equal rectangles. An existing linear algorithm determines the global upper bound exactly. The branching process ends when a branch of a lower bound equal to the global upper bound is found.     

Kronecker Product of Two-dimensional Arrays

Kronecker sequences constructed from short sequences are good sequences for spread spectrum communication systems. In this paper we study a similar problem for two-dimensional arrays, and we determine the linear complexity of the Kronecker product of two arrays, Our result shows that similar good property on linear complexity holds for Kronecker product of arrays.     

Two-dimensional q-differential transformation and its application

The one-dimensional q-differential transformation was introduced in [8] for solving the ordinary q-differential equations. Here, we present the definition and operation of the two-dimensional q-differential transform. A distinctive feature of the q-differential transform is its ability to solve linear and nonlinear partial q-differential equations.     

Fast heuristic for constrained homogenous T-shape cutting patterns

Homogenous T-shape (HTS) cutting patterns are welcomed when the two-phase process is used to produce rectangular pieces from the stock plate, where the plate is cut into homogenous strips at the first phase, and the strips are divided into pieces at the second phase. A heuristic is presented for generating constrained HTS patterns, where the objective is to maximize the pattern value that is equal to the total value of the included pieces, observing the upper bound constraint on the frequency of each piece type. The heuristic is based on dynamic programming and branch-and-bound techniques. It can yield solutions close to optimal with short computation time. By providing good initial solutions, the heuristic can greatly improve the time efficiency of an existing exact branch-and-bound algorithm.     

Characterizations of some two-dimensional cyclic codes correspond to the ideals of F[x,y]/

Two-dimensional cyclic code is one of the natural generalizations of cyclic code. In this paper we study the algebraic structure of some two-dimensional cyclic codes and their dual codes.     

Die unipotenten charaktere von 2F4(q2)

.Alle endlichen Gruppen vom Lie-Typ besitzen eine ausgezeichnete Menge von irreduziblen komplexen Charakteren, die von Lusztig eingeführten unipotenten Charaktere. Diese werden fülr einen vorgegebenen Typ unabhängig vom zugrunde liegenden Körper klassifiziert. Aufgrund der ebenfalls von Lusztig bewiesenen Jordan-Zerlegung der irreduziblen komplexen Charaktere laiit sich die Charaktertafel einer jeden endlichen Gruppe G vom Lie-Typ im wesentlichen zusammenbauen, wenn man die unipotenten Charaktere der halbeinfachen Anteile der Zentralisatoren aller halbeinfachen Elemente in G kennt. Das Problem der Berechnung der Charaktertafel ist somit zurückgeführt auf die Bestimmung aller Werte der unipotenten Charaktere der einfachen Gruppen vom Lie-Typ.     

Relaxation of variational problems in two-dimensional nonlinear elasticity

Consider a plate occupying in a reference configuration a bounded open set Ω ⊂ ℝ ² , and let be its stored-energy function. In this paper we are concerned with relaxation of variational problems of type:

On the solutions and conservation laws of the model for tumor growth in the brain

We study the problem of tumor growth and its monitoring ranging from the simple model for the radially symmetric to the more complex case being the radially non-symmetric one. In each case, we take killing rate of the cancer cells dependent on the concentration of the cells. A number of invariant reductions whose further analysis leads to exact solutions are obtained. Conservation laws for the model are also studied.     

达到极大线性复杂度的前馈阵列

讨论了三类达到极大线性复杂度的前馈阵列的输入阵列的结构。一类是达到极大线性复杂度的乘积前馈阵列,完全确定了其输入阵列的结构;给出了两类输入阵列,证明了它们的任意前馈阵列达到极大线性复杂度。     

Reducing the number of cuts in generating three-staged cutting patterns

Three-staged guillotine patterns are widely used in the manufacturing industry to cut stock plates into rectangular items. The cutting cost often increases with the number of cuts required. This paper focuses on the rectangular two-dimensional cutting stock problem, where three-staged guillotine patterns are used, and the objective is to minimize the sum of plate and cutting costs. The column generation framework is used to solve the problem. It uses a pattern-generation procedure to obtain the patterns. The cutting cost is considered in both the pattern-generation procedure and the objective of the linear programming formulation. The computational results indicate that the approach can reduce the number of cuts, without increasing the plate cost.     

Construction of Two-Dimensional Compactly Supported Orthogonal Wavelets Filters with Linear Phase

In this paper, a large class of two-dimensional orthogonal wavelet filters, (lowpass and highpass), are presented in explicit expression. We also characterize the filters with linear phase in this case. Some examples are also given, including non-separable filters with linear phase. Received September 28, 1999, Accepted July 24, 2000     

The Model for Two-dimensional Layout Optimization Problem with Performance Constraints and Its Optimality Function

This paper studies the two-dimensional layout optimization problem.An optimization model withperformance constraints is presented.The layout problem is partitioned into finite subproblems in terms ofgraph theory,in such a way of that each subproblem overcomes its on-off nature optimal variable.A minimaxproblem is constructed that is locally equivalent to each subproblem.By using this minimax problem,we presentthe optimality function for every subproblem and prove that the first order necessary optimality condition issatisfied at a point if and only if this point is a zero of optimality function.     

Linearization of two-dimensional systems of ODEs without conditions on small denominators

We study the problem of linearizability for two-dimensional systems of ODEs in a neighborhood of the saddle type singular point with rationally incommensurable eigenvalues. It is shown that if the linearizing transformation is convergent in one of the variables, then it is absolutely convergent.     

Two-dimensional weak pseudomanifolds on eight vertices

We explicitly determine all the two-dimensional weak pseudomanifolds on 8 vertices. We prove that there are (up to isomorphism) exactly 95 such weak pseudomanifolds, 44 of which are combinatorial 2-manifolds. These 95 weak pseudomanifolds triangulate 16 topological spaces. As a consequence, we prove that there are exactly three 8-vertex two-dimensional orientable pseudomanifolds which allow degree three maps to the 4-vertex 2-sphere.