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1.
This paper proves a theorem on the decay rate of the oscillatory integral operator with a degenerate C^∞ phase function, thus improving a classical theorem of HSrmander. The proof invokes two new methods to resolve the singularity of such kind of operators: a delicate method to decompose the operator and balance the L^2 norm estimates; and a method for resolution of singularity of the convolution type. The operator is decomposed into four major pieces instead of infinite dyadic pieces, which reveals that Cotlar's Lemma is not essential for the L^2 estimate of the operator. In the end the conclusion is further improved from the degenerate C^∞ phase function to the degenerate C^4 phase function.  相似文献   

2.
1. IntroductionIn bin packing, a list L of items, i.e. numbers in the range (0, 1], are to be packed illtobins, each of which has a capacity 1, and the goal is to minimize the number of bins used.The minimal number of bins into which L can be packed is denoted by OPT (L) for the listL. The first~fit-decreasing (FFD) algorithm first sorts the list into a non-increasing orderand then processes the pieces in that order by placing each item into the first bin icao whiChit fits. For tlist L, l…  相似文献   

3.
In this note, we consider the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle when the vacuum is not involved. The solutions are obtained constructively and globally when the initial data consist of three pieces of constant states. Furthermore, it can be found that the Riemann solutions are stable with respect to such small perturbations of the initial data in this particular situation by investigating the limits of the solutions as the perturbed parameter ε goes to zero.  相似文献   

4.
At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 (0 〈 dl ≤ m) and d2 (0 ≤ d2≤ n), builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.  相似文献   

5.
When I studied at primary school,I learned the ways to calculate the surface area and the volume of rectangle,square and cylinder,and the volume of cone.I knew rectangle and square are measured by the unite square ;we calculate the volume of the cylinder by cutting cylinder into pieces and putting the pieces together approximates the rectan-  相似文献   

6.
Multiplication of Unite FractionA large cake was bought for a class party.First the cake was cut into 20 pieces.These pieceswere too large,so each was cut into 2 smaller pieces.  相似文献   

7.
一维高精度离散GDQ方法   总被引:4,自引:0,他引:4  
郑华盛  赵宁  成娟 《计算数学》2004,26(3):293-302
GDQ method is a kind of high order accurate numerical methods developed several years ago, which have been successfully used to simulate the solution of smooth engineering problems such as structure mechanics and incompressible fluid dynamics. In this paper, extending the traditional GDQ method, we develop a new kind of discontinuous GDQ methods to solve compressible flow problems of which solutions may be discontinuous. In order to capture the local features of fluid flows, firstly, the computational domain is divided into many small pieces of subdomains. Then, in each small subdomain, the GDQ method is implementedand some kinds of numerical flux limitation conditions will be required to keep the correct flow direction. At the boundary interface between subdomains, we also use some kind of flux conditions according to the flow direction. The numerical method obtained by the above steps has the advantages of high order accuracy and easy to treat boundary conditions. It can simulate perfectly nonlinear waves such as shock, rarefaction wave and contact discontinuity. Finally, the numerical experiments on one dimensional Burgers equation and Euler equations are given.The numerical results verify the validation of the method.  相似文献   

8.
A suffcient condition for a set of calibrated submanifolds to be area-minimizing with multiplicities,also call weighted area-minimizing under diffeomorphisms (WAMD) is stated.We construct some WAMD submanifolds by assembling pieces of special Lagrangian (SL) normal bundles including the one of three surfaces meeting at an angle of 120° along soap-film-like singularities.We also mention a symmetry property of SL submanifolds and Bjrling type problem for SL normal bundles.  相似文献   

9.
1 Introduction Let A be a collection of n pairwise disjoint simple closed curves on an orientable closed surface F of genus n ≥2. We say that A is a complete system of F if the surface obtained by cutting F along A is a 2n-punctured sphere. Let A1, A2 be two non-empty subsets of A. We say that (A1,A2) is a partition of A if A1 ∩A2 = (?) and A1 ∪A2 = A. Let (A1, A2) be a partition of A on F, and C a simple closed curve on F. We say that C is separating with respect to (A1, A2) if it is disjoint from A and it cuts F into two pieces F1,F2 with A1(?) F1,A2 (?) F2.  相似文献   

10.
The single-index model with monotonic link function is investigated. Firstly, it is showed that the link function h(.) can be viewed by a graphic method. That is, the plot with the fitted response y on the horizontal axis and the observed y on the vertical axis can be used to visualize the link function. It is pointed out that this graphic approach is also applicable even when the link function is not monotonic. Note that many existing nonparametric smoothers can also be used to assess h(.). Therefore, the I-spline approximation of the link function via maximizing the covariance function with a penalty function is investigated in the present work. The consistency of the criterion is constructed. A small simulation is carried out to evidence the efficiency of the approach proposed in the paper.  相似文献   

11.
The puzzle-assembly problem has many application areas such as restoration and reconstruction of archeological findings, repairing of broken objects, solving jigsaw type puzzles, molecular docking problem, etc. The puzzle pieces usually include not only geometrical shape information but also visual information such as texture, color, and continuity of lines. This paper presents a new approach to the puzzle-assembly problem that is based on using textural features and geometrical constraints. The texture of a band outside the border of pieces is predicted by inpainting and texture synthesis methods. Feature values are derived from these original and predicted images of pieces. An affinity measure of corresponding pieces is defined and alignment of the puzzle pieces is formulated as an optimization problem where the optimum assembly of the pieces is achieved by maximizing the total affinity measure. A Fast Fourier Transform based image registration technique is used to speed up the alignment of the pieces. Experimental results are presented on real and artificial data sets.  相似文献   

12.
Mariana Arghir  Geamilia Solea  Dan Borza 《PAMM》2008,8(1):10397-10398
Longitudinal elasticity modulus, E, is a material specific feature, which,. in general, is establish on the pieces by longitudinal stress. This procedure is possible to apply to the compact material but not to the sintered power parts (or porous material test pieces). For sintered parts, the establishing of Young's modulus, in this paper, it is proposed by transmition of mechanical vibrations along to the test pieces. The test pieces of compact or porous material were strained at longitudinal vibrations. It was establish the linkage between vibration and density, respective between the density and the value of the longitudinal elasticity modulus. Using the test pieces of compact material we realized the methodology to obtain the longitudinal elasticity modulus regarding the compact material, and in this way can be establish the possibility to measure with a good result the longitudinal elasticity modulus for the pieces of sintered powders or of porous material. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

13.
In this paper we study a two-dimensional non-guillotine cutting problem, the problem of cutting rectangular pieces from a large stock rectangle so as to maximize the total value of the pieces cut. The problem has many industrial applications whenever small pieces have to be cut from or packed into a large stock sheet. We propose a tabu search algorithm. Several moves based on reducing and inserting blocks of pieces have been defined. Intensification and diversification procedures, based on long-term memory, have been included. The computational results on large sets of test instances show that the algorithm is very efficient for a wide range of packing and cutting problems.  相似文献   

14.
Abstract

A stochastic differential equation (SDE) is derived and examined for approximately modeling the breaking down of rock surfaces through random processes. The rock surfaces include, for example, surfaces of historical monuments, gravestones, or natural rock formations. Rock surfaces break down through wear, weathering, and erosion. During weathering, rocks are worn away and fractured into smaller pieces while in erosion, the rock pieces are transported through actions, for example, of air, water, and gravity. In the mathematical model developed in the present investigation, it is assumed that environmental actions cause particles or pieces of a rock to gradually break off with erosion occurring simultaneously, that is, the rock pieces are transported away immediately after separation.  相似文献   

15.
We define rectangle exchange transformations analogously to interval exchange transformations. An interval exchange transformation is a mapping of the unit interval onto itself obtained by cutting the interval up into a finite number of subintervals and rearranging the pieces. A rectangle exchange transformation is a mapping of the unit square onto itself obtained by cutting the square up into a finite number of rectangular pieces and rearranging the pieces. We give a minimality condition for rectangle exchange transformations. We deal with various examples of ergodic rectangle exchange transformations. Related questions are discussed.With 2 Figures  相似文献   

16.
We consider the problem of guillotine cutting a rectangular sheet into two rectangular pieces without rotations. The question is whether there exists a cutting pattern with given numbers of occurrences of both rectangular pieces. A polynomial time algorithm is described to construct the convex hull of solutions to this problem.  相似文献   

17.
The irregular strip packing problem consists of cutting a set of convex and non-convex two-dimensional polygonal pieces from a board with a fixed height and infinite length. Owing to the importance of this problem, a large number of mathematical models and solution methods have been proposed. However, only few papers consider that the pieces can be rotated at any angle in order to reduce the board length used. Furthermore, the solution methods proposed in the literature are mostly heuristic. This paper proposes a novel mixed integer quadratically-constrained programming model for the irregular strip packing problem considering continuous rotations for the pieces. In the model, the pieces are allocated on the board using a reference point and its allocation is given by the translation and rotation of the pieces. To reduce the number of symmetric solutions for the model, sets of symmetry-breaking constraints are proposed. Computational experiments were performed on the model with and without symmetry-breaking constraints, showing that symmetry elimination improves the quality of solutions found by the solution methods. Tests were performed with instances from the literature. For two instances, it was possible to compare the solutions with a previous model from the literature and show that the proposed model is able to obtain numerically accurate solutions in competitive computational times.  相似文献   

18.
We consider decompositions of the real line into pairwise disjoint Borel pieces so that each piece is closed under addition. How many pieces can there be? We prove among others that the number of pieces is either at most 3 or uncountable, and we show that it is undecidable in and even in the theory if the number of pieces can be uncountable but less than the continuum. We also investigate various versions: what happens if we drop the Borelness requirement, if we replace addition by multiplication, if the pieces are subgroups, if we partition (0, ∞), and so on.  相似文献   

19.
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.  相似文献   

20.
A cutting stock problem is formulated as follows: a set of rectangular pieces must be cut from a set of sheets, so as to minimize total waste. In our problem the pieces are requested in large quantities and the set of sheets are long rolls of material. For this class of problems we have developed a fast heuristic based on partial enumeration of all feasible patterns. We then tested the effectiveness on a set of test problems ranging from practical to random instances. Finally, the algorithm has been applied to check the asymptotic behaviour of the solution when a continuous stream of pieces is requested and cutting decisions are to be made while orders are still arriving.  相似文献   

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