First-Order Symmetry Energy Induced by Neutron-Proton Mass Difference

The 1st-order symmetry energy coefficient of nuclear matter induced merely by the neutron-proton （n p） mass difference is derived analytically, which turns out to be completely model-independent. Based on this result, （npDM） the 1st-order symmetry energy Esym,1 （A） of heavy nuclei such as 2~spb induced by the np mass difference is investigated with the help of a local density approximation combined with the Skyrme energy density functionals. Although /U（npDM） Esym,1 （A） is small compared with the second-order symmetry energy, it cannot be dropped simply for an accurate estimation of nuclear masses as it is still larger than the rms deviation given by some accurate mass formulas. It is therefore suggested that one perhaps needs to distinguish the neutron mass from the proton one in the construction of nuclear density funetionals.

Numerical Analysis of Upwind Difference Schemes for Two-Dimensional First-Order Hyperbolic Equations with Variable Coefficients

In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.

Application of gray-tone difference matrix-based features of pavement macrotexture in skid resistance evaluation

This paper presents a method to characterize asphalt pavement macrotexture using the gray-tone difference matrix （GTDM）and discusses the potentials of the GTDM indicators for skid resistance evaluation.There are 37 field sites included in the data collection,which cover 6 types of asphalt pavement surfaces. The mean profile depth derived from 3-D macrotexture measurements （MPD3 ） has a significant relationship with the mean texture depth （MTD ）,which can be described by a logarithm model with R2 of 0.962.There is no significant linear relationship between the friction coefficient at a speed of 60 km/h （DFT60 ）and macrotexture indicators.A nonlinear model with British pendulum number （BPN ） incorporated can relate DFT60 to MTD or indicator fcon .A comparison with MTD shows that GTDM-based fcon has a potential to be a macrotexture indicator for skid resistance evaluation,which describes the general height difference and the average local height difference of pavement macrotexture. A relatively high fcon is helpful for improving asphalt pavement skid resistance.

The Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method

A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.

Division of Matrix- and Fracture-Type Shale Oils in the Jiyang Depression and Their Differences

This study discussed the division of matrix- and fracture-type shale oils in the Jiyang Depression, and proposed the concept of fracture development coefficient. The fracture development coefficient is defined as the ratio of fault throw to the distance between a shale oil well and the nearest fault. Based on CO_2 content, state of water, oil production and logging response of shale oil formations, the classification of shale oils was established, i.e., a fracture-type shale oil well has a fracture development coefficient greater than 0.2, while a matrix-type one has a fracture development coefficient less than 0.2. Furthermore, the key control factors of matrix- and fracture-type shale oil enrichment were analyzed using typical anatomical and statistical methods. For matrix-type shale oil enrichment, these factors are lithofacies, total organic carbon（TOC）, shale porosity and abnormal pressure; for fracture-type shale oil enrichment, they are lithofacies, extent of fracture development, and abnormal pressure. This study also first described the differences between matrix- and fracture-type shale oils. The results provide reference for the exploration of terrestrial faulted basins in eastern China.

Linear Quadratic Optimal Control for Systems Governed by First-Order Hyperbolic Partial Differential Equations

This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems.The contributions of this paper consist of the following aspects:(1)The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method.(2)A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed.Meanwhile,the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations(FBPDEs).(3)The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented.It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case,but also support the existing operator results and give a more convenient form of computation.

SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, and e∞^r, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））, and the Schauder basis of the spaces e0^r△^（m））, ec^r△^（m））. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^（m））.

CHARACTERIZATIONS OF COMPACT OPERATORS ON SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar （[17]） defined the Euler spaces of m-th order difference sequences e r 0 （△ （ m ） ）, e r c （△ （ m ） ） and e r ∞ （△ （ m ） ） and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.

ON THE m^(th) ORDER DIFFERENCE SEQUENCE SPACE OF GENERALIZED WEIGHTED MEAN AND COMPACT OPERATORS

In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l（u, v, p; △（m））, which consist of the sequences whose generalized weighted △（m）-difference means are in the linear space l（p） defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from l（u, v, p, △（m）） to l∞, c, and co. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space lp（U, v, △（m）） （1 ≤ p 〈 ∞）.

High Accurate Fourth-Order Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinate

In this work, by extending the method of Hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly. The Poisson equation is approximated by fourth-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results.

Efficient BTCS + CTCS Finite Difference Scheme for General Linear Second Order PDE

This work deals with a second order linear general equation with partial derivatives for a two-variable function. It covers a wide range of applications. This equation is solved with a finite difference hybrid method: BTCS + CTCS. This scheme is simple, precise, and economical in terms of time and space occupancy in memory.

Exact Solution of a Linear Difference Equation in a Finite Number of Steps

An exact solution of a linear difference equation in a finite number of steps has been obtained. This refutes the conventional wisdom that a simple iterative method for solving a system of linear algebraic equations is approximate. The nilpotency of the iteration matrix is the necessary and sufficient condition for getting an exact solution. The examples of iterative equations providing an exact solution to the simplest algebraic system are presented.

A matching algorithm based on hybrid matrices consisting of reference differences and disparities

Unique correct correspondence cannot be obtained only by use of gray correlation technique, which describes gray similar degree of feature points between the left and right images too unilaterally. The gray correlation technique is adopted to extract gray correlation peaks as a coarse matching set called multi-peak set. The disparity gradient limited constraint is utilized to optimize the multi-peak set. Unique match will be obtained by calculating the correlation of hybrid matrices consisting of reference differences and disparities from the multi-peak set. Two of the known corresponding points in the left and right images, respectively, are set as a pair of reference points to determine search direction and search scope at first. After the unique correspondence is obtained by calculating the correlation of the hybrid matrices from the multi-peak set, the obtained match is regarded as a new reference point till all feature points in the left (or right) image have been processed. Experimental results proved that the proposed algorithm was feasible and accurate.

First-order optimality condition of basis pursuit denoise problem

A new first-order optimality condition for the basis pursuit denoise （BPDN） problem is derived. This condition provides a new approach to choose the penalty param- eters adaptively for a fixed point iteration algorithm. Meanwhile, the result is extended to matrix completion which is a new field on the heel of the compressed sensing. The numerical experiments of sparse vector recovery and low-rank matrix completion show validity of the theoretic results.

Solution of 1D Poisson Equation with Neumann-Dirichlet and Dirichlet-Neumann Boundary Conditions, Using the Finite Difference Method

An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;using the finite difference method, in one dimensional case. Two novels matrices are determined allowing a direct and exact formulation of the solution of the Poisson equation. Verification is also done considering an interesting potential problem and the sensibility is determined. This new method has an algorithm complexity of O(N), its truncation error goes like O(h2), and it is more precise and faster than the Thomas algorithm.

Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

This paper deals with the fixed-time adaptive time-varying matrix projective synchronization(ATVMPS)of different dimensional chaotic systems(DDCSs)with time delays and unknown parameters.Firstly,to estimate the unknown parameters,adaptive parameter updated laws are designed.Secondly,to realize the fixed-time ATVMPS of the time-delayed DDCSs,an adaptive delay-unrelated controller is designed,where time delays of chaotic systems are known or unknown.Thirdly,some simple fixed-time ATVMPS criteria are deduced,and the rigorous proof is provided by employing the inequality technique and Lyapunov theory.Furthermore,the settling time of fixed-time synchronization(Fix-TS)is obtained,which depends only on controller parameters and system parameters and is independent of the system’s initial states.Finally,simulation examples are presented to validate the theoretical analysis.

单幅图像局部特征分层模糊挖掘算法仿真

为了能够深入获得图像纹理特征信息,提高后续数据识别精准度。因此,提出了单幅图像局部特征分层模糊挖掘算法。通过直方图均衡化方法,将图像中灰度值集中到对应灰度等级区域。由不均匀分布向均匀分布状态转换,拓展像素的灰度动态范围。分析图像局部特征复杂度与差异度,求出相邻模板灰度等级,得到局部复杂性和差异度矩阵,采用Laplace算法对图像局部特征推荐分类,根据推荐级别分层模糊挖掘所选特征,以此实现对单幅图像的局部特征分层模糊挖掘。通过实验证明,所提算法可准确挖掘出图像特征,不同层级纹理信息都完整,且挖掘时间保持在0.25s内。

阵元失效下稀疏阵列的二维DOA估计算法

本文针对二维稀疏阵列在阵元失效条件下,因数据缺失导致虚拟阵列连续性被破坏及自由度下降的问题,提出了一种二维DOA估计算法。首先基于二维差分共阵构建虚拟阵列,然后利用解耦原子范数最小化理论,以矩阵填充的形式恢复协方差矩阵数据,实现对虚拟阵列中丢失虚拟阵元的内插,最后采用SS-MUSIC算法进行多信源的二维DOA估计。所提方法弥补了物理阵元失效所造成的影响,恢复了原始虚拟阵列的完整孔径特性,保持了虚拟阵列的自由度,从而确保了较高精度的二维DOA估计性能。仿真实验结果表明,在相同阵元数量及阵元失效情况下,本文提出的算法相比已有方法能有效地估计更多信源,并在小快拍数和低信噪比条件下表现出更高的稳健性,最大限度地保留并利用了稀疏阵列在二维DOA估计中的自由度优势。

基于L_(2)灵敏度最小化的数字滤波器状态空间实现稀疏化方法

为解决传统数字滤波器在有限精度实现时因有限字长(Finite Word Length,FWL)效应导致滤波器性能下降的问题,提出一种L_(2)灵敏度最小化的数字滤波器状态空间实现稀疏化方法.推导前向差分算子数字滤波器结构传输函数及其等效状态空间实现,根据可控及可观格莱姆矩阵得到基于相似变换矩阵的L_(2)灵敏度表达式,并进行稀疏化校准,将L_(2)灵敏度最小化问题转换为凸函数求最值问题,求导得到L_(2)灵敏度最小化表达式,代回即得前向差分算子数字滤波器的稀疏化状态空间实现.仿真结果表明,所提方法设计的数字滤波器具有更好的抗FWL效应.

一种基于差异矩阵的光谱复原方法

单透镜成像技术基于计算成像技术发展而来。利用单片透镜构成的光学系统代替传统复杂的光学系统,利用后端的算法处理替代前端的光学处理,不仅简化了光学系统复杂度,而且能够获得满足需求的图像。目前,国内外对于单透镜成像技术在成像光谱领域中的研究较少,因此,开展基于单透镜成像技术的图谱信息获取研究具有较大的研究价值及意义。文章针对单透镜成像光谱仪的混叠图谱数据,提出了1种基于差异矩阵的光谱复原方法。当只考虑光谱信息时,只需对轴上数据进行采集,再根据获取的不同位置处不同波长的强度信息,计算得到差异系数,构建差异矩阵,利用最小二乘法进行求解,即可实现光谱的复原。通过仿真及实验验证,利用SCC及SMSE进行质量评价,验证了上述方法的正确性及可行性。