ELIMINATION AND IDENTITIES WITH THE INTEGRAL SIGN

In this paper,we aim at using the elimination in Weyl algebra to give an algorithm forproving the identities with integral sign.Then,we test several examples that have been proved by D.Zeilberger.     

The Ore-Sato Theorem and Shift Exponents in the q-Difference Case

The authors translate the main results in the paper entitled "Multiplicative Decomposition of Multivariate q-Hypergeometric Terms" from Chinese into English. The paper is written by Shaoshi Chen, Ruyong Feng, Guofeng Fu and Jing Kang, and published in Journal of Mathematics and Systems Science, 32(8), 1019–1032, 2012. Some minor simpli?cation and modi?cation are made during the translation. Based on the results in the above paper, a special form is derived for q-shift exponents appearing in the q-shift quotients of a q-hypergeometric term.     

Testing <Emphasis Type="Italic">k</Emphasis>-edge-connectivity of digraphs

This paper presents an algorithm that tests whether a given degree-bounded digraph is k-edge-connected or ɛ-far from k-edge-connectivity. This is the first testing algorithm for k-edgeconnectivity of digraphs whose running time is independent of the number of vertices and edges. A digraph of n vertices with degree bound d is ɛ-far from k-edge-connectivity if at least ɛdn edges have to be added or deleted to make the digraph k-edge-connected, preserving the degree bound. Given a constant error parameter ɛ and a degree bound d, our algorithm always accepts all k-edge-connected digraphs and rejects all digraphs that is ɛ-far from k-edge-connectivity with probability at least 2/3. It runs in $ O\left( {d\left( {\frac{c} {{\varepsilon d}}} \right)^k log\frac{1} {{\varepsilon d}}O} \right) $ O\left( {d\left( {\frac{c} {{\varepsilon d}}} \right)^k log\frac{1} {{\varepsilon d}}O} \right) (c > 1 is a constant) time when input digraphs are restricted to be (k-1)-edge connected and runs in $ O\left( {d\left( {\frac{{ck}} {{\varepsilon d}}} \right)^k log\frac{k} {{\varepsilon d}}O} \right) $ O\left( {d\left( {\frac{{ck}} {{\varepsilon d}}} \right)^k log\frac{k} {{\varepsilon d}}O} \right) (c > 1 is a constant) time for general digraphs.     

A new <Emphasis Type="Italic">ɛ</Emphasis>-generalized projection method of strongly sub-feasible directions for inequality constrained optimization

In this paper, the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and the ɛ-generalized projection technique, a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented. At each iteration, the search direction is generated by a new ɛ-generalized projection explicit formula, and the step length is yielded by a new Armijo line search. Under some necessary assumptions, not only the algorithm possesses global and strong convergence, but also the iterative points always get into the feasible set after finite iterations. Finally, some preliminary numerical results are reported.     

The determination on weight hierarchies of <Emphasis Type="Italic">q</Emphasis>-ary linear codes of dimension 5 in class IV

The weight hierarchy of a linear [n; k; q] code C over GF(q) is the sequence (d ₁, d ₂, ···, d _k ) where d _r is the smallest support of any r-dimensional subcode of C. “Determining all possible weight hierarchies of general linear codes” is a basic theoretical issue and has important scientific significance in communication system. However, it is impossible for q-ary linear codes of dimension k when q and k are slightly larger, then a reasonable formulation of the problem is modified as: “Determine almost all weight hierarchies of general q-ary linear codes of dimension k”. In this paper, based on the finite projective geometry method, the authors study q-ary linear codes of dimension 5 in class IV, and find new necessary conditions of their weight hierarchies, and classify their weight hierarchies into 6 subclasses. The authors also develop and improve the method of the subspace set, thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV. It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes (classes III and VI), and break through the difficulties. Furthermore, the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough (not most tight nor best), so, it is important to excogitate further new necessary conditions for attacking and solving the k-dimensional problem.     

Fault-tolerant control of linear uncertain systems using H∞ robust predictive control

The robust fault-tolerant control problem of linear uncertain systems is studied. It is shown that a solution for this problem can be obtained from a H∞ robust predictive controller （RMPC） by the method of linear matrix inequality （LMI）. This approach has the advantages of both H∞ control and MPC： the robustness and ability to handle constraints explicitly. The robust closed-loop stability of the linear uncertain system with input and output constraints is proven under an actuator and sensor faults condition. Finally, satisfactory results of simulation experiments verify the validity of this algorithm.     

<Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript> disturbance attenuation for a class of time-delay Hamiltonian systems

This paper considers the problem of L ₂-disturbance attenuation for a class of time-delay port-controlled Hamiltonian systems. A γ-dissipative inequality is established by using a proper control law and a storage function. Then based on the Razumikhin stability theorem, a sufficient condition is proposed for the asymptotically stability of the closed-loop system. Finally, the authors investigate the case that there are time-invariant uncertainties belonging to some convex bounded polytypic domain and an L ₂ disturbance attenuation control law is proposed. Study of illustrative example with simulation shows that the presented method in this paper works very well in the disturbance attenuation of time-delay Hamiltonian systems.     

A family of the local convergence of the improved secant methods for nonlinear equality constrained optimization subject to bounds on variables

This paper studies a family of the local convergence of the improved secant methods for solving the nonlinear equality constrained optimization subject to bounds on variables. The Hessian of the Lagrangian is approximated using the DFP or the BFGS secant updates. The improved secant methods are used to generate a search direction. Combining with a suitable step size, each iterate switches to trial step of strict interior feasibility. When the Hessian is only positive definite in an affine null subspace, one shows that the algorithms generate the sequences converging q-linearly and two-step q-superlinearly. Furthermore, under some suitable assumptions, some sequences generated by the algorithms converge locally one-step q-superlinearly. Finally, some numerical results are presented to illustrate the effectiveness of the proposed algorithms.     

A criterion for the similarity of length-two elements in a noncommutative PID

This paper presents a criterion for the similarity of length-two elements in a noncommutative principal ideal domain. The criterion enables the authors to develop an algorithm for determining whether B ₁ A ₁ and B ₂ A ₂ are similar, where A ₁,A ₂,B ₁,B ₂ are first-order differential (difference) operators. The main step in the algorithm is to find a rational solution of a parametric differential (difference) Risch’s equation, which has been well-studied in symbolic integration (summation).     

基于新网络路由算法的通信网可靠性指标计算

解决通信网络"归一化容量加权可靠性指标"全代数化计算的最关键问题,是寻找能够算出网络节点之间全部路由的代数化路由算法。提出一种网络路由新算法,是按照逻辑代数运算规则,以关联矩阵降阶变换方式计算,对于有m个节点的网络,只需m-2次距阵降阶变换运算,就能够算得网络两节点间全部路由,且不会出现闭环路由问题,完全符合通信传输规则。基于该路由算法研究出通信网络"归一化容量加权可靠性指标"的全代数化算法,由于新算法所有环节均实现了代数化运算,所以易于编写计算机程序,可以很方便地计算出大型通信网络的可靠性指标,解决了大型通信网络可靠性分析困难的问题。通过算例对新算法的各计算过程进行了详细说明,验证了其正确性。     

Inverse Center Location Problem on a Tree

This paper discusses the inverse center location problem restricted on a tree with different costs and bound constraints. The authors first show that the problem can be formulated as a series of combinatorial linear programs, then an O（｜V｜^2 log ｜V｜） time algorithm to solve the problem is presented. For the equal cost case, the authors further give an O（｜V｜） time algorithm.     

Proper reparametrization for inherently improper unirational varieties

In this paper, a class of lattice supports in the lattice space Z ^m is found to be inherently improper because any rational parametrization from C ^m to C ⁿ defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support S is analyzed and shrinking transformations are constructed to transform S to a proper one. For a generic rational parametrization RP defined on an improper support S, we prove that its improper index is the improper index of S and give a proper reparametrization algorithm for RP. Finally, properties for rational parametrizations defined on an improper support and with numerical coefficients are also considered.     

An improved algorithm for solving all <Emphasis Type="Italic">d</Emphasis>-MPs in multi-state networks

Reliability is a desirable performance indicator of many real-world systems to measure the quality level. One general method for evaluating multi-state reliability is using d-minimal paths (d-MPs). However, being an NP-hard problem, searching for all d-MPs is a rather challenging task. This paper proposes an improved algorithm to solve the d-MP problem. To reduce the search space of d-MPs, a concept of lower capacity bound is introduced into the d-MP problem, and an effective technique is developed to find lower capacity bounds. Meanwhile, the fast enumeration method which is a recent improvement to the traditional enumeration method is employed to solve d-MPs. In addition, by introducing the operation of transforming undirected edges into directed edges, the proposed algorithm is applicable to solving both directed networks and undirected networks. Through numerical experiments, it is found that the proposed algorithm holds a distinct advantage over the existing methods in solving all d-MPs.     

IMPROVED ROBUST H-INFINITY ESTIMATION FOR UNCERTAIN CONTINUOUS-TIME SYSTEMS

The design of full-order robust estimators is investigated for continuous-time polytopic uncertain systems. The main purpose is to obtain a stable linear estimator such that the estimation error system remains robustly stable with a prescribed H∞ attenuation level. Firstly, a simple alternative proof is given for an improved LMI representation of H∞ performance proposed recently. Based on the performance criterion which keeps the Lyapunov matrix out of the product of the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameterdependent Lyapunov functions and hence it is less conservative than the earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.     

Semi On-Line Scheduling Problem for Maximizing the Minimum Machine Completion Time on Two Uniform Machines

Ia this paper, we consider a semi on-line version on two uniform machines Mi, i = 1, 2, where the processing time of the largest job is known in advance. A speed si（s1 = 1, 1 ≤s2 = s） is associated with machine Mi. Our goal is to maximize the Cmin. We give a Cmin 2 algorithm and prove its competitive ratio is at most 2s＋1/s＋1 We also claim the Cmin 2 algorithm is tight and the gap between the competitive ratio of Cmin2 algorithm and the optimal value is not greater than 0.555. It is obvious that our result coincides with that given by He for s =1.     

短波信道探测中窄带干扰的去除算法

对于短波信道传播特性的弱信号探测,信号干扰噪声比低,如何减小干扰就显得十分重要。由于基于传统傅里叶变换去干扰算法在去窄带干扰时对幅度和相位的估计不够准确,提出了一种基于傅里叶变换和概率密度相结合的窄带干扰去除算法。仿真结果表明,该算法能很好地去除窄带干扰。但上述算法在去除实测信号中的窄带干扰时性能不佳,所以提出一种改进的傅里叶变换和概率密度相结合的窄带干扰去除算法。实验结果表明,改进后的算法能去除实测信号中的窄带干扰,为解决低信噪比条件下探测信号的参数估计奠定了基础。     

Distributed Consensus-Based <Emphasis Type="Italic">K</Emphasis>-Means Algorithm in Switching Multi-Agent Networks

This paper discusses a distributed design for clustering based on the K-means algorithm in a switching multi-agent network, for the case when data are decentralized stored and unavailable to all agents. The authors propose a consensus-based algorithm in distributed case, that is, the double-clock consensus-based K-means algorithm (DCKA). With mild connectivity conditions, the authors show convergence of DCKA to guarantee a distributed solution to the clustering problem, even though the network topology is time-varying. Moreover, the authors provide experimental results on various clustering datasets to illustrate the effectiveness of the fully distributed algorithm DCKA, whose performance may be better than that of the centralized K-means algorithm.     

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS II： M（n）/G/1/K

We study a single-server queueing system with state-dependent arrivals and general service distribution, or simply M（n）/G/1/K, where the server follows an N policy and takes multiple vacations when the system is empty. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirements are the Laplace-Stieltjes transforms of the service time distribution and the vacation time distribution, and the state-dependent arrival rate. The computational complexity of the algorithm is O（K^3）.     

A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials

This paper presents a new algorithm for computing the extended Hensel construction(EHC) of multivariate polynomials in main variable x and sub-variables u_1, u_2, ···, u_m over a number field K. This algorithm first constructs a set by using the resultant of two initial coprime factors w.r.t. x, and then obtains the Hensel factors by comparing the coefficients of x~i on both sides of an equation. Since the Hensel factors are polynomials of the main variable with coefficients in fraction field K(u_1, u_2, ···, u_m), the computation cost of handling rational functions can be high. Therefore,the authors use a method which multiplies resultant and removes the denominators of the rational functions. Unlike previously-developed algorithms that use interpolation functions or Gr?bner basis, the algorithm relies little on polynomial division, and avoids multiplying by different factors when removing the denominators of Hensel factors. All algorithms are implemented using Magma, a computational algebra system and experiments indicate that our algorithm is more efficient.     

Improve Robustness and Accuracy of Deep Neural Network with L2,∞ Normalization

In this paper, the L_2,∞ normalization of the weight matrices is used to enhance the robustness and accuracy of the deep neural network(DNN) with Relu as activation functions. It is shown that the L_2,∞ normalization leads to large dihedral angles between two adjacent faces of the DNN function graph and hence smoother DNN functions, which reduces over-fitting of the DNN. A global measure is proposed for the robustness of a classification DNN, which is the average radius of th...