A Tight Approximation Algorithm for Multi-Vehicle CVRP with Unsplittable Demands on a Line

In this paper, the authors study the multi-vehicle capacitated vehicle routing problem on a line-shaped network with unsplittable demand. The objective is to find a transportation scheme to minimize the longest distance traveled by a single vehicle such that all the customers are served without violating the capacity constraint. The authors show that this problem has no polynomial-time algorithm with performance ratio less than 2 on condition that P ≠ NP, and then provide a 2-approximation algorithm.

     

Curvature-Based r-Adaptive Isogeometric Analysis with Injectivity-Preserving Multi-Sided Domain Parameterization

Inspired by the r-refinement method in isogeometric analysis, in this paper, the authors propose a curvature-based r-adaptive isogeometric method for planar multi-sided computational domains parameterized by toric surface patches. The authors construct three absolute curvature metrics of isogeometric solution surface to characterize its gradient information, which is more straightforward and effective. The proposed method takes the internal weights as optimization variables and the resulting par...     

High accuracy analysis of tensor-product linear pentahedral finite elements for variable coefficient elliptic equations

For a general second-order variable coefficient elliptic boundary value problem in three dimensions,the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements.In addition,the estimate for the W^1,1 -seminorm of the discrete derivative Green’s function is given.Finally,the authors show that the derivatives of the finite element solution u_h and the corresponding interpolantΠ_u are superclose in the pointwise sense of the L^∞-norm.     

New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

This paper deals with H_∞ control problem for nonlinear conformable fractional order systems. The authors first derive new sufficient condition for exponential stability of nonlinear conformable fractional order systems based on Lyapunov-like function method for conformable fractional order systems and linear matrix inequalities(LMIs) approach. Then, by introducing a new concepts of H_∞ control problem for nonlinear conformable fractional order systems, the authors study H_∞ performance analysis and H_∞ state feedback controller design problems for the considered systems. In terms of LMIs, a sufficient condition is proposed to ensure the nonlinear conformable fractional order systems are not only exponentially stable, but also satisfy H_∞ performance γ. An explicit expression for state feedback controllers is also designed to make the closed-loop system is exponentially stable with H_∞performance γ. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.     

Superconvergence of mixed covolume method on quadrilateral grids for elliptic problems

This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals.Superconvergence results are established in this paper on quadrilateral grids satisfying the h~2-parallelogram condition when the lowest-order Raviart-Thomas space is employed in the mixed covolume method.The authors prove O(h~2) accuracy between the approximate velocity or pressure and a suitable projection of the real velocity or pressure in the L~2 norm.Numerical experiments illustrating the theoretical results are provided.     

The recursive solution of queue length for <Emphasis Type="Italic">Geo/G</Emphasis>/1 queue with <Emphasis Type="Italic">N</Emphasis>-policy

This paper considers a discrete-time queue with N-policy and LAS-DA(late arrival system with delayed access) discipline.By using renewal process theory and probability decomposition techniques,the authors derive the recursive expressions of the queue-length distributions at epochs n~-,n~+,and n.Furthermore,the authors obtain the stochastic decomposition of the queue length and the relations between the equilibrium distributions of the queue length at different epochs(n~-,n~+,n and departure epoch D_n).     

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.     

Distance-Based Regression Analysis for Measuring Associations

Distance-based regression model, as a nonparametric multivariate method, has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies, genomic analyses, and many other research areas. Based on it, a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim. To the best of our knowledge, the statistical properties of the pseudo-F statistic has not yet been well established in the literature. To fill this gap, the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables. Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large, the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root. The asymptotic null distribution of the new test statistic and power of both tests are also investigated. Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test. Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.

     

Straightforward Guess and Determine Analysis Based on Genetic Algorithm

With the development of artificial intelligence, the genetic algorithm has been widely used in many fields. In cryptography, the authors find it is natural to code an individual and design its fitness in a genetic algorithm for a straightforward guess and determine analysis(SGDA, in short).Based on this observation, the authors propose an SGDA based on genetic algorithm. Comparing it with the other three SGDAs based on exhaustive search, MILP method and CPP method respectively,the authors illust...     

Test on Stochastic Block Model: Local Smoothing and Extreme Value Theory

In this paper, to obtain a consistent estimator of the number of communities, the authors present a new sequential testing procedure, based on the locally smoothed adjacency matrix and the extreme value theory. Under the null hypothesis, the test statistic converges to the type I extreme value distribution, and otherwise, it explodes fast and the divergence rate could even reach n in the strong signal case where n is the size of the network, guaranteeing high detection power. This method is simple to use and serves as an alternative approach to the novel one in Lei (2016) using random matrix theory. To detect the change of the community structure, the authors also propose a two-sample test for the stochastic block model with two observed adjacency matrices. Simulation studies justify the theory. The authors apply the proposed method to the political blog data set and find reasonable group structures.

     

L ∞-estimates of mixed finite element methods for general nonlinear optimal control problems

This paper investigates L~∞-estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods.The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions.The authors derive L~∞-estimates for the mixed finite element approximation of nonlinear optimal control problems.Finally,the numerical examples are given.     

A MacWilliams type identity on Lee weight for linear codes over \mathbb{F}_2 + u\mathbb{F}_2^*

In this paper,the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F₂ + uF₂ is determined.As an application of this identity,the authors obtain a MacWilliams type identity on Lee weight for linear codes over F_2^m+ uF_2^m.Furthermore,the authors prove a duality for the m-ply Lee weight distributions by taking advantage of the Krawtchouk polynomials.     

Isogeometric Analysis-Based Topological Optimization for Heterogeneous Parametric Porous Structures

Porous structures widely exist in nature and artifacts, which can be exploited to reduce structural weight and material usage or improve damage tolerance and energy absorption. In this study,the authors develop an approach to design optimized porous structures with Triply Periodic Minimal Surfaces(TPMSs) in the framework of isogeometric analysis(IGA)-based topological optimization.In the developed method, by controlling the density distribution, the designed porous structures can achieve the opt...     

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.     

Minimum Hausdorff distance under rigid motions and comparison of protein structures

Hausdorff distance between two compact sets, defined as the maximum distance from a point of one set to another set, has many application in computer science. It is a good measure for the similarity of two sets. This paper proves that the shape distance between two compact sets in R ⁿ defined by minimum Hausdorff distance under rigid motions is a distance. The authors introduce similarity comparison problems in protein science, and propose that this measure may have good application to comparison of protein structure as well. For calculation of this distance, the authors give one dimensional formulas for problems (2, n), (3, 3), and (3, 4). These formulas can reduce time needed for solving these problems. The authors did some numerical experiments for (2, n). On these sets of data, this formula can reduce time needed to one fifteenth of the best algorithms known on average. As n increases, it would save more time.     

An Adjusted Gray Map Technique for Constructing Large Four-Level Uniform Designs

A uniform experimental design (UED) is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs, limited resources and unknown underlying models. A UED enjoys the following two significant advantages: (i) It is a robust design, since it does not require to specify a model before experimenters conduct their experiments; and (ii) it provides uniformly scatter design points in the experimental domain, thus it gives a good representation of this domain with fewer experimental trials (runs). Many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are needed. Constructing large UEDs using the existing techniques is an NP-hard problem, an extremely time-consuming heuristic search process and a satisfactory result is not guaranteed. This paper presents a new effective and easy technique, adjusted Gray map technique (AGMT), for constructing (nearly) UEDs with large numbers of four-level factors and runs by converting designs with s two-level factors and n runs to (nearly) UEDs with 2^t?1s four-level factors and 2^tn runs for any t ≥ 0 using two simple transformation functions. Theoretical justifications for the uniformity of the resulting four-level designs are given, which provide some necessary and/or sufficient conditions for obtaining (nearly) uniform four-level designs. The results show that the AGMT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large (nearly) UEDs with four-level factors.

     

Finite volume element method with Lagrangian cubic functions

This paper establishes a new finite volume element scheme for Poisson equation on triangular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness matrix is uniformly positive definite and convergence rate to be O(h ³) in H ¹-norm. Some numerical experiments confirm the theoretical considerations.     

Agent’s Optimal Compensation Under Inflation Risk by Using Dynamic Contract Model

This paper studies the problem of principal-agent with moral hazard in continuous time. The firm’s cash flow is described by geometric Brownian motion (hereafter GBM). The agent affects the drift of the firm’s cash flow by her hidden effort. Meanwhile, the firm rewards the agent with corresponding compensation and equity which depend on the output. The model extends dynamic optimal contract theory to an inflation environment. Firstly, the authors obtain the dynamic equation of the firm’s real cash flow under inflation by using the Itô formula. Then, the authors use the martingale representation theorem to obtain agent’s continuation value process. Moreover, the authors derive the Hamilton-Jacobi-Bellman (HJB) equation of investor’s value process, from which the authors derive the investors’ scaled value function by solving the second-order ordinary differential equation. Comparing with He^[1], the authors find that inflation risk affects the agent’s optimal compensation depending on the firm’s position in the market.

     

Good p-ary quasic-cyclic codes from cyclic codes over $$\mathbb{F}_ p + v\mathbb{F}_ p$$

This paper introduces a Gray map from（F_p + uF_p）ⁿ to F_p²ⁿ,and describes the relationship between codes over F_p + vF_p and their Gray images.The authors prove that every cyclic code of arbitrary length n over F_p + vF_p is principal,and determine its generator polynomial as well as the number of cyclic codes.Moreover,the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map.     

An SEIRS epidemic model with two delays and pulse vaccination*

Pulse vaccination is an effective and important strategy to eradicate an infectious disease. The authors investigate an SEIRS epidemic model with two delays and pulse vaccination. By using the discrete dynamical system determined by stroboscopic map, the authors obtain that the infectious population dies out if R△ 〈 1, and the infectious population is uniformly persistent if R^△ 〉 1. The results indicate that a short period of pulse vaccination or a large pulse vaccination rate is a sufficient condition to eradicate the disease.