Showing papers in "Acta Mathematicae Applicatae Sinica in 2017"
TL;DR: It follows that a connected pentavalent symmetric graph of order 16p exists if and only if p = 2 or 31, and that up to isomorphism, there are three such graphs.
Abstract: A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 16p is given for each prime p. It follows from this result that a connected pentavalent symmetric graph of order 16p exists if and only if p = 2 or 31, and that up to isomorphism, there are three such graphs.
15 citations
TL;DR: An infeasible-interior-point algorithm, based on a new wide neighbourhood N(τ1, τ2, η), for linear programming over symmetric cones is presented, and it is proved that if these two directions are equipped with different and appropriate step sizes, then the new algorithm has a polynomial convergence for the commutative class of search directions.
Abstract: In this paper we present an infeasible-interior-point algorithm, based on a new wide neighbourhood N(τ1, τ2, η), for linear programming over symmetric cones. We treat the classical Newton direction as the sum of two other directions. We prove that if these two directions are equipped with different and appropriate step sizes, then the new algorithm has a polynomial convergence for the commutative class of search directions. In particular, the complexity bound is O(r1.5loge−1) for the Nesterov-Todd (NT) direction, and O(r2loge−1) for the xs and sx directions, where r is the rank of the associated Euclidean Jordan algebra and e > 0 is the required precision. If starting with a feasible point (x0, y0, s0) in N(τ1, τ2, η), the complexity bound is $$O\left( {\sqrt r \log {\varepsilon ^{ - 1}}} \right)$$
for the NT direction, and O(rloge−1) for the xs and sx directions. When the NT search direction is used, we get the best complexity bound of wide neighborhood interior-point algorithm for linear programming over symmetric cones.
15 citations
TL;DR: In this paper, the optimal investment and premium control problem in a diffusion approximation to a non-homogeneous compound Poisson process is considered, and closed-form expressions for the optimal policies and the value functions are obtained.
Abstract: This paper considers the optimal investment and premium control problem in a diffusion approximation to a non-homogeneous compound Poisson process. In the nonlinear diffusion model, it is assumed that there is an unspecified monotone function describing the relationship between the safety loading of premium and the time-varying claim arrival rate. Hence, in addition to the investment control, the premium rate can be served as a control variable in the optimization problem. Specifically, the problem is investigated in two cases: (i) maximizing the expected utility of terminal wealth, and (ii) minimizing the probability of ruin respectively. In both cases, some properties of the value functions are derived, and closed-form expressions for the optimal policies and the value functions are obtained. The results show that the optimal investment policy and the optimal premium control policy are dependent on each other. Most interestingly, as an example, we show that the nonlinear diffusion model reduces to a diffusion model with a quadratic drift coefficient when the function associated with the premium rate and the claim arrival rate takes a special form. This example shows that the model of study represents a class of nonlinear stochastic control risk model.
14 citations
TL;DR: In this paper, a special version of Kolmogrov's law of large numbers for independent and identically distributed random variables under one-order type moment condition is presented, which is a special case of Doob's inequality for submartingale.
Abstract: In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob’s inequality for submartingale and Kolmogrov’s inequality. By Kolmogrov’s inequality, we obtain a special version of Kolmogrov’s law of large numbers. Finally, we present a strong law of large numbers for independent and identically distributed random variables under one-order type moment condition.
13 citations
TL;DR: In this paper, it was shown that the connectivity cannot be more than conjectured for k = 3 and conjecture that it is true for all k ∈ N. In this paper, we show that the conjecture holds for n ≥ 2k and k = 1, 2.
Abstract: A subset F ⊂ V (G) is called an R
k
-vertex-cut of a graph G if G − F is disconnected and each vertex of G − F has at least k neighbors in G − F. The R
k
-vertex-connectivity of G, denoted by κ
k
(G), is the cardinality of a minimum R
k
-vertex-cut of G. Let B
n
be the bubble sort graph of dimension n. It is known that κ
k
(B
n
) = 2
k
(n − k − 1) for n ≥ 2k and k = 1, 2. In this paper, we prove it for k = 3 and conjecture that it is true for all k ∈ N. We also prove that the connectivity cannot be more than conjectured.
12 citations
TL;DR: In this paper, a spectral Jacobi rational-Gauss collocation (JRC) method is proposed for solving the multi-pantograph delay differential equations on the half-line.
Abstract: A new spectral Jacobi rational-Gauss collocation (JRC) method is proposed for solving the multi-pantograph delay differential equations on the half-line. The method is based on Jacobi rational functions and Gauss quadrature integration formula. The main idea for obtaining a semi-analytical solution for these equations is essentially developed by reducing the pantograph equations with their initial conditions to systems of algebraic equations in the unknown expansion coefficients. The convergence analysis of the method is analyzed. The method possesses the spectral accuracy. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. Indeed, the present method is compared favorably with other methods.
12 citations
TL;DR: In this paper, the authors studied the Cauchy problem of damped generalized Boussinesq equation and obtained the global existence and finite time blow up of solution, then they obtained some sharp conditions for the well-posedness problem.
Abstract: We study the Cauchy problem of damped generalized Boussinesq equation u
tt
− u
xx
+ (u
xx
+ f(u))
xx
− αu
xxt
= 0. First we give the local existence of weak solution and smooth solution. Then by using potential well method and convexity method we prove the global existence and finite time blow up of solution, then we obtain some sharp conditions for the well-posedness problem.
10 citations
TL;DR: In this paper, a compact finite difference scheme for the coupled nonlinear Schrodinger equations is studied, and the scheme is proved to conserve the original conservative properties with order O(τ 2 + h4).
Abstract: In this article, a compact finite difference scheme for the coupled nonlinear Schrodinger equations is studied. The scheme is proved to conserve the original conservative properties. Unconditional stability and convergence in maximum norm with order O(τ2 + h4) are also proved by the discrete energy method. Finally, numerical results are provided to verify the theoretical analysis.
10 citations
TL;DR: In this article, the authors consider the issue of variable selection in partial linear single-index models under the assumption that the vector of regression coefficients is sparse and apply penalized spline to estimate the nonparametric function and SCAD penalty to achieve sparse estimates of regression parameters in both the linear and single index parts of the model.
Abstract: In this paper, we consider the issue of variable selection in partial linear single-index models under the assumption that the vector of regression coefficients is sparse. We apply penalized spline to estimate the nonparametric function and SCAD penalty to achieve sparse estimates of regression parameters in both the linear and single-index parts of the model. Under some mild conditions, it is shown that the penalized estimators have oracle property, in the sense that it is asymptotically normal with the same mean and covariance that they would have if zero coefficients are known in advance. Our model owns a least square representation, therefore standard least square programming algorithms can be implemented without extra programming efforts. In the meantime, parametric estimation, variable selection and nonparametric estimation can be realized in one step, which incredibly increases computational stability. The finite sample performance of the penalized estimators is evaluated through Monte Carlo studies and illustrated with a real data set.
10 citations
TL;DR: In this article, the existence of nontrivial solutions for some superlinear second order three-point boundary value problems by applying new fixed point theorems in ordered Banach spaces with the lattice structure derived by Sun and Liu was investigated.
Abstract: In this paper, we investigate the existence of nontrivial solutions for some superlinear second order three-point boundary value problems by applying new fixed point theorems in ordered Banach spaces with the lattice structure derived by Sun and Liu.
9 citations
TL;DR: In this article, the relation between orthogonal array and generalized Latin matrices was studied and some useful theorems for their construction were obtained, and a new class of mixed orthogonality arrays were obtained.
Abstract: In this paper, generalized Latin matrix and orthogonal generalized Latin matrices are proposed. By using the property of orthogonal array, some methods for checking orthogonal generalized Latin matrices are presented. We study the relation between orthogonal array and orthogonal generalized Latin matrices and obtain some useful theorems for their construction. An example is given to illustrate applications of main theorems and a new class of mixed orthogonal arrays are obtained.
TL;DR: In this article, the existence of positive solutions of second-order periodic boundary value problem is considered, where 0 0 is a parameter, and positive solutions are obtained by using the positive solution.
Abstract: In this paper, we consider the existence of positive solutions of second-order periodic boundary value problem
$$u'' + {\left( {\frac{1}{2} + \varepsilon } \right)^2}u = \lambda g\left( t \right)f\left( u \right),t \in \left[ {0,2\pi } \right],u\left( 0 \right) = u\left( {2\pi } \right),u'\left( 0 \right) = u'\left( {2\pi } \right)$$
, where 0 0 is a parameter.
TL;DR: In this article, the authors studied M/M/c queues in a Markovian environment with impatient customers, where the arrivals and service rates are modulated by the underlying continuous-time Markov chain.
Abstract: We study M/M/c queues (c = 1, 1 < c < ∞ and c = ∞) in a Markovian environment with impatient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.
TL;DR: In this article, the authors established new oscillation criteria for a non-autonomous second-order delay dynamic equation, which can be applied on different types of time scales such as when T = qℕ for q > 1 and also improve most previous results.
Abstract: In this paper, we establish some new oscillation criteria for a non autonomous second order delay dynamic equation $${\left( {r\left( t \right)g\left( {{x^\Delta }\left( t \right)} \right)} \right)^\Delta } + p\left( t \right)f\left( {x\left( {\tau \left( t \right)} \right)} \right) = 0,$$
on a time scale T. Oscillation behavior of this equation is not studied before. Our results not only apply on differential equations when T=ℝ, difference equations when T=ℕ but can be applied on different types of time scales such as when T=qℕ for q > 1 and also improve most previous results. Finally, we give some examples to illustrate our main results.
TL;DR: In this paper, the authors proposed the lowest order H1-Galerkin mixed finite element method (for short MFEM) for a class of nonlinear sine-Gordon equations with the simplest bilinear rectangular element and zero order Raviart-Thomas element.
Abstract: The lowest order H1-Galerkin mixed finite element method (for short MFEM) is proposed for a class of nonlinear sine-Gordon equations with the simplest bilinear rectangular element and zero order Raviart-Thomas element. Base on the interpolation operator instead of the traditional Ritz projection operator which is an indispensable tool in the traditional FEM analysis, together with mean-value technique and high accuracy analysis, the superclose properties of order O(h2)/O(h2 + τ2) in H1-norm and H(div;Ω)-norm are deduced for the semi-discrete and the fully-discrete schemes, where h, τ denote the mesh size and the time step, respectively, which improve the results in the previous literature.
TL;DR: This paper proposes Bayesian Lasso together with neighborhood regression estimate for Gaussian graphical model, which can obtain parameter estimation and model selection simultaneously and can provide symmetric confidence intervals of all entries of the precision matrix.
Abstract: In this paper, we consider the problem of estimating a high dimensional precision matrix of Gaussian graphical model. Taking advantage of the connection between multivariate linear regression and entries of the precision matrix, we propose Bayesian Lasso together with neighborhood regression estimate for Gaussian graphical model. This method can obtain parameter estimation and model selection simultaneously. Moreover, the proposed method can provide symmetric confidence intervals of all entries of the precision matrix.
TL;DR: In this article, a Kansa's method is designed to solve numerically the Monge-Ampere equation and the solution in some local triangular subdomains by using the combination of some cubic polynomials.
Abstract: In this paper, a Kansa’s method is designed to solve numerically the Monge-Ampere equation. The primitive Kansa’s method is a meshfree method which applying the combination of some radial basis functions (such as Hardy’s MQ) to approximate the solution of the linear parabolic, hyperbolic and elliptic problems. But this method is deteriorated when is used to solve nonlinear partial differential equations. We approximate the solution in some local triangular subdomains by using the combination of some cubic polynomials. Then the given problems can be computed in each subdomains independently. We prove the stability and convergence of the new method for the elliptic Monge-Ampere equation. Finally, some numerical experiments are presented to demonstrate the theoretical results.
TL;DR: In this paper, a new bifactor (ln(1/β)/(1 −β),1+2/(1 − β))-approximation algorithm was proposed for the k-LFLPSC with soft capacities.
Abstract: We consider the k-level facility location problem with soft capacities (k-LFLPSC). In the k-LFLPSC, each facility i has a soft capacity u
i
along with an initial opening cost f
i
≥ 0, i.e., the capacity of facility i is an integer multiple of u
i
incurring a cost equals to the corresponding multiple of f
i
. We firstly propose a new bifactor (ln(1/β)/(1 −β),1+2/(1 −β))-approximation algorithm for the k-level facility location problem (k-LFLP), where β ∈ (0, 1) is a fixed constant. Then, we give a reduction from the k-LFLPSC to the k-LFLP. The reduction together with the above bifactor approximation algorithm for the k-LFLP imply a 5.5053-approximation algorithm for the k-LFLPSC which improves the previous 6-approximation.
TL;DR: In this paper, the existence of weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space was established via Ricceri's result.
Abstract: In this paper, we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in [13].
TL;DR: In this paper, a joint model under Type-I hybrid censoring is addressed in detail, based on the maximum likelihood estimates (MLEs) of unknown parameters, and confidence intervals of parameters are constructed through both the exact method and the parametric bootstrap method.
Abstract: Assuming that the failure time under different risk factors follows the independent exponential distribution, a joint model under Type-I hybrid censoring is addressed in detail. Based on the Maximum likelihood estimates (MLEs) of unknown parameters, we obtain exact distributions of MLEs by using the moment generating function (MGF). Confidence intervals (CIs) of parameters are constructed through both the exact method and the parametric bootstrap method. Then we compare the performances of different methods by Monte Carlo simulations. Finally, the validity of the proposed models and methods are demonstrated by a numerical example.
TL;DR: In this paper, the authors studied the asymptotic behavior of a population dynamics with random diffusion and delayed birth process within a semigroup framework, and discussed the local stability and asynchrony respectively for the considered population system under some conditions.
Abstract: In this paper we devote ourselves to the study of the asymptotic behavior of a size-structured population dynamics with random diffusion and delayed birth process. Within a semigroup framework, we discuss the local stability and asynchrony respectively for the considered population system under some conditions. We use for our discussion the techniques of operator matrices, Hille-Yosida operators, positivity, spectral analysis as well as Perron-Frobenius theory.
TL;DR: In this article, a ratio-dependent predator-prey system with diffusion and cross-diffusion in a bounded domain with no flux boundary condition is considered, and it is shown that under certain hypotheses, the crossdiffusion can create non-constant positive steady states even though the corresponding model without cross diffusion fails.
Abstract: This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross-diffusion in a bounded domain with no flux boundary condition. We show that under certain hypotheses, the cross-diffusion can create non-constant positive steady states even though the corresponding model without cross-diffusion fails.
TL;DR: This paper derives a sequential screening strategy for ovarian cancer by jointly modeling the longitudinal profiles of CA125 and HE4 by constructing a Bayesian hierarchical mixture model with changepoint, and proposes two approaches for diagnosis: the risk of cancer index and the hypothesis test on the true incidence time.
Abstract: The mortality of ovarian cancer is higher than any other female genital malignant tumors, while there exists a strong correlation between early-stage detection and cure for it. CA125 and HE4 are two most common and effective serum markers in recent screening research of ovarian cancer. This paper derives a sequential screening strategy for ovarian cancer by jointly modeling the longitudinal profiles of CA125 and HE4. We construct a Bayesian hierarchical mixture model with changepoint, and propose two approaches for diagnosis: the risk of cancer index and the hypothesis test on the true incidence time. We simulated a 7-year sequential screening research and compared with the standard approach based on a fixed cutoff level. Our approach achieves a 15% higher sensitivity for a fixed specificity, indicating that the sequential strategy combining multiple markers is more effective in the early-stage detection of ovarian cancer.
TL;DR: In this article, the authors derived an optimal 8-order iteration scheme for obtaining simple roots of nonlinear equations using Lagrange interpolation and suitable weight functions, which requires three evaluations of the function and one evaluation of the first derivative per iteration.
Abstract: In this paper, based on fourth order Ostrowski method, we derive an optimal eighth order iteration scheme for obtaining simple roots of nonlinear equations using Lagrange interpolation and suitable weight functions. The scheme requires three evaluations of the function and one evaluation of the first derivative per iteration. Numerical examples are included to confirm the theoretical results and to show the competitive performance of the proposed iteration scheme.
TL;DR: In this paper, the authors study the DeGroot model for continuous opinion dynamics under the influence of innovations and prove that convergence can still be guaranteed in the expectation sense, regardless of the learning topology.
Abstract: We study the DeGroot model for continuous opinion dynamics under the influence of innovations. In the original model, individuals’ opinions, after given their initial values, evolve merely according to the given learning topology. The main contribution of this paper is that external innovation effects are introduced: each individual is given the opportunity to change her opinion to a randomly selected opinion according to a given distribution on the opinion space and then the external opinion is either adapted by the individual, or combined into her learning process. It turns out that all the classical results of the DeGroot model are violated in this new model. We prove that convergence can still be guaranteed in the expectation sense, regardless of the learning topology. We also study the steady distributions of opinions among the society and the time spent to reach a steady state by means of Monte-Carlo simulations.
TL;DR: Application of the generalized Benders decomposition algorithm considers solving the resulting mixed-integer nonlinear programming problem.
Abstract: This paper considers a novel formulation of the multi-period network interdiction problem. In this model, delivery of the maximum flow as well as the act of interdiction happens over several periods, while the budget of resource for interdiction is limit. It is assumed that when an edge is interdicted in a period, the evader considers a rate of risk of detection at consequent periods. Application of the generalized Benders decomposition algorithm considers solving the resulting mixed-integer nonlinear programming problem. Computational experiences denote reasonable consistency with expectations.
TL;DR: In this paper, the authors considered the nonlinear fractional Schrodinger equations with Hartree type nonlinearity in mass-supercritical and energy-subcritical case and established a threshold condition, which leads to a global existence of solutions in energy space.
Abstract: In this paper, we consider the nonlinear fractional Schrodinger equations with Hartree type nonlinearity in mass-supercritical and energy-subcritical case. By sharp Hardy-Littlewood-Sobolev inequality and the Pohozaev identity, we established a threshold condition, which leads to a global existence of solutions in energy space.
TL;DR: In this article, a weighted two-stage local quasi-likelihood estimation method was proposed for additive varying coefficient regression models, in which the coefficients of some factors (covariates) are additive functions of other factors, and the interactions between different factors can be taken into account effectively.
Abstract: We consider a longitudinal data additive varying coefficient regression model, in which the coefficients of some factors (covariates) are additive functions of other factors, so that the interactions between different factors can be taken into account effectively. By considering within-subject correlation among repeated measurements over time and additive structure, we propose a feasible weighted two-stage local quasi-likelihood estimation. In the first stage, we construct initial estimators of the additive component functions by B-spline series approximation. With the initial estimators, we transform the additive varying coefficients regression model into a varying coefficients regression model and further apply the local weighted quasi-likelihood method to estimate the varying coefficient functions in the second stage. The resulting second stage estimators are computationally expedient and intuitively appealing. They also have the advantages of higher asymptotic efficiency than those neglecting the correlation structure, and an oracle property in the sense that the asymptotic property of each additive component is the same as if the other components were known with certainty. Simulation studies are conducted to demonstrate finite sample behaviors of the proposed estimators, and a real data example is given to illustrate the usefulness of the proposed methodology.
TL;DR: In this paper, a general additive-multiplicative hazards model for case-cohort designs with multiple disease outcomes is proposed, and the proposed estimator is consistent and asymptotically normal large sample approximation works well in finite sample studies in simulation.
Abstract: Case-cohort design is an efficient and economical design to study risk factors for diseases with expensive measurements, especially when the disease rate is low When several diseases are of interest, multiple case-cohort design studies may be conducted using the same subcohort To study the association between risk factors and each disease occurrence or death, we consider a general additive-multiplicative hazards model for case-cohort designs with multiple disease outcomes We present an estimation procedure for the regression parameters of the additive-multiplicative hazards model, and show that the proposed estimator is consistent and asymptotically normal Large sample approximation works well in finite sample studies in simulation Finally, we apply the proposed method to a real data example for illustration
TL;DR: In this paper, the authors investigated a class of fourth-order regular differential operators with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the boundary conditions.
Abstract: We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the boundary conditions. We prove that the operator is symmetric, construct basic solutions of differential equation, and give the corresponding Green function of the operator is given.