In this article, the fractional derivatives in the sense of the modified Riemann-Liouville derivatives together with the modified simple equation method and the multiple exp-function method are employed for constructing the exact solutions and the solitary wave solutions for the nonlinear time fractional Sharma-Tasso-Olver equation. With help of Maple, we can get exact explicit 1-wave, 2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton type solutions if we use the multiple exp-function method while we can get only exact explicit 1-wave solution including 1-soliton type solution if we use the modified simple equation method. Two cases with specific values of the involved parameters are plotted for each 2-wave and 3-wave solutions.
The bipolar non-isentropic compressible Navier-Stokes-Poisson (BNSP) system is investigated in R^{3} in the present paper, and the optimal L^{2} time decay rate for the global classical solution is established. It is shown that the total densities, total momenta and total temperatures of two carriers converge to the equilibrium states at the rate (1+t)^{-3/4+ε} in L^{2}-norm for any small and fix ε>0. But, both the difference of densities and the difference of temperatures of two carriers decay at the optimal rate (1+t)^{-3/4}, and the difference of momenta decays at the optimal rate (1+t)^{-1/4}. This phenomenon on the charge transport shows the essential difference between the non-isentropic unipolar NSP and the bipolar NSP system.
In this paper,we consider a class of non-Newtonian fluids for a reacting mixture in one-dimensional bounded interval, provided the initial data satisfying a compatibility condition. The main ingredient is that we allow the initial density vacuum.
The case-cohort design is widely used in large epidemiological studies and prevention trials for cost reduction. In such a design, covariates are assembled only for a subcohort which is a random subset of the entire cohort and any additional cases outside the subcohort. In this paper, we discuss the case-cohort analysis with a class of general additive-multiplicative hazard models which includes the commonly used Cox model and additive hazard model as special cases. Two sampling schemes for the subcohort, Bernoulli sampling with arbitrary selection probabilities and stratified simple random sampling with fixed subcohort sizes, are discussed. In each setting, an estimating function is constructed to estimate the regression parameters. The resulting estimator is shown to be consistent and asymptotically normally distributed. The limiting variance-covariance matrix can be consistently estimated by the case-cohort data. A simulation study is conducted to assess the finite sample performances of the proposed method and a real example is provided.
In this paper we consider the random r-uniform r-partite hypergraph model H(n_{1},n_{2},…,n_{r}; n,p) which consists of all the r-uniform r-partite hypergraphs with vertex partition {V_{1}, V_{2},…, V_{r}} where |V_{i}|=n_{i}=n_{i}(n) (1≤i≤r) are positive integer-valued functions on n with n_{1}+n_{2}+…+n_{r}=n, and each r-subset containing exactly one element in V_{i} (1≤i≤r) is chosen to be a hyperedge of H_{p}∈H (n_{1},n_{2},…,n_{r}; n,p) with probability p=p(n), all choices being independent. Let Δ_{V1}=Δ_{V1}(H) and δ_{V1}=δ_{V1}(H) be the maximum and minimum degree of vertices in V_{1} of H, respectively; X_{d,V1}=X_{d,V1}(H), Y_{d,V1}=Y_{d,V1}(H), Z_{d,V1}=Z_{d,V1}(H) and Z_{c,d,V1}=Z_{c,d,V1}(H) be the number of vertices in V_{1} of H with degree d, at least d, at most d, and between c and d, respectively. In this paper we obtain that in the space H(n_{1},n_{2},…,n_{r}; n,p), X_{d,V1}, Y_{d,V1}, Z_{d,V1}, and Z_{c,d,V1} all have asymptotically Poisson distributions. We also answer the following two questions. What is the range of p that there exists a function D(n) such that in the space H(n_{1},n_{2},…,n_{r}; n,p),P(Δ_{V1}=D(n))=1? What is the range of p such that a.e., H_{p}∈H(n_{1},n_{2},…,n_{r}; n,p) has a unique vertex in V_{1} with degree Δ_{V1}(H_{p})? Both answers are p=o (log n_{1}/N), where N=n_{i}. The corresponding problems on δ_{V1}(H_{p}) also are considered, and we obtained the answers are p≤(1+o(1))(log n_{1}/N) and p=o(log n_{1}/N), respectively.
In this paper, we extend Noether's theorem to nonholonomic constraints systems in optimal control. We present a systematic way to calculate conserved quantities along the Pontryagin extremals for optimal control problems with nonholonomic constraints, which are invariant under the parameter groups of infinitesimal transformations that change all (time, state, control) variables. Meanwhile, the Noether equalities corresponding to the conservation laws are given. Then, we obtain a new version of Noether's theorem to optimal control systems. An example is given to illustrate the application of these results.
A strong k-edge-coloring of a graph G is an assignment of k colors to the edges of G in such a way that any two edges meeting at a common vertex, or being adjacent to the same edge of G, are assigned different colors. The strong chromatic index of G is the smallest integer k for which G has a strong k-edge-coloring. In this paper, we have shown that the strong chromatic index is no larger than 6 for outerplanar graphs with maximum degree 3.
This paper deals with the pos/neg-weighted p-median problem on tree graphs where all customers are modeled as subtrees. We present a polynomial algorithm for the 2-median problem on an arbitrary tree. Then we improve the time complexity to O(n log n) for the problem on a balanced tree, where n is the number of the vertices in the tree.
In this paper, relations between directional derivatives are considered for smooth functions both in 2D and 3D spaces. These relations are established in the form of linear combinations of directional derivatives with their coefficients having simple form and structural regularity. By them, expressions based on directional derivatives for some typical differential operators are derived. This builds up a solid mathematical foundation for further study on numerical computation by the finite point method based on directional difference.
In this paper, we extend to a multivariate setting the bivariate model A introduced by Jin and Ren in 2014 (Recursions and fast Fourier transforms for a new bivariate aggregate claims model, Scandinavian Actuarial Journal 8) to model insurance aggregate claims in the case when different types of claims simultaneously affect an insurance portfolio. We obtain an exact recursive formula for the probability function of the multivariate compound distribution corresponding to this model under the assumption that the conditional multivariate counting distribution (conditioned by the total number of claims) is multinomial. Our formula extends the corresponding one from Jin and Ren.
For American option pricing, the Black-Scholes-Merton model can be discretized as a linear complementarity problem (LCP) by using some finite difference schemes. It is well known that the Projected Successive Over Relaxation (PSOR) has been widely applied to solve the resulted LCP. In this paper, we propose a fixed point iterative method to solve this type of LCPs, where the splitting technique of the matrix is used. We show that the proposed method is globally convergent under mild assumptions. The preliminary numerical results are reported, which demonstrate that the proposed method is more accurate than the PSOR for the problems we tested.
The large time L^{1}-behavior of the strong solution (including the first and second order spacial derivatives) to the incompressible magneto-hydrodynamic (MHD) equations is given in a half-space. The main tool employed in this article is a new weighted estimate for the Stokes flow in L^{1}(R_{+}^{n}), such a study is of independent interest.
In this article, we consider a class of seemingly unrelated single-index regression models. By taking the contemporaneous correlation among equations into account we construct the weighted estimators (WEs) for unknown parameters of the coefficients and the improved local polynomial estimators for the unknown functions, respectively. We establish the asymptotic normalities of these estimators, and show both of them are more asymptotically efficient than those ignoring the contemporaneous correlation. The performances of the proposed procedures are evaluated through simulation studies.
The paper of Dong[Dong, J. Classical solutions to one-dimensional stationary quantum Navier-Stokes equations, J. Math Pure Appl. 2011] which proved the existence of classical solutions to one-dimensional steady quantum Navier-Stokes equations, when the nonzero boundary value u_{0} satisfies some conditions. In this paper, we obtain a different version of existence theorem without restriction to u_{0}. As a byproduct, we get the existence result of classical solutions to the stationary quantum Navier-Stokes equations.
Filter back-projection (FBP) algorithms are available and extensively used methods for tomography. In this paper, we prove the convergence of FBP algorithms at any continuous point of image function, in L^{2}-norm and L^{1}-norm under the certain assumptions of image and window functions of FBP algorithms.
In this paper, we consider two variational models for speckle reduction of ultrasound images. By employing the Γ-convergence argument we show that the solution of the SO model coincides with the minimizer of the JY model. Furthermore, we incorporate the split Bregman technique to propose a fast alterative algorithm to solve the JY model. Some numerical experiments are presented to illustrate the efficiency of the proposed algorithm.
In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.
Fractional factorial split-plot (FFSP) designs are useful in practical experiments. When the numbers of levels of the factors are not all equal in an experiment, mixed-level design is selected. This paper investigates the conditions of a resolution III or IV FFSP design with both two-level and eight-level factors to have various clear effects, including two types of main effects and three types of two-factor interaction components.
The split graph K_{r}∨K_{s} on r+s vertices is denoted by S_{r,s}. A graphic sequence π=(d_{1},d_{2},…,d_{n}) is said to be potentially S_{r,s}-graphic if there is a realization of π containing S_{r,s} as a subgraph. In this paper, a simple sufficient condition for π to be potentially S_{r,s}-graphic is obtained, which extends an analogous condition for π to be potentially K_{r+1}-graphic due to Yin and Li (Discrete Math. 301 (2005) 218-227). As an application of this condition, we further determine the values of σ(S_{r,s},n) for n≥3r+3s-1.
In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a non-autonomous thermoelastic system by using the method of uniform contractive functions. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets. Moreover, we also investigate an alternative result of solutions to the semilinear thermoelastic systems by virtue of the semigroup method.
Longitudinal data often arise when subjects are followed over a period of time, and in many situations, there may exist informative observation times and a dependent terminal event such as death that stops the follow-up. In this article, we propose joint modeling and analysis of longitudinal data with possibly informative observation times and a dependent terminal event in which a common subject-specific latent variable is used to characterize the correlations. A borrow-strength estimation procedure is developed for parameter estimation, and both large-sample and finite-sample properties of the proposed estimators are established. In addition, some goodness-of-fit methods for assessing the adequacy of the model are provided. An application to a bladder cancer study is illustrated.
In this paper, we consider a two-dimensional perturbed risk model with stochastic premiums and certain dependence between the two marginal surplus processes. We obtain the Lundberg-type upper bound for the infinite-time ruin probability by martingale approach, discuss how the dependence affects the obtained upper bound and give some numerical examples to illustrate our results. For the heavy-tailed claims case, we derive an explicit asymptotic estimation for the finite-time ruin probability.
In a connected graph G, the distance d(u,v) denotes the distance between two vertices u and v of G. Let W={w_{1},w_{2},…,w_{k}} be an ordered set of vertices of G and let v be a vertex of G. The representation r(v|W) of v with respect to W is the k-tuple (d(v,w_{1}), d(v,w_{2}),…, d(v,w_{k})). The set W is called a resolving set or a locating set if every vertex of G is uniquely identified by its distances from the vertices of W, or equivalently, if distinct vertices of G have distinct representations with respect to W. A resolving set of minimum cardinality is called a metric basis for G and this cardinality is the metric dimension of G, denoted by β(G). Metric dimension is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). In this paper, we study the metric dimension of barycentric subdivision of Cayley graphs Cay(Z_{n}⊕Z_{2}). We prove that these subdivisions of Cayley graphs have constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of barycentric subdivision of Cayley graphs Cay(Z_{n}⊕Z_{2}).
In this paper, a diffusive predator-prey system of Holling type functional III is considered. For one hand, we considered the possibility of the occurrence of Turing patterns of the system. Our results show that there is no Turing patterns found in the system. On the other hand, we performed detailed Hopf bifurcation analysis to the systems, and showed that the system have multiple oscillatory patterns. Moreover, we also derived the conditions to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solutions. Computer simulations are included to support our theoretical analysis.
In this paper, we consider the problem of the optimal time-consistent investment and proportional reinsurance strategy under the mean-variance criterion, in which the insurer has some inside information at her disposal concerning the future realizations of her claims process. It is assumed that the surplus of the insurer is governed by a Brownian motion with drift, and the insurer has the possibility to reduce the risk by purchasing proportional reinsurance and investing in financial markets. We first formulate the problem and provide a verification theorem on the extended Hamilton-Jacobi-Bellman equations. Then, the closed-form expression is obtained for the optimal strategy of the optimization problem.
The existing methods of projection for solving convex feasibility problem may lead to slow convergence when the sequences enter some narrow "corridor" between two or more convex sets. In this paper, we apply a technique that may interrupt the monotonity of the constructed sequence to the sequential subgradient projection algorithm to construct a non-monotonous sequential subgradient projection algorithm for solving convex feasibility problem, which can leave such corridor by taking a big step at different steps during the iteration. Under some suitable conditions, the convergence is proved.We also compare the numerical performance of the proposed algorithm with that of the monotonous algorithm by numerical experiments.