We define two nonlinear shell models whereby the deformation of an elastic shell with small thickness minimizes ad hoc functionals over sets of admissible deformations of Kirchhoff-Love type. We establish that both models are close in a specific sense to the well-known nonlinear shell model of W.T. Koiter and that one of them has a solution, by contrast with Koiter's model for which such an existence theorem is yet to be proven.

We consider a previously proposed general nonlinear poromechanical formulation, and we derive a linearized version of this model. For this linearized model, we obtain an existence result and we propose a complete discretization strategy-in time and space-with a special concern for issues associated with incompressible or nearly-incompressible behavior. We provide a detailed mathematical analysis of this strategy, the main result being an error estimate uniform with respect to the compressibility parameter. We then illustrate our approach with detailed simulation results and we numerically investigate the importance of the assumptions made in the analysis, including the fulfillment of specific inf-sup conditions.

The advection-diffusion equation y_t^ε -εy_xx^ε + My_x^ε=0, (x, t) ∈ (0, 1)×(0, T) is null controllable for any strictly positive values of the diffusion coefficient ε and of the controllability time T. We discuss here the behavior of the cost of control when the coefficient ε goes to zero, according to the values of T. It is actually known that this cost is uniformly bounded with respect to ε if T is greater than a minimal time T_M, with T_M in the interval[1, 2√3]/M for M > 0 and in the interval[2√2, 2(1 + √3)]/|M|for M < 0. The exact value of T_M is however unknown.
We investigate in this work the determination of the minimal time T_M employing two distincts but complementary approaches. In a first one, we numerically estimate the cost of controllability, reformulated as the solution of a generalized eigenvalue problem for the underlying control operator, with respect to the parameter T and ε. This allows notably to exhibit the structure of initial data leading to large costs of control. At the practical level, this evaluation requires the non trivial and challenging approximation of null controls for the advection-diffusion equation. In the second approach, we perform an asymptotic analysis, with respect to the parameter ε, of the optimality system associated to the control of minimal L²-norm. The matched asymptotic expansion method is used to describe the multiple boundary layers.

The human tricuspid valve, one of the key cardiac structures, plays an important role in the circulatory system. However, there are few mathematical models to accurately simulate it.
In this paper, firstly, we consider the tricuspid valve as an elastic shell with a specific shape and establish its novel geometric model. Concretely, the anterior, the posterior and the septal leaflets of the valve are supposed to be portions of the union of two interfacing semi-elliptic cylindrical shells when they are fully open.
Next, we use Koiter's linear shell model to describe the tricuspid valve leaflets in the static case, and provide a numerical scheme for this elastostatics model. Specifically, we discretize the space variable, i.e., the two tangent components of the displacement are discretized by using conforming finite elements (linear triangles) and the normal component of the displacement is discretized by using conforming Hsieh-Clough-Tocher triangles (HCT triangles).
Finally, we make numerical experiments for the tricuspid valve and analyze the outcome. The numerical results show that the proposed mathematical model describes well the human tricuspid valve subjected to applied forces.

This paper is concerned with the inflow problem for one-dimensional compressible Navier-Stokes equations. For such a problem, Huang, Matsumura, and Shi showed in[4] that there exists viscous shock wave solution to the inflow problem and both the boundary layer solution, the viscous shock wave, and their superposition are time-asymptotically nonlinear stable provided that both the initial perturbation and the boundary velocity are assumed to be sufficiently small. The main purpose of this paper is to show that similar stability results still hold for a class of large initial perturbation which can allow the initial density to have large oscillations. The proofs are given by an elementary energy method and our main idea is to use the smallness of the strength of the viscous shock wave and the boundary velocity to control the possible growth of the solutions induced by the nonlinearity of the compressible Navier-Stokes equations and the inflow boundary condition. The key point in our analysis is to deduce the desired uniform positive lower and upper bounds on the density.

A formal asymptotics leading from a system of Boltzmann equations for mixtures towards either Vlasov-Navier-Stokes or Vlasov-Stokes equations of incompressible fluids was established by the same authors and Etienne Bernard in:A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory Commun. Math. Sci., 15:1703-1741 (2017) and A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures. KRM, 11:43-69 (2018). With the same starting point but with a different scaling, we establish here a formal asymptotics leading to the Vlasov-Euler system of compressible fluids. Explicit formulas for the coupling terms are obtained in two typical situations:for elastic hard spheres on one hand, and for collisions corresponding to the inelastic interaction with a macroscopic dust speck on the other hand.

This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions with the same period for both hard and soft potentials, provided that the time-periodic boundary temperature is sufficiently close to a stationary one which has small variations around a positive constant. The dynamical stability of time-periodic profiles is also proved under small perturbations, and this in turn yields the non-negativity of the profile. For the proof, we develop new estimates in the time-periodic setting.

In this paper, we consider the lifespan of solution to the MHD boundary layer system as an analytic perturbation of general shear flow. By using the cancellation mechanism in the system observed in[12], the lifespan of solution is shown to have a lower bound in the order of ε^-2- if the strength of the perturbation is of the order of ε. Since there is no restriction on the strength of the shear flow and the lifespan estimate is larger than the one obtained for the classical Prandtl system in this setting, it reveals the stabilizing effect of the magnetic field on the electrically conducting fluid near the boundary.

This paper surveys some results on the existence and stability of solutions to some partial differential equations of gaseous stars in the framework of Newtonian mechanics, and presents some key ideas in the proofs.

This paper summarizes the parameter estimation of systems with set-valued signals, which can be classified to three catalogs:one-time completed algorithms, iterative methods and recursive algorithms. For one-time completed algorithms, empirical measure method is one of the earliest methods to estimate parameters by using set-valued signals, which has been applied to the adaptive tracking of periodic target signals. The iterative methods seek numerical solutions of the maximum likelihood estimation, which have been applied to both complex diseases diagnosis and radar target recognition. The recursive algorithms are constructed via stochastic approximation and stochastic gradient methods, which have been applied to adaptive tracking of non-periodic signals.

The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE method guarantees the consistency of its estimators under working correlation structure misspecification, the corresponding efficiency can be severely affected. In this paper, we propose a new two-step estimation method in which the correlation matrix is assumed to be a linear combination of some known working matrices. Asymptotic properties of the new estimators are developed. Simulation studies are conducted to examine the performance of the proposed estimators. We illustrate the methodology with an epileptic data set.

In this article, we consider the varying coefficient multiplicative regression model, which is very useful to model the positive response. The criterion of least product relative error (LPRE) is extended to the varying coefficient multiplicative regression model by kernel smoothing techniques. Consistency and asymptotic normality of the proposed estimator are established. Some numerical simulations are carried out to assess the performance of the proposed estimator. As an illustration, the ethanol data is analyzed.

For the hypersonic inlet and fore-body integrated design, the non-uniform incoming flow generated by the fore-body will bring a relatively big challenge to the inward-turning inlet design. To make the inlet match the non-uniform incoming flow, this paper, based on previous studies, develops a cross-stream marching plus (CSMP) method, by which an aerodynamic surface used to generate a given shock shape can be acquired. The method can correct such solution points as may give rise to grid distortions or flow-field abnormity and overcome the shortcoming of the insufficient stability of previous methods. Numerical simulation results of the conical supersonic flowfield show that the error obtained from the proposed CSMP method drops with the reduction of the grid dimension and the marching step, being less than 0.05% for reducing the marching step to 10%; that with this method the maximum relative error of the pressure on the profile is less than 0.23%. In the design process of the inward-turning inlets that match the fuselage fore-body, it's found that in comparison with the results of the inviscid CFD results, the aerodynamic surface designed with the CSMP method can fully generate the given shock wave shape. Thus, the CSMP method provides a new direction for the inlet/fore-body integrated design.

In this paper, we consider an improved model of pricing vulnerable options with credit risk. We assume that the vulnerable European options not only face default risk, but also face the rare shocks of the underlying assets and the counterparty assets. The dynamics of two correlated assets are modeled as a class of jump diffusion processes. Furthermore, we assume that the dynamic of the corporate liability is a geometric Brownian motion that is related to the underlying asset and the counterparty asset. Under this new framework, we give an explicit pricing formula of the vulnerable European options.

Gutman and Wagner (in the matching energy of a graph, Disc. Appl. Math., 2012) defined the matching energy of a graph and pointed out that its chemical applications go back to the 1970s. Now the research on matching energy mainly focuses on graphs with pendent vertices and only a few papers reported the progress on matching energy of graphs without pendent vertices. For a random six-membered ring spiro chain, the number of k-matchings and the matching energy are random variables. In this paper, we determine the extremal graphs with respect to the matching energy for random six-membered ring spiro chains which have no pendent vertices.

This paper deals with eigenvalue problems for linear Fredholm integral equations of the second kind with weakly singular kernels. A new discrete method is proposed for the approximation of eigenvalues. Compactness of the integral operator in L¹[0, 1] space is obtained. This method is based on the approximation of the integral operator by modified interpolatory projection. Different from traditional methods, norm convergence of operator approximation is proved theoretically. Further, convergence of eigenvalue approximation is obtained by analytical tools. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method.

In this article, we study homogenization of a parabolic linear problem governed by a coefficient matrix with rapid spatial and temporal oscillations in periodically perforated domains with homogeneous Neumann data on the boundary of the holes. We prove results adapted to the problem for characterization of multiscale limits for gradients and very weak multiscale convergence.

In this paper, we present a neighborhood following primal-dual interior-point algorithm for solving symmetric cone convex quadratic programming problems, where the objective function is a convex quadratic function and the feasible set is the intersection of an affine subspace and a symmetric cone attached to a Euclidean Jordan algebra. The algorithm is based on the[13] broad class of commutative search directions for cone of semidefinite matrices, extended by[18] to arbitrary symmetric cones. Despite the fact that the neighborhood is wider, which allows the iterates move towards optimality with longer steps, the complexity iteration bound remains as the same result of Schmieta and Alizadeh for symmetric cone optimization problems.

In this paper, we investigate standing waves in discrete nonlinear Schrödinger equations with nonperiodic bounded potentials. By using the critical point theory and the spectral theory of self-adjoint operators, we prove the existence and infinitely many sign-changing solutions of the equation. The results on the exponential decay of standing waves are also provided.

In this paper, we use the Green's function method to get the pointwise convergence rate of the semilinear pseudo-parabolic equations. By using this precise pointwise structure and introducing negative index Sobolev space condition on the initial data, we release the critical index of the nonlinearity for blowing up. Our result shows that the global existence does not only depend on the nonlinearity but also the initial condition.

As an extension of partially linear models and additive models, partially linear additive model is useful in statistical modelling. This paper proposes an empirical likelihood based approach for testing serial correlation in this semiparametric model. The proposed test method can test not only zero first-order serial correlation, but also higher-order serial correlation. Under the null hypothesis of no serial correlation, the test statistic is shown to follow asymptotically a chi-square distribution. Furthermore, a simulation study is conducted to illustrate the performance of the proposed method.

A dynamic actual demand function was used to portray a market environment for fast moving consumer goods and to establish oligopoly differential games under price competition. We confirmed the stable point in n-player price competition as the saddle point of differential games, and acquired the optimal price and demand at equilibrium. Analysis on optimal price and demand shows that, to obtain more profits, a manufacturer should control costs, rapidly occupy the market, and improve product uniqueness.

Censored regression ("Tobit") model is a special case of limited dependent variable regression model, and plays an important role in econometrics. Based on this model, all kinds of methods for variable or group variable selection have been developed and the corresponding shrinkage parameter estimates are widely studied. However, asymptotic distributions of the shrinkage estimates involve unknown nuisance parameters, such as density function of error term. To avoid estimating nuisance parameters, this paper presents a randomly weighting method to approximate to the asymptotic distribution of the shrinkage estimate. A computation procedure of random approximation is provided and asymptotic properties of the randomly weighting estimates are also obtained. The proposed methods are evaluated with extensively numerical studies and a women labor supply example.

We consider the problems of minimizing the sum of a continuously differentiable convex function and a nonsmooth convex function in this paper. These problems arise in many applications of practical interest. A class of alternating linearization methods is presented for solving these problems. The global convergence rate is also obtained under certain mild conditions. Numerical experiments validate the theoretical convergence analysis and verify the implementation of the proposed algorithm.

A graph is called traceable if it contains a Hamilton path, i.e., a path passing through all the vertices. Let G be a graph on n vertices. G is called claw-_o-1-heavy if every induced claw (K_1,3) of G has a pair of nonadjacent vertices with degree sum at least n - 1 in G. In this paper we show that a claw-_o-1-heavy graph G is traceable if we impose certain additional conditions on G involving forbidden induced subgraphs.

For a graph G=(V, E) without isolated vertex, a function f:E(G) → {-1, 1} is said to be a signed star dominating function of G if ∑_e∈E(v) f(e) ≥ 1 for every v ∈ V (G), where E(v)={uv ∈ E(G)|u ∈ V (G)}. The minimum value of ∑_e∈E(G) f(e), taken over all signed star dominating functions f of G, is called the signed star domination number of G and is denoted by γ_ss(G). This paper studies the bounds and algorithms of signed star domination numbers in some classes of graphs. In particular, sharp bounds for the signed star domination number of a general graph and a linear-time algorithm for the signed star domination problem in a tree is presented.

Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical (in short, fractional ID-k-factor-critical) if G - I has a fractional k-factor for every independent set I of G. In this paper, we present a sufficient condition for a graph to be fractional ID-k-factor-critical, depending on the minimum degree and the neighborhoods of independent sets. Furthermore, it is shown that this result in this paper is best possible in some sense.

A non-increasing sequence π=(d₁, d₂,…, d_n) of nonnegative integers is said to be potentially hamiltonian-graphic (resp. potentially pancyclic-graphic) if it is realizable by a simple graph on n vertices containing a hamiltonian cycle (resp. containing cycles of every length from 3 to n). A.R. Rao and S.B. Rao (J. Combin. Theory Ser.B, 13(1972), 185-191) and Kundu (Discrete Math., 6(1973), 367-376) presented a characterization of π=(d₁, d₂,…, d_n) that is potentially hamiltonian-graphic. S.B. Rao (Lecture Notes in Math., No. 855, Springer Verlag, 1981, 417-440, Unsolved Problem 2) further posed the following problem:present a characterization of π=(d₁, d₂,…, d_n) that is potentially pancyclic-graphic. In this paper, we first give solution to this problem for the case of 4 ≤ n ≤ 11. Moreover, we also show that a near regular graphic sequence π=(d₁, d₂,…, d_n) with d_n ≥ 3 is potentially pancyclic-graphic.

In this paper, we focus on studying the asymptotic stability of the monotone decreasing kink profile solitary wave solutions for the generalized KdV-Burgers equation. We obtain the estimate of the firstorder and second-order derivatives for monotone decreasing kink profile solitary wave solutions, and overcome the difficulties caused by high-order nonlinear terms in the generalized KdV-Burgers equation in the estimate by using L² energy estimating method and Young inequality. We prove that the monotone decreasing kink profile solitary wave solutions are asymptotically stable in H¹. Moreover, we obtain the decay rate of the perturbation ψ in the sense of L² and L^∞ norm, respectively, which are (1 + t)^-1/2 and (1 + t)^-1/4 by using Gargliado-Nirenberg inequality.

This paper considers a nonparametric M-estimator of a regression function for functional stationary ergodic data. More precisely, in the ergodic data setting, we consider the regression of a real random variable Y over an explanatory random variable X taking values in some semi-metric abstract space. Under some mild conditions, the weak consistency and the asymptotic normality of the M-estimator are established. Furthermore, a simulated example is provided to examine the finite sample performance of the M-estimator.

The objective of this paper is to study the issue of uniformity on three-level U-type designs in terms of the wrap-around L²-discrepancy. Based on the known formula, we present a new lower bound of wrap-around L²-discrepancy for three-level U-type designs and compare it with those existing ones through figures, numerical simulation and illustrative examples.

On the one hand, we investigate the Bahadur representation for sample quantiles under φ-mixing sequence with φ(n)=O(n^-3) and obtain a rate as O (n^-3/4 log n), a.s. On the other hand, by relaxing the condition of mixing coefficients to Σ_n=1^∞φ^1/2(n) < ∞, a rate O(n^-1/2(log n)^1/2), a.s., is also obtained.

This paper considers the mathematical programs with equilibrium constraints (MPEC). It is wellknown that, due to the existence of equilibrium constraints, the Mangasarian-Fromovitz constraint qualification does not hold at any feasible point of MPEC and hence, in general, the developed numerical algorithms for standard nonlinear programming problems can not be applied to solve MPEC directly. During the past two decades, much research has been done to develop numerical algorithms and study optimality, stability, and sensitivity for MPEC. However, there are very few results on duality for MPEC in the literature. In this paper, we present a Wolfe-type duality for MPEC and, under some suitable conditions, we establish various duality theorems such as the weak duality, direct duality, converse duality, and strict converse duality theorems. We further show that a linear MPEC is equivalent to a linear programming problem in some sense.

Partly interval censored data frequently occur in many areas including clinical trials, epidemiology research, and medical follow-up studies. When data come from observational studies, we need to carefully adjust for the confounding bias in order to estimate the true treatment effect. Pair matching designs are popular for removing confounding bias without parametric assumptions. With time-to-event outcomes, there are some literature for hypothesis testing with paired right censored data, but not for interval censored data. O'Brien and Fleming extended the Prentice Wilcoxon test to right censored paired data by making use of the PrenticeWilcoxon scores. Akritas proposed the Akritas test and established its asymptotic properties. We extend Akritas test to partly interval censored data. We estimate the survival distribution function by nonparametric maximum likelihood estimation (NPMLE), and prove the asymptotic validity of the new test. To improve our test under small sample size or extreme distributions, we also propose a modified version using the rank of the score difference. Simulation results indicate that our proposed methods have very good performance.

In the article, we investigate a general class of semiparametric hazards regression models for recurrent gap times. The general class includes the proportional hazards model, the accelerated failure time model and the accelerated hazards models as special cases. The model is flexible in modelling recurrent gap times since a covariate effect is identified as having two separate components, namely a time-scale change on hazard progression and a relative hazards ratio. In order to infer the model parameters, the procedure is proposed based on estimating equations. The asymptotic properties of the proposed estimators are established and the finite sample properties are investigated via simulation studies. In addition, a lack of fit test is presented to assess the adequacy of the model and an application of data from a bladder cancer study is reported for illustration.

Using the Mönch fixed point theorem and progressive estimation method, we study the existence, uniqueness and regularity of mild solutions for damped second order impulsive functional differential equations with infinite delay in Banach spaces. The compactness assumption on associated family of operators and the impulsive term, some restrictive conditions on a priori estimation, noncompactness measure estimation and the impulsive term have not been used, our results are different from some known results. Finally, a noncompact semigroup example explains the obtained results.

The degree d(H) of a subgraph H of a graph G is|∪_u∈V(H) N(u)-V(H)|, where N(u) denotes the neighbor set of the vertex u of G. In this paper, we prove the following result on the condition of the degrees of subgraphs. Let G be a 2-connected claw-free graph of order n with minimum degree δ(G) ≥ 3. If for any three non-adjacent subgraphs H₁, H₂, H₃ that are isomorphic to K₁, K₁, K₂, respectively, there is d(H₁) + d(H₂) + d(H₃) ≥ n + 3, then for each pair of vertices u, v ∈ G that is not a cut set, there exists a Hamilton path between u and v.

For the variational inequality with symmetric cone constraints problem, we consider using the inexact modified Newton method to efficiently solve it. It provides a unified framework for dealing with the variational inequality with nonlinear constraints, variational inequality with the second-order cone constraints, and the variational inequality with semi-definite cone constraints. We show that each stationary point of the unconstrained minimization reformulation based on the Fischer-Burmeister merit function is a solution to the problem. It is proved that the proposed algorithm is globally convergent under suitable conditions. The computation results show that the feasibility and efficiency of our algorithm.

Zero-utility principle is one of the main premium pricing principles, which has been widely used in insurance practice. In this paper, the nonparametric estimation of zero-utility premium is given. In addition, the consistency and asymptotic normality of the estimation are proved. Some special cases including linear, exponential and quadratic utility are discussed. Finally, the Monte Carlo method is used to show the convergence rate of premium estimation. Furthermore, the histogram and Normal-Probability-Plot are given to investigate the asymptotic normality of the estimators. The results show that our estimations are good enough to use in practice.