BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES

This paper introduces a method of bootstrap wavelet estimation in a nonparametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.     

The asymptotic limit for a combustion model in regard to infinite reaction rate

The Zeldovich-von Neumann-Doring model and the Chapman-Jouguet model for a simplified combustion model-Majda＇s model is studied.The author proves a uniform maximum norm estimate,then proves that as the rate of chemical reaction tends to infinity the solutions to the Zeldovich-von Neumann-Doring model tend to that of the Chapman-Jouguet model.The type of combustion waves is studied.This result is compared with the result of the projection and finite difference method for the same model.     

一类基于变量分离的稳定化混合有限元方法

Based on a seperated model for saddle-point problems, we develop a new sta-bilized mixed finite element method. Such a model consists of two subproblems with respect to the primal and the dual variables, respectively. We show that the new method is coercive and that optimal error bounds hold. As an application,the nearly incompressible elastic problem is analyzed with our method.     

A Pole Assignment Design Method of Process Control System for Tubular Heat Exchanger

This paper has first studied the simplified model of tubular heat exchanger which is widely used in the industry and other field. On the basis of reference 2,a new pole assignment design method of process control system with derivative control action is found. For the above system, the method and the formation which calculate the feedback matrix K and gain matrix L is given,and the simulation of the system is made.     

A NEW INVERSION METHOD OF TIME-LAPSE SEISMIC

Time-Lapse Seismic improves oil recovery ratio by dynamic reservoir monitoring. Because of the large number of seismic explorations in the process of time-lapse seismic inversion, traditional methods need plenty of inversion calculations which cost high computational works. The method is therefore inefficient. In this paper, in order to reduce the repeating computations in traditional, a new time-lapse seismic inversion method is put forward. Firstly a homotopy-regularization method is proposed for the first time inversion. Secondly, with the first time inversion results as the initial value of following model, a model of the second time inversion is rebuilt by analyzing the characters of time-lapse seismic and localized inversion method is designed by using the model. Finally, through simulation, the comparison between traditional method and the new scheme is given. Our simulation results show that the new scheme could save the algorithm computations greatly.     

SUPER-GEOMETRIC CONVERGENCE OF A SPECTRAL ELEMENT METHOD FOR EIGENVALUE PROBLEMS WITH JUMP COEFFICIENTS

We propose and analyze a C^0 spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise constant coefficients case and verified by numerical tests. Furthermore, the asymptotical equivalence between a Gauss-Lobatto collocation method and a spectral Galerkin method is established for a simplified model.     

Nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization

We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational efforts. The global convergence and Q-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.     

A ROBUST DISCRETIZATION OF THE REISSNER-MINDLIN PLATE WITH ARBITRARY POLYNOMIAL DEGREE

A numerical scheme for the Reissner-Mindlin plate model is proposed.The method is based on a discrete Helmholtz decomposition and can be viewed as a generalization of the nonconforming finite element scheme of Arnold and Falk[SIAM J.Numer.Anal.,26(6):1276-1290,1989].The two unknowns in the discrete formulation are the in-plane rotations and the gradient of the vertical displacement.The decomposition of the discrete shear variable leads to equivalence with the usual Stokes system with penalty term plus two Poisson equations and the proposed method is equivalent to a stabilized discretization of the Stokes system that generalizes the Mini element.The method is proved to satisfy a best-approximation result which is robust with respect to the thickness parameter t.     

Generalized empirical likelihood inference in semiparametric regression model for longitudinal data

In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the model is suggested by introducing the working covariance matrix. It is proved that the proposed statistic is asymptotically standard chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. A simulation study is conducted to compare the proposed method with the generalized least squares method in terms of coverage accuracy and average lengths of the confidence intervals.     

Design of a new dynamical core for global atmospheric models based on some efficient numerical methods

A careful study on the integral properties of the primitive hydrostatic balance equations for baroclinic atmosphere is carried out, and a new scheme to design the global adiabatic model of atmospheric dynamics is presented. This scheme includes a method of weighted equal-area mesh and a fully discrete finite difference method with quadratic and linear conservations for solving the primitive equation system. Using this scheme, we established a new dynamical core with adjustable high resolution acceptable to the available     

Hopf bifurcation in symmetric configuration of predator-prey-mutualist systems

In this paper we apply the equivariant degree method to study Hopf bifurcations in a system of differential equations describing a symmetric predator-prey-mutualist model with diffusive migration between interacting communities. A topological classification (according to symmetry types), of symmetric Hopf bifurcation in configurations of populations with D₈, D₁₂, A₄ and S₄ symmetries, is presented with estimation on minimal number of bifurcating branches of periodic solutions.     

Birth of limit cycles bifurcating from a nonsmooth center

This paper is concerned with a codimension analysis of a two-fold singularity of piecewise smooth planar vector fields, when it behaves itself like a center of smooth vector fields (also called nondegenerate Σ-center). We prove that any nondegenerate Σ-center is Σ  -equivalent to a particular normal form _Z0$Z_0$. Given a positive integer number k   we explicitly construct families of piecewise smooth vector fields emerging from _Z0$Z_0$ that have k hyperbolic limit cycles bifurcating from the nondegenerate Σ  -center of _Z0$Z_0$ (the same holds for k=∞$k=\infty$). Moreover, we also exhibit families of piecewise smooth vector fields of codimension k   emerging from _Z0$Z_0$. As a consequence we prove that _Z0$Z_0$ has infinite codimension.     

Homoclinic orbits and Hopf bifurcations in delay differential systems with T-B singularity

The paper carries the results on Takens-Bogdanov bifurcation obtained in [T. Faria, L.T. Magalhães, Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity, J. Differential Equations 122 (1995) 201-224] for scalar delay differential equations over to the case of delay differential systems with parameters. Firstly, we give feasible algorithms for the determination of Takens-Bogdanov singularity and the generalized eigenspace associated with zero eigenvalue in Rn. Next, through center manifold reduction and normal form calculation, a concrete reduced form for the parameterized delay differential systems is obtained. Finally, we describe the bifurcation behavior of the parameterized delay differential systems with T-B singularity in detail and present an example to illustrate the results.     

Resonance bifurcation from homoclinic cycles

Differential equations that are equivariant under the action of a finite group can possess robust homoclinic cycles that can moreover be asymptotically stable. For differential equations in R⁴ there exists a classification of different robust homoclinic cycles for which moreover eigenvalue conditions for asymptotic stability are known. We study resonance bifurcations that destroy the asymptotic stability of robust ‘simple homoclinic cycles’ in four-dimensional differential equations. We establish that typically a periodic trajectory near the cycle is created, asymptotically stable in the supercritical case.     

Bifurcation and chaos near sliding homoclinics

We study the chaotic behaviour of a time dependent perturbation of a discontinuous differential equation whose unperturbed part has a sliding homoclinic orbit that is a solution homoclinic to a hyperbolic fixed point with a part belonging to a discontinuity surface. We assume the time dependent perturbation satisfies a kind of recurrence condition which is satisfied by almost periodic perturbations. Following a functional analytic approach we construct a Melnikov-like function M(α) in such a way that if M(α) has a simple zero at some point, then the system has solutions that behave chaotically. Applications of this result to quasi-periodic systems are also given.     

On the period of the limit cycles appearing in one-parameter bifurcations

The generic isolated bifurcations for one-parameter families of smooth planar vector fields {X_μ} which give rise to periodic orbits are: the Andronov-Hopf bifurcation, the bifurcation from a semi-stable periodic orbit, the saddle-node loop bifurcation and the saddle loop bifurcation. In this paper we obtain the dominant term of the asymptotic behaviour of the period of the limit cycles appearing in each of these bifurcations in terms of μ when we are near the bifurcation. The method used to study the first two bifurcations is also used to solve the same problem in another two situations: a generalization of the Andronov-Hopf bifurcation to vector fields starting with a special monodromic jet; and the Hopf bifurcation at infinity for families of polynomial vector fields.     

A nondensity property of preperiodic points on Chebyshev dynamical systems

Let k be a number field with algebraic closure , and let S be a finite set of primes of k, containing all the infinite ones. Consider a Chebyshev dynamical system on P². Fix the effective divisor D of P² that is equal to a line nondegenerate on²[−2,2]. Then we will prove that the set of preperiodic points on which are S-integral relative to D is not Zariski dense in P².     

Linear quivers, generic extensions and Kashiwara operators

In the present paper, we introduce the generic extension graph G of a Dynkin or cyclic quiver Q and then compare this graph with the crystal graph C for the quantized enveloping algebra associated to Q via two maps ℘_Q, _Q : Ω → Λ_Q induced by generic extensions and Kashiwara operators, respectively, where Λ_Q is the set of isoclasses of nilpotent representations of Q, and Ω is the set of all words on the alphabet I, the vertex set of Q. We prove that, if Q is a (finite or infinite) linear quiver, then the intersection of the fibres ℘_Q⁻¹ (λ) and KQ⁻¹ (λ) is non-empty for every λ ∈ Λ _Q. We will also show that this non-emptyness property fails for cyclic quivers.     

The σ-isotypic decomposition and the σ-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Γ-reversible-equivariant mappings, where Γ is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the σ-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Γ, two algebraic formulae are established for the computation of the σ-index of a closed subgroup of Γ. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented.     

Dynamic Hopf bifurcations generated by nonlinear terms

We consider the so-called delayed loss of stability phenomenon for singularly perturbed systems of differential equations in case that the associated autonomous system with a scalar parameter undergoes the Hopf bifurcation at the zero equilibrium point. It is assumed that the linearization of the associated system is independent of the parameter and the next terms in the expansion of the right-hand parts at zero are positive homogeneous of order α>1. Simple formulas are presented to estimate the asymptotic delay for the delayed loss of stability phenomenon. More precisely, we suggest sufficient conditions which ensure that zeros of a simple function ψ defined by the positive homogeneous nonlinear terms are the Hopf bifurcation points of the associated system, the sign of ψ at other points determines stability of the zero equilibrium, and the asymptotic delay equals the distance between the bifurcation point and a zero of some primitive of ψ.