Projective vector fields on Finsler manifolds

In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold.     

Stabilization of 4-manifolds

The complex surface X obtained by 8 points blown up on CP2 and Barlow’s surface Y are homeomorphic,but not diffeomorphic.Using the Gromov-Witten invariant Ruan showed that the stabilized manifolds X×S2and Y×S2are not deformation equivalent.In this note,we show that the stabilized manifolds X×S1and Y×S1are diffeomorphic and non-deformation equivalent in cosymplectic sense.     

One Nonparabolic End Theorem on Kahler Manifolds

In this paper, the complete noncompact Kahler manifolds satisfying the weighted Poincare inequality are considered and one nonparabolic end theorem which generalizes Munteanu＇s result is obtained.     

Bifurcation in the stable manifold of a chemostat with general polynomial yields

A three‐dimensional chemostat with nth‐ and mth‐order polynomial yields, instead of the particular ones such as A+BS, A+BS², A+BS³, A+BS⁴, A+BS² + CS³, and A+BSⁿ, is proposed. The existence of limit cycles in the two‐dimensional stable manifold, the Hopf bifurcation, and the stability of the periodic solution created by the bifurcation is proved. Copyright © 2009 John Wiley & Sons, Ltd.     

Periodic problem for a nonlinear‐damped wave equation on the boundary

In this work we investigate the existence of periodic solutions in t for the following problem: We employ elliptic regularization and monotone method. We consider $\mbox{\boldmath{$\Omega$}}\mbox{\boldmath{$\subset$}}{\mathbb{R}}^{{{n}}} \ (n\geqslant 1)$ an open bounded set that has regular boundary Γ and Q=Ω ×(0,T), T>0, a cylinder of ${\mathbb{R}}^{n+1}$ with lateral boundary Σ = Γ × (0,T). Copyright © 2009 John Wiley & Sons, Ltd.     

Globally Hyperbolic Regularization of Grad's Moment System

In this paper, we propose a globally hyperbolic regularization to the general Grad's moment system in multidimensional spaces. Systems with moments up to an arbitrary order are studied. The characteristic speeds of the regularized moment system can be analytically given and depend only on the macroscopic velocity and the temperature. The structure of the eigenvalues and eigenvectors of the coefficient matrix is fully clarified. The regularization together with the properties of the resulting moment systems is consistent with the simple one‐dimensional case discussed in ¹. In addition, all characteristic waves are proven to be genuinely nonlinear or linearly degenerate, and the studies on the properties of rarefaction waves, contact discontinuities, and shock waves are included. © 2014 Wiley Periodicals, Inc.     

Remarks on the controllability of fractional differential equations

In this paper, we study the approximate controllability of a linear fractional differential equation by using the method of regularization of Tikhonov. New concepts and results about controllability are established. Then, under the condition of the positivity of the controllability operator, we obtain that the linear system can be steered to an arbitrary small neighbourhood of the fractional integral of the state at final time.     

Estimation of vector ARMAX models

The asymptotic properties of maximum likelihood estimates of a vector ARMAX system are considered under general conditions, relating to the nature of the exogenous variables and the innovation sequence and to the form of the parameterization of the rational transfer functions, from exogenous variables and innovations to the output vector. The exogenous variables are assumed to be such that the sample serial covariances converge to limits. The innovations are assumed to be martingale differences and to be nondeterministic in a fairly weak sense. Stronger conditions ensure that the asymptotic distribution of the estimates has the same covariance matrix as for Gaussian innovations but these stronger conditions are somewhat implausible. With each ARMAX structure may be associated an integer (the McMillan degree) and all structures for a given value of this integer may be topologised as an analytic manifold. Other parameterizations and topologisations of spaces of structures as analytic manifolds may also be considered and the presentation is sufficiently general to cover a wide range of these. Greater generality is also achieved by allowing for general forms of constraints.     

Numerical integration of ordinary differential equations on manifolds

Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions” defined by nonvanishing Lie brackets.     

The Totally Geodesic Coisotropic Submanifolds in Kähler Manifolds

In this paper, we consider the coisotropic submanifolds in a Kähler manifold of nonnegative holomorphic curvature. We prove an intersection theorem for compact totally geodesic coisotropic submanifolds and discuss some topological obstructions for the existence of such submanifolds. Our results apply to Lagrangian submanifolds and real hypersurfaces since the class of coisotropic submanifolds includes them. As an application, we give a fixed-point theorem for compact Kähler manifolds with positive holomorphic curvature. Also, our results can be further extended to nearly Kähler manifolds.