We study solutions of almost periodic linear differential systems. This field is called the Favard theory what is based on the famous Favard result in [10] (see, e.g., [3, Theorem 1.2] or [28, Theorem 1]). It is a well-known corollary of the Favard (and the Floquet) theory that any bounded solution of a periodic linear differential system is almost periodic (see [12, Corollary 6.5] and [13] for...

in this paper, we are going to study the g-natural metrics on the tangent bundle of finslermanifolds. we concentrate on the complex and kählerian and hermitian structures associated with finslermanifolds via g-natural metrics. we prove that the almost complex structure induced by this metric is acomplex structure on tangent bundle if and only if the finsler metric is of scalar flag curvature. t...

In this paper, we study the iterative algorithms for saddle point problems(SPP). Bai, Golub and Pan recently studied a class of preconditioned Hermitian and skew-Hermitian splitting methods(PHSS). By further accelerating it with another parameters, using the Hermitian/skew-Hermitian splitting iteration technique we present the generalized preconditioned Hermitian and skew-Hermitian splitting me...

We show (a) that any entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C with the Euclidean metric is flat; (b) that any space-like entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C with the pseudo-Euclidean metric is flat if the Hessian of the potential is bounded below quadratically; and (c) the Hermitian counterpart of (b) for the...

With the change of variables U = U*q, substitution into (21) results in UCU*q = Ud. Consequently, the solution vector U of (20) can be obtained from the solution vector q of (22) or q can be obtained from U. Note that if a system of real equations is Toeplitz-plus-Hankel (T + H) , where T i s symmetric Toeplitz and H i s skew-centrosym-metric Hankel, then the equations may be transformed into H...

Comparing the lopsided Hermitian/skew-Hermitian splitting (LHSS) method and Hermitian/skewHermitian splitting (HSS) method, a new criterion for choosing the above two methods is presented, which is better than that of Li, Huang and Liu [Modified Hermitian and skew-Hermitian splitting methods for nonHermitian positive-definite linear systems, Numer. Lin. Alg. Appl., 14 (2007): 217-235]. Key-Word...

We describe an extension to ScaLAPACK for computing with symmetric (and hermitian) matrices stored in a packed form. This is similar to the compact storage for symmetric (and hermitian) matrices available in LAPACK [2]. This enables more efficient use of memory by storing only the lower or upper triangular part of a symmetric matrix. The capabilities include Choleksy factorization (PxSPTRF) and...

We describe a new extension to ScaLAPACK [2] for computing with symmetric (Hermi-tian) matrices stored in a packed form. The new code is built upon the ScaLAPACK routines for full dense storage for a high degree of software reuse. The original ScaLAPACK stores a symmetric matrix as a full matrix but accesses only the lower or upper triangular part. The new code enables more efficient use of mem...

We investigate Monge-Ampère type equations on almost Hermitian manifolds and show an \(a\) \(priori\) \(L^\infty\) estimate for a smooth solution of these equations.