非正曲率度量空间的若干性质

我们讨论了非正曲率度量空间（ＮＰＣ空间）的弱收敛、弱紧性、正规结构、不动点性质,证明了该空间具有正规结构以及在有界闭凸集上的非扩张映射具有不动点。     

Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization

In this paper, we propose a robust sequential quadratic programming (SQP) method for nonlinear programming without using any explicit penalty function and filter. The method embeds the modified QP subproblem proposed by Burke and Han (Math Program 43:277–303, 1989) for the search direction, which overcomes the common difficulty in the traditional SQP methods, namely the inconsistency of the quadratic programming subproblems. A non-monotonic technique is employed further in a framework in which the trial point is accepted whenever there is a sufficient relaxed reduction of the objective function or the constraint violation function. A forcing sequence possibly tending to zero is introduced to control the constraint violation dynamically, which is able to prevent the constraint violation from over-relaxing and plays a crucial role in global convergence and the local fast convergence as well. We prove that the method converges globally without the Mangasarian–Fromovitz constraint qualification (MFCQ). In particular, we show that any feasible limit point that satisfies the relaxed constant positive linear dependence constraint qualification is also a Karush–Kuhn–Tucker point. Under the strict MFCQ and the second order sufficient condition, furthermore, we establish the superlinear convergence. Preliminary numerical results show the efficiency of our method.     

A nonmonotone filter method for nonlinear optimization

We propose a new nonmonotone filter method to promote global and fast local convergence for sequential quadratic programming algorithms. Our method uses two filters: a standard, global g-filter for global convergence, and a local nonmonotone l-filter that allows us to establish fast local convergence. We show how to switch between the two filters efficiently, and we prove global and superlinear local convergence. A special feature of the proposed method is that it does not require second-order correction steps. We present preliminary numerical results comparing our implementation with a classical filter SQP method.     

Nontrivial solutions for asymptotically linear hamiltonian systems with Lagrangian boundary conditions

In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory developed by the first author.     

On the Range of the Pseudomonotone Second-Order Cone Linear Complementarity Problem

In this paper, we provide a complete characterization of the range of the pseudomonotone second-order cone linear complementarity problem. In particular, by answering the three questions that under what conditions the range is the whole space, convex and closed, respectively, we explicitly characterize and formulate the range of the pseudomonotone second-order cone linear complementarity problem.     

Communication: A dramatic transition from nonferromagnet to ferromagnet in finite fused-azulene chain

One-dimensional fused-azulene oligomers (n = 2-6) are studied with the effective valence bond as well as density functional theory methods. A nonferromagnetic (closed-shell singlet) to ferromagnetic (triplet) ground state transformation is witnessed with increasing length of oligomers. The computational results are interpreted in terms of spin coupling between the unpaired electrons of two nonbonding molecular orbitals localized, respectively, on the top and bottom chains of the oligomers. The present study provides a theoretical suggestion for understanding the ferromagnetic spin polarizations that has been observed very recently in graphene nanoribbons.     

Excitation energy calculation of conjugated hydrocarbons: a new Pariser-Parr-Pople model parameterization approaching CASPT2 accuracy

A new parameterization for the Pariser-Parr-Pople (PPP) model for conjugated hydrocarbons is proposed in this work. The distance-dependence of PPP parameters are obtained from CASPT2 ground state and low-lying excited state energies of ethylene and its cation at various C-C single bond lengths and are fitted to a set of carefully chosen mathematical functions. Our new PPP model is applied to the calculation of vertical singlet-triplet energy gaps and the excitation energies for low-lying π→π(*) valence excitations in various π-conjugated molecules. Results with the new PPP model are consistently better than the standard PPP model in use. It often surpasses density functional theory and single-reference excited state methods such as configuration interaction singles or time-dependent density functional theory in terms of its accuracy and agrees reasonably well with high-level theories or experiments.     

Magnetic anisotropy properties of CoZrNb thin films deposited on PET substrate by magnetron sputtering

Soft magnetism and magnetic anisotropy properties of CoZrNb thin films deposited on polyethylene terephthalate (PET) substrate by magnetron sputtering were investigated. As the film thickness increases, the coercivity of films decreases from 7 to 4 Oe. It exhibits an in-plane uniaxial magnetic anisotropy as the thickness of CoZrNb thin films increases. An easy axis is observed in CoZrNb films along the direction transverse to the rolling direction of the polymer web.     

Theoretical study of very high spin organic pi-conjugated polyradicals

Different forms of pi-conjugated polyarylmethyl systems, such as diradicals, polyradicals, spin clusters, and polymers, were studied with valence bond (VB) calculations within the density matrix renormalization group (DMRG) framework. For these systems, the energy gap between the high-spin ground state and the lowest low-spin excited state (DeltaE(L-H)) was computed and found to correlate well with their stability. On the basis of our analysis, medium-sized polyarylmethyl cycles are suggested to be potential key building blocks of very high spin spin clusters and polymers.