Influence of ionization on the conformational preferences of peptide models. Ramachandran surfaces of N‐formyl‐glycine amide and N‐formyl‐alanine amide radical cations

Ramachandran maps of neutral and ionized HCO–Gly–NH₂ and HCO–Ala–NH₂ peptide models have been built at the B3LYP/6‐31++G(d,p) level of calculation. Direct optimizations using B3LYP and the recently developed MPWB1K functional have also been carried out, as well as single‐point calculations at the CCSD(T) level of theory with the 6‐311++G(2df,2p) basis set. Results indicate that for both peptide models ionization can cause drastic changes in the shape of the PES in such a way that highly disallowed regions in neutral PES become low‐energy regions in the radical cation surface. The structures localized in such regions, and are highly stabilized due to the formation of 2‐centre‐3‐electron interactions between the two carbonyl oxygens. Inclusion of solvent effects by the conductor‐like polarizable continuum model (CPCM) shows that the solute‐solvent interaction energy plays an important role in determining the stability order. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

Translation-invariant maps and applications

In this paper we study translation-invariant maps on a linear space. A method for estimating quantities induced by such maps is presented. Applications for differences of operators, commutators, G-contractive maps and Grüss type inequalities are also given.     

Nonlinear conditions for weighted composition operators between Lipschitz algebras

Let T:Lip₀(X)→Lip₀(Y) be a surjective map between pointed Lipschitz ^∗-algebras, where X and Y are compact metric spaces. On the one hand, we prove that if T satisfies the non-symmetric norm ^∗-multiplicativity condition:

     

Automorphisms of Ehresmann connections

We prove that a diffeomorphism of a manifold with an Ehresmann connection is an automorphism of the Ehresmann connection, if and only if, it is a totally geodesic map (i.e., sends the geodesies, considered as parametrized curves, to geodesies) and preserves the strong torsion of the Ehresmann connection. This result generalizes and to some extent strengthens the classical theorem on the automorphisms of a D-manifold (manifold with covariant derivative). The second author is supported by the Hungarian Nat. Sci. Found. (OTKA), Grant No. NK68040.     

Best approximation, coincidence and fixed point theorems for quasi-lower semicontinuous set-valued maps in hyperconvex metric spaces

Suppose X is a compact admissible subset of a hyperconvex metric spaces M, and suppose F:XM is a quasi-lower semicontinuous set-valued map whose values are nonempty admissible. Suppose also G:XX is a continuous, onto quasi-convex set-valued map with compact, admissible values. Then there exists an x₀X such that

As applications, we give some coincidence and fixed point results for weakly inward set-valued maps. Our results, generalize some well-known results in literature.     

Strong convergence of composite iterative schemes for zeros of m-accretive operators in Banach spaces

We introduce a new composite iterative scheme to approximate a zero of an m$m$-accretive operator A$A$ defined on uniform smooth Banach spaces and a reflexive Banach space having a weakly continuous duality map. It is shown that the iterative process in each case converges strongly to a zero of A$A$. The results presented in this paper substantially improve and extend the results due to Ceng et al. [L.C. Ceng, H.K. Xu, J.C. Yao, Strong convergence of a hybrid viscosity approximation method with perturbed mappings for nonexpansive and accretive operators, Taiwanese J. Math. (in press)], Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005) 51–60] and Xu [H.K. Xu, Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631–643]. Our work provides a new approach for the construction of a zero of m$m$-accretive operators.     

Application of the GALI method to localization dynamics in nonlinear systems

We investigate localization phenomena and stability properties of quasiperiodic oscillations in N$N$ degree of freedom Hamiltonian systems and N$N$ coupled symplectic maps. In particular, we study an example of a parametrically driven Hamiltonian lattice with only quartic coupling terms and a system of N$N$ coupled standard maps. We explore their dynamics using the Generalized Alignment Index (GALI), which constitutes a recently developed numerical method for detecting chaotic orbits in many dimensions, estimating the dimensionality of quasiperiodic tori and predicting slow diffusion in a way that is faster and more reliable than many other approaches known to date.     

The critical groups of a family of graphs and elliptic curves over finite fields

Let q be a power of a prime, and E be an elliptic curve defined over  . Such curves have a classical group structure, and one can form an infinite tower of groups by considering E over field extensions for all k≥1. The critical group of a graph may be defined as the cokernel of L(G), the Laplacian matrix of G. In this paper, we compare elliptic curve groups with the critical groups of a certain family of graphs. This collection of critical groups also decomposes into towers of subgroups, and we highlight additional comparisons by using the Frobenius map of E over  . This work was partially supported by the NSF, grant DMS-0500557 during the author’s graduate school at the University of California, San Diego, and partially supported by an NSF Postdoctoral Fellowship.     

基于统计特性与边缘特性融合的阴影检测方法

针对视频监视系统中的阴影检测问题,提出了一种基于灰度比值统计与边缘特征分析相融合的阴影检测方法.根据阴影的面积和灰度特征,采用灰度统计和正态分布曲线拟合的方法估计出阴影灰度的分布区域,实现对阴影的初分割.利用熵判据对初分割的结果进行判断,对于过分割的情况,依据目标与阴影间的位置关系,利用阴影的边缘特性进行目标重构.不同光照环境下的视频监控图像测试结果表明,该方法可以用于灰度图像和彩色图像,能够有效检测出阴影区域并保持目标的完整性.     

Integrable generalizations of Schrödinger maps and Heisenberg spin models from Hamiltonian flows of curves and surfaces

A moving frame formulation of non-stretching geometric curve flows in Euclidean space is used to derive a 1+1 dimensional hierarchy of integrable SO(3)$SO\left(3\right)$-invariant vector models containing the Heisenberg ferromagnetic spin model as well as a model given by a spin vector version of the mKdV equation. These models describe a geometric realization of the NLS hierarchy of soliton equations whose bi-Hamiltonian structure is shown to be encoded in the Frenet equations of the moving frame. This derivation yields an explicit bi-Hamiltonian structure, recursion operator, and constants of motion for each model in the hierarchy. A generalization of these results to geometric surface flows is presented, where the surfaces are non-stretching in one direction while stretching in all transverse directions. Through the Frenet equations of a moving frame, such surface flows are shown to encode a hierarchy of 2+1 dimensional integrable SO(3)$SO\left(3\right)$-invariant vector models, along with their bi-Hamiltonian structure, recursion operator, and constants of motion, describing a geometric realization of 2+1 dimensional bi-Hamiltonian NLS and mKdV soliton equations. Based on the well-known equivalence between the Heisenberg model and the Schrödinger map equation in 1+1 dimensions, a geometrical formulation of these hierarchies of 1+1 and 2+1 vector models is given in terms of dynamical maps into the 2-sphere. In particular, this formulation yields a new integrable generalization of the Schrödinger map equation in 2+1 dimensions as well as a mKdV analog of this map equation corresponding to the mKdV spin model in 1+1 and 2+1 dimensions.