Charge density analysis of some processes involving intramolecular hydrogen transfer

The variations in topology of the electron density along the reaction paths of the keto-enol tautomerism of acetaldehyde, the pinacol rearrangement of protonated 1,2-ethanediol, and the unimolecular decomposition of methanediol, were studied as examples of hydrogen transfer between, respectively, C?O, C?C, and O?O atoms. The evolution of atomic charges, determined using two different atomic partitionings (AIM and Hirshfeld), indicates that the main electronic charge transfer in keto-enol tautomerism takes place between the migrating hydrogen and the carbon of the carbonyl group. The topology of the electron density demonstrates that a hydrogen-bridge structure is never formed along the reaction path of the pinacol rearrangement. The methanediol decomposition follows a concerted mechanism with very small variations in the atomic charges.     

大型稀疏无约束最优化的列分划校正Cholesky因子算法

我们考虑求解无约束优化问题1引言(?)f(x),(1)其中f：D(?)R~n→R为R~n上的二次连续可微函数,且f(x)的二阶Hesse阵H(x)稀疏、正定．为了求解问题(1),我们考虑下列Newton型方法x~(k 1)=x~k-(B~k)~(-1)▽f(x~k),k=0,1,…,(2)其中B~k是和Hesse阵H(x~k)具有相同稀疏性的近似．由于Hesse阵对称,我们假定B~k对称．为了具体说明给定矩阵B的稀疏性,我们使用M来定义指标对(i,j)的集合,其     

Compact linearization for binary quadratic problems

We show that a well-known linearization technique initially proposed for quadratic assignment problems can be generalized to a broader class of quadratic 0–1 mixed-integer problems subject to assignment constraints. The resulting linearized formulation is more compact and tighter than that obtained with a more usual linearization technique. We discuss the application of the compact linearization to three classes of problems in the literature, among which the graph partitioning problem.      

Another greedy heuristic for the constrained forest problem

The constrained forest problem seeks a minimum-weight spanning forest in an undirected edge-weighted graph such that each tree spans at least a specified number of vertices. We present a greedy heuristic for this NP-hard problem, whose solutions are at least as good as, and often better than, those produced by the best-known 2-approximate heuristic.     

New diphenylhexatriene derivatives as fluorescent membrane probes: Partitioning properties

Three new diphenylhexatriene derivatives, two phospholipids and one single-chain amphiphilic molecule, have been synthesized and considered as probes for measuring membrane fluidity by fluorescence anisotropy. The possibility of using these probes to determine specifically fluidity of inner leaflets of cellular plasma membranes was inferred from their partitioning properties between gel and liquid crystalline phases of phospholipid vesicles of binary composition.     

A comparative post-Hartree–Fock and density functional theory study of monochalcogenide diatomic molecules

HOMO and LUMO (FMOs) play important role in the optical properties of meridianal isomer of tris(8-hydroxyquinolino)aluminum (mer-Alq3) and its derivatives. The frontier molecular orbitals (FMOs) also play a vital role in the process of charge transport. It is urgent to find the reason of FMO distribution pattern among the ligands. The structures of mer-Alq3 and its “CH”/N substituted derivatives have been optimized at the B3LYP/6-31G^* level. Energy decomposition analysis has been performed at the B3LYP/DZP level. The results of energy-partitioning analysis of ground states are discussed. It has been explained that HOMOs are on A-ligands due to weaker electrostatic interaction energy between L_a-AlL_bL_c fragments while LUMOs are on B-ligands due to weaker orbital interaction energy between L_b-AlL_aL_c fragments.     

Analysis of the performance of the parallel quicksort method

In this paper a theoretical analysis of the performance of a parallel form of the Quicksort algorithm is presented and shown to be in qualitative agreement with experiments carried out on the Loughborough University NEPTUNE parallel system.     

On the complete set packing and set partitioning polytopes: Properties and rank 1 facets

This paper studies two polytopes: the complete set packing and set partitioning polytopes, which are both associated with a binary $n$-row matrix having all possible columns. Cuts of rank 1 for the latter polytope play a central role in recent exact algorithms for many combinatorial problems, such as vehicle routing. We show the precise relation between the two polytopes studied, characterize the multipliers that induce rank 1 clique facets and give several families of multipliers that yield other facets.     

An improved approximation algorithm for requirement cut

This note presents improved approximation guarantees for the requirement cut problem: given an n-vertex edge-weighted graph G=(V,E), and g groups of vertices X₁,…,X_g⊆V with each group X_i having a requirement r_i between 0 and |X_i|, the goal is to find a minimum cost set of edges whose removal separates each group X_i into at least r_i disconnected components. We give a tight Θ(logg) approximation ratio for this problem when the underlying graph is a tree, and show how this implies an O(logk⋅logg) approximation ratio for general graphs, where .     

Stability Estimates for Coefficients of Magnetic Schrödinger Equation from Full and Partial Boundary Measurements

In this paper we establish a log log-type estimate which shows that in dimension n ≥ 3 the magnetic field and the electric potential of the magnetic Schrödinger equation depends stably on the Dirichlet to Neumann (DN) map even when the boundary measurement is taken only on a subset that is slightly larger than half of the boundary ?Ω – a notion made more precise later. Furthermore, we prove that in the case when the measurement is taken on all of ?Ω one can establish a better estimate that is of log-type.