The charge-charge flux-overlap model for the interpretation of atomic polar tensors and infrared intensities

The interpretation of infrared intensities using the concepts of atomic polar tensors divided according to contributions from charge-charge flux-overlap (CCFO) terms appears in general to be quite useful. Here we shall illustrate this analysis for the F and H atoms in chemically related molecules to show how their properties vary for CF, CH, OF and OH bonds as R varies in RCF, RCH and ROH molecules.     

Products of graceful trees

We give some conditions on H and $\text{G}$ for the rooted product H($\text{G}$) to be graceful. These conditions extend and unify previous results.     

Two theorems on graceful trees

Let T be a tree on n vertices which are labelled by the integers in N = {1,2,…,n} such that each vertex of T is associated with a distinct number in N. The weight of an edge is defined to be the absolute value of the difference between the two numbers labelled at its end vertices. If the weights of all edges of T are distinct, we call T a graceful tree. In this note, two methods for constructing bigger graceful trees from a given one and a given pair of graceful trees are provided.     

Optimal and robust contracts for a risk-constrained principal

The theory of risk measurement has been extensively developed over the past ten years or so, but there has been comparatively little effort devoted to using this theory to inform portfolio choice. One theme of this paper is to study how an investor in a conventional log-Brownian market would invest to optimize expected utility of terminal wealth, when subjected to a bound on his risk, as measured by a coherent law-invariant risk measure. Results of Kusuoka lead to remarkably complete expressions for the solution to this problem. The second theme of the paper is to discuss how one would actually manage (not just measure) risk. We study a principal/agent problem, where the principal is required to satisfy some risk constraint. The principal proposes a compensation package to the agent, who then optimises selfishly ignoring the risk constraint. The principal can pick a compensation package that induces the agent to select the principal’s optimal choice.     

Unified semi‐analytical wall boundary conditions for inviscid,laminar or turbulent flows in the meshless SPH method

Wall boundary conditions in smoothed particle hydrodynamics (SPH) is a key issue to perform accurate simulations. We propose here a new approach based on a renormalising factor for writing all boundary terms. This factor depends on the local shape of a wall and on the position of a particle relative to the wall, which is described by segments (in two‐dimensions), instead of the cumbersome fictitious or ghost particles used in most existing SPH models. By solving a dynamic equation for the renormalising factor, we significantly improve traditional wall treatment in SPH, for pressure forces, wall friction and turbulent conditions. The new model is demonstrated for cases including hydrostatic conditions for still water in a tank of complex geometry and a dam break over triangular bed profile with sharp angle where significant improved behaviour is obtained in comparison with the conventional boundary techniques. The latter case is also compared with a finite volume and volume‐of‐fluid scheme. The performance of the model for a two‐dimensional laminar flow in a channel is demonstrated where the profiles of velocity are in agreement with the theoretical ones, demonstrating that the derived wall shear stress balances the pressure gradient. Finally, the performance of the model is demonstrated for flow in a schematic fish pass where both the velocity field and turbulent viscosity fields are satisfactorily reproduced compared with mesh‐based codes. Copyright © 2012 John Wiley & Sons, Ltd.     

Identities for the Ramanujan zeta function

We prove formulas for special values of the Ramanujan tau zeta function. Our formulas show that L(Δ,k)$L(\mathrm{\Delta },k)$ is a period in the sense of Kontsevich and Zagier when k?12$k?12$. As an illustration, we reduce L(Δ,k)$L(\mathrm{\Delta },k)$ to explicit integrals of hypergeometric and algebraic functions when k∈{12,13,14,15}$k\in \{12,13,14,15\}$.     

Neutron and proton transverse emission ratio measurements and the density dependence of the asymmetry term of the nuclear equation of state

Recent measurements of preequilibrium neutron and proton transverse emission from (112,124)Sn+(112,124)Sn reactions at 50 MeV/A have been completed at the National Superconducting Cyclotron Laboratory. Free nucleon transverse emission ratios are compared to those of A=3 mirror nuclei. Comparisons are made to Boltzmann-Uehling-Uhlenbeck (BUU) transport calculations and conclusions concerning the density dependence of the asymmetry term of the nuclear equation of state at subnuclear densities are made. Comparison to BUU model predictions indicate a density dependence of the asymmetry energy that is closer to a form in which the asymmetry energy increases as the square root of the density for the density region studied. A coalescent-invariant analysis is introduced as a means of reducing suggested difficulties with cluster emission in total nucleon emission.     

The neural correlates of calculation ability in children: an fMRI study

Most studies investigating mental numerical processing involve adult participants and little is known about the functioning of these systems in children. The current study used functional magnetic resonance imaging (fMRI) to investigate the neural correlates of numeracy and the influence of age on these correlates with a group of adults and a group of third graders who had average to above average mathematical ability. Participants performed simple and complex versions of exact and approximate calculation tasks while in the magnet. Like adults, children activated a network of brain regions in the frontal and parietal lobes during the calculation tasks, and they recruited additional brain regions for the more complex versions of the tasks. However, direct comparisons between adults and children revealed significant differences in level of activation across all tasks. In particular, patterns of activation in the parietal lobe were significantly different as a function of age. Findings support previous claims that the parietal lobe becomes more specialized for arithmetic tasks with age.     

Fastest Coupling of Random Walks

A new coupling of one-dimensional random walks is describedwhich tries to control the coupling by keeping the separationof the two random walks of constant sign. It turns out thatamong such monotone couplings there is an optimal one-step couplingwhich maximises the second moment of the difference (assumingthis is finite), and this coupling is ‘fast’ inthe sense that for a random walk with a unimodal step distributionthe coupling time achieved by using the new coupling at eachstep is stochastically no larger than any other coupling. Thisis applied to the case of symmetric unimodal distributions.     

The adsorption of C6H5Cl on Si(111)7 × 7 studied by STM

The adsorption of chlorobenzene on Si(111)7 × 7 at room temperature was studied by scanning tunneling microscopy (STM). Selective chemisorption was observed at different adatom sites. It was found that the center adatoms were more reactive than the corner adatoms, and the faulted half of the unit cell was more reactive than the unfaulted. The mechanism is discussed in terms of the electronic and atomic structures in Si(111)7 × 7. Both preferences indicate that chlorobenzene was present initially in a mobile precursor state.