Free boundary problem for a fully nonlinear and degenerate parabolic equation in an angular domain

This paper concerns with the problem of how to running an insurance company to maximize his total discounted expected dividends. In our model, the dividend rate is limited in $[0,M]$ and the company is allowed to transfer any proportion of risk by reinsuring. So there are two strategies which we call dividend strategy and reinsurance strategy. The objective function and the corresponding optimal two strategies are the solution and the two free boundaries of the following Barenblatt parabolic equation

$v_t?\underset{0\le a\le 1}{\max }?(\frac{1}{2}{a}^2{\sigma }^2{v}_{xx}+a\mu v_x)+cv?\underset{0\le l\le M}{\max }?[(1?v_x)l]=0$

under certain boundary conditions on an angular domain

$Q_T=\{(x,t)|0<x<Mt,0<t\le T\}.$

The main effort is to analyze the properties of the solution and the free boundaries to show the optimal decision for the insurance company.     

Quantum-chemical study on the catalytic activity of TinRumO2(1 1 0) surfaces on chlorine evolution

Based on the generalized gradient approximation (GGA), Perdew-Wang-91 (PW91) combined with a periodic slab model has been applied to study the catalytic activity of chlorine evolution on TinRumO2(1 1 0) surface. Metal oxide model TinRumO2 has been established with pure TiO2 and RuO2 on the basis set of Double Numerical plus polarization (DNP), in which the proportion of n:m was 3:1, 1:1, or 1:3. Analysis on the reaction activity in the electrochemical reaction and the electrochemical desorption reaction was based on Frontiermolecular orbital theory. The results show that the TinRumO2 with a ratio of Ti:Ru at 3:1 is best facilitates the electrochemical reaction and electrochemical desorption reaction to produce M-Clads intermediate and precipitate Cl2. In addition, the adsorption energy of Cl on the surface of Ti3Ru1O2 possesses the minimum value of 2.514 eV, and thus electrochemical desorption reaction could occur most easily.     

Shock and traveling wave phenomena on an externally damped, non-linear string

We examine the propagation of shocks and traveling wave phenomena on a one-dimensional string that is executing finite-amplitude, transverse vibrations in a resisting medium. As part of our study, we develop an approach that allows us to describe, albeit approximately, the evolution and propagation of a shock front using analytical methods. In addition, exact traveling wave solutions, one of which involves the Lambert W-function, of the string's equation of motion are determined and analyzed. Lastly, a possible new form of the solution to the linearized problem is presented and extensions and other applications of the present work are briefly discussed.     

A mean-reverting SDE on correlation matrices

We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright–Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit. We also shed light on a useful connection with Wishart processes that makes understand how we get the full SDE. Then, we focus on the simulation of this diffusion and present discretization schemes that achieve a second-order weak convergence. Last, we give a possible application of these processes in finance and argue that they could easily replace and improve the standard assumption of a constant correlation.     

A diversity oriented synthesis of d-erythro-sphingosine and siblings

An efficient building block-based synthetic protocol has been developed for the synthesis of 3-ketosphingoids with various chain lengths using cross metathesis of a Garner’s aldehyde-derived α,β-unsaturated ketone as the key step. Stereoselective reduction of the biomimetic precursors thus obtained provided d-erythro-sphingosine and truncated anaogues in good overall yields.     

Resolution,absolute configuration and antifilarial activity of coumarinyl amino alcohols

The resolution of racemic coumarinyl amino alcohols 5–10 was achieved by using the inexpensive and readily accessible chiral resolving agent N-carbethoxy-l-proline (S)-11. Direct esterification of rac-5–10 with (S)-11 furnished diastereomeric esters, which were easily separated by column chromatography. The obtained diastereomers yielded the desired enantiopure coumarinyl amino alcohols (S)-(+)-5–10 and (R)-(?)-5–10 in good yields with high enantiomeric excess on saponification. The absolute configurations were determined by X-ray crystal analysis and/or by comparison of the specific rotations. Furthermore, in in vitro antifilarial motility inhibition assays, enantiopure coumarins (S)-(+)-9, (R)-(?)-9 and (S)-(+)-10, (R)-(?)-10 were found to be less efficient in affecting the viability of macrofilariae of Brugia malayi than their racemic forms 9 and 10, respectively, indicating the synergistic effect of the enantiomers in evoking antifilarial action.     

Variations on selective separability in non-regular spaces

We study various variations on selective separability in non-regular topological spaces. We use the notions of θ-closure and θ-density to define selective versions of θ-separability. These properties are also related to topological games.     

Ratio-conjugation tool and its application in linear optimization models†

The ratio-conjugation-tool (RC) is constructed systematically, and its applicability for analysis of economic models is demonstrated. One of the main results establishes a general formula for RC of aggregative function. This tool is applied to the analysis of linear economic dynamics models of Neumann–Gale type which can be solved by a dynamic programming method: for each direct problem we construct the corresponding dual RC-problem. Moreover, we consider three examples of the most important economic dynamics models and look at these now from a unified general position.