Total synthesis of PDE-I and -II by copper-mediated double aryl amination

A concise total synthesis of PDE-I and -II featuring copper-mediated double aryl amination with the combination of CuI, CsOAc, and Cs₂CO₃ is described. The highly substituted pyrroloindole skeleton was constructed by a one-pot five-step sequence including double aryl amination, β-elimination, deprotection of a Cbz group, and unexpected formation of an indole via removal of an Ns group followed by rearomatization. The undesired elimination of the protecting group (Ns group) was hampered by using the Boc group as a protecting group in the second-generation synthesis, which excluded the reduction of the indole required in the first-generation synthesis.     

Photoinduced alignment of polymer liquid crystals containing azobenzene moieties in the side group VII. On He-Ne laser beam irradiation

Photoinduced alignment in a polymer liquid crystal prepared from 6-{1-[4-(2-cyano-4-nitrophenylazo)phenyl]piperazino}hexyl acrylate and 4'-[6-(methacryloyloxy)hexyloxy]-4-cyanobiphenyl was investigated for the first time on irradiation with a polarized He-Ne laser beam at 633 nm. The azobenzene moieties as well as the inert cyanobiphenyl mesogenic units were aligned with the molecular long axis perpendicular to the polarization direction of the irradiation light. Alignment induced on short irradiation was reversible, while that induced under prolonged irradiation was irreversible due to the occurrence of crosslinking which might be caused by photoinduced decomposition of the azobenzene moieties during the photoirradiation process.     

A simultaneous approach to inverse source problem by Green's function

In this paper, we consider an inverse source problem of identification of F(t) function in the linear parabolic equation u_t = u_xx + F(t) and u₀(x) function as the initial condition from the measured final data and local boundary data. Based on the optimal control framework by Green's function, we construct Fréchet derivative of Tikhonov functional. The stability of the minimizer is established from the necessary condition. The CG algorithm based on the Fréchet derivative is applied to the inverse problem, and results are presented for a test example. Copyright © 2014 John Wiley & Sons, Ltd.     

An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition

In this paper, the inverse problem of finding the time‐dependent coefficient of heat capacity together with the solution periodic boundary and integral overdetermination conditions is considered. Under some natural regularity and consistency conditions on the input data, the existence, uniqueness, and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example. Copyright © 2014 John Wiley & Sons, Ltd.     

A stochastic control model of investment,production, and consumption on a finite horizon

In this paper, we consider a stochastic control problem on a finite time horizon. The unit price of capital obeys a logarithmic Brownian motion, and the income from production is also subject to the random Brownian fluctuations. The goal is to choose optimal investment and consumption policies to maximize the finite horizon expected discounted hyperbolic absolute risk aversion utility of consumption. A dynamic programming principle is used to derive a time‐dependent Hamilton–Jacobi–Bellman equation. The Leray–Schauder fixed point theorem is used to obtain existence of solution of the HJB equation. At last, we derive the optimal investment and consumption policies by the verification theorem. The main contribution in this paper is the use of PDE technique to the finite time problem for obtaining optimal polices. Copyright © 2014 John Wiley & Sons, Ltd.     

Multilevel preconditioning and low‐rank tensor iteration for space–time simultaneous discretizations of parabolic PDEs

This paper addresses the solution of parabolic evolution equations simultaneously in space and time as may be of interest in, for example, optimal control problems constrained by such equations. As a model problem, we consider the heat equation posed on the unit cube in Euclidean space of moderately high dimension. An a priori stable minimal residual Petrov–Galerkin variational formulation of the heat equation in space–time results in a generalized least squares problem. This formulation admits a unique, quasi‐optimal solution in the natural space–time Hilbert space and serves as a basis for the development of space–time compressive solution algorithms. The solution of the heat equation is obtained by applying the conjugate gradient method to the normal equations of the generalized least squares problem. Starting from stable subspace splittings in space and in time, multilevel space–time preconditioners for the normal equations are derived. In order to reduce the complexity of the full space–time problem, all computations are performed in a compressed or sparse format called the hierarchical Tucker format, supposing that the input data are available in this format. In order to maintain sparsity, compression of the iterates within the hierarchical Tucker format is performed in each conjugate gradient iteration. Its application to vectors in the hierarchical Tucker format is detailed. Finally, numerical results in up to five spatial dimensions based on the recently developed htucker toolbox for MATLAB are presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Design,Synthesis, and Evaluation of Dihydropyranopyrazole Derivatives as Novel PDE2 Inhibitors for the Treatment of Alzheimer’s Disease

Phosphodiesterase 2 (PDE2) has been regarded as a novel target for the treatment of Alzheimer’s disease (AD). In this study, we obtained (R)-LZ77 as a hit compound with moderate PDE2 inhibitory activity (IC₅₀ = 261.3 nM) using a high-throughput virtual screening method based on molecular dynamics. Then, we designed and synthesized 28 dihydropyranopyrazole derivatives as PDE2 inhibitors. Among them, compound (+)-11h was the most potent PDE2 inhibitor, with an IC₅₀ value of 41.5 nM. The molecular docking of PDE2-(+)-11h reveals that the 4-(trifluoromethyl)benzyl)oxyl side chain of the compound enters the H-pocket and forms strong hydrophobic interactions with L770/L809/F862, which improves inhibitory activity. The above results may provide insight for further structural optimization of highly potent PDE2 inhibitors and may lay the foundation for their use in the treatment of AD.     

An ignition-temperature model with two free interfaces in premixed flames†

In this paper we consider an ignition-temperature zero-order reaction model of thermo-diffusive combustion. This model describes the dynamics of thick flames, which have recently received considerable attention in the physical and engineering literature. The model admits a unique (up to translations) planar travelling wave solution. This travelling wave solution is quite different from those usually studied in combustion theory. The main qualitative feature of this travelling wave is that it has two interfaces: the ignition interface where the ignition temperature is attained and the trailing interface where the concentration of deficient reactants reaches zero. We give a new mathematical framework for studying the cellular instability of such travelling front solutions. Our approach allows the analysis of a free boundary problem to be converted into the analysis of a boundary value problem having a fully nonlinear system of parabolic equations. The latter is very suitable for both mathematical and numerical analysis. We prove the existence of a critical Lewis number such that the travelling wave solution is stable for values of Lewis number below the critical one and is unstable for Lewis numbers that exceed this critical value. Finally, we discuss the results of numerical simulations of a fully nonlinear system that describes the perturbation dynamics of planar fronts. These simulations reveal, in particular, some very interesting ‘two-cell’ steady patterns of curved combustion fronts.     

基于大功率LED扩展光源的均匀光斑光辐射模拟器设计

基于边缘光线原理和光学扩展量守恒思想,结合复合抛物面聚光器和轴对称自由曲面透镜,设计并研制了大功率发光二极管扩展光源的反射/折射准直器.运用Tracepro软件对系统进行光束追迹模拟仿真和实验,研制出均匀光斑的光辐射模拟器.模拟器输出发散角为±12°光束,测量距离出射面50cm处光屏的光斑,在尺寸为14cm×14cm的光照范围内,测得光斑水平方向中心线上的光度均匀度优于4.1%,竖直方向中心线上的光度均匀度优于3.8%.     

A macroscopic model for an intermediate state between type‐I and type‐II superconductivity

A vectorial nonlocal and nonlinear parabolic problem on a bounded domain for an intermediate state between type‐I and type‐II superconductivity is proposed. The domain is for instance a multiband superconductor that combines the characteristics of both types. The nonlocal term is represented by a (space) convolution with a singular kernel arising in Eringen's model. The nonlinearity is coming from the power law relation by Rhyner. The well‐posedness of the problem is discussed under low regularity assumptions and the error estimate for a semi‐implicit time‐discrete scheme based on backward Euler approximation is established. In the proofs, the monotonicity methods and the Minty–Browder argument are used. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1551–1567, 2015