Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line

Consider an evolution family U=(U(t,s))_t?s?0 on a half-line R₊ and an integral equation . We characterize the exponential dichotomy of the evolution family through solvability of this integral equation in admissible function spaces which contain wide classes of function spaces like function spaces of Lp type, the Lorentz spaces Lp,q and many other function spaces occurring in interpolation theory. We then apply our results to study the robustness of the exponential dichotomy of evolution families on a half-line under small perturbations.     

Asymptotic Behavior of Solutions to the Cahn-Hilliard Equation in Spherically Symmetric Domains

The Cahn-Hilliard equation is a fourth-order parabolic partial differential equation that is one of the leading models for the study of phase separation in isothermal, isotropic, binary mixtures, such as molten alloys. The asymptotic behavior of solutions to the Cahn-Hilliard equation with Dirichlet boundary conditions and the associated stationary problem have been studied. In particular, it is proved that the only possible stable equilibrium solutions in spherically symmetric domains are spherically symmetric and monotone in the radial direction.     

Characterizations of proximinal,semichebychevian and chebychevian subspaces in real normed spaces

A simple model optimal control problem for continuous casting with state-space constraints is approximated, as usual, by a penalty method and by a numerical discretization of the nonlinear heat equation. The convergence of the approximate problems directly to the original problem is proven under a stability criterion linking the penalty parameter with the discretization parameters. For this purpose, known discretization error estimates for the Stefan problem are extended for the case of time varying boundary conditions.     

On the Geometric Densities of Random Closed Sets

Abstract

In many applications it is of great importance to handle evolution equations about random closed sets of different (even though integer) Hausdorff dimensions, including local information about initial conditions and growth parameters. Following a standard approach in geometric measure theory such sets may be described in terms of suitable measures. For a random closed set of lower dimension with respect to the environment space, the relevant measures induced by its realizations are singular with respect to the Lebesgue measure, and so their usual Radon–Nikodym derivatives are zero almost everywhere. In this paper we suggest to cope with these difficulties by introducing random generalized densities (distributions) á la Dirac–Schwarz, for both the deterministic case and the stochastic case. In this last one we analyze mean generalized densities, and relate them to densities of the expected values of the relevant measures. Many models of interest in material science and in biomedicine are based on time dependent random closed sets, as the ones describing the evolution of (possibly space and time inhomogeneous) growth processes; in such a situation, the Delta formalism provides a natural framework for deriving evolution equations for mean densities at all (integer) Hausdorff dimensions, in terms of the local relevant kinetic parameters of birth and growth. In this context connections with the concepts of hazard function, and spherical contact distribution function are offered.     

Chemo‐ and Regioselective Dihydroxylation of Benzene to Hydroquinone Enabled by Engineered Cytochrome P450 Monooxygenase

Hydroquinone (HQ) is produced commercially from benzene by multi‐step Hock‐type processes with equivalent amounts of acetone as side‐product. We describe an efficient biocatalytic alternative using the cytochrome P450‐BM3 monooxygenase. Since the wildtype enzyme does not accept benzene, a semi‐rational protein engineering strategy was developed. Highly active mutants were obtained which transform benzene in a one‐pot sequence first into phenol and then regioselectively into HQ without any overoxidation. A computational study shows that the chemoselective oxidation of phenol by the P450‐BM3 variant A82F/A328F leads to the regioselective formation of an epoxide intermediate at the C3=C4 double bond, which departs from the binding pocket and then undergoes fragmentation in aqueous medium with exclusive formation of HQ. As a practical application, an E. coli designer cell system was constructed, which enables the cascade transformation of benzene into the natural product arbutin, which has anti‐inflammatory and anti‐bacterial activities.     

Directed Evolution of a Bacterial Laccase (CueO) for Enzymatic Biofuel Cells

Escherichia coli's copper efflux oxidase (CueO) has rarely been employed in the cathodic compartment of enzymatic biofuel cells (EBFCs) due to its low redox potential (0.36 V vs. Ag/AgCl, pH 5.5) towards O₂ reduction. Herein, directed evolution of CueO towards a more positive onset potential was performed in an electrochemical screening system. An improved CueO variant (D439T/L502K) was obtained with a significantly increased onset potential (0.54 V), comparable to that of high‐redox‐potential fungal laccases. Upon coupling with an anodic compartment, the EBFC exhibited an open‐circuit voltage (V_oc) of 0.56 V. Directed enzyme evolution by tailoring enzymes to application conditions in EBFCs has been validated and might, in combination with molecular understanding, enable future breakthroughs in EBFC performance     

Computer simulation of arising of diploid genomes

The haploid–diploid cycle where, under unfavorable conditions the population becomes diploid, is modeled by a Monte-Carlo method in the framework of the Jan–Stauffer–Moseley hypothesis. Diploidy and sex may have first arisen as a way to escape death, when a simple unicellular individual is threatened by too many deleterious mutations. Using a bit string model, we find that in a system where competition is present (through the Verhulst factor), diploids dominate. In this case the transition from haploid to essentially diploid population takes place in a short time interval reminiscent of phase transitions in physical systems.     

Density matrix of a quantum field in a particle-creating background

We examine the time evolution of a quantized field in external backgrounds that violate the stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the final quantum state (the density operator at the final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of evolution. We find a generating functional that allows one to obtain density operators for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles). Analyzing one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons. We discuss the question (and its relation to the initial stage of quark–gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not in thermal equilibrium. In this respect, we discuss some cases when pair-creation by an electric-like field can mimic the one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the mean numbers of created particles, provided that the effects of switching the external field on and off are negligible. It is demonstrated that at high temperatures and in slowly varying electric fields the rate of particle-creation is essentially time-dependent.     

强光一号2.4 MV 环-板型水介质开关光学诊断

 利用ns级时间分辨可见光分幅相机和光纤传感器对“强光一号”环-板型水介质开关进行光学测量,得到了电流通道发展图像以及整个放电过程的光强变化信号。实验结果表明:环-板型水介质开关开始击穿时的平均场强约为190 kV/cm,同时存在多个放电通道,流注呈树枝状分布,发展速度为几十cm/ms。