Doubly nonlinear evolution equations with non-monotone perturbations in reflexive Banach spaces

Let V and V* be a real reflexive Banach space and its dual space, respectively. This paper is devoted to the abstract Cauchy problem for doubly nonlinear evolution equations governed by subdifferential operators with non-monotone perturbations of the form: ?_V y^t (u￠(t)) + ?_V j(u(t)) + B(t, u(t)) ' f(t){\partial_V \psi^t (u{^\prime}(t)) + \partial_V \varphi(u(t)) + B(t, u(t)) \ni f(t)} in V*, 0 < t < T, u(0) = u ₀, where ?_V y^t, ?_V j: V ? 2^V*{\partial_V \psi^t, \partial_V \varphi : V \to 2^{V^*}} denote the subdifferential operators of proper, lower semicontinuous and convex functions y^t, j: V ? (-￥, +￥]{\psi^t, \varphi : V \to (-\infty, +\infty]}, respectively, for each t ? [0,T]{t \in [0,T]}, and f : (0, T) → V* and u₀ ? V{u_0 \in V} are given data. Moreover, let B be a (possibly) multi-valued operator from (0, T) × V into V*. We present sufficient conditions for the local (in time) existence of strong solutions to the Cauchy problem as well as for the global existence. Our framework can cover evolution equations whose solutions might blow up in finite time and whose unperturbed equations (i.e., B o 0{B \equiv 0}) might not be uniquely solved in a doubly nonlinear setting. Our proof relies on a couple of approximations for the equation and a fixed point argument with a multi-valued mapping. Moreover, the preceding abstract theory is applied to doubly nonlinear parabolic equations.     

Enantioselective ester synthesis in the presence of optically active polymers

Enantiomer-differentiating ester syntheses from acid salts, chlorides, and an anhydride were studied in the presence of optically active polyamines. Enantiomer selection occurred in reactions of a racemic salt with an achiral alkyl bromide and vice versa, which is good evidence of the importance of activation of the carboxylate group by complexation of the counterion and activation of alkyl bromide by the formation of a quaternary salt with polyamine under solid–liquid, phase-transfer reaction conditions. Only small optical activity was observed in the products of acid anhydride or chloride with alcohol.     

Nonlinear diffusion equations driven by the p(·)-Laplacian

This paper is concerned with nonlinear diffusion equations driven by the p(·)-Laplacian with variable exponents in space. The well-posedness is first checked for measurable exponents by setting up a subdifferential approach. The main purposes are to investigate the large-time behavior of solutions as well as to reveal the limiting behavior of solutions as p(·) diverges to the infinity in the whole or in a subset of the domain. To this end, the recent developments in the studies of variable exponent Lebesgue and Sobolev spaces are exploited, and moreover, the spatial inhomogeneity of variable exponents p(·) is appropriately controlled to obtain each result.     

A study of the multiple pinhole coded aperture and the application of the minicomputer in image decoding.

Research has been done on optically reconstructed imaging employing the Multiple Pinhole Coded Aperture (hereafter abreviated as MPCA) in radioisotope tomographic imaging. However, problems remain in the optically reconstructed image method. Therefore, we employed a minicomputer (hereafter abbreviated as CPU) and developed the software for decoding and managing the radioisotope tomographic image. Combining the MPCA and the CPU system, we were able to decode and manage the radioisotope tomographic image. 1) In comparison to the optically decoded MPCA image, various input commands are possibly in the CPU method according to the dialogue between the CPU and the on line typewriter. In addition to this, decoded tomographic images of unrestricted depth are readily attainable. 2) In the CPU method noise elimination and other aspects of image management can be easily performed.     

A practical synthesis of L-ribose

L-Ribose was synthesized by a simple four-step method with overall yield of 76.3% from a protected L-arabinose derivative, which is a compatible intermediate for the synthesis of L-deoxyribose. The key step of this strategy is the Swern oxidation and subsequent stereoselective reduction accompanied by inversion of the 2-hydroxy group of protected L-arabinose.