Separation of D‐psicose and D‐fructose using simulated moving bed chromatography

Simulated moving bed (SMB) processes have been widely used in the sugar industries with ion‐exchange resin as a stationary phase. D ‐Psicose, a rare monosaccharide known as a valuable pharmaceutical substrate, was synthesized by the enzymatic conversion from D ‐fructose. The SMB process was adopted to separate D ‐psicose from D ‐fructose. Before the SMB experiment, the reaction mixture including D ‐psicose and D ‐fructose was treated by a deashing process to remove contaminants, such as buffers, proteins, and other organic materials. Four columns packed with Dowex 50WX4‐Ca²⁺ (200–400 mesh) ion‐exchange resins were used in the four‐zone SMB. Single‐step frontal analysis was performed to estimate the isotherm parameters of each monosaccharide. The operating conditions of the SMB process were determined based on the Equilibrium Theory. According to the simulation of the SMB process, the purity and yield of extract product (D ‐psicose) achieved were 99.04 and 97.46%, respectively and those of raffinate product (D ‐fructose) were 99.06 and 99.53%, respectively. Under the optimized operating condition, complete separation (extract purity = 99.36%, raffinate purity = 99.67%) was achieved experimentally.     

Enhanced electrophoretic DNA separation in photonic crystal fiber

Joule heating generated by the electrical current in capillary electrophoresis leads to a temperature gradient along the separation channel and consequently affects the separation quality. We describe a method of reducing the Joule heating effect by incorporating photonic crystal fiber into a micro capillary electrophoresis chip. The photonic crystal fiber consists of a bundle of extremely narrow hollow channels, which ideally work as separation columns. Electrophoretic separation of DNA fragments was simultaneously but independently carried out in 54 narrow capillaries with a diameter of 3.7 μm each. The capillary bundle offers more efficient heat dissipation owing to the high surface-to-volume ratio. Under the same electrical field strength, notable improvement in resolution was obtained in the capillary bundle chip.     

New Quenching Procedure for Preservation of Initial Polymer/Catalyst Particle Morphology in Ziegler–Natta Olefin Polymerization

Preservation of initial polymer/catalyst particle morphology under air, was examined using stopped‐flow Ziegler–Natta polymerization with various quenching conditions and post‐chemical treatments. The exposure of the initial particles to air caused the fast formation of cracks on the surface, finally leading to significant reformation of the particle shape, when polymerizing particles were washed with heptane at ?65 °C under N₂ or under CO₂. On the other hand, when the particles were washed with heptane containing an appropriate amount of tetrahydrofuran under CO₂, the particle morphology under air was almost completely maintained even after 1 h exposure. The present results are useful for various ex situ characterizations of unstable initial polymer/catalyst particles.

     

On the restriction of cross characteristic representations of 2 F 4(q) to proper subgroups

We prove that the restriction of any nontrivial representation of the Ree groups ² F ₄(q), q = 2²ⁿ⁺¹ ≥ 8 in odd characteristic to any proper subgroup is reducible. We also determine all triples (K, V, H) such that ${K \in \{^2F_4(2), ^2F_4(2)'\} }We prove that the restriction of any nontrivial representation of the Ree groups ² F ₄(q), q = 2²ⁿ⁺¹ ≥ 8 in odd characteristic to any proper subgroup is reducible. We also determine all triples (K, V, H) such that K ? {²F₄(2), ²F₄(2)￠}{K \in \{^2F_4(2), ^2F_4(2)'\} } , H is a proper subgroup of K, and V is a representation of K in odd characteristic restricting absolutely irreducibly to H.     

A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity

We revisit the asymptotic formulas originally derived in [D.J. Cedio-Fengya, S. Moskow, M.S. Vogelius, Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction, Inverse Problems 14 (1998) 553–595; A. Friedman, M. Vogelius, Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence, Arch. Ration. Mech. Anal. 105 (1989) 299–326]. These formulas concern the perturbation in the voltage potential caused by the presence of diametrically small conductivity inhomogeneities. We significantly extend the validity of the previously derived formulas, by showing that they are asymptotically correct, uniformly with respect to the conductivity of the inhomogeneities. We also extend the earlier formulas by allowing the conductivities of the inhomogeneities to be completely arbitrary L^∞$L^{\infty }$, positive definite, symmetric matrix-valued functions. We briefly discuss the relevance of the uniform asymptotic validity, and the admission of arbitrary anisotropically conducting inhomogeneities, as far as applications of the perturbation formulas to “approximate cloaking” are concerned.     

Operational Properties of Two Integral Transforms of Fourier Type and their Convolutions

In this paper we present the operational properties of two integral transforms of Fourier type, provide the formulation of convolutions, and obtain eight new convolutions for those transforms. Moreover, we consider applications such as the construction of normed ring structures on L₁(\mathbbR)L_{1}({\mathbb{R}}), further applications to linear partial differential equations and an integral equation with a mixed Toeplitz-Hankel kernel.     

Variational analysis of extended generalized equations via coderivative calculus in Asplund spaces

This paper is devoted to the development of variational analysis and generalized differentiation in the framework of Asplund spaces. We mainly concern the study of a special class of set-valued mapping given in the form

where both F and Q are set-valued mappings between Asplund spaces. Models of this type are associated with solutions maps to the so-called (extended) generalized equations and play a significant role in many aspects of variational analysis and its applications to optimization, stability, control theory, etc. In this paper we conduct a local variational analysis of such extended solution maps S and their remarkable specifications based on dual-space generalized differential constructions of the coderivative type. The major part of our analysis revolves around coderivative calculus largely developed and implemented in this paper and then applied to establishing verifiable conditions for robust Lipschitzian stability of extended generalized equations and related objects.     

Tikhonov regularization method for a system of equilibrium problems in Banach spaces

The purpose of this paper is to investigate the Tikhonov regularization method for solving a system of ill-posed equilibrium problems in Banach spaces with a posteriori regularization-parameter choice. An application to convex minimization problems with coupled constraints is also given.     

A new regularized method for two dimensional nonhomogeneous backward heat problem

We consider the problem of finding, from the final data u(x,y,T)=g(x,y), the initial data u(x,y,0) of the temperature function u(x,y,t),(x,y)I=(0,π)×(0,π),t[0,T] satisfying the following system

The problem is severely ill-posed. In this paper a simple and convenient new regularization method for solving this problem is considered. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively.