Solutions of sturm-liouville boundary value problems for higher-order differential equations

The existence of solutions of a class of two-point boundary value problems for higher order differential equations is studied. Sufficient conditions for the existence of at least one solution are established. It is of interest that the nonlinearityf in the equation depends on all lower derivatives, and the growth conditions imposed onf are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don’t apply the Green’s functions of the corresponding problem and the method to obtain a priori bound of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.     

On the entropy of fusion

The asymptotic value of the melting entropy, i.e. ΔS_f = R ln 2 for vanishing relative change of volume on melting, can be derived from the vibrational entropy due to vibrating dislocations, which are introduced into a material on melting.     

Improved coating method for uniform polymer layer in infrared hollow fiber

An improved coating method was proposed in order to form a uniform polymer layer in the fabrication of cyclic olefin polymer-coated silver (COP/Ag) hollow fiber. A COP solution was flowed in a closed loop, in which the silver-coated tube was used as a part of the loop. Owing to the constant flowing speed of the COP solution and the airtight flowing environment, a COP layer was uniformly formed. The hollow fibers attain high performance and deliver multi-wavelength laser light from the infrared to the visible simultaneously. The method was successfully applied to the fabrication of practical hollow fibers with 2 m length for the near and mid-infrared lasers.     

Synthesis and properties of poly(amic acid)s and polyimides based on 2,2′,6,6′‐biphenyltetracarboxylic dianhydride

Poly(amic acid)s (PAAs) having the high solution stability and transmittance at 365 nm for photosensitive polyimides have been developed. PAAs with a twisted conformation in the main chains were prepared from 2,2′,6,6′‐biphenyltetracarboxylic dianhydride (2,2′,6,6′‐BPDA) and aromatic diamines. Imidization of PAAs was achieved by chemical treatment using trifluoroacetic anhydride. Among them, the PAA derived from 2,2′,6,6′‐BPDA and 4,4′‐(1,3‐phenylenedioxy)dianiline was converted to the polyimide by thermal treatment. The heating at 300 °C under nitrogen did not complete thermal imidization of PAAs having glass‐transition temperatures (T_g)s higher than 300 °C to the corresponding PIs. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6385–6393, 2006     

Characteristics of a protein error in determination of serum protein in the presence of inorganic salt.

There is a possibility that the color development of the dye-binding method based on a protein error of a pH indicator is affected by the coexisting inorganic salt. Thus, the author theoretically and experimentally investigated the effect of the inorganic salt on the protein error. In a theoretical analysis, the anion of an inorganic salt, like the dissociated dye and buffer anions, was assumed to react with the protein, forming a colorless anion-protein complex. The calculated results were compared with those obtained by experiments using three pH indicators and various kinds of inorganic salts. The calculated results obtained are as follows: (1) The color development decreases with increasing the concentration of the inorganic salt and the equilibrium constant of the reaction between the inorganic salt and protein; (2) The rate of the absorbance decrease is larger for a lower concentration of the inorganic salt than for a higher one; (3) The larger is the equilibrium constant, the larger is the absorbance decrease. The absorbance decrease was caused by the anion, and was increased by increasing the anion concentration. The magnitude of the effect of the anion was iodide > bromide > chloride, which was associated with their ionic radius. The difference in the effect of the anion was thought to indicate that the equilibrium constant, in other words, the bonding strength of the anion to protein is iodide > bromide > chloride.     

Important role of the 3-mercaptopropionamide moiety in glutathione: promoting effect on decomposition of the adduct of glutathione with the oxoammonium ion of TEMPO

Cyclic voltammetry of TEMPO in aqueous 0.1 M NaOH in the presence of glutathione (GSH) or cysteine (Cys) indicated the following points: (i) Both of the thiols rapidly formed adducts 3 with oxoammonium ion 1 anodically generated from TEMPO. (ii) 3 generated from GSH entered a succeeding reaction that generated N-oxide anion 2- (the reduced TEMPO). (iii) 3 produced from Cys remained intact over the time scale of voltammetry. A structural feature of GSH was considered to contribute to the observed behavior of this tripeptide. Possible structural features were evaluated by screening various thiols on the basis of whether they provided GSH-like voltammetric results. The 3-mercaptopropionamide group with an amide hydrogen in GSH was determined to be responsible for the observed difference between GSH and Cys. The likely function is to transform 3 from GSH into a 5-imino-1,2-oxathiolane intermediate, thereby releasing 2-. Product analysis for reactions of model thiols representing GSH and Cys with 1 provided support for this argument and suggested that the reaction of GSH or Cys with 1 would produce the corresponding disulfides, regardless of whether a five-membered ring intermediate was formed. The proposed function of the 3-mercaptopropionamide moiety of GSH may provide useful insight for the molecular design of exogenous thiol compounds as novel drugs for the treatment of GSH-depletion-related disorders.