A Quantitative Determination of the Interaction of Pentamethylenetetrazole with the Sodium Ion by Sodium-23 NMR

The importance of the sodium ion transport in biological systems is well known. Numerous studies have dealt with compounds which affect ion transport across membrane systems. However, the mechanism of ion transport across the membrane is still not clear. Hence it is of interest to investigate the interaction of the sodium ion with biologically active compounds in a system where the complex membrane is absent. Such a method of investigation must be able to detect very weak interactions. Sodium-23 nuclear magnetic resonance fits well into this classification. This technique has been used by others¹ and by us² to investigate electrolyte solutions and biological or model systems. We have been interested in the chemistry of cyclopolymethy-lenetetrazoles for some time.³ These compounds are characterized by their strong stimulating action on the central nervous system and, in     

Unital affine semigroups

Affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable. They were introduced by Cohen and Collins in 1959. We look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups. Most notably we improve a result of Wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups.     

Cyano terminated tolane compounds for polymer dispersed liquid crystal application: relationship between cyano terminated tolane based molecular structures and electro-optical properties

ABSTRACT

The structures of the liquid crystal (LC) molecules have a key role in impacting the electro-optical performance of a polymer dispersed liquid crystal (PDLC) film. In this paper, the relationship between the LC molecular structures and the electro-optical properties of PDLC films is investigated based on an unexplored cyano-terminated tolane compounds (CTTCs) doped E8 LCs/UV polymers system. Due to the high polarity of CTTCs, LCs doped with the cyano-terminated tolane (CTT) molecules exhibit high birefringence and large positive dielectric anisotropy. On the whole, PDLC films doped with the CTT molecules exhibit a lower driving voltage than that doped with the pure E8. More excitingly, PDLC films based on CTT molecules with larger length-to-width ratio and longer conjugated system show higher contrast ratio (CR) and faster response time. Eventually, the mechanism of the effects of CTT-based molecular structures and the relationship between the electro-optical performance of PDLC films and CTT molecules are illustrated. This work paves a new way for optimising the electro-optical properties of PDLC films.     

Detailed comparison of the pnicogen bond with chalcogen,halogen, and hydrogen bonds

The characteristics of the pnicogen bond are explored using a variety of quantum chemical techniques. In particular, this interaction is compared with its halogen and chalcogen bond cousins, as well as with the more common H‐bond. In general, these bonds are all of comparable strength. More specifically, they are strengthened by the presence of an electronegative substituent on the electron‐acceptor atom, and each gains strength as one moves down the appropriate column of the periodic table, for example, from N to P to As. These noncovalent bonds owe their stability to a mixture in nearly equal parts of electrostatic attraction and charge transfer, along with a smaller dispersion component. The charge transfer arises from the overlap between the lone pair of the electron donor and a σ* antibond of the acceptor. The angular characteristics of the equilibrium geometry result primarily from a compromise between electrostatic and induction forces. Angular distortions of the H‐bond are typically less energetically demanding than comparable bends of the other noncovalent bonds. © 2012 Wiley Periodicals, Inc.     

Sur les Transformations Simultanées de Deux Équations Différentielles Linéaires du Deuxième Ordre dans Elles-mêmes

AMS (MOS) Classification 34C20     

POSITIVE SOLUTIONS TO(k,n-k) NONHOMOGENEOUS BOUNDARYVALUE PROBLEM

By the Schauder fixed point theory,this paper establishes the existence of positive solutions to a(k,n k) m-point boundary value problem.We show that there exists a positive constant b such that the problem has at least one positive solution when the homogeneous boundary parameter is smaller than b,and no positive solution when this parameter is greater than b.     

On solitary wave solutions to the nonlinear Schrödinger equations with two parameters

In this paper, we discuss the existence and multiplicity of positive solitary wave solutions for nonlinear Schrödinger equations with two parameters. The proof is based on the method of upper and lower solutions and the fixed point index.