The determination of starting conditions for modifier optimization in reversed-phase HPLC

Summary After a brief introduction of the subject, the paper focusses on the first step in any optimization procedure: the delineation of the parameter space, wherein the global optimum is to be found. For organic modifier optimization in reversed-phase liquid chromatography it is shown that the necessary information can be derived from a single water-methanol gradient. It first yields an estimate of the total number of solutes in the sample, which is vital to define the peak capacity needed to achieve separation at a certain confidence level. Next, the gradient allows the prediction of suitable isocratic methanol binary solvents, and transfer rules formulate the iso-eluotropic composition of the common binary solvents (tetrahydrofuran and acetonitrile). Because all predictions are based on a statistical analysis of a limited data base, attention is given to the practical situation where an actual sample deviates from the average solute behaviour. Such deviations are revealed in the first isocratic run and can be used to arrive at a better estimate of solute retention.     

SYNTHESIS OF CROSS-CONJUGATED （p-PHENYLENE）S-POLY（p- PHENYLENEVINYLENE）S HYBRIDS WITH LOW CONTENT OF STRUCTURAL DEFECTS

The novel shish-kebab-type liquid crystalline cross-conjugated （p-phenylene）s-poly（p-phenylenevinylene）s hybrid was synthesized through Gilch polymerization. Their structures and properties were characterized by NMR, GPC, DSC, X-ray diffraction and polarizing optical microscope （POM）. ^1H-NMR investigation of the polymers indicates that the shish-kebab-structure has a strong ability to suppress the structural defects in the polymers. The polymers are enantiotropic liquid crystals. The melting point （Tm） of the polymers decreases when the length of the alkoxy tails of the mesogenic units increases. The mesophase was identified by X-ray diffraction method. They showed not only a smectic LC phase, but also a strong green fluorescence in chloroform. The maximum absorption band of the ＂kebabs＂ of the two, 5-bis（4＇- alkoxyphenyl）benzene at 280 nm did not appear in absorption spectra of the polymers. The same phenomena were also observed in the fluorescence spectra. These results imply that the polymers have formed a cross-conjugated uniform structure and achieved an extended n-conjugation polymer.     

A Basis for Orbital Symmetry Rules

The influence of molecular symmetry on reaction rates is examined with an approach in which reactions are viewed as electronic transitions between states of reacants and products (described, in turn by quasiadiabatic potential surface). The moleculer Hamiltonian is used to derive selection rules for these transitions. The complete Hamilatonian has no useful symmetery. Neglect of non-Born-Oppenheimer and spin-orbit terms (and of other angular momentum coupling terms) leads to an apporixmate Hamiltonian and to selection rules which from the basis of the Woodward-Hoffmann rules. This apporch provides an alternative to the adiabatic potantial surfaces, reaction coordinates, and transition state theory used in more familiar discussions of the Woodward-Hoffmann rules. Further, it provides a particulary clear method for discussing violations of these symmetry rules, and for differentiating concerted and nonconcerted reactions.     

ELECTROCHEMICAL POLYMERIZATION OF ANILINE IN PHOSPHORIC ACID AND THE PROPERTIES OF POLYANILINE

The behavior of the electrochemical polymerization of aniline in a weak acid, phosphoric acid, is very similar to that in strong acids, i.e. its polymerization rate increases quickly with the electrolysis time. The FTIR spectra of polyaniline samples synthesized in phosphoric acid indicate that the counter ion H2PO4^- is present in both the oxidized form and the reduced form of polyaniline. The counter ion plays an important role in adjusting the pH value at the electrode surface of polyaniline during the oxidation and reduction processes. As a result, a pair of redox peaks still appear in cyclic voltammograms of polyaniline in a solution of sodium sulfate of pH 5.5 and in a solution of NaH2PO4 of pH 7.0,respectively, at low potential scan rate; and the color of polyaniline film also changes with applied potential at pH 7.0. Thus,the pH region for the electrochemical activity and the electrochromism of polyaniline is extended to pH 5.5 for a solution of sodium sulfate and to pH 7.0 for a solution of NaH2PO4. The conductivity of polyaniline is 3.3 S cm^-1, depending on the concentration of phosphoric acid used in the stage of polymerization of aniline. The result of elemental analysis of polyaniline is presented here.     

Pore size distributions in microporous membranes. A critical analysis of the bubble point extended method

An extended bubble point method has been used to examine the porous morphology of several track-etched microporous polycarbonate membranes with nominal pore sizes ranging from 0.1 to 5.0 μm. The technique has been carefully analyzed and corrected to take into account the diverse non-ideal factors in flow along with the prevalence of Knudsen flow over the Hagen-Poiseuille one in the smaller pores.     

Lipschitzian inverse functions,directional derivatives,and applications inC 1,1 optimization

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC ^1,1 optimization problems.Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets f(x; u), the author is indebted to Prof. L. Thibault.     

Higher-order necessary conditions for infinite and semi-infinite optimization

In this paper, we present a unified theory of first-order and higher-order necessary optimality conditions for abstract vector optimization problems in normed linear spaces. We prove general multiplier rules, from which nearly all known first-order, second-order, and higher-order necessary conditions can be derived. In the last section, we prove higher-order necessary conditions for semi-infinite programming problems.This work was developed within the Forschungsschwerpunkt Dynamische Systeme, Universität Bremen, Bremen, West Germany.The author wishes to thank Prof. Dr. D. Hinrichsen for his helpful remarks and discussions during the preparation of this work.     

The extended Hulburt–Hirschfelder‐long‐range oscillator model for direct‐potential‐fit analysis

In the present work, an extended Hulburt–Hirschfelder oscillator model is proposed as a means of simplifying potential energy functions for direct‐potential‐fit analyses. The new potential energy function is joined smoothly to the long‐range inverse‐power dispersion energy expression. The new model is employed in direct‐potential‐fits using spectroscopic line positions that involve the ground electronic states of the principal isotopologues of hydrogen iodide and carbon monoxide, and the ground and first singlet‐sigma excited states of hydrogen fluoride and hydrogen chloride. The present methodology is found to lead to compact, flexible, and robust representations for the potential energy that compare favorably with the results of past work where more complicated models were employed.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.