A Note About the Nowicki Conjecture on Weitzenböck Derivations

2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.

An algorithm to detect linearly separable clusters of binary patterns

The clusters of binary patterns can be considered as Boolean functions of the (binary) features. Such a relationship between the linearly separable (LS) Boolean functions and LS clusters of binary patterns is examined. An algorithm is presented to answer the questions of the type: “Is the cluster formed by the subsets of the (binary) data set having certain features AND/NOT having certain other features, LS from the remaining set?” The algorithm uses the sequences of Numbered Binary Form (NBF) notation and some elementary (NPN) transformations of the binary data.

An algorithm to detect linearly separable clusters of binary patterns

The clusters of binary patterns can be considered as Boolean functions of the (binary) features. Such a relationship between the linearly separable (LS) Boolean functions and LS clusters of binary patterns is examined. An algorithm is presented to answer the questions of the type: “Is the cluster formed by the subsets of the (binary) data set having certain features AND/NOT having certain other features, LS from the remaining set?” The algorithm uses the sequences of Numbered Binary Form (NBF) notation and some elementary (NPN) transformations of the binary data.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.

Effect of binary block-selective solvents on self-assembly of ABA triblock copolymer in dilute solution

We have studied the self-assembly of the ABA triblock copolymer (P4VP-b-PS-b-P4VP) in dilute solution by using binary block-selective solvents, that is, water and methanol. The triblock copolymer was first dissolved in dioxane to form a homogeneous solution. Subsequently, a given volume of selective solvent was added slowly to the solution to induce self-assembly of the copolymer. It was found that the copolymer (P4VP(43)-b-PS366-b-P4VP(43)) tended to form spherical aggregate or bilayer structure when we used methanol or water as the single selective solvent, respectively.

Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy (2) + 2b(x, y) dx dy + c(x, y)dx (2) = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf`s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F (p) = 0, and F (pp) not equal aEuro parts per thousand 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form omega = dy -aEuro parts per thousand pdx defined on the singular surface F = 0.

The use of binary polymeric networks in stabilising polyethylene oxide solid dispersions

The objective of this study was to determine if a high Tg polymer (Eudragit® S100) could be used to stabilize amorphous domains of polyethylene oxide (PEO) and hence improve the stability of binary polymer systems containing celecoxib (CX). We propose a novel method of stabilizing the amorphous PEO solid dispersion through inclusion of a miscible, high Tg polymer, namely, that can form strong inter-polymer interactions. The effects of inter-polymer interactions and miscibility between PEO and Eudragit S100 are considered. Polymer blends were first manufactured via hot-melt extrusion at different PEO/S100 ratios (70/30, 50/50, and 30/70 wt/wt). Differential scanning calorimetry and dynamic mechanical thermal analysis data suggested a good miscibility between PEO and S100 polymer blends, particularly at the 50/50 ratio. To further evaluate the system, CX/PEO/S100 ternary mixtures were extruded. Immediately after hot-melt extrusion, a single Tg that increased with increasing S100 content (anti-plasticization) was observed in all ternary systems. The absence of powder X-ray diffractometry crystalline Bragg’s peaks also suggested amorphization of CX. Upon storage (40°C/75% relative humidity), the formulation containing PEO/S100 at a ratio of 50:50 was shown to be most stable. Fourier transform infrared studies confirmed the presence of hydrogen bonding between Eudragit S100 and PEO suggesting this was the principle reason for stabilization of the amorphous CX/PEO solid dispersion system.

Respecting contractual intentions : balancing consumer expectations with the sanctity of contract in the context of standard form insurance contracts

It is the purpose of this article to examine the means curently available to judges to achieve a workable balance between providing appropriate consumer protection to signatories of standard form contractors while still retaining adequate respect for the sanctity of contract, and, based on this analysis, to determine whether a significantly greater scope of contract (re)construction is likely to become the norm in most common law jurisdictions in the coming decades.

Legal Reasoning in Environmental Law : a Study of Structure, Form and Language

This book analyses the structure, form and language of a selected number of international and national legal instruments and reviews how an illustrative range of international and national judicial institutions have responded to the issues before them and the processes of legal reasoning engaged by them in reaching their decisions. This involves a very detailed discussion of these primary sources of international and national environmental law with a view to determining their jurisprudential architecture and the processes of reasoning expected of those responsible for implementing these architectural arrangements. This book is concerned not with the effectiveness or the quality of an environmental legal system but only with its jurisprudential characteristics and their associated processes of legal reasoning.

Permutation polynomials of the form (xp −x +δ)s +L(x)

Recently, several classes of permutation polynomials of the form (x2 + x + δ)s + x over F2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp − x + δ)s + L(x) over Fpm is investigated, where L(x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on F2m are derived. Three classes of permutation polynomials over F3m are also presented.

Control of core-shell structure and elemental composition of binary quantum dots

The possibility of initial stage control of the elemental composition and core/shell structure of binary SiC quantum dots by optimizing temporal variation of Si and C incoming fluxes and surface temperatures is shown via hybrid numerical simulations. Higher temperatures and influxes encourage the formation of a stoichiometric outer shell over a small carbon-enriched core, whereas lower temperatures result in a larger carbon-enriched core, Si-enriched undershell, and then a stoichiometric SiC outer shell. This approach is generic and is applicable to a broad range of semiconductor materials and nanofabrication techniques. © 2007 American Institute of Physics.