An Algorithm Based on Simple Rules for the Determination of the Architecture of Branched Polymer Molecules from the Number of Branching Points per Molecule

2007 ◽  
Vol 16 (3) ◽  
pp. 240-246 ◽  
Author(s):  
Jean-Charles Majesté ◽  
Christian Carrot ◽  
Paul-Octavian Stanescu ◽  
Coralie Mardon
Keyword(s):  
Branched Polymer ◽  
Polymer Molecules ◽  
Branching Points ◽  
Simple Rules

Excess entropy of the systems of molecules differing in size and shape

1983 ◽  
Vol 48 (1) ◽  
pp. 192-198 ◽  
Author(s):  
Tomáš Boublík
Keyword(s):  
Equation Of State ◽  
Hard Spheres ◽  
Excess Entropy ◽  
Convex Bodies ◽  
Pure Substance ◽  
Liquid Equilibrium ◽  
Simple Rules ◽  
Different Shapes ◽  
The Mean

The excess entropy of mixing of mixtures of hard spheres and spherocylinders is determined from an equation of state of hard convex bodies. The obtained dependence of excess entropy on composition was used to find the accuracy of determining ΔSE from relations employed for the correlation and prediction of vapour-liquid equilibrium. Simple rules were proposed for establishing the mean parameter of nonsphericity for mixtures of hard bodies of different shapes allowing to describe the P-V-T behaviour of solutions in terms of the equation of state fo pure substance. The determination of ΔSE by means of these rules is discussed.

Determination of Concentration of Amphiphilic Polymer Molecules on the Surface of Encapsulated Semiconductor Nanocrystals

Langmuir ◽  
2016 ◽  
Vol 32 (8) ◽  
pp. 1955-1961 ◽  
Author(s):  
Aleksandra Fedosyuk ◽  
Aliaksandra Radchanka ◽  
Artsiom Antanovich ◽  
Anatol Prudnikau ◽  
Maksim V. Kvach ◽  
...  
Keyword(s):  
Semiconductor Nanocrystals ◽  
Amphiphilic Polymer ◽  
Polymer Molecules

The Structure of Neoprene. II. Determination of End Groups by Means of Radiosulfur

1949 ◽  
Vol 22 (4) ◽  
pp. 1092-1102 ◽  
Author(s):  
W. E. Mochel ◽  
J. H. Peterson
Keyword(s):  
Chain Transfer ◽  
Potassium Persulfate ◽  
Polymer Molecule ◽  
Cleavage Reaction ◽  
Polymer Molecules ◽  
Simple Chain ◽  
The One ◽  
Tetraethylthiuram Disulfide ◽  
Molecular Weight Fractions

Abstract By use of radioactive sulfur it has been shown that sulfur-modified Neoprene, i.e., Neoprene Type GN, is essentially a copolymer of chloroprene and sulfur in the approximate ratio of 100 chloroprene units per sulfur atom. The sulfur units, possibly disulfides, are cleaved by an alkaline emulsion of tetraethylthiuram disulfide, so that a gel polymer containing combined sulfur can thus be converted to a soluble, plastic product. The mechanism of this cleavage reaction has not been completely elucidated as yet. Potassium persulfate, used as initiator for the polymerization of Neoprene, appears to be combined with the polymer in Neoprene Type GN in amounts equivalent to 8–17 polymer molecules formed for each sulfur-cpntaining initiator fragment. However, when dodecanethiol is used as modifier, a large proportion of the polymer molecules contain essentially no combined sulfur from the persulfate, and it appears that the true initiator is the RS free radical formed by reaction of the thiol with potassium persulfate. Dodecanethiol used as a polymerization modifier or chain transfer agent is combined in a greater amount than the one thiol per polymer molecule expected on the basis of simple chain transfer. High molecular-weight fractions contained 3–4 thiol sulfur atoms per polymer molecule and the results suggest that thiol addition to the double bonds of the polymer had occurred.

The direct observation of polymer molecules and determination of their molecular weight

1964 ◽  
Vol 279 (1376) ◽  
pp. 50-61 ◽  
Keyword(s):  
Molecular Weight ◽  
Direct Observation ◽  
Particle Diameter ◽  
Dilute Solution ◽  
Crystalline Polymers ◽  
Polymer Molecules ◽  
Molecular Weights ◽  
Preferential Evaporation ◽  
Poor Solvent

An experimental investigation of the conditions necessary for the production of compact, single polymer molecules, in a form suitable for direct observation in the electron microscope, is described. Molecules are isolated by dispersing a dilute solution of the polymer as fine droplets on to a suitable substrate: ideally each droplet should contain either one or no polymer molecules. The solution is a mixture of two solvents, a good one and a poor one. Initially the good solvent predominates so that the probability of polymer aggregation is low. Preferential evaporation of the relatively volatile solvent on the substrate itself gives the poor solvent conditions needed for the formation of well-defined molecular spheres. Factors determining the choice of solvent, precipitant, and the composition of the mixture are discussed. There is little difficulty in obtaining single molecules with glassy amorphus polymers; rubbery polymers collapse and spherical molecules are formed only if the entire preparation is carried out at a temperature below that of the glass transition; crystalline polymers are not amenable to this technique. To obtain sufficient contrast the particles have to be shadowed and it is shown that, although certain dimensions are distorted by the metal coating, the shadow length faithfully represents the true particle diameter. Molecular weights, and their distribution, when of the order of a million and above, can readily be accurately determined. Conventional methods are unreliable in this region of high molecular weight.

scholarly journals Linguistically Defined Clustering of Data

2018 ◽  
Vol 28 (3) ◽  
pp. 545-557 ◽  
Author(s):  
Jacek M. Leski ◽  
Marian P. Kotas
Keyword(s):  
State Of The Art ◽  
Sequential Search ◽  
High Data ◽  
Linguistic Rule ◽  
Linguistic Rules ◽  
Simple Rules ◽  
Benchmark Datasets ◽  
Clustering Approach ◽  
The Subject

Abstract This paper introduces a method of data clustering that is based on linguistically specified rules, similar to those applied by a human visually fulfilling a task. The method endeavors to follow these remarkable capabilities of intelligent beings. Even for most complicated data patterns a human is capable of accomplishing the clustering process using relatively simple rules. His/her way of clustering is a sequential search for new structures in the data and new prototypes with the use of the following linguistic rule: search for prototypes in regions of extremely high data densities and immensely far from the previously found ones. Then, after this search has been completed, the respective data have to be assigned to any of the clusters whose nuclei (prototypes) have been found. A human again uses a simple linguistic rule: data from regions with similar densities, which are located exceedingly close to each other, should belong to the same cluster. The goal of this work is to prove experimentally that such simple linguistic rules can result in a clustering method that is competitive with the most effective methods known from the literature on the subject. A linguistic formulation of a validity index for determination of the number of clusters is also presented. Finally, an extensive experimental analysis of benchmark datasets is performed to demonstrate the validity of the clustering approach introduced. Its competitiveness with the state-of-the-art solutions is also shown.

Numerical determination of the singularity order of a system of differential equations

2020 ◽  
Vol 28 (1) ◽  
pp. 17-34
Author(s):  
Ali Baddour ◽  
Mikhail D. Malykh ◽  
Alexander A. Panin ◽  
Leonid A. Sevastianov
Keyword(s):  
Differential Equations ◽  
Integrable Hamiltonian System ◽  
Computer Experiments ◽  
Completely Integrable Hamiltonian System ◽  
Painlevé Property ◽  
Branching Points ◽  
Present Context ◽  
Singularity Order ◽  
Complex Scheme

We consider moving singular points of systems of ordinary differential equations. A review of Painlevé’s results on the algebraicity of these points and their relation to the Marchuk problem of determining the position and order of moving singularities by means of finite difference method is carried out. We present an implementation of a numerical method for solving this problem, proposed by N. N. Kalitkin and A. Al’shina (2005) based on the Rosenbrock complex scheme in the Sage computer algebra system, the package CROS for Sage. The main functions of this package are described and numerical examples of usage are presented for each of them. To verify the method, computer experiments are executed (1) with equations possessing the Painlevé property, for which the orders are expected to be integer; (2) dynamic Calogero system. This system, well-known as a nontrivial example of a completely integrable Hamiltonian system, in the present context is interesting due to the fact that coordinates and momenta are algebraic functions of time, and the orders of moving branching points can be calculated explicitly. Numerical experiments revealed that the applicability conditions of the method require additional stipulations related to the elimination of superconvergence points.

Numerical determination of the singularity order of a system of differential equations

2020 ◽  
Vol 28 (1) ◽  
pp. 17-34
Author(s):  
Ali Baddour ◽  
Mikhail D. Malykh ◽  
Alexander A. Panin ◽  
Leonid A. Sevastianov
Keyword(s):  
Differential Equations ◽  
Integrable Hamiltonian System ◽  
Computer Experiments ◽  
Completely Integrable Hamiltonian System ◽  
Painlevé Property ◽  
Branching Points ◽  
Present Context ◽  
Singularity Order ◽  
Complex Scheme

We consider moving singular points of systems of ordinary differential equations. A review of Painlevé’s results on the algebraicity of these points and their relation to the Marchuk problem of determining the position and order of moving singularities by means of finite difference method is carried out. We present an implementation of a numerical method for solving this problem, proposed by N. N. Kalitkin and A. Al’shina (2005) based on the Rosenbrock complex scheme in the Sage computer algebra system, the package CROS for Sage. The main functions of this package are described and numerical examples of usage are presented for each of them. To verify the method, computer experiments are executed (1) with equations possessing the Painlevé property, for which the orders are expected to be integer; (2) dynamic Calogero system. This system, well-known as a nontrivial example of a completely integrable Hamiltonian system, in the present context is interesting due to the fact that coordinates and momenta are algebraic functions of time, and the orders of moving branching points can be calculated explicitly. Numerical experiments revealed that the applicability conditions of the method require additional stipulations related to the elimination of superconvergence points.

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