scholarly journals Elasticity in certain block monoids via the Euclidean table

2007 ◽  
Vol 57 (5) ◽  
Author(s):  
SooAh Chang ◽  
Scott Chapman ◽  
William Smith
Keyword(s):  
Prime Integer ◽  
Irreducible Elements ◽  
Complete Set ◽  
Block Monoids ◽  
János Bolyai

AbstractThis paper continues the study begun in [GEROLDINGER, A.: On non-unique factorizations into irreducible elements II, Colloq. Math. Soc. János Bolyai 51 (1987), 723–757] concerning factorization properties of block monoids of the form ℬ(ℤn, S) where S = $$\{ \bar 1,\bar a\} $$ (hereafter denoted ℬa(n)). We introduce in Section 2 the notion of a Euclidean table and show in Theorem 2.8 how it can be used to identify the irreducible elements of ℬa(n). In Section 3 we use the Euclidean table to compute the elasticity of ℬa(n) (Theorem 3.4). Section 4 considers the problem, for a fixed value of n, of computing the complete set of elasticities of the ℬa(n) monoids. When n = p is a prime integer, Proposition 4.12 computes the three smallest possible elasticities of the ℬa(p).

scholarly journals ON FACTORIZATION IN BLOCK MONOIDS FORMED BY $\{\bar{1},\bar{a}\}$ IN $\mathbb{Z}_{n}$

2003 ◽  
Vol 46 (2) ◽  
pp. 257-267 ◽  
Author(s):  
Scott T. Chapman ◽  
William W. Smith
Keyword(s):  
Class Group ◽  
Subject Classification ◽  
Division Algorithm ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Irreducible Elements ◽  
Complete Set ◽  
Cross Number ◽  
Block Monoids ◽  
Block Monoid

AbstractWe consider the factorization properties of block monoids on $\mathbb{Z}_n$ determined by subsets of the form $S_a=\{\bar{1},\bar{a}\}$. We denote such a block monoid by $\mathcal{B}_a(n)$. In §2, we provide a method based on the division algorithm for determining the irreducible elements of $\mathcal{B}_a(n)$. Section 3 offers a method to determine the elasticity of $\mathcal{B}_a(n)$ based solely on the cross number. Section 4 applies the results of §3 to investigate the complete set of elasticities of Krull monoids with divisor class group $\mathbb{Z}_n$.AMS 2000 Mathematics subject classification: Primary 20M14; 20D60; 13F05

Bonded Force Constant Derivation of Lysine-Arginine Cross-linked Advanced Glycation End-Products

2018 ◽  
Author(s):  
Anthony Nash ◽  
Nora H de Leeuw ◽  
Helen L Birch
Keyword(s):  
Molecular Dynamics ◽  
Force Constant ◽  
Computational Study ◽  
Force Constants ◽  
Quantum Mechanical ◽  
Advanced Glycation ◽  
Partial Charges ◽  
Cross Links ◽  
Complete Set ◽  
Dynamics Simulations

<div> <div> <div> <p>The computational study of advanced glycation end-product cross- links remains largely unexplored given the limited availability of bonded force constants and equilibrium values for molecular dynamics force fields. In this article, we present the bonded force constants, atomic partial charges and equilibrium values of the arginine-lysine cross-links DOGDIC, GODIC and MODIC. The Hessian was derived from a series of <i>ab initio</i> quantum mechanical electronic structure calculations and from which a complete set of force constant and equilibrium values were generated using our publicly available software, ForceGen. Short <i>in vacuo</i> molecular dynamics simulations were performed to validate their implementation against quantum mechanical frequency calculations. </p> </div> </div> </div>

A flux-based stoichiometric model of enhanced biological phosphorus removal metabolism

1998 ◽  
Vol 37 (4-5) ◽  
pp. 609-613
Author(s):  
J. Pramanik ◽  
P. L. Trelstad ◽  
J. D. Keasling
Keyword(s):  
Phosphorus Removal ◽  
Reaction Network ◽  
Bacterial Biomass ◽  
Enhanced Biological Phosphorus Removal ◽  
Biological Phosphorus Removal ◽  
Stoichiometric Model ◽  
Aerobic Reactor ◽  
Complete Set ◽  
Biological Phosphorus

Enhanced biological phosphorus removal (EBPR) in wastewater treatment involves metabolic cycling through the biopolymers polyphosphate (polyP), polyhydroxybutyrate (PHB), and glycogen. This cycling is induced through treatment systems that alternate between carbon-rich anaerobic and carbon-poor aerobic reactor basins. While the appearance and disappearance of these biopolymers has been documented, the intracellular pressures that regulate their synthesis and degradation are not well understood. Current models of the EBPR process have examined a limited number of metabolic pathways that are frequently lumped into an even smaller number of “reactions.” This work, on the other hand, uses a stoichiometric model that contains a complete set of the pathways involved in bacterial biomass synthesis and energy production to examine EBPR metabolism. Using the stoichiometric model we were able to analyze the role of EBPR metabolism within the larger context of total cellular metabolism, as well as predict the flux distribution of carbon and energy fluxes throughout the total reaction network. The model was able to predict the consumption of PHB, the degradation of polyP, the uptake of acetate and the release of Pi. It demonstrated the relationship between acetate uptake and Pi release, and the effect of pH on this relationship. The model also allowed analysis of growth metabolism with respect to EBPR.

Design of GA and Ontology based NLP Frameworks for Online Opinion Mining

2019 ◽  
Vol 13 (2) ◽  
pp. 159-165
Author(s):  
Manik Sharma ◽  
Gurvinder Singh ◽  
Rajinder Singh
Keyword(s):  
Genetic Algorithm ◽  
Natural Language Processing ◽  
Natural Language ◽  
Language Processing ◽  
Opinion Mining ◽  
Hybrid Genetic Algorithm ◽  
Online Reviews ◽  
Middle Tier ◽  
Complete Set ◽  
Mining Model

Background: For almost every domain, a tremendous degree of data is accessible in an online and offline mode. Billions of users are daily posting their views or opinions by using different online applications like WhatsApp, Facebook, Twitter, Blogs, Instagram etc. Objective: These reviews are constructive for the progress of the venture, civilization, state and even nation. However, this momentous amount of information is useful only if it is collectively and effectively mined. Methodology: Opinion mining is used to extract the thoughts, expression, emotions, critics, appraisal from the data posted by different persons. It is one of the prevailing research techniques that coalesce and employ the features from natural language processing. Here, an amalgamated approach has been employed to mine online reviews. Results: To improve the results of genetic algorithm based opining mining patent, here, a hybrid genetic algorithm and ontology based 3-tier natural language processing framework named GAO_NLP_OM has been designed. First tier is used for preprocessing and corrosion of the sentences. Middle tier is composed of genetic algorithm based searching module, ontology for English sentences, base words for the review, complete set of English words with item and their features. Genetic algorithm is used to expedite the polarity mining process. The last tier is liable for semantic, discourse and feature summarization. Furthermore, the use of ontology assists in progressing more accurate opinion mining model. Conclusion: GAO_NLP_OM is supposed to improve the performance of genetic algorithm based opinion mining patent. The amalgamation of genetic algorithm, ontology and natural language processing seems to produce fast and more precise results. The proposed framework is able to mine simple as well as compound sentences. However, affirmative preceded interrogative, hidden feature and mixed language sentences still be a challenge for the proposed framework.

The light-scattering Mueller matrices for Rayleigh and Rayleigh-Gans-Debye approximation

1990 ◽  
Vol 55 (12) ◽  
pp. 2889-2897
Author(s):  
Jaroslav Holoubek
Keyword(s):  
Light Scattering ◽  
Theoretical Work ◽  
Matrix Elements ◽  
Elastic Light Scattering ◽  
Yield Information ◽  
Recent Theoretical Work ◽  
Particle Parameters ◽  
Complete Set ◽  
Single Matrix ◽  
Scattering Matrix Elements

Recent theoretical work has shown that the complete set of polarized elastic light-scattering studies should yield information about scatterer structure that has so far hardly been utilized. We present here calculations of angular dependences of light-scattering matrix elements for spheres near the Rayleigh and Rayleigh-Gans-Debye limits. The significance of single matrix elements is documented on examples that show how different matrix elements respond to changes in particle parameters. It appears that in the small-particle limit (Rg/λ < 0.1) we do not loose much information by ignoring "large particle" observables.

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