scholarly journals Two staged pattern formation and spontaneous wave breakup in the ferroin-bromate-pyrocatechol reaction

2011 ◽  
Vol 9 (3) ◽  
pp. 379-385
Author(s):  
Mohammad Harati ◽  
Jichang Wang
Keyword(s):  
Dimensional Space ◽  
Wave Activity ◽  
Reaction Conditions ◽  
One Dimensional ◽  
Second Stage ◽  
Quiescent Period ◽  
Dimensional Space Time ◽  
Spatiotemporal Behavior ◽  
Two Stages ◽  
Time Plot

AbstractThis report investigated nonlinear spatiotemporal behavior in the ferroin-bromate-pyrocatechol reaction, in which two stages of wave formation, separated by several hours of quiescent period, were observed. In addition to its great photosensitivity, the second stage wave activity could undergo spontaneous breakups at broad reaction conditions. Analysis based on one-dimensional space-time plot suggests that the breakup was caused by propagation slowdown of the leading wave. Due to the presence of coupled autocatalytic reactions, the propagation of the initial and the second stage waves exhibited different and subtle responses to the variation of the concentration of each reagent.

One-dimensional space-time vector light sheet

2021 ◽  
Author(s):  
Mbaye Diouf ◽  
Mitchell Harling ◽  
Murat Yessenov ◽  
Layton A. Hall ◽  
Ayman Abouraddy ◽  
...  
Keyword(s):  
Dimensional Space ◽  
Light Sheet ◽  
Space Time ◽  
One Dimensional ◽  
Dimensional Space Time

scholarly journals Extrapolation of Functions of Many Variables by Means of Metric Analysis

2018 ◽  
Vol 173 ◽  
pp. 03014 ◽  
Author(s):  
Alexandr Kryanev ◽  
Victor Ivanov ◽  
Anastasiya Romanova ◽  
Leonid Sevastianov ◽  
David Udumyan
Keyword(s):  
Dimensional Space ◽  
Straight Line Segment ◽  
Interpolation Scheme ◽  
Second Stage ◽  
Metric Analysis ◽  
Several Variables ◽  
Straight Line ◽  
Extrapolation Problem ◽  
Two Stages ◽  
Auto Regression

The paper considers a problem of extrapolating functions of several variables. It is assumed that the values of the function of m variables at a finite number of points in some domain D of the m-dimensional space are given. It is required to restore the value of the function at points outside the domain D. The paper proposes a fundamentally new method for functions of several variables extrapolation. In the presented paper, the method of extrapolating a function of many variables developed by us uses the interpolation scheme of metric analysis. To solve the extrapolation problem, a scheme based on metric analysis methods is proposed. This scheme consists of two stages. In the first stage, using the metric analysis, the function is interpolated to the points of the domain D belonging to the segment of the straight line connecting the center of the domain D with the point M, in which it is necessary to restore the value of the function. In the second stage, based on the auto regression model and metric analysis, the function values are predicted along the above straight-line segment beyond the domain D up to the point M. The presented numerical example demonstrates the efficiency of the method under consideration.

scholarly journals SYNTHESIS OF ACILGLYCERIDES WITH HIGH NUTRITIONAL VALUE BY AN ENZYMATIC TWO-STEP PROCESS

2019 ◽  
Vol 49 (2) ◽  
pp. 137-142
Author(s):  
Daniel Alberto Sánchez ◽  
María Luján Ferreira ◽  
Gabriela Marta Tonetto
Keyword(s):  
Burkholderia Cepacia ◽  
Nutritional Value ◽  
Extraction Procedure ◽  
Capric Acid ◽  
Simple Liquid ◽  
Reaction Conditions ◽  
Burkholderia Cepacia Lipase ◽  
Second Stage ◽  
Acid Catalyzed ◽  
Two Stages

Acylglycerides are esters formed from glycerol and fatty acids. The structure of these glycerides affects their digestion and absorption. In this work, the synthesis of acylglycerides with high nutritional value by an enzymatic process in two stages is presented. In the first stage, the esterification of glycerol and capric acid catalyzed by Lipozyme RM IM was carried out. In this reaction, 73% conversion of capric acid and 71% selectivity to 1,3-dicaprin was achieved. The diglyceride was separated and purified efficiently by a simple liquid-liquid extraction procedure. The dicaprin was esterified with palmitic acid using Burkholderia cepacia lipase immobilized on chitosan as the catalyst. In this second stage conversions of 1,3-dicaprin with values between 48 and 87% and with high selectivity towards the esterification of the sn-2 position were achieved. The reaction product had between 76 and 90% of acylglycerides with high nutritional value, depending on the reaction conditions.

scholarly journals A-topology for Minkowski space

1979 ◽  
Vol 21 (1) ◽  
pp. 53-64 ◽  
Author(s):  
Sribatsa Nanda
Keyword(s):  
Minkowski Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
One Dimensional ◽  
Group Of Homeomorphisms ◽  
Dimensional Space Time ◽  
The One ◽  
Induced Topology ◽  
Time Continuum ◽  
Inhomogeneous Lorentz Group

AbstractWe consider in this paper a topology (which we call the A-topology) on Minkowski space, the four-dimensional space–time continuum of special relativity and derive its group of homeomorphisms. We define the A-topology to be the finest topology on Minkowski space with respect to which the induced topology on time-like and light-like lines is one-dimensional Euclidean and the induced topology on space-like hyperplanes is three- dimensional Euclidean. It is then shown that the group of homeomorphisms of this topology is precisely the one generated by the inhomogeneous Lorentz group and the dilatations.

Study on Dynamics Model of Solid Trajectory Analysis and Pneumatics Based on Space-Time Four-Dimensional Data

2014 ◽  
Vol 556-562 ◽  
pp. 3856-3859
Author(s):  
Jun Zhang
Keyword(s):  
Mathematical Model ◽  
Dimensional Space ◽  
Space Time ◽  
Flight Trajectory ◽  
Time Data ◽  
One Dimensional ◽  
Dimensional Space Time ◽  
The One ◽  
Steady State Simulation ◽  
The Mathematical Model

In this paper we use elastic-plastic mechanics and air dynamic to establish the mathematical model of badminton flight trajectory and deformation, and use the ANSYS software to do simulation on badminton flight process, and obtain the flight path and deformation of badminton. In order to analyze the badminton four-dimensional space-time data, we establish the one-dimensional time measurement, and use one-dimensional time transient stress to establish flight trajectory and deformation, and design the four-dimensional space-time steady-state simulation process. Through calculation we eventually get the force of badminton flight process and deformation nephogram. Comparing four times results of numerical simulation results, the mathematical model of this design model meets the design requirements. It provides technical reference for badminton athlete's training and teaching.

scholarly journals Global Optimization Algorithm Based on One-Dimensional Chaotic Maps and Gradient Descent Technique

2017 ◽  
Vol 15 (1) ◽  
pp. 17-22
Author(s):  
D. Tsankova ◽  
S. Lekova
Keyword(s):  
Optimization Algorithm ◽  
Hybrid Algorithm ◽  
Gradient Descent ◽  
Chaotic Maps ◽  
Initial Point ◽  
One Dimensional ◽  
Second Stage ◽  
Gradient Descent Algorithm ◽  
Multimodal Function ◽  
Two Stages

Abstract A hybrid algorithm for searching the global minimum of a multimodal function is proposed in the paper. It is a two stages search technique, the first stage is the twice carrier wave based chaotic optimization algorithm (COA) for global searching, and the second stage is the gradient descent algorithm (GDA) for accurate local searching. The chaotic dynamics is realized through one-dimensional map in three variants: logistic, cubic and sine map. Three testing functions are used. A hundred simulations (each starting from different initial point generated randomly) were carried out for each of the test functions using two optimization algorithms: the proposed hybrid algorithm and the GDA working alone. The success and accuracy of locating the extremum, as well as the convergence of the algorithms using the three different chaotic maps were discussed.

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