scholarly journals THE REPRODUCING KERNEL ALGORITHM FOR NUMERICAL SOLUTION OF VAN DER POL DAMPING MODEL IN VIEW OF THE ATANGANA–BALEANU FRACTIONAL APPROACH

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040010 ◽  
Author(s):  
SHAHER MOMANI ◽  
BANAN MAAYAH ◽  
OMAR ABU ARQUB
Keyword(s):  
Numerical Simulations ◽  
Numerical Solution ◽  
Reproducing Kernel ◽  
Computational Algorithm ◽  
Mathematical Structure ◽  
The Other ◽  
Modern Trend ◽  
Van Der Pol ◽  
New Approach ◽  
Damping Model

The aim of this paper is to propose the Atangana–Baleanu fractional methodology for fathoming the Van der Pol damping model by using the reproducing kernel algorithm. To this end, we discuss the mathematical structure of this new approach and some other numerical properties of solutions. Furthermore, all needed requirements for characterizing solutions by applying the reproducing kernel algorithm are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate Atangana–Baleanu fractional solutions are proposed. Finally, numerical simulations in fractional emotion is constructed one next to the other with tabulated data and graphical portrayals.

scholarly journals Classical and Higher Order Runge-Kutta Methods with Nonlinear Shooting Technique for Solving Van der Pol (VdP) Equation

2018 ◽  
Vol 66 (1) ◽  
pp. 43-47
Author(s):  
Farhana Ahmed Simi ◽  
Goutam Saha
Keyword(s):  
Exact Solution ◽  
Perturbation Method ◽  
Numerical Solution ◽  
Accurate Result ◽  
Research Work ◽  
Single Step ◽  
The Other ◽  
Van Der Pol ◽  
Shooting Technique ◽  
Runge Kutta

The goal of the research work is to examine the improvement of numerical solution of VdP equation. The well-known VdP equation is governed by the second order nonlinear ODE and then solved numerically using the classical Runge-Kutta (RK) method, RK-Fehlberg method of order five, Verner method of order eight and Cash-Karp method of order six with nonlinear shooting technique. In this work, numerical simulations have been carried out using NVdP code which is written in MATHEMATICA. Also, the accuracy and efficiency of the solution of VdP equation using different RK methods with nonlinear shooting technique has been investigated. For analysis of accuracy, the approximate exact solution obtained by perturbation method is used for the comparison. It is observed that all the different RK methods give accurate result of the VdP equation. But the classical RK method shows slightly better performance than the other single step techniques. Dhaka Univ. J. Sci. 66(1): 43-47, 2018 (January)

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

MAPPING CONTEMPORARY ISLAMIC JURISPRUDENCE OF MUḤAMMAD SAʻĪD AL-‘ASHMĀWĪ AND MUḤAMMAD SHAḤRŪR

2018 ◽  
Vol 1 (1) ◽  
pp. 32
Author(s):  
Yusroh Yusroh ◽  
Mohd. Zaki Abd. Rahman
Keyword(s):  
The Other ◽  
Russian Philosophy ◽  
New Approach ◽  
Marriage And Divorce ◽  
Other Hand ◽  
Islamic Jurisprudence

Muḥammad Saʻīd Al-‘Ashmāwī and Muḥammad Shaḥrūr are well known as contemporary Muslim thinkers. This article tries to map their contemporary ideas on Islamic jurisprudence. The main data of this research taken mainly from the works both of Al-‘Ashmāwī and Shaḥrūr. In particular, the paper tries to analyze Al-‘Ashmāwī‘s ideas on sharia, politics, hijab, marriage and divorce. On the other hand, the ideas of Shahrour on al-Qur'an, Sunnah and Fiqh, the theory of borders, pluralism, the commandment, inheritance, hijab, marriage, divorce, dowry, politics, and imamate are also critizised. After analyzing their lives and their ideas on Islamic jurisprudence, the paper found that their social, educational and practical backgrounds have affected their intellectual formations and ideas. Ashmawi is encouraged by diligence and enlightenment and is believed to be enlightened. Shahrour, however, takes a new approach in order to create the ḥudūd theory as a new way. As well as their intellectual background, Ashmawi has a good queen in Arabic, English and French as well as religion, Sharia, jurisprudence and theology. Shahrour is a good queen in Arabic, English, Russian, philosophy, philology and historical language.

A NEW APPROACH TO THE STUDY OF COORDINATIVE CONSTRUCTIONS

2019 ◽  
pp. 175-187
Author(s):  
Anna Varnayeva
Keyword(s):  
Characteristic Property ◽  
Mathematical Concept ◽  
The Other ◽  
New Approach ◽  
Logical Aspect ◽  
First Case

Coordinative constructions are traditionally opposed to subordinative constructions. However, this opposition comes down to denial of dependence in coordinative constructions. Thereby the parity of these two constructions does not come to light: subordinative construction can be described without coordinative one. This situation is not improved by detection of a coordinative triangle in all coordinative constructions. The article shows a new approach in the study of coordinative constructions: a coordinative construction is a system; there are not only specific relations – a coordinative triangle, – but also specific elements. Novelty of the study consists in the address to extralinguistic facts, viz. a mathematical concept of a set and its elements. There are a lot of similarities between them. A set in mathematics includes generalizing elements and the composed row in coordinative constructions; in the first case the set is not partitioned, in the second case it is partitioned. In mathematics equivalent components in coordinative constructions correspond to the set elements. A characteristic property in mathematics is homogeneity in coordinative constructions and etc. It is firstly demonstrated, that coordinative and subordinative constructions are correlative and the study of one construction is impossible without the study of the other one. Their parity is shown in coordinative constructions with elements of one set, in subordinative ones with elements of different sets. Cf.: roses and tulips –red roses. In the coordinatiму construction elements of one set are called: «flowers »; in the subordinative construction there are elements of different sets: «flowers » and «colors». It should be noted that the mathematical concept of a set relates to so called logical aspect in linguistics or thinking about reality.

NUMERICAL SOLUTION FOR DUFFING-VAN DER POL OSCILLATOR VIA BLOCK METHOD

2020 ◽  
Vol 10 (1) ◽  
pp. 1857-8365
Author(s):  
A. F. Nurullah ◽  
M. Hassan ◽  
T. J. Wong ◽  
L. F. Koo
Keyword(s):  
Numerical Solution ◽  
Van Der Pol Oscillator ◽  
Block Method ◽  
Van Der Pol

Stress Testing to Assess Recovery from Extreme Events

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
M. John Plodinec
Keyword(s):  
Climate Change ◽  
United States ◽  
Financial Institutions ◽  
Extreme Events ◽  
Stress Testing ◽  
The United States ◽  
The Other ◽  
New Approach ◽  
Rapid Spread ◽  
Potential Benefits

Abstract Over the last decade, communities have become increasingly aware of the risks they face. They are threatened by natural disasters, which may be exacerbated by climate change and the movement of land masses. Growing globalization has made a pandemic due to the rapid spread of highly infectious diseases ever more likely. Societal discord breeds its own threats, not the least of which is the spread of radical ideologies giving rise to terrorism. The accelerating rate of technological change has bred its own social and economic risks. This widening spectrum of risk poses a difficult question to every community – how resilient will the community be to the extreme events it faces. In this paper, we present a new approach to answering that question. It is based on the stress testing of financial institutions required by regulators in the United States and elsewhere. It generalizes stress testing by expanding the concept of “capital” beyond finance to include the other “capitals” (e.g., human, social) possessed by a community. Through use of this approach, communities can determine which investments of its capitals are most likely to improve its resilience. We provide an example of using the approach, and discuss its potential benefits.

Closed Sets of Boolean Terms in Relational Databases

1991 ◽  
Vol 14 (3) ◽  
pp. 367-385
Author(s):  
Andrzej Jankowski ◽  
Zbigniew Michalewicz
Keyword(s):  
Computational Complexity ◽  
Incomplete Information ◽  
Relational Databases ◽  
The Other ◽  
New Approach ◽  
Closed Sets ◽  
Null Value ◽  
Algebraic Operations

A number of approaches have been taken to represent compound, structured values in relational databases. We review a few such approaches and discuss a new approach, in which every set is represented as a Boolean term. We show that this approach generalizes the other approaches, leading to more flexible representation. Boolean term representation seems to be appropriate in handling incomplete information: this approach generalizes some other approaches (e.g. null value mark, null variables, etc). We consider definitions of algebraic operations on such sets, like join, union, selection, etc. Moreover, we introduce a measure of computational complexity of these operations.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

scholarly journals Exploring the Effect of Silicon on the High Temperature Corrosion of Lean FeCrAl Alloys in Humid Air

2021 ◽  
Author(s):  
T. Sand ◽  
A. Edgren ◽  
C. Geers ◽  
V. Asokan ◽  
J. Eklund ◽  
...  
Keyword(s):  
Corrosion Resistance ◽  
High Temperature ◽  
Oxidation Behavior ◽  
High Temperature Corrosion ◽  
The Other ◽  
Oxide Scales ◽  
Protective Oxide ◽  
New Approach ◽  
Fecral Alloys ◽  
Cr Evaporation

AbstractA new approach to reduce the chromium and aluminium concentrations in FeCrAl alloys without significantly impairing corrosion resistance is to alloy with 1–2 wt.% silicon. This paper investigates the “silicon effect” on oxidation by comparing the oxidation behavior and scale microstructure of two FeCrAl alloys, one alloyed with silicon and the other not, in dry and wet air at 600 °C and 800 °C. Both alloys formed thin protective oxide scales and the Cr-evaporation rates were small. In wet air at 800 °C the Si-alloyed FeCrAl formed an oxide scale containing mullite and tridymite together with α- and γ-alumina. It is suggested that the reported improvement of the corrosion resistance of Al- and Cr-lean FeCrAl’s by silicon alloying is caused by the appearance of Si-rich phases in the scale.

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