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6: Paper Source PDF document

Paper's Title:

Shape Diagrams for 2D Compact Sets - Part I: Analytic Convex Sets.

Author(s):

S. Rivollier, J. Debayle and J.-C. Pinoli

Ecole Nationale Supérieure des Mines de Saint-Etienne,

CIS - LPMG, UMR CNRS 5148, 158 cours Fauriel,

42023 Saint-Etienne Cedex 2, France.


 
rivollier@emse.fr; debayle@emse.fr; pinoli@emse.fr
 

Abstract:

Shape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. Such a set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow thirty-one shape diagrams to be built. Most of these shape diagrams can also been applied to more general compact sets than compact convex sets. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these thirty-one shape diagrams. The purpose of this paper is to present the first part of this study, by focusing on analytic compact convex sets. A set will be called analytic if its boundary is piecewise defined by explicit functions in such a way that the six geometrical functionals can be straightforwardly calculated. The second and third part of the comparative study are published in two following papers [19.20]. They are focused on analytic simply connected sets and convexity discrimination for analytic and discretized simply connected sets, respectively.



6: Paper Source PDF document

Paper's Title:

Shape Diagrams for 2D Compact Sets - Part II: Analytic Simply Connected Sets.

Author(s):

S. Rivollier, J. Debayle and J.-C. Pinoli

Ecole Nationale Supérieure des Mines de Saint-Etienne,

CIS - LPMG, UMR CNRS 5148, 158 cours Fauriel,

42023 Saint-Etienne Cedex 2, France.


 
rivollier@emse.fr; debayle@emse.fr; pinoli@emse.fr
 

Abstract:

Shape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. However, they can also been applied to more general compact sets than compact convex sets. A compact set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow twenty-two shape diagrams to be built. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these twenty-two shape diagrams. The first part of this study is published in a previous paper 16. It focused on analytic compact convex sets. A set will be called analytic if its boundary is piecewise defined by explicit functions in such a way that the six geometrical functionals can be straightforwardly calculated. The purpose of this paper is to present the second part, by focusing on analytic simply connected compact sets. The third part of the comparative study is published in a following paper 17. It is focused on convexity discrimination for analytic and discretized simply connected compact sets.



6: Paper Source PDF document

Paper's Title:

Application of Equivalence Method to Classify Monge-Ampère Equations of Elliptic Type

Author(s):

Moheddine Imsatfia

E-mail: imsatfia@math.jussieu.fr 

Abstract:

In this paper, we apply Cartan's equivalence method to give a local classification of Monge-Ampère equations of elliptic type. Then we find a necessary and sufficient conditions such that a Monge-Ampère equation is either contactomorphic to the Laplace equation or to an Euler-Lagrange equation.



3: Paper Source PDF document

Paper's Title:

Shape Diagrams for 2D Compact Sets - Part III: Convexity Discrimination for Analytic and Discretized Simply Connected Sets.

Author(s):

S. Rivollier, J. Debayle and J.-C. Pinoli

Ecole Nationale Supérieure des Mines de Saint-Etienne,
CIS - LPMG, UMR CNRS 5148, 158 cours Fauriel,
42023 Saint-Etienne Cedex 2, France.


 
rivollier@emse.fr; debayle@emse.fr; pinoli@emse.fr
 

Abstract:

Shape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. However, they can also been applied to more general compact sets than compact convex sets. A compact set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow twenty-two shape diagrams to be built. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these twenty-two shape diagrams. The two first parts of this study are published in previous papers 8,9. They focus on analytic compact convex sets and analytic simply connected compact sets, respectively. The purpose of this paper is to present the third part, by focusing on the convexity discrimination for analytic and discretized simply connected compact sets..



3: Paper Source PDF document

Paper's Title:

Coexisting Attractors and Bubbling Route to Chaos in Modified Coupled Duffing Oscillators

Author(s):

B. Deruni1, A. S. Hacinliyan1,2, E. Kandiran3, A. C. Keles2, S. Kaouache4, M.-S. Abdelouahab4, N.-E. Hamri4

1Department of Physics,
University of Yeditepe,
Turkey.

2Department of Information Systems and Technologies,
University of Yeditepe,
Turkey

3Department of Software Development,
University of Yeditepe,
Turkey.

4Laboratory of Mathematics and their interactions,
University Center of Abdelhafid Boussouf,
Mila 43000,
Algeria.

E-mail: berc890@gmail.com
ahacinliyan@yeditepe.edu.tr
engin.kandiran@yeditepe.edu.tr
cihan.keles@yeditepe.edu.tr
s.kaouache@centr-univ-mila.dz
medsalah3@yahoo.fr
n.hamri@centre-univ-mila.dz

Abstract:

In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modification. The oscillators have cubic damping instead of linear one. Although single duffing oscillator has complex dynamics, coupled duffing systems possess a much more complex structure. The dynamical behavior of the system is investigated both numerically and analytically. Numerical results indicate that the system has double scroll attractor with suitable parameter values. On the other hand, bifurcation diagrams illustrate rich behavior of the system, and it is seen that, system enters into chaos with different routes. Beside classical bifurcations, bubbling route to chaos is observed for suitable parameter settings. On the other hand, Multistability of the system is indicated with the coexisting attractors, such that under same parameter setting the system shows different periodic and chaotic attractors. Moreover, chaotic synchronization of coupled oscillators is illustrated in final section.



2: Paper Source PDF document

Paper's Title:

Weyl Transform Associated With Bessel and Laguerre Functions

Author(s):

E. Jebbari and M . Sifi

Department of Mathematics Faculty of Sciences of Tunis,
1060 Tunis,
Tunisia.
mohamed.sifi@fst.rnu.tn


Abstract:

We define and study the Wigner transform associated to Bessel and Laguerre transform and we prove an inversion formula for this transform. Next we consider a class of symbols which allows to define the Bessel-Laguerre Weyl transform. We establish a relation between the Wigner and Weyl transform. At last, we discuss criterion in term of symbols for the boundedness and compactness of the Bessel-Laguerre Weyl transform.



2: Paper Source PDF document

Paper's Title:

On the Asymptotic Behavior of Solutions of Third Order Nonlinear Differential Equations

Author(s):

Ivan Mojsej and Alena Tartaľová

Institute of Mathematics,
Faculty of Science, P. J. Šafárik University,
Jesenná 5, 041 54 Košice,
Slovak Republic
ivan.mojsej@upjs.sk

Department of Applied Mathematics and Business Informatics,
Faculty of Economics, Technical University,
Nemcovej 32, 040 01 Košice,
Slovak Republic
alena.tartalova@tuke.sk


Abstract:

This paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third order with quasiderivatives. Mainly, we present the necessary and sufficient conditions for the existence of nonoscillatory solutions with specified asymptotic behavior as t tends to infinity. These conditions are presented as integral criteria and involve only the coefficients of investigated differential equations. In order to prove some of the results, we use a topological approach based on the Schauder fixed point theorem.



2: Paper Source PDF document

Paper's Title:

Hyperbolic Barycentric Coordinates

Author(s):

Abraham A. Ungar

Department of Mathematics, North Dakota State University,
Fargo, ND 58105,
USA
Abraham.Ungar@ndsu.edu
URL
: http://math.ndsu.nodak.edu/faculty/ungar/

Abstract:

A powerful and novel way to study Einstein's special theory of relativity and its underlying geometry, the hyperbolic geometry of Bolyai and Lobachevsky, by analogies with classical mechanics and its underlying Euclidean geometry is demonstrated. The demonstration sets the stage for the extension of the notion of barycentric coordinates in Euclidean geometry, first conceived by Möbius in 1827, into hyperbolic geometry. As an example for the application of hyperbolic barycentric coordinates, the hyperbolic midpoint of any hyperbolic segment, and the centroid and orthocenter of any hyperbolic triangle are determined.



2: Paper Source PDF document

Paper's Title:

Optimization and Approximation for Polyhedra in Separable Hilbert Spaces

Author(s):

Paolo d'Alessandro

Department of Mathematics,
Third University of Rome,
Italy.

E-mail: pdalex45@gmail.com

Abstract:

This paper studies infinite dimensional polyhedra, covering the case in which range spaces of operators defining inequality systems are not closed. A rangespace method of linear programming is generalized to infinite dimensions and finite dimensional methods of approximation are introduced.



2: Paper Source PDF document

Paper's Title:

Kinematic Model for Magnetic Null-points in 2 Dimensions

Author(s):

Ali Khalaf Hussain Al-Hachami

Department of Mathematics,
College of Education For Pure Sciences,
Wasit University,
Iraq.
E-mail: alhachamia@uowasit.edu.iq

Abstract:

The adjacent configurations of two-dimensional magnetic null point centers are analyzed by an immediate examination about the null. The configurations are classified as either potential or non-potential. By then the non-potential cases are subdivided into three cases depending upon whether the component of current is less than, equal to or greater than a threshold current. In addition the essential structure of reconnection in 2D is examined. It unfolds that the manner by which the magnetic flux is rebuilt. In this paper, we center on the ramifications of kinematic arrangements; that is, we fathom just Maxwell's conditions and a resistive Ohm's law.



1: Paper Source PDF document

Paper's Title:

Asymptotic Behavior of Mixed Type Functional Equations

Author(s):

J. M. Rassias

Pedagogical Department, E.E., National and Capodistrian University of Athens, Section of Mathematics And Informatics, 4, Agamemnonos Str., Aghia Paraskevi, Athens 15342,Greece
jrassias@primedu.uoa.gr
URL: http://www.primedu.uoa.gr/~jrassias/

Abstract:

In 1983 Skof [24] was the first author to solve the Ulam problem for additive mappings on a restricted domain. In 1998 Jung [14] investigated the Hyers-Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve the bounds and thus the results obtained by Jung [14], in 1998 and by the author [21], in 2002. Besides we establish new theorems about the Ulam stability of mixed type functional equations on restricted domains. Finally, we apply our recent results to the asymptotic behavior of functional equations of different types.



1: Paper Source PDF document

Paper's Title:

On Perturbed Reflection Coefficients

Author(s):

J. L. Díaz-Barrero and J. J. Egozcue

Applied Mathematics III,
Universidad Politécnica de Cataluña,
Barcelona, Spain
jose.luis.diaz@upc.edu
juan.jose.egozcue@upc.edu


Abstract:

Many control and signal processing applications require testing stability of polynomials. Classical tests for locating zeros of polynomials are recursive, but they must be stopped whenever the so called "singular polynomials" appear. These ``singular cases'' are often avoided by perturbing the "singular polynomial". Perturbation techniques although always successful are not proven to be well-founded. Our aim is to give a mathematical foundation to a perturbation method in order to overcome "singular cases" when using Levinson recursion as a testing method. The non-singular polynomials are proven to be dense in the set of all polynomials respect the L²-norm on the unit circle . The proof is constructive and can be used algorithmically.



1: Paper Source PDF document

Paper's Title:

Positive Periodic Time-Scale Solutions for Functional Dynamic Equations

Author(s):

Douglas R. Anderson and Joan Hoffacker

Department of Mathematics and Computer Science
Concordia College
Moorhead, MN 56562 USA
andersod@cord.edu
URL:
http://www.cord.edu/faculty/andersod/

Department of Mathematical Sciences
Clemson University
Clemson, SC 29634 USA
johoff@clemson.edu
URL:
http://www.math.clemson.edu/facstaff/johoff.htm


Abstract:

Using Krasnoselskii's fixed point theorem, we establish the existence of positive periodic solutions to two pairs of related nonautonomous functional delta dynamic equations on periodic time scales, and then extend the discussion to higher-dimensional equations. Two pairs of corresponding nabla equations are also provided in an analogous manner.



1: Paper Source PDF document

Paper's Title:

On the Optimal Buckling Loads of Clamped Columns

Author(s):

Samir Karaa

Department of Mathematics and Statistics
Sultan Qaboos University, P.O. Box 36, Alkhod 123
Muscat, Sultanate of Oman
skaraa@squ.edu.om

URL: http://ajmaa.org/EditorsU/SKaraa.php


Abstract:

We consider the problem of determining the optimal shape of a clamped column of given length and volume, without minimum cross section constraints. We prove that the necessary condition of optimality derived by Olhoff and Rasmussen is sufficient when 0<α<1. The number alpha appears in Equation 2.1. For the case α =1 it is shown that the value 48 is optimal. We also determine the exact values of the optimal shape at the extremities, and take advantage of a robust nonlinear ordinary differential equation solver COLSYS to compute the optimal buckling load with a high accuracy.



1: Paper Source PDF document

Paper's Title:

Analysis of the Flow Field in Stenosed Bifurcated Arteries Through a Mathematical Model

Author(s):

S. Chakravarty and S. Sen

Department of Mathematics, Visva-Bharati University,
Santiniketan 731235,
India
santabrata2004@yahoo.co.in


Abstract:

The present study is dealt with an appropriate mathematical model of the arotic bifurcation in the presence of constrictions using which the physiological flow field is analized. The geometry of the bifurcated arterial segment having constrictions in both the parent and its daughter arterial lumen frequently occurring in the diseased arteries causing malfunction of the cardiovascular system , is formed mathematically with the introduction of appropriate curvatures at the lateral junctions and the flow divider. The flowing blood contained in the stenosed bifurcated artery is treated to be Newtonian and the flow is considered to be two dimensional. The motion of the arterial wall and its effect on local fluid mechanics is not ruled out from the present pursuit. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier-Stokes equations for Newtonian fluid. The flow field can be obtained primarily following the radial coordinate transformation and using the appropriate boundary conditions and finally adopting a suitable finite difference scheme numerically. The influences of the arterial wall distensibility and the presence of stenosis on the flow field, the flow rate and the wall shear stresses are quantified in order to indicate the susceptibility to atherosclerotic lesions and thereby to validate the applicability of the present theoretical model.



1: Paper Source PDF document

Paper's Title:

A Sum Form Functional Equation and Its Relevance in Information Theory

Author(s):

Prem Nath and Dhiraj Kumar Singh

Department of Mathematics
University of Delhi
Delhi - 110007
India
pnathmaths@gmail.com
dksingh@maths.du.ac.in


Abstract:

The general solutions of a sum form functional equation containing four unknown mappings have been investigated. The importance of these solutions in relation to various entropies in information theory has been emphasised.



1: Paper Source PDF document

Paper's Title:

Equilibria and Periodic Solutions of Projected Dynamical Systems on Sets with Corners

Author(s):

Matthew D. Johnston and Monica-Gabriela Cojocaru

Department of Applied Mathematics, University of Waterloo,
Ontario, Canada
mdjohnst@math.uwaterloo.ca

Department of Mathematics & Statistics, University of Guelph,
Ontario, Canada
mcojocar@uoguelph.ca


Abstract:

Projected dynamical systems theory represents a bridge between the static worlds of variational inequalities and equilibrium problems, and the dynamic world of ordinary differential equations. A projected dynamical system (PDS) is given by the flow of a projected differential equation, an ordinary differential equation whose trajectories are restricted to a constraint set K. Projected differential equations are defined by discontinuous vector fields and so standard differential equations theory cannot apply. The formal study of PDS began in the 90's, although some results existed in the literature since the 70's. In this paper we present a novel result regarding existence of equilibria and periodic cycles of a finite dimensional PDS on constraint sets K, whose points satisfy a corner condition. The novelty is due to proving existence of boundary equilibria without using a variational inequality approach or monotonicity type conditions.



1: Paper Source PDF document

Paper's Title:

Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions

Author(s):

Árpád Száz

Institute of Mathematics, University of Debrecen,
H-4010 Debrecen, Pf. 12,
Hungary
szaz@math.klte.hu

Abstract:

By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2-homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.



1: Paper Source PDF document

Paper's Title:

Generalizing Polyhedra to Infinite Dimension

Author(s):

Paolo d'Alessandro


Department of Mathematics, Third University of Rome,
Lgo S.L. Murialdo 1, 00146 Rome, Italy.


dalex@mat.uniroma3.it.


URL: http://www.mat.uniroma3.it/users/dalex/dalex.html.

Abstract:

This paper generalizes polyhedra to infinite dimensional Hilbert spaces as countable intersections of closed semispaces. Highlights are the structure theory that shows that a polyhedron is the sum of compact set (in a suitable topology) plus a closed pointed cone plus a closed subspace, giving the internal representation of polyhedra. In the final part the dual range space technique is extended to the solution of infinite dimensional LP problems.



1: Paper Source PDF document

Paper's Title:

Ellipses Inscribed in Parallelograms

Author(s):

A. Horwitz

Penn State University,
25 Yearsley Mill Rd.
Media, PA 19063
U. S. A. 
alh4@psu.edu
 

Abstract:

We prove that there exists a unique ellipse of minimal eccentricity, EI, inscribed in a parallelogram, Ð. We also prove that the smallest nonnegative angle between equal conjugate diameters of $EI equals the smallest nonnegative angle between the diagonals of Ð. We also prove that if EM is the unique ellipse inscribed in a rectangle, R, which is tangent at the midpoints of the sides of R, then EM is the unique ellipse of minimal eccentricity, maximal area, and maximal arc length inscribed in R. Let Ð be any convex quadrilateral. In previous papers, the author proved that there is a unique ellipse of minimal eccentricity, EI, inscribed in Ð, and a unique ellipse, EO, of minimal eccentricity circumscribed about Ð. We defined Ð to be bielliptic if EI and EO have the same eccentricity. In this paper we show that a parallelogram, Ð, is bielliptic if and only if the square of the length of one of the diagonals of Ð equals twice the square of the length of one of the sides of Ð .



1: Paper Source PDF document

Paper's Title:

Expected Utility with Subjective Events

Author(s):

Jacob Gyntelberg and Frank Hansen

Bank for International Settlements,
Basel,
Switzerland

jacob.gyntelberg@bis.org


Tohoku University, Institute for International Education,
Sendai,
Japan

frank.hansen@m.tohoku.ac.jp

Abstract:

We provide a new theory of expected utility with subjective events modeled by a lattice of projections. This approach allows us to capture the notion of a ``small world'' as a context dependent or local state space embedded into a subjective set of events, the ``grand world''. For each situation the decision makers' subjective ``small world'' reflects the events perceived to be relevant for the act under consideration. The subjective set of events need not be representable by a classical state space. Maintaining preference axioms similar in spirit to the classical axioms, we obtain an expected utility representation which is consistent across local state spaces and separates subjective probability and utility. An added benefit is that this alternative expected utility representation allows for an intuitive distinction between risk and uncertainty.



1: Paper Source PDF document

Paper's Title:

To a Banach *-algebra in a Semipartial Dynamical System

Author(s):

Bahman Tabatabaie Shourijeh and Seyed Mostafa Zebarjad

Department of Mathematics,
College of Sciences,
Shiraz University, Shiraz 71454,
Iran.

E-mail: tabataba@math.susc.ac.ir    
zebarjad@mail.yu.ac.ir
URL: http://research.shirazu.ac.ir/faculty/More.asp?ID=207

Abstract:

By a partial dynamical system, we mean a triple containing a C*-algebra A, a discrete group G and a partial action of G on A. There are two C*--algebras associated to a given partial dynamical system. These are nothing but the certain C*-completions of a Banach *-algebra. In constructing such a Banach *-algebra, usually, a tedious limit process is used to apply. In this paper, we prove some theorems in this context without any limit process.



1: Paper Source PDF document

Paper's Title:

Credibility Based Fuzzy Entropy Measure

Author(s):

G. Yari, M. Rahimi, B. Moomivand and P. Kumar

Department of Mathematics,
Iran University of Science and Technology,
Tehran,
Iran.
E-mail: Yari@iust.ac.ir
E-mail: Mt_Rahimi@iust.ac.ir
URL: http://www.iust.ac.ir/find.php?item=30.11101.20484.en
URL: http://webpages.iust.ac.ir/mt_rahimi/en.html

Qarzol-hasaneh
Mehr Iran Bank, Tehran,
Iran.
E-mail: B.moomivand@qmb.ir

Department of Mathematics and Statistics,
University of Northern British Columbia,
Prince George, BC,
Canada.
E-mail: Pranesh.Kumar@unbc.ca

Abstract:

Fuzzy entropy is the entropy of a fuzzy variable, loosely representing the information of uncertainty. This paper, first examines both previous membership and credibility based entropy measures in fuzzy environment, and then suggests an extended credibility based measure which satisfies mostly in Du Luca and Termini axioms. Furthermore, using credibility and the proposed measure, the relative entropy is defined to measure uncertainty between fuzzy numbers. Finally we provide some properties of this Credibility based fuzzy entropy measure and to clarify, give some examples.



1: Paper Source PDF document

Paper's Title:

Mapped Chebyshev Spectral Methods for Solving Second Kind Integral Equations on the Real Line

Author(s):

Ahmed Guechi and Azedine Rahmoune

Department of Mathematics, University of Bordj Bou Arréridj,
El Anasser, 34030, BBA,
Algeria.
E-mail: a.guechi2017@gmail.com
E-mail: a.rahmoune@univ-bba.dz

Abstract:

In this paper we investigate the utility of mappings to solve numerically an important class of integral equations on the real line. The main idea is to map the infinite interval to a finite one and use Chebyshev spectral-collocation method to solve the mapped integral equation in the finite interval. Numerical examples are presented to illustrate the accuracy of the method.



1: Paper Source PDF document

Paper's Title:

Inequalities for Discrete F-Divergence Measures: A Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: http://rgmia.org/dragomir 

Abstract:

In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated f-divergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of Kullback-Leibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the f-divergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.



1: Paper Source PDF document

Paper's Title:

A Comparison Between Two Different Stochastic Epidemic Models with Respect to the Entropy

Author(s):

Farzad Fatehi and Tayebe Waezizadeh

Department of Mathematics,
University of Sussex,
Brighton BN1 9QH,
UK.
E-mail: f.fatehi@sussex.ac.uk
URL: http://www.sussex.ac.uk/profiles/361251

Department of Pure Mathematics, Faculty of Mathematics and Computer,
Shahid Bahonar University of Kerman,
Kerman 76169-14111,
Iran.
E-mail: waezizadeh@uk.ac.ir
URL: http://academicstaff.uk.ac.ir/en/tavaezizadeh

Abstract:

In this paper at first a brief history of mathematical models is presented with the aim to clarify the reliability of stochastic models over deterministic models. Next, the necessary background about random variables and stochastic processes, especially Markov chains and the entropy are introduced. After that, entropy of SIR stochastic models is computed and it is proven that an epidemic will disappear after a long time. Entropy of a stochastic mathematical model determines the average uncertainty about the outcome of that random experiment. At the end, we introduce a chain binomial epidemic model and compute its entropy, which is then compared with the DTMC SIR epidemic model to show which one is nearer to reality.



1: Paper Source PDF document

Paper's Title:

Sweeping Surfaces with Darboux Frame in Euclidean 3-space E3

Author(s):

F. Mofarreh, R. Abdel-Baky and N. Alluhaibi

Mathematical Science Department, Faculty of Science,
Princess Nourah bint Abdulrahman University
Riyadh  11546,
Saudi Arabia.
E-mail: fyalmofarrah@pnu.edu.sa

 
Department of Mathematics, Faculty of Science,
University of Assiut,
Assiut 71516,
Egypt.
E-mail: rbaky@live.com

Department of Mathematics Science and Arts, College Rabigh Campus,
 King Abdulaziz University
Jeddah,
Saudi Arabia.
E-mail: nallehaibi@kau.edu.sa

Abstract:

The curve on a regular surface has a moving frame and it is called Darboux frame. We introduce sweeping surfaces along the curve relating to the this frame and investigate their geometrical properties. Moreover, we obtain the necessary and sufficient conditions for these surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced.



1: Paper Source PDF document

Paper's Title:

Lie Group Theoretic Approach of One-Dimensional Black-Scholes Equation

Author(s):

P. L. Zondi and M. B. Matadi

Department of Mathematical sciences,
Faculty of Sciences & Agriculture, University of Zululand,
P Bag X1001, Kwa-Dlangezwa 3886,
South Africa.
E-mail: matadim@unizulu.ac.za
zondip@unizulu.ac.za

Abstract:

This study discusses the Lie Symmetry Analysis of Black-Scholes equation via a modified local one-parameter transformations. It can be argued that the transformation of the Black-Scholes equation is firstly obtained by means of riskless rate. Thereafter, the corresponding determining equations to the reduced equation are found. Furthermore, new symmetries of the Black-Scholes equation are constructed and lead to invariant solutions.


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