Abstract:

This paper deals with the global asymptotic stability character of solutions of a discrete time deterministic model proposed by Wikan and Eide in Bulletin of Mathematical Biology, 66, 2004, 1685-1704. A stochastic extension of this model is proposed and discussed. Computer simulations suggest that the dynamics of the stochastic model includes a mixture of the dynamics observed in the deterministic model.

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.

Paper's Title:

On the Sendov Conjecture for a Root Close to the Unit Circle

Author(s):

Indraneel G. Kasmalkar

Department of Mathematics,
University of California,
Berkeley, CA 94720
United States of America

E-mail: indraneelk@berkeley.edu 

Abstract:

On Sendov's conjecture, T. Chijiwa quantifies the idea stated by V. Vâjâitu and A. Zaharescu (and M. J. Miller independently), namely that if a polynomial with all roots inside the closed unit disk has a root sufficiently close to the unit circle then there is a critical point at a distance of at most one from that root. Chijiwa provides an estimate of exponential order for the required 'closeness' of the root to the unit circle so that such a critical point may exist. In this paper, we will improve this estimate to polynomial order by making major modifications and strengthening inequalities in Chijiwa's proof.

Paper's Title:

On the Hyers-Ulam Stability of Homomorphisms and Lie Derivations

Author(s):

Javad Izadi and Bahmann Yousefi

Department of Mathematics, Payame Noor University,
P.O. Box: 19395-3697, Tehran,
Iran.
E-mail: javadie2003@yahoo.com, b_yousefi@pnu.ac.ir

Abstract:

Let A be a Lie Banach^*-algebra. For each elements (a, b) and (c, d) in A²:= A * A, by definitions

 (a, b) (c, d)= (ac, bd),
 |(a, b)|= |a|+ |b|,
(a, b)^*= (a^*, b^*),

A² can be considered as a Banach^*-algebra. This Banach^*-algebra is called a Lie Banach^*-algebra whenever it is equipped with the following definitions of Lie product:

for all a, b, c, d in A. Also, if A is a Lie Banach^*-algebra, then D: A²→A² satisfying

 D ([ (a, b), (c, d)])= [ D (a, b), (c, d)]+ [(a, b), D (c, d)]

for all $a, b, c, d∈A, is a Lie derivation on A². Furthermore, if A is a Lie Banach^*-algebra, then D is called a Lie^* derivation on A² whenever D is a Lie derivation with D (a, b)^*= D (a^*, b^*) for all a, b∈A. In this paper, we investigate the Hyers-Ulam stability of Lie Banach^*-algebra homomorphisms and Lie^* derivations on the Banach^*-algebra A².

Paper's Title:

Introducing the Dorfmanian: A Powerful Tool for the Calculus Of Variations

Author(s):

Olivier de La Grandville

Department of Management Science and Engineering,
Stanford University,
475 Via Ortega, Stanford, CA 94305,
U. S. A.

E-mail: odelagrandville@gmail.com

Abstract:

We show how a modified Hamiltonian proposed by Robert Dorfman [1] to give intuitive sense to the Pontryagin maximum principle can be extended to easily obtain all high-order equations of the calculus of variations. This new concept is particularly efficient to determine the differential equations leading to the extremals of functionals defined by n-uple integrals, while a traditional approach would require -- in some cases repeatedly -- an extension of Green's theorem to n-space.
Our paper is dedicated to the memory of Robert Dorfman (1916 - 2002).

Paper's Title:

A Multivalued Version of the Radon-Nikodym Theorem, via the Single-valued Gould Integral

Author(s):

Domenico Candeloro¹, Anca Croitoru², Alina Gavriluţ², Anna Rita Sambucini¹

¹Dept. of Mathematics and Computer Sciences,
University of Perugia,
1, Via Vanvitelli -- 06123, Perugia,
Italy.
E-mail:  domenico.candeloro@unipg.it, anna.sambucini@unipg.it

²Faculty of Mathematics,
Al. I. Cuza University,
700506 Iaşi,
Romania.
E-mail: croitoru@uaic.ro, gavrilut@uaic.ro

Abstract:

In this paper we consider a Gould type integral of real functions with respect to a compact and convex valued not necessarily additive measure. In particular we will introduce the concept of integrable multimeasure and, thanks to this notion, we will establish an exact Radon-Nikodym theorem relative to a fuzzy multisubmeasure which is new also in the finite dimensional case. Some results concerning the Gould integral are also obtained.

Paper's Title:

Generalised Models for Torsional Spine Reconnection

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:

Three-dimensional (3D) null points are available in wealth in the solar corona, and the equivalent is probably going to be valid in other astrophysical situations. On-going outcomes from sun oriented perceptions and from reproductions propose that reconnection at such 3D nulls may assume a significant job in the coronal dynamics. The properties of the torsional spine method of magnetic reconnection at 3D nulls are researched. Kinematic model are created, which incorporate the term ηJ that is spatially localised around the null, stretching out along the spine of the null. The null point is to research the impact of shifting the level of asymmetry of the null point magnetic field on the subsequent reconnection process where past examinations constantly considered a non-nonexclusive radially symmetric null. Specifically we analyse the rate of reconnection of magnetic flux at the spine of null point. Logical arrangements are determined for the enduring kinematic equation, and contrasted and the after effects of torsional spine reconnection models when the current is restricted in which the Maxwell conditions are illuminated. The geometry of the current layers inside which torsional spine reconnection happen is autonomous on the symmetry of the magnetic field. Torsional spine reconnection happens in a thin cylinder around the spine, with circular cross-segment when the fan eigenvalues are extraordinary. The short axis of the circle being along the solid field bearing. Just as it was discovered that the fundamental structure of the method of attractive reconnection considered is unaffected by changing the magnetic field symmetry, that is, the plasma flow is discovered rotational around the spine of null point. The spatiotemporal pinnacle current, and the pinnacle reconnection rate achieved, are found not to rely upon the level of asymmetry.

Paper's Title:

Accuracy of Implicit DIMSIMs with Extrapolation

Author(s):

A. J. Kadhim, A. Gorgey, N. Arbin and N. Razali

Mathematics Department, Faculty of Science and Mathematics,
Sultan Idris Education University,
35900 Tanjong Malim, Perak,
Malaysia
E-mail: annie_gorgey@fsmt.upsi.edu.my

Unit of Fundamental Engineering Studies,
Faculty of Engineering, Built Environment,
The National University of Malaysia,
43600 Bangi,
Malaysia.

Abstract:

The main aim of this article is to present recent results concerning diagonal implicit multistage integration methods (DIMSIMs) with extrapolation in solving stiff problems. Implicit methods with extrapolation have been proven to be very useful in solving problems with stiff components. There are many articles written on extrapolation of Runge-Kutta methods however fewer articles on extrapolation were written for general linear methods. Passive extrapolation is more stable than active extrapolation as proven in many literature when solving stiff problems by the Runge-Kutta methods. This article takes the first step by investigating the performance of passive extrapolation for DIMSIMs type-2 methods. In the variable stepsize and order codes, order-2 and order-3 DIMSIMs with extrapolation are investigated for Van der Pol and HIRES problems. Comparisons are made with ode23 solver and the numerical experiments showed that implicit DIMSIMs with extrapolation has greater accuracy than the method itself without extrapolation and ode23.

Paper's Title:

Analysis of a Dynamic Elasto-viscoplastic Frictionless Antiplan Contact Problem with Normal Compliance

Author(s):

A. Ourahmoun¹, B. Bouderah², T. Serrar³

^1,2Applied Mathematics Laboratory,
M'sila University, 28000,
Algeria.
E-mail: ourahmounabbes@yahoo.fr

³Applied Mathematics Laboratory,
Setif 1 University, 19000,
Algeria.

Abstract:

We consider a mathematical model which describes the dynamic evolution of a thermo elasto viscoplastic contact problem between a body and a rigid foundation. The mechanical and thermal properties of the obstacle coating material near its surface. A variational formulation of this dynamic contact phenomenon is derived in the context of general models of thermo elasto viscoplastic materials. The displacements and temperatures of the bodies in contact are governed by the coupled system consisting of a variational inequality and a parabolic differential equation. The proof is based on a classical existence and uniqueness result on parabolic inequalities,differential equations and fixed point arguments.

Paper's Title:

Existence, Global Regularity and Uniqueness of Solutions of the Navier-Stokes Equations in Space Dimension 3 when the Initial Data are Regular

Author(s):

Moulay D. Tidriri

Email: mtctyasa@gmail.com

Abstract:

The existence, regularity, and uniqueness of global solutions of the Navier-Stokes equations in are given for when the initial velocity for all integers q ≥ 0 and div u₀ = 0.

Paper's Title:

A Generalization of a Partial b-metric and Fixed Point Theorems

Author(s):

Pravin Singh and Virath Singh

Department of Mathematics, University of KwaZulu-Natal,
Private Bag X54001, Durban,
South Africa.
E-mail: singhp@ukzn.ac.za
singhv@ukzn.ac.za

Abstract:

The purpose of this paper is to introduce the concept of a Partial α, β b-metric as a generalization of a partial b-metric and prove theorems for some contractive type mapping.

Paper's Title:

A Caratheodory's Approximate Solutions of Stochastic Differential Equations Under the Hölder Condition

Author(s):

Bo-Kyeong Kim and Young-Ho Kim

Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnam-do 51140,
Korea.
E-mail: claire9576@naver.com
yhkim@changwon.ac.kr

Abstract:

In this paper, based on the theorem of the uniqueness of the solution of the stochastic differential equation, the convergence possibility of the Caratheodory's approximate solution was studied by approximating the unique solution. To obtain this convergence theorem, we used a Hölder condition and a weakened linear growth condition. Furthermore, The auxiliary theorems for the existence and continuity of the Caratheodory's approximate solution were investigated as a prerequisite.

Paper's Title:

On the Oldest Problem in the Calculus of Variations: A New Message from Queen Dido

Author(s):

Olivier de La Grandville

Faculty of Economics,
Goethe University Frankfurt,
Theodore Adorno Platz 4, 60323 Frankfurt,
Germany.
E-mail: odelagrandville@gmail.com

Abstract:

We consider the problem of finding the optimal curve of given length linking two points in a plane such as it encloses a maximal area. We show that if the curve is not described by a single-valued function, its determination does not necessarily imply to work with a parametric representation of the curve. We show that a simpler approach is at hand -- and, who knows? -- this might well be the method Queen Dido used.

Paper's Title:

Lozi Maps With Max Function and its Application

Author(s):

Abdellah Menasri

Higher National School of Forests,
Khenchela,
Algeria.
E-mail: abdellah.menasri70@gmail.com

Abstract:

In this paper, we study the Lozi map by replacing the piecewise linear term in the first equation by the function max (f(x,y);g(x,y)) such that f and g are two arbitrary functions in R². This is a family model that allows us to study several new piecewise-smooth maps. We demonstrate that these models converge to a robust chaotic attractor and give some applications of these models in the real world.

Paper's Title:

Metric Functionals for the Hästö Metric

Author(s):

G. Bettencourt and S. Mendes

Departamento de Matemática,
Universidade da Beira Interior -
Covilhã Portugal,
Centro de Matemática e Aplicações
Universidade da Beira Interior -
Covilhã Portugal.
E-mail: gastao@ubi.pt

 
ISCTE - University Institute of Lisbon - Lisbon Portugal,
Centro de Matemática e Aplicações
Universidade da Beira Interior -
Covilhã Portugal.
E-mail: sergio.mendes@iscte-iul.pt

Abstract:

In 2002, new classes of weighted metrics on Rⁿ were introduced by Peter Hästö. In this article we compute the metric functionals for such classes of metrics.

Paper's Title:

Jordan Canonical Form of Interval Matrices and Applications

Author(s):

S. Hema Surya, T. Nirmala and K. Ganesan

Department of Mathematics, College of Engineering and Technology,
SRM Institute of Science and Technology,
Kattankulathur,
Chennai-603203,
India.
E-mail: nirmalat@srmist.edu.in
URL: https://www.srmist.edu.in/faculty/dr-t-nirmala/

Abstract:

A square interval matrix over R can be converted to diagonal form if certain prerequisites are satisfied. However not all square matrices can be diagonalized. As a consequence, we strive the next simplest form to which it can be reduced while retaining important properties such as eigenvalues, rank, nullity, and so on. It turns out that any real interval matrix has a Jordan Canonical Form (JCF) over E if it has n interval eigenvalues in IR. We discuss in this paper a method for computing the Jordan canonical form of an interval matrix using a new pairing technique and a new type of interval arithmetic that will make classifying and analyzing interval matrices easier and more efficient. We conclude with a numerical example that supports the theory and application of predator-prey model.

Paper's Title:

The Degree of Homogeneity: Definition, Geometric Interpretation and New, Direct Proofs of Euler's Theorem

Author(s):

Olivier de La Grandville

Faculty of Economics, Goethe University Frankfurt,
Theodore Adorno Platz 4, 60323 Frankfurt,
Germany.
E-mail: odelagrandville@gmail.com

Abstract:

We show how the degree of homogeneity of a function is a highly useful, precise measure of the sensitivity of a function to a change in its variables. This measure can be evaluated directly thanks to a simple geometric construct, entirely independently of measurement units. The usefulness of this concept is also illustrated by the fact that it leads to new, direct proofs, geometric as well as algebraic, of Euler's theorem; this is in contrast to the traditional approach that requires a limiting process.

Paper's Title:

On a Novel Class of Advanced Integrals of MacRobert Type Incorporating Generalized Hypergeometric Functions

Author(s):

Shwetha S Shetty and Shantha Kumari Kurumujji

Department of Mathematics, A J Institute of Engineering and Technology,
(Affiliated to Visvesvaraya Technological University (VTU), Belagavi),
Mangaluru, Karnataka,
India.
E-mail: shwethashetty576@gmail.com, shanthakk99@gmail.com

Abstract:

The main objective of this study is to evaluate two master formulas expressed as integrals over the interval from zero to π/2. These integrals involve exponential functions and trigonometric functions sine and cosine, along with ₃F₂ hypergeometric functions parameterized by general variables i and j, where i = j = 0, ± 1, ± 2, .... From these master formulas, we derive twenty-six MacRobert-type integrals by evaluating them at specific values of i and j. The results are expressed using Gamma functions. The findings given here are derived from summation formulas for the series ₄ F₃ obtained recently by Choi and Rathie along with a general result attributed to MacRobert.

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