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15: 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.



9: Paper Source PDF document

Paper's Title:

Topological Aspects of Discrete Switch Dynamical Systems

Author(s):

Faiz Imam and Sharan Gopal

Department of Mathematics,
BITS - Pilani, Hyderabad Campus,
India.
E-mail: mefaizy@gmail.com

Department of Mathematics,
BITS - Pilani, Hyderabad Campus,
India.
E-mail: sharanraghu@gmail.com

ABSTRACT NOT FOUND. WEBSITE ERROR

Abstract:



8: Paper Source PDF document

Paper's Title:

Inclusion and Neighborhood Properties for Certain Subclasses of Analytic Functions Associated with Convolution Structure

Author(s):

M. K. Aouf

Mathematics Department,
Faculty of Science,
Mansoura University 35516,
Egypt.
mkaouf127@yahoo.com

Abstract:

In this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order defined by using the familiar convolution structure of analytic functions. In this paper we obtain the coefficient estimates and the consequent inclusion relationships involving the neighborhoods of the p-valently analytic functions.



5: Paper Source PDF document

Paper's Title:

Some Double λ-Convergent Sequence Spaces Over n-Normed Spaces

Author(s):

Kuldip Raj, Renu Anand and Seema Jamwal

School of Mathematics,
Shri Mata Vaishno Devi University Katra-182320,
Jammu and Kashmir,
India.

E-mail: kuldipraj68@gmail.comrenuanand71@gmail.com, seemajamwal8@gmail.com

Abstract:

In this paper we introduce some double generalized λ-convergent sequence spaces over n-normed spaces defined by Musielak-Orlicz function M = (Mk,l). We also made an attempt to study some topological and algebraic properties of these sequence spaces.



5: Paper Source PDF document

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).



5: Paper Source PDF document

Paper's Title:

Improved Oscillation Criteria of Second-Order Advanced Non-canonical Difference Equation

Author(s):

G. E. Chatzarakis1, N. Indrajith2, S. L. Panetsos1, E. Thandapani3

1Department of Electrical and Electronic Engineering Educators
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
E-mail: gea.xatz@aspete.gr, geaxatz@otenet.gr
spanetsos@aspete.gr

2Department of Mathematics,
Presidency College, Chennai - 600 005,
India.
E-mail: indrajithna@gmail.com

3Ramanujan Institute for Advanced Study in Mathematics,
University of Madras Chennai - 600 005,
India.
E-mail: ethandapani@yahoo.co.in

Abstract:

Employing monotonic properties of nonoscillatory solutions, we derive some new oscillation criteria for the second-order advanced non-canonical difference equation

Our results extend and improve the earlier ones. The outcome is illustrated via some particular difference equations.



4: Paper Source PDF document

Paper's Title:

A general theory of decision making

Author(s):

Frank Hansen

Department of Economics,
University of Copenhagen,
Studiestraede 6, DK-1455 Copenhagen K
Denmark Frank.Hansen@econ.ku.dk
URL: http://www.econ.ku.dk/okofh


Abstract:

We formulate a general theory of decision making based on a lattice of observable events, and we exhibit a large class of representations called the general model. Some of the representations are equivalent to the so called standard model in which observable events are modelled by an algebra of measurable subsets of a state space, while others are not compatible with such a description. We show that the general model collapses to the standard model, if and only if an additional axiom is satisfied. We argue that this axiom is not very natural and thus assert that the standard model may not be general enough to model all relevant phenomena in economics. Using the general model we are (as opposed to Schmeidler [16]) able to rationalize Ellsberg's paradox without the introduction of non-additive measures.



4: 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.



4: Paper Source PDF document

Paper's Title:

A Study of the Effect of Density Dependence in a Matrix Population Model

Author(s):

N. Carter and M. Predescu

Department of Mathematical Sciences,
Bentley University,
Waltham, MA 02452,
U.S.A.
ncarter@bentley.edu
 mpredescu@bentley.edu

Abstract:

We study the behavior of solutions of a three dimensional discrete time nonlinear matrix population model. We prove results concerning the existence of equilibrium points, boundedness, permanence of solutions, and global stability in special cases of interest. Moreover, numerical simulations are used to compare the dynamics of two main forms of the density dependence function (rational and exponential).



4: Paper Source PDF document

Paper's Title:

Uniqueness of Meromorphic Functions and Weighted Sharing

Author(s):

Indrajit Lahiri and Rupa Pal

Department of Mathematics, University of
Kalyani, West Bengal 741235, India

indr9431@dataone.in


 Jhargram Raj College,
Jhargram, Midnapur(W),
West Bengal 721507,
India
rupa.a.pal@gmail.com

Abstract:

With the help of the notion of weighted sharing of values, we prove a result on uniqueness of meromorphic functions and as a consequence we improve a result of P. Li



4: Paper Source PDF document

Paper's Title:

On Generalized Triangle Inequality in p-Freéchet Spaces, 0<p<1

Author(s):

M. A. Latif

Department of Mathematics,
University of Hail, Hail,
Saudi Arabia
m_amer_latif@hotmail.com

Abstract:

In this paper generalized triangle inequality and its reverse in a p-Fréchet space where, 0<p<1 are obtained.



4: Paper Source PDF document

Paper's Title:

Positive Solutions to a System of Boundary Value Problems for Higher-Dimensional Dynamic Equations on Time Scales

Author(s):

I. Y. Karaca

Department of Mathematics,
Ege University,
35100 Bornova, Izmir,
Turkey

ilkay.karaca@ege.edu.tr

URL: http://ege.edu.tr
 

Abstract:

In this paper, we consider the system of boundary value problems for higher-dimensional dynamic equations on time scales. We establish criteria for the existence of at least one or two positive solutions. We shall also obtain criteria which lead to nonexistence of positive solutions. Examples applying our results are also given.



4: Paper Source PDF document

Paper's Title:

Wavelet Frames in Higher Dimensional Sobolev Spaces

Author(s):

Raj Kumar, Manish Chauhan, and Reena

Department of Mathematics,
Kirori Mal College, University of Delhi,
New Delhi-110007,
India.
E-mail: rajkmc@gmail.com

Department of Mathematics,
University of Delhi,
New Delhi-110007,
India
E-mail: manish17102021@gmail.com

Department of Mathematics,
Hans Raj College, University of Delhi,
New Delhi-110007,
India
E-mail: reena.bhagwat29@gmail.com

Abstract:

In this paper, we present sufficient condition for the sequence of vectors to be a frame for Hs(Rd) are derived. Necessary and sufficient conditions for the sequence of vectors to be tight wavelet frames in Hs(Rd) are obtained. Further, as an application an example of tight wavelet frames for Hs(R2) as bivariate box spline over 3-direction are given.



4: Paper Source PDF document

Paper's Title:

Inequalities for Functions of Selfadjoint Operators on Hilbert Spaces:
a Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, College 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: https://rgmia.org/dragomir 

Abstract:

The main aim of this survey is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.



4: Paper Source PDF document

Paper's Title:

Uniqueness Problems for Difference Polynomials Sharing a Non-Zero Polynomial of Certain Degree With Finite Weight

Author(s):

V. Priyanka, S. Rajeshwari and V. Husna

Department of Mathematics,
School of Engineering,
Presidency University,
Bangalore-560064,
India.
E-mail: priyapriyankaram1994@gmail.com rajeshwaripreetham@gmail.com
husnav43@gmail.com

Abstract:

In this paper, we prove a result on the value distribution of difference polynomials sharing higher order derivatives of meromorphic functions which improves some earlier results. At the same time, we also prove possible uniqueness relation of entire functions when the difference polynomial generated by them sharing a non zero polynomial of certain degree. The result obtained in the paper will improve and generalize a number of recent results in a compact and convenient way.



3: 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.



3: Paper Source PDF document

Paper's Title:

Ostrowski Type Inequalities for Lebesgue Integral: 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:

The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and real-valued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.



3: 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.



3: Paper Source PDF document

Paper's Title:

Estimates of Norms on Krein Spaces

Author(s):

Satheesh K. Athira, P. Sam Johnson and K. Kamaraj

Department of Mathematical and Computational Sciences,
National Institute of Technology Karnataka,
Surathkal, Mangaluru 575 025,
India.
E-mail: athirachandri@gmail.com

Department of Mathematical and Computational Sciences,
National Institute of Technology Karnataka,
Surathkal, Mangaluru 575 025,
India.
E-mail:sam@nitk.edu.in

Department of Mathematics,
University College of Engineering Arni,
Anna University, Arni 632 326,
India.
E-mail: krajkj@yahoo.com

Abstract:

Various norms can be defined on a Krein space by choosing different underlying fundamental decompositions. Some estimates of norms on Krein spaces are discussed and a few results in Bognar's paper are generalized.



3: 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.



3: Paper Source PDF document

Paper's Title:

On Admissible Mapping via Simulation Function

Author(s):

Anantachai Padcharoen and Pakeeta Sukprasert

Department of Mathematics,
Faculty of Science and Technology,
Rambhai Barni Rajabhat University,
Chanthaburi 22000,
Thailand.
E-mail: anantachai.p@rbru.ac.th
 
Department of Mathematics and Computer Science
Faculty of Science and Technology
Rajamangala University of Technology Thanyaburi (RMUTT),
Thanyaburi, Pathumthani 12110,
Thailand.
E-mail: pakeeta_s@rmutt.ac.th

Abstract:

In this paper, we present some fixed point results in complete metric spaces by using generalized admissible mapping embedded in the simulation function. Its applications, Our results used to study the existence problem of nonlinear Hammerstein integral equations.



3: Paper Source PDF document

Paper's Title:

Hankel Functional Connected to Lemniscate of Bernoulli

Author(s):

K. Ramanuja Rao, Rajnesh Lal and Kaushal Singh

Fiji National University,
Department of Mathematics & Statistics,
P.O. Box 5529, Lautoka,
Fiji.
E-mail: ramanuja.kotti@fnu.ac.fj
 rajnesh.lal@fnu.ac.fj
kaushal.singh@fnu.ac.fj

Abstract:

The aim of present paper is to derive a higher bound (HB) of 3rd order Hankel determinant for a collection of holomorphic mappings connected with exactly to the right side of the lemniscate of Bernoulli, whose polar coordinates form is r2 = 2cos2(2θ). The method carried in this paper is more refined than the method adopted by the authors (see [1]), who worked on this problem earlier.



3: Paper Source PDF document

Paper's Title:

Oscillatory Behavior of Second-Order Non-Canonical Retarded Difference Equations

Author(s):

G.E. Chatzarakis1, N. Indrajith2, E. Thandapani3 and K.S. Vidhyaa4

1Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
E-mail:  gea.xatz@aspete.gr, geaxatz@otenet.gr

 

2Department of Mathematics,
Presidency College, Chennai - 600 005,
India.
E-mail: indrajithna@gmail.com

3Ramanujan Institute for Advanced Study in Mathematics,
University of Madras,
Chennai - 600 005,
India.
E-mail: ethandapani@yahoo.co.in

4Department of Mathematics,
SRM Easwari Engineering College,
Chennai-600089,
India.
E-mail: vidyacertain@gmail.com

Abstract:

Using monotonic properties of nonoscillatory solutions, we obtain new oscillatory criteria for the second-order non-canonical difference equation with retarded argument

Our oscillation results improve and extend the earlier ones. Examples illustrating the results are provided.



3: Paper Source PDF document

Paper's Title:

SQIRV Model for Omicron Variant with Time Delay

Author(s):

S. Dickson, S. Padmasekaran, G. E. Chatzarakis and S. L. Panetsos

Mathematics, Periyar University, Periyar Palkalai Nagar, Salem,
636011, Tamilnadu,
India.
E-mail: dickson@periyaruniversity.ac.in, padmasekarans@periyaruniversity.ac.in

Electrical and Electronic Engineering Educators, School of
Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens,
Greece.
E-mail: geaxatz@otenet.gr, spanetsos@aspete.gr

Abstract:

In order to examine the dynamics of the Omicron variant, this paper uses mathematical modelling and analysis of a SQIRV model, taking into account the delay in the conversion of susceptible individuals into infected individuals and infected individuals into recovered individuals. The pandemic was eventually controlled as a result of the massive delays. To assure the safety of the host population, this concept incorporates quarantine and the COVID-19 vaccine. Both local and global stability of the model are examined. It is found that the fundamental reproduction number affects both local and global stability conditions. Our findings show that asymptomatic cases caused by an affected population play an important role in increasing Omicron infection in the general population. The most recent data on the pandemic Omicron variant from Tamil Nadu, India, is verified.



3: Paper Source PDF document

Paper's Title:

Bicomplex Univalent Functions

Author(s):

Mohd Arif, Amjad Ali, Rajat Singh* and Romesh Kumar

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: azizymaths@gmail.com

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: amjadladakhi687@gmail.com

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: *rajat.singh.rs634@gmail.com

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: romeshmath@gmail.com

Abstract:

In this paper we introduce bicomplex univalent functions and also discuss the properties of a specific class of univalent functions.



3: Paper Source PDF document

Paper's Title:

Li-Yorke and Expansivity for Composition Operators on Lorentz Space

Author(s):

Rajat Singh and Romesh Kumar

Department of Mathematics,
University of Jammu,
Jammu 180006,
INDIA.
E-mail: rajat.singh.rs634@gmail.com

Department of Mathematics,
University of Jammu,
Jammu 180006,
INDIA.
E-mail: romeshmath@gmail.com

Abstract:

In this paper, we investigate Li-Yorke composition operators and some of its variations on Lorentz spaces. Further, we also study expansive composition operators on these spaces. The work of the paper is essentially based on the work in [3], [6], [8] and [15].



2: Paper Source PDF document

Paper's Title:

Viability Theory And Differential Lanchester Type Models For Combat.
Differential Systems.

Author(s):

G. Isac and A. Gosselin

Department Of Mathematics, Royal Military College Of Canada,
P.O. Box 17000, S
tn Forces, Kingston, Ontario, Canada K7k 7b4

isac-g@rmc.ca
gosselin-a@rmc.ca

URL
:
http://www.rmc.ca/academic/math_cs/isac/index_e.html
URL
:
http://www.rmc.ca/academic/math_cs/gosselin/index_e.html

Abstract:

In 1914, F.W. Lanchester proposed several mathematical models based on differential equations to describe combat situations [34]. Since then, his work has been extensively modified to represent a variety of competitions including entire wars. Differential Lanchester type models have been studied from many angles by many authors in hundreds of papers and reports. Lanchester type models are used in the planning of optimal strategies, supply and tactics. In this paper, we will show how these models can be studied from a viability theory stand point. We will introduce the notion of winning cone and show that it is a viable cone for these models. In the last part of our paper we will use the viability theory of differential equations to study Lanchester type models from the optimal theory point of view.



2: Paper Source PDF document

Paper's Title:

On a Criteria for Strong Starlikeness

Author(s):

V. Ravichandran, M. Darus, and N. Seenivasagan

School Of Mathematical Sciences, Universiti Sains Malaysia,
11800 Usm Penang, Malaysia
vravi@cs.usm.my
URL: http://cs.usm.my/~vravi

School of Mathematical Sciences, Faculty of Sciences and Technology,
Ukm, Bangi 43600, Malaysia
maslina@pkrisc.cc.ukm.my

Sindhi College, 123, P. H. Road, Numbal,
Chennai 600 077 India
vasagan2000@yahoo.co.in

 

Abstract:

In this paper, we are concerned with finding sufficient condition for certain normalized analytic function f(z) defined on the open unit disk in the complex plane to be strongly starlike of order α. Also we have obtained similar results for certain functions defined by Ruscheweyh derivatives and Sălăgean derivatives. Further extension of these results are given for certain p-valent analytic functions defined through a linear operator.



2: Paper Source PDF document

Paper's Title:

On Vector Variational Inequality Problem in Terms of Bifunctions

Author(s):

C. S. Lalitha and Monika Mehta

Department of Mathematics, Rajdhani College,
University of Delhi, Raja Garden,
Delhi 110015, India
cslalitha@rediffmail.com

Department of Mathematics, Satyawati College,
University Of Delhi, Ashok Vihar,
Phase-III, Delhi 110052, India
mridul_in@yahoo.com


Abstract:

In this paper, we consider a generalized vector variational inequality problem expressed in terms of a bifunction and establish existence theorems for this problem by using the concepts of cone convexity and cone strong quasiconvexity and employing the celebrated Fan's Lemma. We also give two types of gap functions for this problem.



2: Paper Source PDF document

Paper's Title:

C*-valued metric projection and Moore-Penrose inverse on Hilbert C*-modules

Author(s):

M. Eshaghi Gordji, H. Fathi and S.A.R. Hosseinioun

Department of Mathematics,
Semnan University, P.O. Box 35195-363, Semnan,
Iran.
Center of Excellence in Nonlinear Analysis and Applications (CENAA),
Semnan University,
Iran.
E-mail: Madjid.Eshaghi@gmail.com

Department of Mathematics,
Shahid Beheshti University, Tehran,
Iran.
E-mail: Hedayat.fathi@yahoo.com

Department of Mathematical Sciences,
University of Arkansas, Fayetteville, Arkansas 72701,
USA.
E-mail: shossein@uark.net

 

Abstract:

Let t be a regular operator between Hilbert C*-modules and t be its Moore-Penrose inverse. We give some characterizations for t based on C*-valued metric projection. Moore-Penrose inverse of bounded operators and elements of a C*-algebra is studied as a special case.



2: Paper Source PDF document

Paper's Title:

On an extension of Edwards's double integral with applications

Author(s):

I. Kim, S. Jun, Y. Vyas and A. K. Rathie

Department of Mathematics Education,
Wonkwang University,
Iksan, 570-749,
Republic of Korea.

General Education Institute,
Konkuk University,
Chungju 380-701,
Republic of Korea.

Department of Mathematics, School of Engineering,
Sir Padampat Singhania University,
Bhatewar, Udaipur, 313601, Rajasthan State,
India.

Department of Mathematics,
Vedant College of Engineering and Technology,
(Rajasthan Technical University),
Bundi-323021, Rajasthan,
India.

E-mail: iki@wku.ac.kr sjun@kku.ac.kr
yashoverdhan.vyas@spsu.ac.in arjunkumarrathie@gmail.com

Abstract:

The aim of this note is to provide an extension of the well known and useful Edwards's double integral. As an application, new class of twelve double integrals involving hypergeometric function have been evaluated in terms of gamma function. The results are established with the help of classical summation theorems for the series 3F2 due to Watson, Dixon and Whipple. Several new and interesting integrals have also been obtained from our main findings.



2: Paper Source PDF document

Paper's Title:

On Ruled Surfaces According to Quasi-Frame in Euclidean 3-Space

Author(s):

M. Khalifa Saad and R. A. Abdel-Baky

Department of Mathematics, Faculty of Science,
Islamic University of Madinah,
KSA.
Department of Mathematics, Faculty of Science,
Sohag University, Sohag,
EGYPT.
E-mail: mohamed_khalifa77@science.sohag.edu.eg, mohammed.khalifa@iu.edu.sa

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

Abstract:

This paper aims to study the skew ruled surfaces by using the quasi-frame of Smarandache curves in the Euclidean 3-space. Also, we reveal the relationship between Serret-Frenet and quasi-frames and give a parametric representation of a directional ruled surface using the quasi-frame. Besides, some comparative examples are given and plotted which support our method and main results.



2: Paper Source PDF document

Paper's Title:

The Effect of Harvesting Activities on Prey-Predator Fishery Model with Holling type II in Toxicant Aquatic Ecosystem

Author(s):

Moh Nurul Huda, Fidia Deny Tisna Amijaya, Ika Purnamasari

Department of Mathematics, Faculty of Mathematics and Natural Science,
Mulawarman University,
Samarinda, East Kalimantan,75123
Indonesia.
E-mail: muh.nurulhuda@fmipa.unmul.ac.id
 fidiadta@fmipa.unmul.ac.id
ika.purnamasari@fmipa.unmul.ac.id

Abstract:

This paper discussed prey-predator fishery models, in particular by analysing the effects of toxic substances on aquatic ecosystems. It is assumed in this model, that the prey population is plankton and the predator population is fish.\ Interaction between the two populations uses the Holling type II function. The existence of local and global critical points of the system are shown and their stability properties are analysed. Furthermore, Bionomic equilibrium and optimal control of harvesting are discussed. Finally, numerical simulations have been carried out to show in the interpretation of results.



2: Paper Source PDF document

Paper's Title:

Construction of a Frame Multiresolution Analysis on Locally Compact Abelian Groups

Author(s):

R. Kumar and Satyapriya

Department of Mathematics,
Kirori Mal College,
University of Delhi,
Delhi,
India.
E-mail: rajkmc@gmail.com

 
Department of Mathematics,
University of Delhi,
Delhi,
India.
E-mail: kmc.satyapriya@gmail.com

Abstract:

The frame multiresolution analysis (FMRA) on locally compact Abelian groups has been studied and the results concerning classical MRA have been worked upon to obtain new results. All the necessary conditions, which need to be imposed on the scaling function φ to construct a wavelet frame via FMRA, have been summed up. This process of construction of FMRA has aptly been illustrated by sufficient examples.



2: 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:

Linear System of Singularly Perturbed Initial Value Problems with Robin Initial Conditions

Author(s):

S. Dinesh, G. E. Chatzarakis, S. L. Panetsos and S. Sivamani

Department of Mathematics,
Saranathan College of Engineering,
Tiruchirappalli-620012,
Tamil Nadu,
India.

Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.

E-mail: geaxatz@otenet.gr, dineshselvaraj24@gmail.com,
spanetsos@aspete.gr, winmayi2012@gmail.com

Abstract:

On the interval (0,1], this paper considers an initial value problem for a system of n singularly perturbed differential equations with Robin initial conditions. On a piecewise uniform Shishkin mesh, a computational approach based on a classical finite difference scheme is proposed. This approach is shown to be first-order convergent in the maximum norm uniformly in the perturbation parameters. The theory is illustrated by a numerical example.



2: Paper Source PDF document

Paper's Title:

Using Direct and Fixed Point Technique of Cubic Functional Equation and its Hyers-Ulam Stability

Author(s):

Ramanuja Rao Kotti, Rajnesh Krishnan Mudaliar, Kaushal Neelam Devi, Shailendra Vikash Narayan

Fiji National University,
Department of Mathematics & Statistics,
P.O. Box 5529, Lautoka,
Fiji.
E-mail: ramanuja.kotti@fnu.ac.fj
URL: https://www.fnu.ac.fj

Abstract:

In this present work, we introduce a new type of finite dimensional cubic functional equation of the form

where Φ≥4 is an integer, and derive its general solution. The main purpose of this work is to investigate the Hyers-Ulam stability results for the above mentioned functional equation in Fuzzy Banach spaces by means of direct and fixed point methods.



1: Paper Source PDF document

Paper's Title:

Uniqueness of Meromorphic Functions that Share Three Values

Author(s):

Abhijit Banerjee

Department of Mathematics
Kalyani Government Engineering College
West Bengal 741235
India.
abanerjee_kal@yahoo.co.in
abanerjee@mail15.com
abanerjee_kal@rediffmail.com


Abstract:

In the paper dealing with the uniqueness problem of meromorphic functions we prove five theorems one of which will improve a result given by Lahiri \cite{5} and the remaining will supplement some previous results.



1: Paper Source PDF document

Paper's Title:

Numerical Studies on Dynamical Systems Method for Solving Ill-posed Problems with Noise

Author(s):

N. H. Sweilam and A. M. Nagy

Mathematics Department, Faculty of Science,
Cairo University,
Giza, Egypt.
n_sweilam@yahoo.com

Mathematics Department, Faculty of Science,
Benha University,
Benha, Egypt.
abdelhameed_nagy@yahoo.com


Abstract:

In this paper, we apply the dynamical systems method proposed by A. G. RAMM, and the the variational regularization method to obtain numerical solution to some ill-posed problems with noise. The results obtained are compared to exact solutions. It is found that the dynamical systems method is preferable because it is easier to apply, highly stable, robust, and it always converges to the solution even for large size models.



1: Paper Source PDF document

Paper's Title:

On the Numerical Solution for Deconvolution Problems with Noise

Author(s):

N. H. Sweilam

Cairo University, Faculty of Science, Mathematics Department,
Giza, Egypt.
n-sweilam@yahoo.com


Abstract:

In this paper three different stable methods for solving numerically deconvolution problems with noise are studied. The methods examined are the variational regularization method, the dynamical systems method, and the iterative regularized processes. Gravity surveying problem with noise is studied as a model problem. The results obtained by these methods are compared to the exact solution for the model problem. It is found that these three methods are highly stable methods and always converge to the solution even for large size models. The relative higher accuracy is obtained by using the iterative regularized processes.



1: Paper Source PDF document

Paper's Title:

Refinements of the Trace Inequality of Belmega, Lasaulce and Debbah

Author(s):

Shigeru Furuichi and Minghua Lin


Department of Computer Science and System Analysis,
College of Humanities and Sciences, Nihon University,
3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan.
 

Department of Mathematics and Statistics,
 University of Regina, Regina, Saskatchewan, Canada S4S 0A2.

furuichi@chs.nihon-u.ac.jp, lin243@uregina.ca.

Abstract:

 In this short paper, we show a certain matrix trace inequality and then give a refinement of the trace inequality proven by Belmega, Lasaulce and Debbah. In addition, we give an another improvement of their trace inequality.



1: Paper Source PDF document

Paper's Title:

A New Property of General Means of Order p with an Application to the Theory of Economic Growth

Author(s):

Olivier de La Grandville

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

lagrandvil@aol.com

 

Abstract:

The purpose of this note is to demonstrate a new property of the general mean of order p of m ordered positive numbers . If p < 0 and if , the elasticity of with respect to xm, defined by , tends towards zero, and therefore . This property is then applied to optimal growth theory.



1: Paper Source PDF document

Paper's Title:

A Note On The Global Behavior Of A Nonlinear System of Difference Equations

Author(s):

Norman H. Josephy, Mihaela Predescu and Samuel W. Woolford

Department of Mathematical Sciences,
Bentley University,
Waltham, MA 02452,
U.S.A.

mpredescu@bentley.edu
njosephy@bentley.edu
swoolford@bentley.edu


 

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.



1: Paper Source PDF document

Paper's Title:

Szegö Limits and Haar Wavelet Basis

Author(s):

M. N. N. Namboodiri and S. Remadevi

Dept. of Mathematics, Cochin University of Science and Technology,
Cochin-21, Kerala,
India.

nambu@cusat.ac.in

Dept. of Mathematics, College of Engineering,
Cherthala, Kerala,
India.

rema@mec.ac.in
 

Abstract:

This paper deals with Szegö type limits for multiplication operators on L2 (R) with respect to Haar orthonormal basis. Similar studies have been carried out by Morrison for multiplication operators Tf using Walsh System and Legendre polynomials [14]. Unlike the Walsh and Fourier basis functions, the Haar basis functions are local in nature. It is observed that Szegö type limit exist for a class of multiplication operators Tf , f∈ L (R) with respect to Haar (wavelet) system with appropriate ordering. More general classes of orderings of Haar system are identified for which the Szegö type limit exist for certain classes of multiplication operators. Some illustrative examples are also provided.



1: Paper Source PDF document

Paper's Title:

New Implicit Kirk-Type Schemes for General Class of Quasi-Contractive Operators in Generalized Convex Metric Spaces

Author(s):

K. Rauf, O. T. Wahab and A. Ali

Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
E-mail: krauf@unilorin.edu.ng

Department of Statistics and Mathematical Sciences,
Kwara State University, Malete,
Nigeria.

Department of Mathematics,
Mirpur University of Science and Technology, Mirpur,
Pakistan.

Abstract:

In this paper, we introduce some new implicit Kirk-type iterative schemes in generalized convex metric spaces in order to approximate fixed points for general class of quasi-contractive type operators. The strong convergence, T-stability, equivalency, data dependence and convergence rate of these results were explored. The iterative schemes are faster and better, in term of speed of convergence, than their corresponding results in the literature. These results also improve and generalize several existing iterative schemes in the literature and they provide analogues of the corresponding results of other spaces, namely: normed spaces, CAT(0) spaces and so on.



1: Paper Source PDF document

Paper's Title:

Generalized k-distance-balanced Graphs

Author(s):

Amir Hosseini and Mehdi Alaeiyan

Department of mathematics, Karaj Branch,
Islamic Azad university, Karaj,
Iran.
E-mail: amir.hosseini@kiau.ac.ir, hosseini.sam.52@gmail.com

Department of Mathematics,
Iran University of Science and Technology, Tehran,
Iran.
E-mail: alaeiyan@iust.ac.ir

Abstract:

A nonempty graph Γ is called generalized k-distance-balanced, whenever every edge ab has the following property: the number of vertices closer to a than to b, k, times of vertices closer to b than to a, or conversely, k N .In this paper we determine some families of graphs that have this property, as well as to prove some other result regarding these graphs.



1: Paper Source PDF document

Paper's Title:

Polynomial Dichotomy of C0-Quasi Semigroups in Banach Spaces

Author(s):

Sutrima1,2, Christiana Rini Indrati2, Lina Aryati2

1Department of Mathematics,
Universitas Sebelas Maret,
PO Box 57126, Surakarta,
Indonesia.
E-mail: sutrima@mipa.uns.ac.id

2Department of Mathematics,
Universitas Gadjah Mada,
PO Box 55281, Yogyakarta,
Indonesia.
E-mail: rinii@ugm.ac.id, lina@ugm.ac.id 

Abstract:

Stability of solutions of the problems is an important aspect for application purposes. Since its introduction by Datko [7], the concept of exponential stability has been developed in various types of stability by various approaches. The existing conditions use evolution operator, evolution semigroup, and quasi semigroup approach for the non-autonomous problems and a semigroup approach for the autonomous cases. However, the polynomial stability based on C0-quasi semigroups has not been discussed in the references. In this paper we propose a new stability for C0-quasi semigroups on Banach spaces i.e the polynomial stability and polynomial dichotomy. As the results, the sufficient and necessary conditions for the polynomial and uniform polynomial stability are established as well as the sufficiency for the polynomial dichotomy. The results are also confirmed by the examples.



1: Paper Source PDF document

Paper's Title:

Convergence Speed of Some Random Implicit-Kirk-type Iterations for Contractive-type Random Operators

Author(s):

H. Akewe, K.S. Eke

Department of Mathematics,
Covenant University, 
Canaanland, KM 10, Idiroko Road, P. M. B. 1023, Ota, Ogun State,
Nigeria.
E-mail: hudson.akewe@covenantuniversity.edu.ng, kanayo.eke@covenantuniversity.edu.ng

Abstract:

The main aim of this paper is to introduce a stochastic version of multistep type iterative scheme called a modified random implicit-Kirk multistep iterative scheme and prove strong convergence and stability results for a class of generalized contractive-type random operators. The rate of convergence of the random iterative schemes are also examined through an example. The results show that our new random implicit kirk multistep scheme perform better than other implicit iterative schemes in terms of convergence and thus have good potentials for further applications in equilibrium problems in computer science, physics and economics.



1: Paper Source PDF document

Paper's Title:

On a New Class of Eulerian's Type Integrals Involving Generalized Hypergeometric Functions

Author(s):

Sungtae Jun, Insuk Kim and Arjun K. Rathie

General Education Institute,
Konkuk University, Chungju 380-701,
Republic of Korea.

Department of Mathematics Education,
Wonkwang University, Iksan, 570-749,
Republic of Korea.

Department of Mathematics,
Vedant College of Engineering and Technology (Rajasthan Technical University),
Bundi-323021, Rajasthan,
India.

E-mail: sjun@kku.ac.kr, iki@wku.ac.kr, arjunkumarrathie@gmail.com

Abstract:

Very recently Masjed-Jamei and Koepf established interesting and useful generalizations of various classical summation theorems for the 2F1, 3F2, 4F3, 5F4 and 6F5 generalized hypergeometric series. The main aim of this paper is to establish eleven Eulerian's type integrals involving generalized hypergeometric functions by employing these theorems. Several special cases have also been given.



1: Paper Source PDF document

Paper's Title:

A New Interpretation of the Number e

Author(s):

Olivier de La Grandville

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

Abstract:

We show that e is the amount that 1 becomes when it is invested during an arbitrary time span of length T, at any continuously compounded interest rates as long as their average is equal to 1/T . A purely mathematical interpretation of e is the amount a unit quantity becomes after any duration T when the average of its instantaneous growth rates is 1/T. This property can be shown to remain valid if T tends to infinity as long as the integral of the growth rates converges to unity.



1: Paper Source PDF document

Paper's Title:

An Analytical Solution of Perturbed Fisher's Equation Using Homotopy Perturbation Method (HPM), Regular Perturbation Method (RPM) and Adomian Decomposition Method (ADM)

Author(s):

Moussa Bagayogo, Youssouf Minoungou, Youssouf Pare

Departement de Mathematique,
Universite Ouaga I Pr Joseph Ki-Zerbo,
Burkina Faso.
E-mail: moussabagayogo94@gmail.com, m.youl@yahoo.fr, pareyoussouf@yahoo.fr.

Abstract:

In this paper, Homotopy Perturbation Method (HPM), Regular Pertubation Method (RPM) and Adomian decomposition Method (ADM) are applied to Fisher equation. Then, the solution yielding the given initial conditions is gained. Finally, the solutions obtained by each method are compared



1: Paper Source PDF document

Paper's Title:

Solving Non-Autonomous Nonlinear Systems of Ordinary Differential Equations Using Multi-Stage Differential Transform Method

Author(s):

K. A. Ahmad, Z. Zainuddin, F. A. Abdullah

School of Mathematical Sciences Universiti Sains Malaysia
11800 USM Penang
Malaysia.
E-mail: abumohmmadkh@hotmail.com
zarita@usm.my
farahaini@usm.my

Abstract:

Differential equations are basic tools to describe a wide variety of phenomena in nature such as, electrostatics, physics, chemistry, economics, etc. In this paper, a technique is developed to solve nonlinear and linear systems of ordinary differential equations based on the standard Differential Transform Method (DTM) and Multi-stage Differential Transform Method (MsDTM). Comparative numerical results that we are obtained by MsDTM and Runge-Kutta method are proposed. The numerical results showed that the MsDTM gives more accurate approximation as compared to the Runge-Kutta numerical method for the solutions of nonlinear and linear systems of ordinary differential equations



1: Paper Source PDF document

Paper's Title:

Evaluation of a New Class of Double Integrals Involving Generalized Hypergeometric Function 4F3

Author(s):

Joohyung Kim, Insuk Kim and Harsh V. Harsh

Department of Mathematics Education,
Wonkwang University, Iksan, 570-749,
Korea.
E-mail: joohyung@wku.ac.kr
 
Department of Mathematics Education,
Wonkwang University, Iksan, 570-749,
Korea.
E-mail: iki@wku.ac.kr

Department of Mathematics, Amity School of Eng. and Tech.,
Amity University Rajasthan
NH-11C, Jaipur-303002, Rajasthan,
India.
E-mail: harshvardhanharsh@gmail.com

Abstract:

Very recently, Kim evaluated some double integrals involving a generalized hypergeometric function 3F2 with the help of generalization of Edwards's well-known double integral due to Kim,  et al. and generalized classical Watson's summation theorem obtained earlier by Lavoie,  et al. In this research paper we evaluate one hundred double integrals involving generalized hypergeometric function 4F3 in the form of four master formulas (25 each) viz. in the most general form for any integer. Some interesting results have also be obtained as special cases of our main findings.



1: Paper Source PDF document

Paper's Title:

Trace Inequalities for Operators in Hilbert Spaces: 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: https://rgmia.org/dragomir 

Abstract:

In this paper we survey some recent trace inequalities for operators in Hilbert spaces that are connected to Schwarz's, Buzano's and Kato's inequalities and the reverses of Schwarz inequality known in the literature as Cassels' inequality and Shisha-Mond's inequality. Applications for some functionals that are naturally associated to some of these inequalities and for functions of operators defined by power series are given. Further, various trace inequalities for convex functions are presented including refinements of Jensen inequality and several reverses of Jensen's inequality. Hermite-Hadamard type inequalities and the trace version of Slater's inequality are given. Some Lipschitz type inequalities are also surveyed. Examples for fundamental functions such as the power, logarithmic, resolvent and exponential functions are provided as well.



1: Paper Source PDF document

Paper's Title:

Several New Closed-form Evaluations of the Generalized Hypergeometric Function with Argument 1/16

Author(s):

B. R. Srivatsa Kumar, Insuk Kim and Arjun K. Rathie

Department of Mathematics,
Manipal Institute of Technology,
Manipal Academy of Higher Education,
Manipal 576 104,
India.
E-mail: sri_vatsabr@yahoo.com

Department of Mathematics Education,
Wonkwang University,
Iksan, 54538,
Republic of Korea.
E-mail: iki@wku.ac.kr

Department of Mathematics,
Vedant College of Engineering and Technology,
Rajasthan Technical University,
Bundi, 323021, Rajasthan,
India.
E-mail: arjunkumarrathie@gmail.com 

Abstract:

The main objective of this paper is to establish as many as thirty new closed-form evaluations of the generalized hypergeometric function q+1Fq(z) for q= 2, 3, 4. This is achieved by means of separating the generalized hypergeometric function q+1Fq(z) for q=1, 2, 3, 4, 5 into even and odd components together with the use of several known infinite series involving central binomial coefficients obtained earlier by Ji and Hei \& Ji and Zhang.



1: Paper Source PDF document

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.



1: Paper Source PDF document

Paper's Title:

Complete Analysis of Global Behavior of Certain System of Piecewise Linear Difference Equations

Author(s):

Atiratch Laoharenoo, Ratinan Boonklurb and Watcharapol Rewlirdsirikul

Department of Mathematics and Computer Science,
Kamnoetvidya Science Academy, Rayong 21210
Thailand.
E-mail: atiratch.l@kvis.ac.th

 
Department of Mathematics and Computer Science,
Faculty of Science, Chulalongkorn University, Bangkok 10330
Thailand.
E-mail: ratinan.b@chula.ac.th

Department of Mathematics and Computer Science,
Faculty of Science, Chulalongkorn University, Bangkok 10330
Thailand.
E-mail: 6570104323@student.chula.ac.th

 

Abstract:

Our goal is to study the system of piecewise linear difference equations x{n+1} = |xn|-yn-b and y{n+1} = xn - |yn| + 1 where n 0 and b6. We can prove that the behavior of the solution can be divided into 2 types depending on the region of initial condition (x0,y0). That is, the solution eventually becomes the equilibrium point. Otherwise, the solution eventually becomes the periodic solution of prime period 5. All regions of initial condition for each type of solution are determined.



1: Paper Source PDF document

Paper's Title:

A General Fractional Control Scheme for Compound Combination Synchronization Between Different Fractional-Order Identical Chaotic Systems

Author(s):

Soumia Bensimessaoud and Smail Kaouache

Laboratory of Mathematics and their interactions, Abdelhafid Boussouf University Center, Mila, Algeria.
E-mail: soumiabensimessaoud@gmail.com, smailkaouache@gmail.com

Abstract:

In this paper, we aim to investigate the problem of compound combination synchronization (CCS) between four different fractional-order identical chaotic systems. Based on Laplace transformation and stability theory of linear dynamical systems, a new control law is proposed to assure the achievement of this kind of synchronization. Secondly, this control scheme is applied to realised CCS between four identical unified chaotic systems. Recall, that the proposed control scheme can be applied to wide classes of chaotic and hyperchaotic systems. Numerical simulations are given to show the effectiveness of the proposed method.



1: Paper Source PDF document

Paper's Title:

Optimal Conditions using Multi-valued G-Presic type Mapping

Author(s):

Deb Sarkar, Ramakant Bhardwaj, Vandana Rathore, and Pulak Konar

Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: debsarkar1996@gmail.com

Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: drrkbhardwaj100@gmail.com

School of Engineering and Technology,
Jagran Lakecity University, Bhopal, MP-462044,
India.
E-mail: drvandana@jlu.edu.in

Department of Mathematics,
VIT University, Chennai, Tamil Nadu-600127,
India.
E-mail: pulakkonar@gmail.com

Abstract:

In the present paper, some best proximity results have been presented using the concept of G-Presic type multi-valued mapping. These results are the extensions of Presic's theorem in the non-self mapping. A suitable example has also been given. Here, some applications are presented in θ-chainable space and ordered metric space.


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