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

Abstract:

The well known Jordan decomposition theorem gives the useful characterization that any function of bounded variation can be written as the difference of two increasing functions. Functions which can be expressed in this way can be used to formulate an exclusion test for the recent Cellular Exclusion Algorithms for numerically computing all zero points or the global minima of functions in a given cellular domain [2,8,9]. In this paper we give an algorithm to approximate such increasing functions when only the values of the function of bounded variation can be computed. For this purpose, we are led to introduce the idea of ε-increasing functions. It is shown that for any Lipschitz continuous function, we can find two ε-increasing functions such that the Lipschitz function can be written as the difference of these functions.

Paper's Title:

Oscillation and Boundedness of Solutions to First and Second Order Forced Dynamic Equations with Mixed Nonlinearities

Author(s):

Ravi P. Agarwal and Martin Bohner

Department of Mathematical Sciences, Florida Institute of Technology
Melbourne, FL 32901,
U.S.A.
bohner@mst.edu
URL:http://web.mst.edu/~bohner

Department of Economics and Finance, Missouri University of Science and Technology
Rolla, MO 65401,
U.S.A.
agarwal@fit.edu

Abstract:

Some oscillation and boundedness criteria for solutions to certain first and second order forced dynamic equations with mixed nonlinearities are established. The main tool in the proofs is an inequality due to Hardy, Littlewood and Pólya. The obtained results can be applied to differential equations, difference equations and q-difference equations. The results are illustrated with numerous examples.

Paper's Title:

Sufficient Conditions for Certain Types of Functions to be Parabolic Starlike

Author(s):

A. Gangadharan and S. Chinthamani

Department of Mathematics,
Easwari Engineering College,
Ramapuram, Chennai - 89,
India.

Research Scholar,
Anna University,
Chennai

E-mail: ganga.megalai@gmail.com

E-mail: chinvicky@rediffmail.com

Abstract:

In this paper sufficient conditions are determined for functions of the form and certain other types of functions to be parabolic starlike.

Paper's Title:

A New Relaxed Complex-valued b-metric Type and Fixed Point Results

Author(s):

P. Singh, V. Singh and T. C. M. Jele

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

Abstract:

In this paper, we study the existence and uniqueness of fixed point in complex valued b-metric spaces and introduce a new relaxed α, β Complex-valued b-metric type by relaxing the triangle inequality and determine whether the fixed point theorems are applicable in these spaces.

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.

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:

Fekete-Szegö Inequality for Sakaguchi Type of functions in Petal Shaped Domain

Author(s):

E. K. Nithiyanandham and B. Srutha Keerthi

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: nithiyankrish@gmail.com

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: keerthivitmaths@gmail.com

Abstract:

In this paper, we estimate coefficient bounds,|a_2|,|a_3| and |a_4|, Fekete-Szegö inequality and Toeplitz determinant T₂(2) and T₃(1) for functions belonging to the following class

the function being holomorphic, we expand using Taylor series and obtain several corollaries and consequences for the main result.

Paper's Title:

Toeplitz Determinant for Sakaguchi Type Functions Under Petal Shaped Domain

Author(s):

B. Nandhini and B. Srutha Keerthi

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: nandhinibaskar1996@gmail.com

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: keerthivitmaths@gmail.com

Abstract:

We introduce a new general subclass GP^t,ρ of Sakaguchi kind function on a Petal shaped domain. We obtain coefficients bounds and upper bounds for the Fekete-Szegö functional over the class. From these functions we obtain the bounds of first four coefficients, and then we have derived the Toeplitz determinant T₂(2) and T₃(1) whose diagonal entries are the coefficients of functions.

Paper's Title:

An Easy and Efficient Way for Solving A class of Singular Two Point Boundary Value Problems

Author(s):

Muhammed I. Syam, Muhammed N. Anwar and Basem S. Attili

Mathematical Sciences Department
United Arab Emirates University, P. O. Box 17551
Al-Ain, United Arab Emirates
b.attili@uaeu.ac.ae

Abstract:

We will consider an efficient and easy way for solving a certain class of singular two point boundary value problems. We will employ the least squares method which proved to be efficient for this type of problems. Enough examples that were considered by others will be solved with comparison with the results presented there.

Paper's Title:

A Reverse of the Triangle Inequality in Inner Product Spaces and Applications for Polynomials

Author(s):

I. Brnetić, S. S. Dragomir, R. Hoxha and J. Pečarić

Department of Applied Mathematics, Faculty of Electrical Engineering and Computing,
University of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr

School of Computer Science & Mathematics, Victoria University
Po Box 14428, Melbourne Vic 8001
Australia
sever.dragomir@vu.edu.au
URL:http://rgmia.vu.edu.au/dragomir

Faculty of Applied Technical Sciences, University of Prishtina,
Mother Theresa 5, 38 000 Prishtina
Kosova
razimhoxha@yahoo.com

Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia
pecaric@hazu.hr

Abstract:

A reverse of the triangle inequality in inner product spaces related to the celebrated Diaz-Metcalf inequality with applications for complex polynomials is given.

Paper's Title:

A Subclass of Meromorphically Multivalent Functions with Applications to Generalized Hypergeometric Functions

Author(s):

M. K. Aouf

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

Abstract:

In this paper a new subclass of meromorphically multivalent functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically p-valent functions. The main object of the present paper is to investigate the various important properties and characteristics of this subclass of meromorphically multivalent functions. We also derive many interesting results for the Hadamard products of functions belonging to this subclass. Also we consider several applications of our main results to generalized hypergeomtric functions.

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.

Paper's Title:

Uniform Convergence of Schwarz Method for Noncoercive Variational Inequalities Simple Proof

Author(s):

M. Haiour and E. Hadidi.

Department of mathematics, LANOS Laboratory,
Faculty of the Sciences, University Badji Mokhtar,
P.O 23000 Annaba,
Algeria.

haiourm@yahoo.fr,
ehadidi71@yahoo.fr

Abstract:

In this paper we study noncoercive variational inequalities, using the Schwarz method. The main idea of this method consists in decomposing the domain in two subdomains. We give a simple proof for the main result concerning L^∞ error estimates, using the Zhou geometrical convergence and the L^∞ approximation given for finite element methods by Courty-Dumont.  

Paper's Title:

Certain Compact Generalizations of Well-Known Polynomial Inequalities

Author(s):

N. A. Rather and Suhail Gulzar

Department of Mathematics,
University of Kashmir, Hazratbal Srinagar-190006,
India.

dr.narather@gmail.com

sgmattoo@gmail.com

Abstract:

In this paper, certain sharp compact generalizations of well-known Bernstien-type inequalities for polynomials, from which a variety of interesting results follow as special cases, are obtained.

Paper's Title:

Schwarz Method for Variational Inequalities Related to Ergodic Control Problems

Author(s):

S. Saadi, H. Mécheri

Department of Mathematics, Badji Mokhtar University, Annaba 23000,
P.O.Box. 12, Annaba 23000, Algeria

signor_2000@yahoo.fr

Mcherihalima@yahoo.fr

Abstract:

In this paper, we study variational inequalities related to ergodic control problems studied by M. Boulbrachčne and H. Sissaoui [11], where the "discount factor" (i.e., the zero order term) is set to 0, we use an overlapping Schwarz method on nomatching grid which consists in decomposing the domain in two subdomains. For α ∈ ]0.1[ we provide the discretization on each subdomain converges in L^∞ -norm.

Paper's Title:

L∞- Error Estimate of Schwarz Algorithm for Elliptic Quasi-Variational Inequalities Related to Impulse Control Problem

Author(s):

Saadi Samira and Mehri Allaoua

Lab. LANOS, Department of Mathematics,
University Badji Mokhtar Annaba,
P.O.Box 12, Annaba 23000,
Algeria.

Lab. LAIG, Department of Mathematics,
University May 8th 1945,
P.O.Box 401, Guelma 24000,
Algeria.

E-mail: saadisamira69@yahoo.fr
allmehri@yahoo.fr

Abstract:

In this work, we study Schwarz method for a class of elliptic quasi-variational inequalities. The principal result of this investigation is to prove the error estimate in ∞-norm for two domains with overlapping nonmatching grids, using the geometrical convergence, and the uniform convergence of Cortey Dumont.

Paper's Title:

Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results

Author(s):

Sever S. Dragomir^1,2

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.

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:

On Closed Range C^*-modular Operators

Author(s):

Javad Farokhi-Ostad and Ali Reza Janfada

Department of Mathematics,
Faculty of Mathematics and Statistics Sciences,
University of Birjand, Birjand,
Iran.
E-mail: j.farokhi@birjand.ac.ir ajanfada@birjand.ac.ir

Abstract:

In this paper, for the class of the modular operators on Hilbert C^*-modules, we give the conditions to closedness of their ranges. Also, the equivalence conditions for the closedness of the range of the modular projections on Hilbert C^*-modules are discussed. Moreover, the mixed reverse order law for the Moore-Penrose invertible modular operators are given.

Paper's Title:

Action of Differential Operators On Chirpsconstruct On L^∞

Author(s):

Taoufik El Bouayachi and Naji Yebari

Laboratoire de Mathematiques et applications,
Faculty of sciences and techniques, Tangier,
Morocco.
E-mail: figo407@gmail.com, yebarinaji@gmail.com

Abstract:

We will study in this work the action of differential operators on L∞ chirps and we will give a new definition of logarithmic chirp. Finally we will study the action of singular integral operators on chirps by wavelet characterization and Kernel method.

Paper's Title:

On a subset of Bazilevic functions

Author(s):

Marjono and D. K. Thomas

Department of Mathematics,
Faculty of Mathematics and Natural Sciences,
Brawajaya University,
Malang, Jawa Timur 65145,
Indonesia.
E-mail: marjono@ub.ac.id

Department of Mathematics,
Swansea University, Singleton Park,
Swansea, SA2 8PP,
United Kingdom.
E-mail: d.k.thomas@swansea.ac.uk

Abstract:

Let S denote the class of analytic and univalent functions in of the form For α≥0, the subclass B₁α of S of Bazilevic functions has been extensively studied. In this paper we determine various properties of a subclass of B₁α, for α≥0 which extends early results of a class of starlike functions studied by Ram Singh.

Paper's Title:

Some fixed point results in partial S-metric spaces

Author(s):

M. M. Rezaee, S. Sedghi, A. Mukheimer, K. Abodayeh, and Z. D. Mitrovic

Department of Mathematics, Qaemshahr Branch,
Islamic Azad University, Qaemshahr,
Iran.
E-mail: Rezaee.mohammad.m@gmail.com

Department of Mathematics, Qaemshahr Branch,
Islamic Azad University, Qaemshahr,
Iran.
E-mail: sedghi.gh@qaemiau.ac.ir

Department of Mathematics and General Sciences,
Prince Sultan University, Riyadh,
KSA.
E-mail: mukheimer@psu.edu.sa

Department of Mathematics and General Sciences,
Prince Sultan University, Riyadh,
KSA.
E-mail: kamal@psu.edu.sa

Nonlinear Analysis Research Group,
Faculty of Mathematics and Statistics,
Ton Duc Thang University, Ho Chi Minh City,
Vietnam.
E-mail: zoran.mitrovic@tdtu.edu.vn

Abstract:

We introduce in this article a new class of generalized metric spaces, called partial S-metric spaces. In addition, we also give some interesting results on fixed points in the partial S-metric spaces and some applications.

Paper's Title:

The Higher Coefficients for Bazilevic Functions B₁(α)

Author(s):

Marjono, Sa'adatul Fitri, and Krisna Adilia Daniswara

Department of Mathematics,
Faculty of Mathematics and Natural Sciences,,
Brawijaya University, Malang Jawa Timur 65145
Indonesia.
E-mail: marjono@ub.ac.id
saadatulfitri@ub.ac.id
krisnaadiliadaniswara@gmail.com
 

Abstract:

Let f be analytic in D{z: |z|< 1} with , and normalized by the conditions f(0)=f'(0)-1=0. We give sharp estimates for the seventh and eighth coefficients for the class of Bazilevic functions with logarithmic growth, B₁α, defined by for α≥0.

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

Paper's Title:

A New Relaxed b-metric Type and Fixed Point Results

Author(s):

P. Singh, V. Singh and Thokozani Cyprian Martin Jele

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

Abstract:

The purpose of this paper is to introduce a new relaxed α, β b-metric type by relaxing the triangle inequality. We investigate the effect that this generalization has on fixed point theorems.

Paper's Title:

Existence of Solution of Differential and Riemann-Liouville Equation Via Fixed Point Approach in Complex Valued b-Metric Spaces

Author(s):

K. Afassinou, A. A. Mebawondu, H. A. Abass and O. K. Narain

Department of Science Access,
University of Zululand, KwaDlangezwa,
South Africa.
E-mail: komia@aims.ac.za

DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: dele@aims.ac.za

DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: hammedabass548@gmail.com

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

In this paper, we establish some fixed point and common fixed point results for a new type of generalized contractive mapping using the notion of C-class function in the framework of complex valued b-metric spaces. As an application, we establish the existence and uniqueness of a solution for Riemann-Liouville integral and ordinary differential equation in the framework of a complete complex valued b-metric spaces. The obtained results generalize and improve some fixed point results in the literature.

Paper's Title:

Numerical Solution of Certain Types of Fredholm-Volterra Integro-Fractional Differential Equations via Bernstein Polynomials

Author(s):

Alias B. Khalaf¹, Azhaar H. Sallo² and Shazad S. Ahmed³

¹Department of Mathematics, College of Science,
University of Duhok,
Kurdistan Region,
Iraq.
E-mail:  aliasbkhalaf@uod.ac

²Department of Mathematics, College of Science,
University of Duhok,
Kurdistan Region,
Iraq.
E-mail:  azhaarsallo@uod.ac

³Department of Mathematics, College of Science,
University of Sulaimani,
Kurdistan Region,
Iraq.
E-mail: shazad.ahmed@univsul.edu

Abstract:

In this article we obtain a numerical solution for a certain fractional order integro-differential equations of Fredholm-Volterra type, where the fractional derivative is defined in Caputo sense. The properties of Bernstein polynomials are applied in order to convert the fractional order integro-differential equations to the solution of algebraic equations. Some numerical examples are investigated to illustrate the method. Moreover, the results obtained by this method are compared with the exact solution and with the results of some existing methods as well.

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.

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+1F_q(z) for q= 2, 3, 4. This is achieved by means of separating the generalized hypergeometric function _q+1F_q(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.

Paper's Title:

Introducing the Picard-S3 Iteration for Fixed Points

Author(s):

Pravin Singh, Virath Singh and Shivani Singh

University of KwaZulu-Natal,
School of Mathematics Statistics and Computer Sciences,
Private Bag X54001,
Durban, 4000
South Africa.

Unisa,
Department of Decision Sciences,
PO Box 392,
Pretoria, 0003
South Africa.
E-mail: singhprook@gmail.com
singhv@ukzn.ac.za
shivstarsingh@gmail.com

Abstract:

In this paper we introduce a three step iteration method and show that it can be used to approximate the fixed point of a weak contraction mapping. Furthermore, we prove that this scheme is equivalent to the Mann iterative scheme. A comparison is made with other three step iterative methods by examining the speed of convergence. Results are presented in tables to support our conclusion.

Paper's Title:

Bounds for the Extremal Eigenvalues of Positive Definite Matrices

Author(s):

Shivani Singh and Pravin Singh

Unisa, Department of Decision Sciences,
PO Box 392,
Pretoria,
0003,
South Africa.
E-mail: singhs2@unisa.ac.za

University of KwaZulu-Natal,
School of Mathematics Statistics and Computer Sciences
Private Bag X54001,
Durban,
4000,
South Africa.
E-mail: singhprook@gmail.com

Abstract:

We use a projection to achieve bounds for a vector function of the eigenvalues of a positive definite matrix. For various choices of the monotonic function we are able to obtain bounds for the extremal eigenvalues in terms of the traces of the matrix and its powers. These bounds are relatively simple to compute.

Paper's Title:

High Order Collocation Method for the Generalized Kuramoto-Sivashinsky Equation

Author(s):

Zanele Mkhize, Nabendra Parumasur and Pravin Singh

School of Mathematics, Statistics and Computer Sciences,
University of KwaZulu-Natal,
Private Bag X 54001,
Durban 4000.
E-mail: mkhizez2@ukzn.ac.za
parumasurn1@ukzn.ac.za
 singhp@ukzn.ac.za
URL: https://www.ukzn.ac.za

Abstract:

In this paper, we derive the heptic Hermite basis functions and use them as basis functions in the orthogonal collocation on finite elements (OCFE) method. We apply the method to solve the generalized Kuramoto-Sivashinsky equation. Various numerical simulations are presented to justify the computational efficiency of the proposed method.

Paper's Title:

Higher Order Accurate Compact Schemes for Time Dependent Linear and Nonlinear Convection-Diffusion Equations

Author(s):

S. Thomas, Gopika P.B. and S. K. Nadupuri

Department of Mathematics
National Institute of Technology Calicut
Kerala
673601
India.
E-mail: sobinputhiyaveettil@gmail.com pbgopika@gmail.com nsk@nitc.ac.in
 

Abstract:

The primary objective of this work is to study higher order compact finite difference schemes for finding the numerical solution of convection-diffusion equations which are widely used in engineering applications. The first part of this work is concerned with a higher order exponential scheme for solving unsteady one dimensional linear convection-diffusion equation. The scheme is set up with a fourth order compact exponential discretization for space and cubic $C^1$-spline collocation method for time. The scheme achieves fourth order accuracy in both temporal and spatial variables and is proved to be unconditionally stable. The second part explores the utility of a sixth order compact finite difference scheme in space and Huta's improved sixth order Runge-Kutta scheme in time combined to find the numerical solution of one dimensional nonlinear convection-diffusion equations. Numerical experiments are carried out with Burgers' equation to demonstrate the accuracy of the new scheme which is sixth order in both space and time. Also a sixth order in space predictor-corrector method is proposed. A comparative study is performed of the proposed schemes with existing predictor-corrector method. The investigation of computational order of convergence is presented.

Paper's Title:

Geometrical Properties of Subclass of Analytic Function with Odd Degree

Author(s):

K. Sivagami Sundari and B. Srutha Keerthi

Divison of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology, Chennai Campus, Chennai - 600 127,
India.
E-mail: sivagamisundari.2298@gmail.com 

Divison of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology, Chennai Campus, Chennai - 600 127,
India.
E-mail: keerthivitmaths@gmail.com
 

Abstract:

The objective of the paper is to study the geometrical properties of the class B(λ, t). For which we have proved that the radius is optimal ,(i.e) the number cannot be replaced by a larger one. Additionally, the graphs for various values of t and λ are compared in order to study the sharpness of the coefficient bounds.

Paper's Title:

On the Equiform Geometry of the Involute-evolute Curve Couple in Hyperbolic and de Sitter Spaces

Author(s):

M. Khalifa Saad, H. S. Abdel-Aziz and A. A. Abdel-Salam

Department of Mathematics,
Faculty of Science,
Islamic University of Madinah,
KSA.
E-mail: mohammed.khalifa@iu.edu.sa

Department of Mathematics,
Faculty of Science,
Sohag University, Sohag,
EGYPT.
E-mail: habdelaziz2005@yahoo.com

Department of Mathematics,
Faculty of Science,
Sohag University, Sohag,
EGYPT.
E-mail: asem2e@yahoo.com

Abstract:

In this paper, we aim to investigate the equiform differential geometric properties of the involute-evolute curve couple with constant equiform curvatures in three-dimensional hyperbolic and de Sitter spaces. Also, we obtain some relations between the curvature functions of these curves and investigate some special curves with respect to their equiform curvatures. Finally, we defray two computational examples to support our main findings.

Paper's Title:

Eigenvalue Bounds based on Projections

Author(s):

Pravin Singh, Shivani Singh, Virath Singh

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.

University of South Africa,
Department of Decision Sciences, PO Box 392,
 Pretoria,0003,
South Africa.

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.

E-mail: singhp@ukzn.ac.za, singhs2@unisa.ac.za, singhv@ukzn.ac.za
 

Abstract:

In this paper, we derive expressions for the bounds of the extremal eigenvalues of positive definite matrices. Our approach is to use a symmetric projection operator onto an n-2 dimensional subspace of the real space of n tuples. These bounds are based on traces of the matrix and its powers. They are relatively easy and inexpensive to compute.

Paper's Title:

On the Oscillatory Behavior of Self Adjoint Fractional Extensible Beam Equations

Author(s):

S. Priyadharshini¹, G.E. Chatzarakis², S. L. Panetsos² and V. Sadhasivam¹

¹Post Graduate and Research Department of Mathematics,
Thiruvalluvar Government Arts College,
Rasipuram - 637 401, Namakkal Dt., Tamil Nadu,
India.
E-mail: s.priya25april@gmail.com, ovsadha@gmail.com

²Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education(ASPETE),
Marousi 15122, Athens,
Greece.
E-mail: geaxatz@otenet.gr, gea.xatz@aspete.gr, spanetsos@aspete.gr

Abstract:

The main objective of this paper is to study the oscillatory behavior of the solutions of self adjoint fractional extensible beam equations by using integral average method. Some new sufficient conditions are established with various boundary conditions over a cylindrical domains. Examples illustrating the results are given.

Paper's Title:

Recursive Bounds for the Eigenvalues of Symmetric Positive Definite Matrices

Author(s):

Pravin Singh, Shivani Singh, Virath Singh

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.

University of South Africa,
Department of Decision Sciences, PO Box 392,
 Pretoria,0003,
South Africa.

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.

E-mail: singhp@ukzn.ac.za, singhs2@unisa.ac.za, singhv@ukzn.ac.za
 

Abstract:

In this paper, we bound the extremal eigenvalues of a positive definite real symmetric matrix by considering a part of the characteristic equation in the region of the smallest and largest eigenvalues. An expansion around these values leads to a sequence of monotonic functions, whose zeros coincide with the extremal zeros of associated polynomials. The latter is shown to yield bounds that are fairly accurate.

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