


Paper's Title:
Orthogonal Collocation on Finite Elements Using Quintic Hermite Basis
Author(s):
P. Singh, N. Parumasur and C. Bansilal
University of KwaZuluNatal,
School of Mathematics Statistics and Computer Sciences,
Private Bag X54001,
Durban, 4000,
South Africa.
Email: singhprook@gmail.com
parumasurn1@ukzn.ac.za
christelle18@gmail.com
Abstract:
In this paper we consider the orthogonal collocation on finite elements (OCFE) method using quintic Hermite (second degree smooth) basis functions and use it to solve partial differential equations (PDEs). The method is particularly tailored to solve third order BVPS and PDEs and to handle their special solutions such as travelling waves and solitons, which typically is the case in the KdV equation. The use of quintic polynomials and collocation using Gauss points yields a stable high order superconvergent method. OCFE using quintic Hermite basis is optimal since it is computationally more efficient than collocation methods using (first degree smooth) piecewisepolynomials and more accurate than the (third degree smooth) Bsplines basis. Various computational simulations are presented to demonstrate the computational efficiency and versatility of the OCFE method.
Paper's Title:
High Order Collocation Method for the Generalized KuramotoSivashinsky Equation
Author(s):
Zanele Mkhize, Nabendra Parumasur and Pravin Singh
School of Mathematics, Statistics and
Computer Sciences,
University of KwaZuluNatal,
Private Bag X 54001,
Durban 4000.
Email: 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 KuramotoSivashinsky equation. Various numerical simulations are presented to justify the computational efficiency of the proposed method.
Paper's Title:
On Weighted Toeplitz Operators
Author(s):
S. C. Arora and Ritu Kathuria
Department of Mathematics,
University of Delhi,
Delhi 110007,
India.
Department of Mathematics,
Motilal Nehru College, University of Delhi,
Delhi 110021,
India.
Abstract:
A weighted Toeplitz operator on H^{2}(β) is defined as T_{φ}f=P(φf) where P is the projection from L^{2}(β) onto H^{2}(β) and the symbol φ ∈ L^{2}(β) for a given sequence β=‹β_{n}›_{n∈ Z} of positive numbers. In this paper, a matrix characterization of a weighted multiplication operator on L^{2}β is given and it is used to deduce the same for a weighted Toeplitz operator. The eigenvalues of some weighted Toeplitz operators are also determined.
Paper's Title:
FeketeSzegö 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.
Email: nithiyankrish@gmail.com
Division of Mathematics, School of
Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai  600 048,
India.
Email: keerthivitmaths@gmail.com
Abstract:
In this paper, we estimate coefficient bounds,a_2,a_3 and a_4, FeketeSzegö inequality and Toeplitz determinant T_{2}(2) and T_{3}(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:
Hyponormal and KQuasiHyponormal Operators On SemiHilbertian Spaces
Author(s):
Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali
Mathematics Department,
College of Science,
Aljouf University,
Aljouf 2014,
Saudi Arabia.
Email:
sididahmed@ju.edu.sa
Mathematics Department, Faculty of
Science,
Hassiba Benbouali, University of Chlef,
B.P. 151 Hay Essalem, Chlef 02000,
Algeria.
Email:
benali4848@gmail.com
Abstract:
Let H be a Hilbert space and let A be a positive bounded operator on H. The semiinner product < uv>_{A}:=<Auv>, u,v ∈ H induces a seminorm  ._{A} on H. This makes H into a semiHilbertian space. In this paper we introduce the notions of hyponormalities and kquasihyponormalities for operators on semi Hilbertian space (H,._{A}), based on the works that studied normal, isometry, unitary and partial isometries operators in these spaces. Also, we generalize some results which are already known for hyponormal and quasihyponormal operators. An operator T ∈ B_{A} (H) is said to be (A, k)quasihyponormal if
Paper's Title:
Some properties of kquasi class Q* operators
Author(s):
Shqipe Lohaj and Valdete Rexhëbeqaj Hamiti
Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
Email: shqipe.lohaj@unipr.edu
Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
Email: valdete.rexhebeqaj@unipr.edu
Abstract:
In this paper, we give some results of kquasi class Q^{*} operators. We proved that if T is an invertible operator and N be an operator such that N commutes with T^{*}T, then N is kquasi class Q^{*} if and only if TNT^{1} is of kquasi class Q^{*}. With example we proved that exist an operator kquasi class Q^{*} which is quasi nilpotent but it is not quasi hyponormal.
Paper's Title:
Some properties of quasinormal, paranormal and 2k^{*} paranormal operators
Author(s):
Shqipe Lohaj
Department of Mathematics,
University of Prishtina,
10000,
Kosova.
Email: shqipe.lohaj@unipr.edu
Abstract:
In the beginning of this paper some conditions under which an operator is partial isometry are given. Further, the class of 2k^{*} paranormal operators is defined and some properties of this class in Hilbert space are shown. It has been proved that an unitarily operator equivalent with an operator of a 2k^{*} paranormal operator is a 2k^{*} paranormal operator, and if is a 2k^{*} paranormal operator, that commutes with an isometric operator, then their product also is a $2k^*$ paranormal operator.
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 380701,
Republic of Korea.
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Republic of Korea.
Department of Mathematics,
Vedant College of Engineering and Technology (Rajasthan Technical University),
Bundi323021, Rajasthan,
India.
Email: sjun@kku.ac.kr, iki@wku.ac.kr, arjunkumarrathie@gmail.com
Abstract:
Very recently MasjedJamei and Koepf established interesting and useful generalizations of various classical summation theorems for the _{2}F_{1}, _{3}F_{2}, _{4}F_{3}, _{5}F_{4} and _{6}F_{5} 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.
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