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6: Paper Source PDF document

Paper's Title:

An Approximation of Jordan Decomposable Functions for a Lipschitz Function

Author(s):

Ibraheem Alolyan

Mathematics Department,
College of Science, King Saud University
P.O.Box: 2455, Riyadh 11451,
Saudi Arabia
ialolyan05@yahoo.com


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.



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.



2: Paper Source PDF document

Paper's Title:

A Simple New Proof of Fan-Taussky-Todd Inequalities

Author(s):

Zhi-Hua Zhang and Zhen-Gang Xiao

Zixing Educational Research Section,
Chenzhou City, Hunan 423400, P. R. China.
Zhi-hua Zhang
Url: http://www.hnzxslzx.com/zzhweb/
 

Department Of Mathematics, Hunan Institute Of Science And Technology,
Yueyang City, Hunan 423400, P. R. China.
Zhen-gang Xiao 

Abstract:

In this paper we present simple new proofs of the inequalities:

which holds for all real numbers a0 = 0, a1, · · · , an, an+1 = 0 and the coefficients 2(1 - cos(π/(n + 1))) and 2(1 + cos(π/(n + 1))) are the best possible; and

which holds for all real numbers a0 = 0, a1, · · · , an and the coefficients 2(1-cos(π/(2n + 1))) and 2(1 + cos(π/(2n + 1))) are the best possible.



2: Paper Source PDF document

Paper's Title:

On the Boundedness of Hardy's Averaging Operators

Author(s):

Dah-Chin Luor

Department of Applied Mathematics,
I-Shou University, Dashu District,
Kaohsiung City 84001,
Taiwan, R.O.C.
dclour@isu.edu.tw

Abstract:

In this paper we establish scales of sufficient conditions for the boundedness of Hardy's averaging operators on weighted Lebesgue spaces. The estimations of the operator norms are also obtained. Included in particular are the Erdélyi-Kober operators.



2: Paper Source PDF document

Paper's Title:

A Geometric Generalization of Busemann-Petty Problem

Author(s):

Liu Rong and Yuan Jun

Shanghai Zhangjiang Group Junior Middle School,
Huo Xiang Road, Shanghai, 201203,
China

yuanjun_math@126.com

liurong@shu.edu.cn

Abstract:

The norm defined by Busemann's inequality establishes a class of star body - intersection body. This class of star body plays a key role in the solution of Busemann-Petty problem. In 2003, Giannapoulos [1] defined a norm for a new class of half-section. Based on this norm, we give a geometric generalization of Busemann-Petty problem, and get its answer as a result



2: Paper Source PDF document

Paper's Title:

Hankel Operators on Copson's Spaces

Author(s):

Nicolae Popa

Institute of Mathematics of Romanian Academy,
P.O. BOX 1-764 RO-014700 Bucharest,
Romania.

E-mail: Nicolae.Popa@imar.ro, npopafoc@gmail.com

Abstract:

We give a characterization of boundedness of a Hankel matrix, generated by a pozitive decreasing sequence, acting on Copson's space cop(2).



2: Paper Source PDF document

Paper's Title:

Generalised Models for Torsional Spine Reconnection

Author(s):

Ali Khalaf Hussain Al-Hachami

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

Abstract:

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



1: Paper Source PDF document

Paper's Title:

Positive Solution For Discrete Three-Point Boundary Value Problems

Author(s):

Wing-Sum Cheung And Jingli Ren


Department of Mathematics,
The University of Hong Kong,
Pokfulam, Hong Kong
wscheung@hku.hk

Institute of Systems Science,
Chinese Academy of Sciences,
Beijing 100080, P.R. China
renjl@mx.amss.ac.cn

Abstract:

This paper is concerned with the existence of positive solution to the discrete three-point boundary value problem

,

where , and f is allowed to change sign. By constructing available operators, we shall apply the method of lower solution and the method of topology degree to obtain positive solution of the above problem for on a suitable interval. The associated Green’s function is first given.



1: Paper Source PDF document

Paper's Title:

Two Classes of Completely Monotonic Functions Involving Gamma and Polygamma Functions

Author(s):

Bai-Ni Guo, Xiao-Ai Li and Feng Qi

School of Mathematics and Informatics, Henan Polytechnic University,
Jiaozuo City, Henan Province, 454010,
China.
bai.ni.guo@gmail.com

College of Mathematics and Information Science,
Henan Normal University, Xinxiang City,
Henan Province, 453007,
China.
lxa.hnsd@163.com

Research Institute of Mathematical Inequality Theory,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
qifeng618@gmail.com
qifeng618@hotmail.com
qifeng618@qq.com
URLhttp://rgmia.vu.edu.au/qi.html

Abstract:

The function

is logarithmically completely monotonic in (0,∞) if and only if c≥1 and its reciprocal is logarithmically completely monotonic in (0,∞) if and only if c≤0. The function

is completely monotonic in (0,∞) if and only if c≥1 and its negative is completely monotonic in (0,∞)  if and only if c≤0.



1: Paper Source PDF document

Paper's Title:

Isoperimetric Inequalities for Dual Harmonic Quermassintegrals

Author(s):

Yuan Jun, Zao Lingzhi and Duan Xibo

School of Mathematics and Computer Science,
Nanjing Normal University, Nanjing, 210097,
China.
yuanjun_math@126.com

Department of Mathematics, Nanjing Xiaozhuang University,
Nanjing, 211171,
China.
lzhzhao@163.com

Department of Mathematics, Shandong Water Polytechnic,
Shandong, 276826,
China
dxb1111@sohu.com


Abstract:

In this paper, some isoperimetric inequalities for the dual harmonic quermassintegrals are established.



1: Paper Source PDF document

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. Boulbrachène 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.



1: Paper Source PDF document

Paper's Title:

Commutators of Hardy Type Operators

Author(s):

Chunping Xie

Department of Mathematics,
Milwaukee School of Engineering,
1025 N. Broadway,
Milwaukee, Wisconsin 53202,
USA.

E-mail: xie@msoe.edu
URL: http://www.msoe.edu/people/chunping.xie

Abstract:

The note deals with commutaors of the Hardy operator, Hardy type operators on Morrey spaces on R+. We have proved that the commutators generated by Hardy operator and Hardy type operators with a BMO function b are bounded on the Morrey spaces.



1: Paper Source PDF document

Paper's Title:

Coefficient Estimates for Certain Subclasses of Bi-univalent Sakaguchi Type Functions by using Faber Polynomial

Author(s):

P. Murugabharathi, B. Srutha Keerthi

Mathematics Division,
School of Advanced Sciences,
VIT Chennai, Vandaloor, Kelambakkam Road,
Chennai - 600 127, India.
E-mail: bharathi.muhi@gmail.com
E-mail: sruthilaya06@yahoo.co.in

Abstract:

In this work, considering a general subclass of bi-univalent Sakaguchi type functions, we determine estimates for the general Taylor-Maclaurin coefficients of the functions in these classes. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.



1: Paper Source PDF document

Paper's Title:

Sweeping Surfaces with Darboux Frame in Euclidean 3-space E3

Author(s):

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

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

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

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

Abstract:

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


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