AJMAA

The Australian Journal of Mathematical Analysis and Applications

ISSN 1449-5910

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8: Paper Source PDF document

Paper's Title:

Inequalities Relating to the Gamma Function

Author(s):

Chao-Ping Chen and Feng Qi

Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo City, Henan 454000, China
chenchaoping@hpu.edu.cn

Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo City, Henan 454000, China
qifeng@hpu.edu.cn, fengqi618@member.ams.org
Url: http://rgmia.vu.edu.au/qi.html, http://dami.hpu.edu.cn/qifeng.html

Abstract:

For , we have

For,

And equality occurs for x=1.

4: Paper Source PDF document

Paper's Title:

Positive Periodic Time-Scale Solutions for Functional Dynamic Equations

Author(s):

Douglas R. Anderson and Joan Hoffacker

Department of Mathematics and Computer Science
Concordia College
Moorhead, MN 56562 USA
andersod@cord.edu
URL: http://www.cord.edu/faculty/andersod/

Department of Mathematical Sciences
Clemson University
Clemson, SC 29634 USA
johoff@clemson.edu
URL: http://www.math.clemson.edu/facstaff/johoff.htm

Abstract:

Using Krasnoselskii's fixed point theorem, we establish the existence of positive periodic solutions to two pairs of related nonautonomous functional delta dynamic equations on periodic time scales, and then extend the discussion to higher-dimensional equations. Two pairs of corresponding nabla equations are also provided in an analogous manner.

3: Paper Source PDF document

Paper's Title:

Generalized Fuglede-Putnam Theorem and Orthogonality

Author(s):

A. Bachir and A. Sagres

Department of Mathematics, Faculty of Science, King Khaled University, Abha, P.O. Box 9004 Kingdom Saudi Arabia
bachir_ahmed@hotmail.com
sagres@hotmail.com

Abstract:

An asymmetric Fuglede-Putnam’s theorem for dominant operators and p-hyponormal operators is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.

3: Paper Source PDF document

Paper's Title:

A Wallis Type Inequality and a Double Inequality for Probability Integral

Author(s):

Jian Cao, Da-Wei Niu and Feng Qi

School of Mathematics and Informatics,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
21caojian@163.com

School of Mathematics and Informatics,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
nnddww@tom.com

Research Institute of Mathematical Inequality Theory,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
qifeng@hpu.edu.cn
fengqi618@member.ams.org
qifeng618@hotmail.com
qifeng618@msn.com
qifeng618@qq.com
URL: http://rgmia.vu.edu.au/qi.html

Abstract:

In this short note, a Wallis type inequality with the best upper and lower bounds is established. As an application, a double inequality for the probability integral is found.

1: Paper Source PDF document

Paper's Title:

On the Generalized Inverse over Integral Domains

Author(s):

Yaoming Yu and Guorong Wang

College of Education, Shanghai Normal University
Shanghai 200234
People's Republic of China.
yuyaoming@online.sh.cn
grwang@shnu.edu.cn

Abstract:

In this paper, we study further the generalized inverse of a matrix A over an integral domain. We give firstly some necessary and sufficient conditions for the existence of the generalized inverse , an explicit expression for the elements of the generalized inverse and an explicit expression for the generalized inverse , which reduces to the {1} inverse. Secondly, we verify that the group inverse, the Drazin inverse, the Moore-Penrose inverse and the weighted Moore-Penrose inverse are identical with the generalized inverse for an appropriate matrix G, respectively, and then we unify the conditions for the existence and the expression for the elements of the weighted Moore-Penrose inverse, the Moore-Penrose inverse, the Drazin inverse and the group inverse over an integral domain. Thirdly, as a simple application, we give the relation between some rank equation and the existence of the generalized inverse , and a method to compute the generalized inverse . Finally, we give an example of evaluating the elements of without calculating .

1: Paper Source PDF document

Paper's Title:

Local and Global Existence and Uniqueness Results for Second and Higher Order Impulsive Functional Differential Equations with Infinite Delay

Author(s):

Johnny Henderson and Abdelghani Ouahab

Department of Mathematics, Baylor University,
Waco, Texas 76798-7328
USA.
Johnny_Henderson@baylor.edu

Laboratoire de Mathématiques, Université de Sidi Bel Abbés
BP 89, 22000 Sidi Bel Abbées,
Algérie.
ouahab@univ-sba.dz

Abstract:

In this paper, we discuss the local and global existence and uniqueness results for second and higher order impulsive functional differential equations with infinite delay. We shall rely on a nonlinear alternative of Leray-Schauder. For the global existence and uniqueness we apply a recent Frigon and Granas nonlinear alternative of Leray-Schauder type in Fréchet spaces.

1: Paper Source PDF document

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.

1: Paper Source PDF document

Paper's Title:

Long Correlations Applied to the Study of Agricultural Indices in Comparison with the S&P500 index

Author(s):

M. C. Mariani, J. Libbin, M.P. Beccar Varela,
V. Kumar Mani, C. Erickson, D.J. Valles Rosales

Department of Mathematical Sciences,
Science Hall 236, New Mexico State University,
Las Cruces, NM 88003-8001,
USA.
mmariani@nmsu.edu

Abstract:

Long-time correlations in agricultural indices are studied and their behavior is compared to the well-established S&P500 index. Hurst exponent and Detrended Fluctuation Analysis (DFA) techniques are used in this analysis. We detected long-correlations in the agricultural indices and briefly discussed some features specific in comparison to the S&P500 index.

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