325 research outputs found
Generalized Abstracted Mean Values
No full textIn this article, the author introduces the generalized abstracted mean values which extend the concepts of most means with two variables, and researches their basic properties and monotonicities
2010-2011 Academic Excellence Research - Dr. Lokenath Debnath
No full textAcademic Excellence Research - Dr. Lokenath Debnath.https://scholarworks.utrgv.edu/utpamedia/1055/thumbnail.jp
A Further Generalization of Hardy-Hilbert's Integral Inequality with Parameter and Applications
No full textIn this paper, by introducing some parameters and by employing
a sharpening of Hölder’s inequality, a new generalization of Hardy-Hilbert
integral inequality involving the Beta function is established. At the same
time, an extension of Widder’s theorem is given
Other Proofs of Monotonicity for Generalized Weighted Mean Values
No full textIn this article, another two simple and short proofs of monotonicity for the generalized weighted mean values with two parameters are given
University Faculty Excellence Award in Service: Dr. Lokenath Debnath
No full textDebnath served as chair of the Mathematics Department from the year he arrived at UTPA in 2001 until 2011. Under his leadership, a program was established to enhance passing rates of introductory math courses, a Ph.D. program in mathematics was submitted and approved by The University of Texas System Board of Regents, and a mathematics faculty mentor program and external review process for faculty evaluation were developed and implemented, among many other achievements to enhance mathematics education. He constructed this department from basically a service department into one of the best mathematical departments in the state, said Dr. John Trant, dean of the College of Science and Mathematics. Debnath extended his service beyond the department, college and University to a national scale by serving as the founding managing editor of the International Journal of the Mathematics and Mathematical Sciences. His many undergraduate and graduate level text books and research monographs are relied upon worldwide. Debnath has been called driven in his mission to make a difference. I am a professor. I teach and I also write books and papers to expand knowledge, to create knowledge so others get benefit from that, Debnath said. Students are our assets for our future generations. We inspire them, we stimulate them, we try to impart knowledge and educate them so they can become successful in their lives.https://scholarworks.utrgv.edu/utpamedia/1326/thumbnail.jp
Introduction to hilbert spaces with apllications, Ed. 2nd/ Debnath
No full textxviii, 551 hal.: ill.; 21 cm
Studies of nonlinear interactions of ocean waves.
No full textNonlinear wave interactions in both inviscid and weakly viscous fluid are studied. Using the averaged variational method, new interaction equations are derived. It is shown that results reduce to those obtained earlier for weak second-order resonant interactions in the limit of zero viscosity. The nonlinear resonant evolution of amplitude triads has been investigated for different values of viscosity. A variational principle for the Rossby waves in -plane approximation is formulated. Some conservation laws are derived from full nonlinear equations of Rossby waves. The variational principle and the concept of virtual work are used to derive the basic equations of motion, boundary and free surface conditions for capillary waves. Resonant interactions among surface gravity waves and capillary-gravity waves are described. Numerical results with graphical representations are included.PhDApplied SciencesEnvironmental engineeringMathematicsOcean engineeringPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/131013/2/9825268.pd
Sir James Lighthill and modern fluid mechanics: a memorial tribute
No full textThis memorial tribute commemorates Sir James Lighthill the man and the mathematical scientist. A brief biographical information is presented with my personal reminiscences. His major contributions to fluid mechanics with special reference to nonlinear dispersive waves are discussed. By any standards, his legacy of research and publications of six books and one hundred fifty papers will remain forever as a remarkable example of scholarly work
Srinivasa Ramanujan (1887-1920) and the theory of partitions of numbers and statistical mechanics a centennial tribute
No full textThis centennial tribute commemorates Ramanujan the Mathematician and
Ramanujan the Man. A brief account of his life, career, and remarkable mathematical contributions is given to describe the gifted talent of Srinivasa Ramanujan. As an example of his creativity in mathematics, some of his work on the theory of partition of numbers has been presented with its application to statistical mechanics
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