Next Issue
Volume 1, September
Previous Issue
Volume 1, March

Mathematics, Volume 1, Issue 2 (June 2013) – 2 articles , Pages 46-75

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
Order results
Result details
Select all
Export citation of selected articles as:
Article
On the Class of Dominant and Subordinate Products
Mathematics 2013, 1(2), 65-75; https://doi.org/10.3390/math1020065 - 15 May 2013
Cited by 2 | Viewed by 2393
Abstract
In this paper we provide proofs of two new theorems that provide a broad class of partition inequalities and that illustrate a na¨ıve version of Andrews’ anti-telescoping technique quite well. These new theorems also put to rest any notion that including parts of [...] Read more.
In this paper we provide proofs of two new theorems that provide a broad class of partition inequalities and that illustrate a na¨ıve version of Andrews’ anti-telescoping technique quite well. These new theorems also put to rest any notion that including parts of size 1 is somehow necessary in order to have a valid irreducible partition inequality. In addition, we prove (as a lemma to one of the theorems) a rather nontrivial class of rational functions of three variables has entirely nonnegative power series coefficients. Full article
Article
Stability of Solutions to Evolution Problems
Mathematics 2013, 1(2), 46-64; https://doi.org/10.3390/math1020046 - 13 May 2013
Cited by 3 | Viewed by 2653
Abstract
Large time behavior of solutions to abstract differential equations is studied. The results give sufficient condition for the global existence of a solution to an abstract dynamical system (evolution problem), for this solution to be bounded, and for this solution to have a [...] Read more.
Large time behavior of solutions to abstract differential equations is studied. The results give sufficient condition for the global existence of a solution to an abstract dynamical system (evolution problem), for this solution to be bounded, and for this solution to have a finite limit as t , in particular, sufficient conditions for this limit to be zero. The evolution problem is: u ˙ = A(t)u + F(t, u) + b(t), t 0; u(0) = u 0 . (*) Here u ˙ := du dt , u = u(t) H, H is a Hilbert space, t R + := [0,), A(t) is a linear dissipative operator: Re(A(t)u,u) γ(t)(u, u) where F(t, u) is a nonlinear operator, F(t, u) c 0 u p , p > 1, c 0 and p are positive constants, b(t) β(t) , and β(t)0 is a continuous function. The basic technical tool in this work are nonlinear differential inequalities. The non-classical case γ(t) 0 is also treated. Full article
Previous Issue
Next Issue
Back to TopTop