The heat equation on time scales

We present the use of a Fourier transform on time scales to solve a dynamic heat IVP. This is done by inverting a certain exponential function via contour integral. We include some specific examples and directions for further study

Optimality conditions for the calculus of variations with higher-order delta derivatives

We prove the Euler-Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives.Comment: Submitted 26/Jul/2009; Revised 04/Aug/2010; Accepted 09/Aug/2010; for publication in "Applied Mathematics Letters

Generalized retarded integral inequalities

We prove some new retarded integral inequalities. The results generalize those in [J. Math. Anal. Appl. 301 (2005), no. 2, 265--275].Comment: Changes suggested by the referee don

Isoperimetric problems of the calculus of variations with fractional derivatives

In this paper we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered.Comment: Submitted 02-Oct-2009; revised 30-Jun-2010; accepted 10-May-2011; for publication in the journal Acta Mathematica Scienti

Generalizations of Gronwall-Bihari Inequalities on Time Scales

We establish some nonlinear integral inequalities for functions defined on a time scale. The results extend some previous Gronwall and Bihari type inequalities on time scales. Some examples of time scales for which our results can be applied are provided. An application to the qualitative analysis of a nonlinear dynamic equation is discussed.Comment: This is a preprint of an article accepted (16/May/2008) for publication in the "Journal of Difference Equations and Applications"; J. Difference Equ. Appl. is available online at http://www.informaworld.co

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least 4 m. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the 6.5 m James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 yr, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit. © 2023. The Author(s). Published by IOP Publishing Ltd on behalf of the Astronomical Society of the Pacific (ASP). All rights reserved.Open access articleThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]