Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations

We establish some new criteria for the oscillation of second-order nonlinear dynamic equations on a time scale. We study the case of strongly superlinear and the case of strongly sublinear equations subject to various conditions.     

Optimal Existence Theory for Single and Multiple Positive Periodic Solutions of Functional Differential Equations

This paper deals with a new optimal existence theory for single and multiple positive periodic solutions of functional differential equations using a fixed-point theorem in cones. We illustrate our theory by examining several biomathematical models. The paper improves and extends previous results in the literature.     

Approximations of solutions to neutral functional differential equations with nonlocal history conditions

This work is concerned with a class of neutral functional differential equations with nonlocal history conditions in a Hilbert space. The approximation of solution to a class of such problems is studied. Moreover, the convergence of Faedo-Galerkin approximation of solution is shown. For illustration, an example is worked out.     

An upper and lower solution approach for singular boundary value problems with sign changing non‐linearities

We obtain via Schauder's fixed point theorem new results for singular second‐order boundary value problems where our non‐linear term f(t,y,z) is allowed to change sign. In particular, our problem may be singular at y=0, t=0 and/or t=1. Copyright © 2002 John Wiley & Sons, Ltd.     

On the number of views of polyhedral terrains

We show that the number of topologically different orthographic views of a polyhedral terrain withn edges isO(n ^5+ɛ ), and that the number of topologically different perspective views of such a terrain isO(n ^8+ɛ ), for any ɛ>0. Both bounds are almost tight in the worst case. The proofs are simple consequences of the recent almost-tight bounds of [11] on the complexity of lower envelopes in higher dimensions. Pankaj Agarwal has been supported by National Science Foundation Grant CCR-91-06514. Micha Sharir has been supported by National Science Foundation Grant CCR-91-22103, and by grants from the U.S.—Israeli Binational Science Foundation, the G.I.F.—the German Israeli Foundation for Scientific Research and Development- and the Fund for Basic Research administered by the Israeli Academy of Sciences.     

Euclidean minimum spanning trees and bichromatic closest pairs

We present an algorithm to compute a Euclidean minimum spanning tree of a given setS ofN points inE ^d in timeO(F _d (N,N) log ^d N), whereF _d (n,m) is the time required to compute a bichromatic closest pair amongn red andm green points inE ^d . IfF _d (N,N)=Ω(N ^1+ε), for some fixed ɛ>0, then the running time improves toO(F _d (N,N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in expected timeO((nm logn logm)^2/3+m log² n+n log² m) inE ₃, which yields anO(N ^4/3 log^4/3 N) expected time, algorithm for computing a Euclidean minimum spanning tree ofN points inE ³. Ind≥4 dimensions we obtain expected timeO((nm)^{1−1/([d/2]+1)+ε}+m logn+n logm) for the bichromatic closest pair problem andO(N ^{2−2/([d/2]+1)ε}) for the Euclidean minimum spanning tree problem, for any positive ɛ. The first, second, and fourth authors acknowledge support from the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), a National Science Foundation Science and Technology Center under NSF Grant STC 88-09648. The second author's work was supported by the National Science Foundation under Grant CCR-8714565. The third author's work was supported by the Deutsche Forschungsgemeinschaft under Grant A1 253/1-3, Schwerpunktprogramm “Datenstrukturen und effiziente Algorithmen”. The last two authors' work was also partially supported by the ESPRIT II Basic Research Action of the EC under Contract No. 3075 (project ALCOM).     

Existence of multiple positive solutions for second order nonlinear dynamic BVPs by variational methods

The aim of this paper is to employ variational techniques and critical point theory to prove some sufficient conditions for the existence of multiple positive solutions to a nonlinear second order dynamic equation with homogeneous Dirichlet boundary conditions.     

The generalized Thomas–Fermi singular boundary value problems for neutral atoms

This paper presents an upper and lower solution theory for singular boundary value problems modelling the Thomas–Fermi equation, subject to a boundary condition corresponding to the neutral atom with Bohr radius equal to its existence interval. Furthermore, we derive sufficient conditions for the existence–construction of the above‐mentioned upper–lower solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

A novel programmed shrinkage dilatometer for optimized sintering of powder ceramics

A fast-firing shrinkage rate controlled dilatometer was developed as a tool for optimizing sintering of powder compacts. The instrument described in this work features an infrared imaging radiation furnace and a low thermal mass dilatometer assembly which allowed controlled heating and cooling rates of up to 500°C min^?1. Shrinkage control was accomplished using a computer interfaced PID control algorithm. Adjustments were made to hardware and software which reduced specimen creep under dilatometer pushrod load, eliminated non-uniform pushrod expansion, fostered reproducible specimen temperature determination, accounted for thermal expansion during sintering, and generated instantaneous termination of sintering at the specified end of RCS. Tests performed on ZnO samples demonstrated very rapid thermal response and excellent shrinkage control.