Comparison and oscillatory behavior for certain second order nonlinear dynamic equations

We present some new necessary and sufficient conditions for the oscillation of second order nonlinear dynamic equation $$\bigl(a\bigl(x^{\Delta }\bigr)^{\alpha }\bigr)^{\Delta }(t)+q(t)x^{\beta }(t)=0$$ on an arbitrary time scale $\mathbb{T}$ , where α and β are ratios of positive odd integers, a and q are positive rd-continuous functions on $\mathbb{T}$ . Comparison results with the inequality $$\bigl(a\bigl(x^{\Delta }\bigr)^{\alpha }\bigr)^{\Delta }(t)+q(t)x^{\beta }(t)\leqslant 0\quad (\geqslant 0)$$ are established and application to neutral equations of the form $$\bigl(a(t)\bigl(\bigl[x(t)+p(t)x[\tau (t)]\bigr]^{\Delta }\bigr)^{\alpha }\bigr)^{\Delta }+q(t)x^{\beta }\bigl[g(t)\bigr]=0$$ are investigated.     

A resource-dependent competition model: Effects of toxicants emitted from external sources as well as formed by precursors of competing species

In this paper, a nonlinear mathematical model is proposed and analyzed to study the survival of resource-dependent competing species. It is assumed that competing species and its resource are affected simultaneously by a toxicant emitted into the environment from external sources as well as formed by precursors of competing species. Stabilities of all the equilibria are studied using the theory of differential equations and computer simulation. A condition which determines the persistence of the system is also obtained. It is concluded from the analysis that as the cumulative rates of emission and formation of toxicants into the environment increase, the densities of both competing species and its resource decrease. It is also concluded that the usual competitive outcomes for the resource biomass altered in the presence of precursors.     

Importance of compositional homogeneity of macromolecular chains for UCST‐type transitions in water: Controlled versus conventional radical polymerization

The change of polymerization method from conventional free radical polymerization to the reversible addition fragmentation chain transfer (RAFT) method provided thermoresponsive behavior of upper critical solution temperature (UCST)‐type in water to copolymers of styrene (St) and acrylamide (AAm). Sample preparation conditions (temperature and time of dissolution) for turbidity measurements could also significantly influence the thermoresponsive behavior of polymers based on AAm. Poly(AAm‐co‐St)s made by RAFT method till high conversions showed sharp cloud points ranging 50–62 °C with low hysteresis in water depending upon the copolymer composition. Samples for turbidity measurements were prepared under optimized conditions, that is, 70 °C for 1.5 h. In contrast, the copolymers made by conventional radical polymerization in all copolymer composition range were not thermoresponsive. The example [poly(AAm‐co‐St)] emphasizes the importance of compositional homogeneity of macromolecular chains for showing UCST‐type transitions in water for a system with wide difference in reactivity ratios of the comonomers. Since, examples of polymeric systems showing UCST in water are not too many, this work highlights how compositional homogeneity would help in developing many more systems with tuned cloud points. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1878–1884     

Synthesis of de novo designed small-molecule inhibitors of bacterial RNA polymerase

The de novo molecular design program SPROUT has been used in conjunction with the X-ray crystal structure of RNA polymerase (RNAP) from Thermus aquaticus to produce a novel enzyme inhibitor scaffold. A short and efficient synthesis of molecules corresponding to this scaffold has been developed and in keeping with the design predictions, the resulting inhibitors displayed useful levels of inhibition of Escherichia coli RNAP.     

Solutions of Volterra integral equations with infinite delay

We present several new existence results for a Volterra integral equation with infinite delay. We discuss periodic and bounded solutions. Sufficient conditions for the existence of positive periodic solutions are also provided. The techniques we employ have not been used for this equation before. Our results generalize and complement those in the literature and several examples are presented to show their applicability. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mechanism design for a multicommodity flow game in service network alliances

We study a collaborative multicommodity flow game where individual players own capacity on the edges of the network and share this capacity to deliver commodities. We present membership mechanisms, by adopting a rationality based approach using notions from game theory and inverse optimization, to allocate benefits among the players in such a game.     

Optimal Existence Conditions for the Periodic Delay ϕ-Laplace Equation with upper and lower Solutions in the Reverse order

In this paper, we show that the monotone iterative technique produces two monotone sequences that converge uniformly to extremal solutions for the periodic delay ?-Laplace equation. Moreover, we obtain optimal existence conditions with upper and lower solutions in the reverse order.     

Quasi-planar graphs have a linear number of edges

A graph is calledquasi-planar if it can be drawn in the plane so that no three of its edges are pairwise crossing. It is shown that the maximum number of edges of a quasi-planar graph withn vertices isO(n).Work on this paper by Pankaj K. Agarwal, Boris Aronov and Micha Sharir has been supported by a grant from the U.S.-Israeli Binational Science Foundation. Work on this paper by Pankaj K. Agarwal has also been supported by NSF Grant CCR-93-01259, by an Army Research Office MURI grant DAAH04-96-1-0013, by an NYI award, and by matching funds from Xerox Corporation. Work on this paper by Boris Aronov has also been supported by NSF Grant CCR-92-11541 and by a Sloan Research Fellowship. Work on this paper by János Pach, Richard Pollack, and Micha Sharir has been supported by NSF Grants CCR-91-22103 and CCR-94-24398. Work by János Pach was also supported by Grant OTKA-4269 and by a CUNY Research Award. Work by Richard Pollack was also supported by NSF Grants CCR-94-02640 and DMS-94-00293. Work by Micha Sharir was also supported by NSF Grant CCR-93-11127, by a Max-Planck Research Award, and by grants from the Israel Science Fund administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development. Part of the work on this paper was done during the participation of the first four authors in the Special Semester on Computational and Combinatorial Geometry organized by the Mathematical Research Institute of Tel Aviv University, Spring 1995.     

Coincidence Points and Invariant Approximation Results for Multimaps

Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either extended or improved.     

Label placement by maximum independent set in rectangles

Motivated by the problem of labeling maps, we investigate the problem of computing a large non-intersecting subset in a set of n rectangles in the plane. Our results are as follows. In O(n log n) time, we can find an O(log n)-factor approximation of the maximum subset in a set of n arbitrary axis-parallel rectangles in the plane. If all rectangles have unit height, we can find a 2-approximation in O(n log n) time. Extending this result, we obtain a (1 + 1/k)-approximation in time O(n log n + n^2k−1) time, for any integer k ≥ 1.