The Lax conjecture is true

In 1958 Lax conjectured that hyperbolic polynomials in three variables are determinants of linear combinations of three symmetric matrices. This conjecture is equivalent to a recent observation of Helton and Vinnikov.Comment: 7 pages, Proceedings to the AMS, to appear. Added background materia

Experimental Evidence of Time Delay Induced Death in Coupled Limit Cycle Oscillators

Experimental observations of time delay induced amplitude death in a pair of coupled nonlinear electronic circuits that are individually capable of exhibiting limit cycle oscillations are described. In particular, the existence of multiply connected death islands in the parameter space of the coupling strength and the time delay parameter for coupled identical oscillators is established. The existence of such regions was predicted earlier on theoretical grounds in [Phys. Rev. Lett. 80, 5109 (1998); Physica 129D, 15 (1999)]. The experiments also reveal the occurrence of multiple frequency states, frequency suppression of oscillations with increased time delay and the onset of both in-phase and anti-phase collective oscillations.Comment: 4 aps formatted RevTeX pages; 6 figures; to appear in Phys. Rev. Let

Design of an Implantable Device for Ocular Drug Delivery

Ocular diseases, such as, glaucoma, age-related macular degeneration (AMD), diabetic retinopathy, and retinitis pigmentosa require drug management in order to prevent blindness and affecting million of adults in USA and worldwide. There is an increasing need to develop devices for drug delivery to address ocular diseases. This study focuses on the design, simulation, and development of an implantable ocular drug delivery device consisting of micro-/nanochannels embedded between top and bottom covers with a drug reservoir made from polydimethylsiloxane (PDMS) which is silicon-based organic and biodegradable polymer. Several simulations were carried out with six different micro-channel configurations in order to see the feasibility for ocular drug delivery applications. Based on the results obtained, channel design of osmotic I and osmotic II satisfied the diffusion rates required for ocular drug delivery. Finally, a prototype illustrating the three components of the drug delivery design is presented. In the future, the device will be tested for its functionality and diffusion characteristics

Strong duality in conic linear programming: facial reduction and extended duals

The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$(P) \sup {<c, x> | Ax \leq_K b}$$ in the absence of any constraint qualification. The facial reduction algorithm solves a sequence of auxiliary optimization problems to obtain such a dual. Ramana's dual is applicable when (P) is a semidefinite program (SDP) and is an explicit SDP itself. Ramana, Tuncel, and Wolkowicz showed that these approaches are closely related; in particular, they proved the correctness of Ramana's dual using certificates from a facial reduction algorithm. Here we give a clear and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual: -- we state a simple facial reduction algorithm and prove its correctness; and -- building on this algorithm we construct a family of extended duals when $K$ is a {\em nice} cone. This class of cones includes the semidefinite cone and other important cones.Comment: A previous version of this paper appeared as "A simple derivation of a facial reduction algorithm and extended dual systems", technical report, Columbia University, 2000, available from http://www.unc.edu/~pataki/papers/fr.pdf Jonfest, a conference in honor of Jonathan Borwein's 60th birthday, 201

Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling

Small lattices of $N$ nearest neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied, and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in N=2 case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case $N>2$. Bifurcations found include inverse and direct Hopf and fold limit cycle bifurcations. Typical dynamics for different small time-lags and coupling intensities could be excitable with a single globally stable equilibrium, asymptotic oscillatory with symmetric limit cycle, bi-stable with stable equilibrium and a symmetric limit cycle, and again coherent oscillatory but non-symmetric and phase-shifted. For an intermediate range of time-lags inverse sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo oscillators with the same type of coupling.Comment: accepted by Phys.Rev.

Effect of organic farming practices on soil and performance of soybean (Glycine max) under semi-arid tropical conditions in Central India

A field experiment was conducted to evaluate the influence of organic farming practices on soil health and crop performance of Soybean (Glycine max).The crop cultivar JS-335 of soybean was grown with 30:26.2:16.6 kg ha-1 (NPK) recommended dose of fertilizers under three management practices viz., organic, chemical and integrated (50:50) in randomized block design, replicated three times. Soil organic carbon, available N, P and K, microbial enzymatic activities, total biomass, seed yield and harvest index (HI) were analysed during the study. It was observed that soil organic carbon (11.3 g kg-1), available N (125 mg kg-1), P (49.7 mg kg-1) and soil enzyme activities viz., dehydrogenase (DHA) (98.20 µ grams TPF/g soil/24 h) and alkaline phosphatase (178.2 µ grams p-nitro phenol/g soil/h) were found significantly higher in the plot managed organically while available K (320.1 mg kg-1) was not significant with respect to chemical and integrated practices. The total biomass (1927 kg ha-1) and seed yield (601 kg ha-1) of soybean was found highest in organic farming practices followed by integrated and chemical practices. Very poor microbial activities were observed in chemically managed plots. Thus, the study demonstrated that the organic farming practice improved soil health and performance of soybean crop

Thermodynamic structure of the Atmospheric Boundary Layer over the Arabian Sea and the Indian Ocean during pre-INDOEX and INDOEX-FFP campaigns

Spatial and temporal variability of the Marine Atmospheric Boundary Layer (MABL) height for the Indian Ocean Experiment (INDOEX) study period are examined using the data collected through Cross-chained LORAN (Long-Range Aid to Navigation) Atmospheric Sounding System (CLASS) launchings during the Northern Hemispheric winter monsoon period. This paper reports the results of the analyses of the data collected during the pre-INDOEX (1997) and the INDOEX-First Field Phase (FFP; 1998) in the latitude range 14&amp;deg;N to 20&amp;deg;S over the Arabian Sea and the Indian Ocean. Mixed layer heights are derived from thermodynamic profiles and they indicated the variability of heights ranging from 400m to 1100m during daytime depending upon the location. Mixed layer heights over the Indian Ocean are slightly higher during the INDOEX-FFP than the pre-INDOEX due to anomalous conditions prevailing during the INDOEX-FFP. The trade wind inversion height varied from 2.3km to 4.5km during the pre-INDOEX and from 0.4km to 2.5km during the INDOEX-FFP. Elevated plumes of polluted air (lofted aerosol plumes) above the marine boundary layer are observed from thermodynamic profiles of the lower troposphere during the INDOEX-FFP. These elevated plumes are examined using 5-day back trajectory analysis and show that one group of air mass travelled a long way from Saudi Arabia and Iran/Iraq through India before reaching the location of measurement, while the other air mass originates from India and the Bay of Bengal