Graphically balanced equilibria and stationary measures of reaction networks

The graph-related symmetries of a reaction network give rise to certain special equilibria (such as complex balanced equilibria) in deterministic models of dynamics of the reaction network. Correspondingly, in the stochastic setting, when modeled as a continuous time Markov chain, these symmetries give rise to certain special stationary measures. Previous work by Anderson, Craciun, and Kurtz [Bull Math. Biol., 72 (2010), pp. 1947-1970] identified stationary distributions of a complex balanced network; later, Cappelletti and Wiuf [SIAM J. Appl. Math., 76 (2016), pp. 411-432] developed the notion of complex balancing for stochastic systems. We define and establish the relations between reaction balanced measure, complex balanced measure, reaction vector balanced measure, and cycle balanced measure and prove that with mild additional hypotheses, the former two are stationary distributions. Furthermore, in the spirit of an earlier work by Joshi [Discrete Contin. Dyn. Syst. Ser. B, 20 (2015), pp. 1077-1105] we give sufficient conditions under which detailed balance of the stationary distribution of Markov chain models implies the existence of positive detailed balance equilibria for the related deterministic reaction network model. Finally, we provide a complete map of the implications between balancing properties of deterministic and corresponding stochastic reaction systems, such as complex balance, reaction balance, reaction vector balance, and cycle balance

A complete radio study of SNR G15.4+0.1 from new GMRT observations

The supernova remnant G15.4+0.1 is considered to be the possible counterpart of the gamma-ray source HESSJ1818-154. With the goal of getting a complete view of this remnant and understanding the nature of the gamma-ray flux, we conducted a detailed radio study that includes the search for pulsations and a model of the broadband emission for the G15.4+0.1/HESSJ1818-154 system. Low-frequency imaging at 624 MHz and pulsar observations at 624 and 1404 MHz towards G15.4+0.1 were carried out with the Giant Metrewave Radio Telescope (GMRT). We correlated the new radio data with observations of the source at X-ray and infrared wavelengths from XMM-Newton and Herschel observatories, respectively. To characterize the neutral hydrogen medium (HI) towards G15.4+0.1, we used data from the Southern Galactic Plane Survey. We modelled the spectral energy distribution using both hadronic and leptonic scenarios. From the combination of the new GMRT observations with existing data, we derived a continuum spectral index alpha=-0.62+-0.03 for the whole remnant. The local synchrotron spectra of G15.4+0.1, calculated from the combination of the GMRT data with 330 MHz observations from the VLA, tends to be flatter in the central part of the remnant, accompanying the region where the blast wave is impinging molecular gas. No spectral index trace was found indicating the radio counterpart to the pulsar wind nebula proposed from X-ray observations. In addition, the search for radio pulsations yielded negative results. Emission at far-infrared wavelengths is observed in the region where the SNR shock is interacting with dense molecular clumps. We also identified HI features forming a shell that wraps most of the outer border of G15.4+0.1. Characteristic parameters were estimated for the shocked HI gas. We found that either a purely hadronic or leptonic model is compatible with the broadband emission known so far.Comment: 11 pages, 9 figures, accepted for publication in Astronomy & Astrophysic

North-South Distribution of Solar Flares during Cycle 23

In this paper, we investigate the spatial distribution of solar flares in the northern and southern hemisphere of the Sun that occurred during the period 1996 to 2003. This period of investigation includes the ascending phase, the maximum and part of descending phase of solar cycle 23. It is revealed that the flare activity during this cycle is low compared to previous solar cycle, indicating the violation of Gnevyshev-Ohl rule. The distribution of flares with respect to heliographic latitudes shows a significant asymmetry between northern and southern hemisphere which is maximum during the minimum phase of the solar cycle. The present study indicates that the activity dominates the northern hemisphere in general during the rising phase of the cycle (1997-2000). The dominance of northern hemisphere is shifted towards the southern hemisphere after the solar maximum in 2000 and remained there in the successive years. Although the annual variations in the asymmetry time series during cycle 23 are quite different from cycle 22, they are comparable to cycle 21.Comment: 6 pages, 2 figures, 1 table; Accepted for the publication in the proceedings of international solar workshop held at ARIES, Nainital, India on "Transient Phenomena on the Sun and Interplanetary Medium" in a special issue of "Journal of Astrophysics and Astronomy (JAA)

Connections between normalized Wright functions with families of analytic functions with negative coefficients

In this article we present sufficient conditions that ensures that normalized Wright functions belong to certain subclasses of analytic univalent functions with negative coefficients in the unit disc U. We also provide some geometric properties of integral transforms involving normalized Wright functions

Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations

The truncation method is a collective name for techniques that arise from truncating a Laurent series expansion (with leading term) of generic solutions of nonlinear partial differential equations (PDEs). Despite its utility in finding Backlund transformations and other remarkable properties of integrable PDEs, it has not been generally extended to ordinary differential equations (ODEs). Here we give a new general method that provides such an extension and show how to apply it to the classical nonlinear ODEs called the Painleve equations. Our main new idea is to consider mappings that preserve the locations of a natural subset of the movable poles admitted by the equation. In this way we are able to recover all known fundamental Backlund transformations for the equations considered. We are also able to derive Backlund transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages

Gravitational collapse of an isentropic perfect fluid with a linear equation of state

We investigate here the gravitational collapse end states for a spherically symmetric perfect fluid with an equation of state $p=k\rho$. It is shown that given a regular initial data in terms of the density and pressure profiles at the initial epoch from which the collapse develops, the black hole or naked singularity outcomes depend on the choice of rest of the free functions available, such as the velocities of the collapsing shells, and the dynamical evolutions as allowed by Einstein equations. This clarifies the role that equation of state and initial data play towards determining the final fate of gravitational collapse.Comment: 7 Pages, Revtex4, To appear in Classical and Quantum Gravit

Structure Related to Morphine

Synthesis of 2-N-heptyl-5,9-dimethyl-6,7-benzomorphan from 3,4-lutidine was effected in three step process and only a-form could be obtained through phosphoric acid cyclisation. This a-form of benzomorphan was converted in three steps to a-2N-hepthyl-2-hydroxy-5,9-dimethyl-6,7-benzomorphan, which was also synthesised from alternative route. Infrared spectrum of the base confirmed the presence of a-from