In the field of phytohormone defense, the general perception is that salicylate (SA)-mediated defense is induced against biotrophic pathogens while jasmonate (JA)-mediated defense functions against necrotrophic pathogens. Our goals were to observe the behavior of the necrotrophic pathogen Rhizoctonia solani in the vicinity, on the surface, and within the host tissue after priming the host with SA or JA, and to see if priming with these phytohormones would affect the host defense differently upon infection. It was observed for the first time, that R. solani could not only distinguish between JA versus SA-primed tomato plants from a distance, but surprisingly avoided SA-primed plants more than JA-primed plants. To corroborate these findings, early infection events were monitored and compared through microscopy, Scanning Electron Microscopy, and Confocal Laser Scanning Microscopy using transformed R. solani expressing green fluorescence protein gene (gfp). Different histochemical and physiological parameters were compared between the unprimed control, JA-primed, and SA-primed plants after infection. The expression of a total of fifteen genes, including the appressoria-related gene of the pathogen and twelve marker genes functioning in the SA and JA signaling pathways, were monitored over a time course during early infection stages. R. solani being traditionally designated as a necrotroph, the major unexpected observations were that Salicylate priming offered better tolerance than Jasmonate priming and that it was mediated through the activation of SA-mediated defense during the initial phase of infection, followed by JA-mediated defense in the later phase. Hence, the present scenario of biphasic SA-JA defense cascades during R. solani infection, with SA priming imparting maximum tolerance, indicate a possible hemibiotrophic pathosystem that needs to be investigated further.
Geodesic motion has significant characteristics of space-time. We calculate the principle Lyapunov exponent (LE), which is the inverse of the instability timescale associated with this geodesics and Kolmogorov–Senai (KS) entropy for our rotating Kerr–Kiselev (KK) black hole. We have investigate the existence of stable/unstable equatorial circular orbits via LE and KS entropy for time-like and null circular geodesics. We have shown that both LE and KS entropy can be written in terms of the radial equation of innermost stable circular orbit (ISCO) for time-like circular orbit. Also, we computed the equation marginally bound circular orbit, which gives the radius (smallest real root) of marginally bound circular orbit (MBCO). We found that the null circular geodesics has larger angular frequency than time-like circular geodesics ($$Q_o > Q_{\sigma }$$ Q o > Q σ ). Thus, null-circular geodesics provides the fastest way to circulate KK black holes. Further, it is also to be noted that null circular geodesics has shortest orbital period $$(T_{photon}< T_{ISCO})$$ ( T photon < T ISCO ) among the all possible circular geodesics. Even null circular geodesics traverses fastest than any stable time-like circular geodesics other than the ISCO.
We derive proper time Lyapunov exponent [Formula: see text] and coordinate time Lyapunov exponent [Formula: see text] for a regular Hayward class of black hole. The proper time corresponds to [Formula: see text] and the coordinate time corresponds to [Formula: see text], where [Formula: see text] is measured by the asymptotic observers both for Hayward black hole and for special case of Schwarzschild black hole. We compute their ratio as [Formula: see text] for time-like geodesics. In the limit of [Formula: see text] that means for Schwarzschild black hole this ratio reduces to [Formula: see text]. Using Lyapunov exponent, we investigate the stability and instability of equatorial circular geodesics. By evaluating the Lyapunov exponent, which is the inverse of the instability time scale, we show that, in the eikonal limit, the real and imaginary parts of quasi-normal modes (QNMs) is specified by the frequency and instability time scale of the null circular geodesics. Furthermore, we discuss the unstable photon sphere and radius of shadow for this class of black hole.
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