arXiv subjects
Publications and source records attributed to Pankaj Jain.
The main aim of this paper to provide several scales of equivalent conditions for the bilinear Hardy inequalities in the case $1< q, p_1, p_2<\infty$ with $q \geq \max(p_1,p_2)$.
We obtain a pointwise description of functions belonging to function spaces with the lattice property. In particular, it is valid for Banach function spaces provided that the Hardy-Littlewood maximal operator is bounded. We also study weighted grand Sobolev spaces, defined on arbitrary open sets (of finite or infinite measure), and provide pointwise description of them.
In this paper, the $L^p_v(\R)$-boundedness of the Dunkl-Hausdorff operator $\displaystyle H_{\al,ϕ} f(x)=\ent\frac{ |ϕ(t)|}{|t|^{2\al+2}}f\lf(\frac{x}{t}\rh) dt $ has been characterized and for a certain type of weight $v$, the precise value of the norm $\|H_{\al,ϕ}\|_{L^p_v(\R)\to L^p_v(\R)}$ has been obtained. This covers several of the existing results. Analogous results in two dimensions have also been proved.
In this paper, we have derived certain classical inequalities, namely, Young's, Hölder's, Minkowski's and Hermite-Hadamard inequalities for pseudo-integral (also known as $g$-integral). For Young's, Hölder's, Minkowski's inequalities, both the cases $p>1$ as well as $p<1,\,p\ne 0$ have been covered. Moreover, in the case of Hermite-Hadamard inequality, a refinement has also been proved and as a special case, $g$-analogue of geometric-logarithmic-arithmetic inequality has been deduced.
We have analyzed AstroSat observations of the galactic micro-quasar system GRS 1915+105, when the system exhibited C-type Quasi-periodic Oscillations (QPOs) in the frequency range of 3.4-5.4 Hz. The broad band spectra (1-50 keV) obtained from simultaneous LAXPC and SXT can be well described by a dominant relativistic truncated accretion disk along with thermal Comptonization and reflection. We find that while the QPO frequency depends on the inner radii with a large scatter, a much tighter correlation is obtained when both the inner radii and accretion rate of the disk are taken into account. In fact, the frequency varies just as the dynamic frequency (i.e. the inverse of the sound crossing time) as predicted decades ago by the relativistic standard accretion disk theory for a black hole with spin parameter of ~0.9. We show that this identification has been possible due to the simultaneous broad band spectral coverage with temporal information as obtained from AstroSat.
We introduce a pixel space method to detect dipole modulation or hemispherical power asymmetry in the cosmic microwave background (CMB) polarization. The method relies on the use of squared total polarized flux whose ensemble average picks up a dipole due to the dipole modulation in the CMB polarization. The method is useful since it can be applied easily to partial sky. We define several statistics to characterize the amplitude of the detected signal. By simulations we show that the method can be used to reliably extract the signal at 2.7$σ$ level or higher in future CORE-like missions, assuming that the signal is present in the CMB polarization at the level detected by the Planck mission in the CMB temperature. An application of the method to the 2018 Planck data does not detect a significant effect, when taking into account the presence of correlated detector noise and residual systematics in data. Using the FFP10 we find the presence of a very strong bias which might be masking any real effect.
We study the collider, astrophysical and cosmological constraints on the dark matter sector of a conformal model within the framework of both the freeze out as well as the freeze in mechanism. The model has a dark sector with strong self interactions. This sector couples weakly with the Standard Model (SM) particles via a scalar messenger. The lightest dark sector particle is a pion-like fermion anti-fermion bound state. We find that the model successfully satisfies the constraints coming from the Higgs decay to the visible as well as the invisible sector. We have used the results of the dark matter direct detection experiments, such as, XENON1T in order to impose bounds on the parameters of the model. The model satisfies the indirect detection constraints of gamma ray from the galactic center and Dwarf spheroidal galaxies. We also determine the parameter range for which it satisfies the astrophysical constraints on the dark matter self coupling.
We explore the large to moderate scale anisotropy in distant radio sources using the TGSS ADR1 catalog. We use different measures, i.e. number counts, sky brightness and flux per source, for this study. In agreement with earlier results, we report a significant excess of clustering signal above the angular scale of roughly $10$ degrees (i.e. $l\lessapprox 20-30$). We find that some survey areas have a systematically low/high flux and argue this may be the cause of the observed signal of excess power at low multipoles. With mocks we demonstrate the effect of such large scale flux systematics and recover TGSS like excess clustering signal by assuming $20\%$ flux uncertainties over $\sim 10^\circ \times 10^\circ$ size patches. We argue that that TGSS at this stage, i.e. TGSS ADR1, is not suitable for large scale clustering measurements. We find that the measure, flux per source, shows evidence of isotropy for all multipoles $l > 2$ despite the presence of systematics in the data.
We study precession dynamics of generic binary black holes in eccentric orbits using an effective potential based formalism derived in [M. Kesden et al., PRL {\bf 114}, 081103 (2015)]. This effective potential is used to classify binary black holes into three mutually exclusive spin morphologies. During the inspiral phase, binaries make transitions from one morphology to others. We evolve a population of binary black holes from an initial separation of $1000\mathbf{M}$ to a final separation of $10\mathbf{M}$ using post-Newtonian accurate evolution equations. We find that, given suitable initial conditions, a binary's eccentricity can follow one of three distinct evolutionary patterns: (i) eccentricity monotonically increasing until final separation, (ii) eccentricity rising after decaying to a minimum value, and (iii) eccentricity monotonically decreasing throughout the inspiral. The monotonic growth or growth after reaching a certain minimum of eccentricity is due to the effect of 2PN spin-spin coupling. Further, we investigate the morphology transitions in eccentric binaries and find that the probability of such binaries transiting from one to other is similar to those in circular orbits, implying that eccentricity plays a sub-dominant role in spin morphology evolution of a precessing binary black hole. We, hence, argue that the morphological classification of spin precession dynamics is a robust tool to constrain the formation channels of binaries with arbitrary eccentricity as well.
We develop a general formalism to treat reflection of spherical electromagnetic waves from a spherical surface. Our main objective is interpretation of radio wave signals produced by cosmic ray interactions with Earth's atmosphere which are observed by the Antarctica based ANITA detector after reflection off the ice surface. The incident wave is decomposed into plane waves and each plane wave is reflected off the surface using the standard Fresnel formalism. For each plane wave the reflected wave is assumed to be locally a plane wave. This is a very reasonable assumption and there are no uncontrolled approximations in our treatment of the reflection phenomenon. The surface roughness effects are also included by using a simple model. We apply our formalism to the radiation produced by the balloon-borne HiCal radio-frequency (RF) transmitter. Our final results for the reflected power are found to be in good agreement with data for all elevation angles. We also study the properties of reflected radio pulses in order to study their phase relationship with direct pulses. We find that for some roughness models the pulse shape can be somewhat distorted and may be misidentified as a direct pulse. However this is a rather small effect and is unable to provide an explanation for the observed mystery events by ANITA.
We investigate weak lensing effect on cosmic microwave background (CMB) in the presence of dipole anisotropy. The approach of flat-sky approximation is considered. We determine the functions $σ_0^2$ and $σ_2^2$ that appear in expressions of the lensed CMB power spectrum in the presence of a dipole anisotropy. We determine the correction to B-mode power spectrum which is found to be appreciable at low multipoles ($l$). However, the temperature and E-mode power spectrum are not altered significantly.
We test the isotropy of radio polarization angle orientations with a robust and reliable dual frequency polarimetric survey of active galactic nuclei (AGN). We find that the polarization orientations are consistent with the assumption of isotropy for scales larger than or equal to $\sim 800$ Mpc. This provides further evidence of isotropy at large distance scales and is likely to impose strong constraints on some of the physical mechanisms that may be invoked to explain past observations of alignment of radio and optical polarizations at large distance scales.
In this work, we present a $\sim$90 ks continuous monitoring of the Galactic micro-quasar GRS 1915+105 with AstroSat when the source undergoes a major transition from a non-variable, $χ$ class (similar to radio-quiet $χ$ class) to a structured, large amplitude, periodic heartbeat state (similar to $ρ$ class). We show that such transition takes place via an intermediate state when the large-amplitude, irregular variability of the order of hundreds of seconds in the soft X-ray band turned into a 100-150 sec regular, structured, nearly periodic flares. The properties of a strong low-frequency quasi-periodic oscillations (LF QPO) in the frequency range 3-5 Hz also evolve marginally during these variability transitions. We also study time-lag and rms spectra at the QPO and harmonic component and the dynamic power spectra. We note few important differences between the heartbeat state and the $ρ$ class. Interestingly, the time-averaged LF QPO properties in the hard X-ray band is relatively stable in three states when compared to the significant evolution observed in the slow variability properties at mHz frequencies. Such relative stability of LF QPOs implies the inner disk-corona coupled accretion flow which determines the LF QPO properties, may be uninterrupted by the launch of long, large-amplitude flares.
We compute the top quark threshold contributions to the $γγ$ production at the LHC. They appear when the invariant mass of the photon pair, $M_{γγ}$ just exceeds two times the mass of the top quark and induce some feature in the $M_{γγ}$ distribution. We determine the magnitude of this threshold effect and characterize this feature with a simple empirical fitting function to show that it is possible to observe this effect at the LHC in future. We also explore some possible improvements that may enhance its significance.
We present X-ray spectral and timing behavior of Cyg X-3 as observed by AstroSat during the onset of a giant radio flare on 01-02 April 2017. Within a time-scale of few hours, the source shows a transition from the hypersoft state (HPS) to a more luminous state (we termed as the very high state) which coincides with the time of the steep rise in radio flux density by an order of magnitude. Modeling the SXT and LAXPC spectra jointly in 0.5-70.0 keV, we found that the first few hours of the observation is dominated by the HPS with no significant counts above 17 keV. Later, an additional flat powerlaw component suddenly appeared in the spectra which extends to very high energies with the powerlaw photon index of 1.49 +/- 0.04. Such a flat powerlaw component has never been reported from Cyg X-3. Interestingly the fitted powerlaw model in 25-70 keV, when extrapolated to the radio frequency, predicts the radio flux density consistent with the trend measured from RATAN-600 telescope at 11.2 GHz. This provides a direct evidence of the synchrotron origin of flat X-ray powerlaw component and the most extensive monitoring of the broadband X-ray behavior at the moment of decoupling the giant radio jet base from the compact object in Cyg X-3. Using SXT and LAXPC observations, we determine the giant flare ejection time as MJD 57845.34 +/- 0.08 when 11.2 GHz radio flux density increases from ~100 to ~478 mJy.
The hemispherical power asymmetry, observed in the CMBR data, has generally been interpreted in terms of the dipole modulation model for the temperature fluctuations. Here we point out that this model leads to several predictions, which can be directly tested in the current data. We suggest tests of the hemispherical power asymmetry both in real and multipole space. We find a significant signal of the dipole modulation model in WMAP and PLANCK data with our tests. The dipole amplitude and direction also agrees, within errors, with earlier results based on hemispherical analysis in multipole space. We also find evidence that the effective dipole modulation amplitude increases with the multipole l in the range l=2-64.
We propose a dipole modulation model for the Cosmic Microwave Background Radiation (CMBR) polarization field. We show that the model leads to correlations between l and l+1 multipoles, exactly as in the case of temperature. We obtain results for the case of TE, EE and BB correlations. An anisotropic or inhomogeneous model of primordial power spectrum which leads to such correlations in temperature field also predicts similar correlations in CMBR polarization. We analyze the CMBR temperature and polarization data in order to extract the signal of these correlation between l and l+1 multipoles. Our results for the case of temperature using the latest PLANCK data agree with those obtained by an earlier analysis. A detailed study of the correlation in the polarization data is not possible at present. Hence we restrict ourselves to a preliminary investigation in this case.
We consider an inhomogeneous model and independently an anisotropic model of primordial power spectrum in order to describe the observed hemispherical anisotropy in Cosmic Microwave Background Radiation. This anisotropy can be parametrized in terms of the dipole modulation model of the temperature field. Both the models lead to correlations between spherical harmonic coefficients corresponding to multipoles, l and l \pm 1. We obtain the model parameters by making a fit to TT correlations in CMBR data. Using these parameters we predict the signature of our models for correlations among different multipoles for the case of the TE and EE modes. These predictions can be used to test whether the observed hemispherical anisotropy can be correctly described in terms of a primordial power spectrum. Furthermore these may also allow us to distinguish between an inhomogeneous and an anisotropic model.