7,107 research outputs found
Optimal error estimates of a mixed finite element method for\ud parabolic integro-differential equations with non smooth initial data
In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments and without using parabolic type duality technique, optimal L2-error estimates are derived for semidiscrete approximations, when the initial data is in L2. Due to the presence of the integral term, it is, further, observed that estimate in dual of H(div)-space plays a role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof technique used for deriving optimal error estimates of finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, the proposed analysis can be easily extended to other mixed method for PIDE with rough initial data and provides an improved result
CSPOB-Continuous Spectrophotometry of Black Holes
The goal of a small and dedicated satellite called the "Continuous
Spectro-Photometry of Black Holes" or CSPOB is to provide the essential tool
for the theoretical understanding of the hydrodynamic and magneto-hydrodynamic
flows around black holes. In its life time of about three to four years, only a
half a dozen black holes will be observed continuously with a pair of CSPOBs.
Changes in the spectral and temporal variability properties of the high-energy
emission would be caught as they happen. Several important questions are
expected to be answered and many puzzles would be sorted out with this mission.Comment: 4 Pages, 3 Figures, Proceeding of the 2nd Kolkata Conference on
"Observational Evidence for the Black Holes in the Universe", Published in
AIP, 200
Mass function and dynamical study of the open clusters Berkeley 24 and Czernik 27
We present a photometric study of the open clusters Berkeley 24 (Be
24) and Czernik 27 (Cz 27). The radii of the clusters are determined as
2\farcm7 and 2\farcm3 for Be 24 and Cz 27, respectively. We use the Gaia Data
Release 2 (GDR2) catalogue to estimate the mean proper motions for the
clusters. We found the mean proper motion of Be 24 as mas
yr and mas yr in right ascension and declination
for Be 24 and mas yr and mas yr for
Cz 27. We used probable cluster members selected from proper motion data for
the estimation of fundamental parameters. We infer reddenings =
mag and mag for the two clusters. Analysis of
extinction curves towards the two clusters show that both have normal
interstellar extinction laws in the optical as well as in the near-IR band.
From the ultraviolet excess measurement, we derive metallicities of [Fe/H]=
dex and dex for the clusters Be 24 and Cz 27,
respectively. The distances, as determined from main sequence fitting, are
kpc and kpc. The comparison of observed CMDs with
isochrones, leads to an age of Gyr and Gyr for
Be 24 and Cz 27, respectively.
In addition to this, we have also studied the mass function and dynamical
state of these two clusters for the first time using probable cluster members.
The mass function is derived after including the corrections for data
incompleteness and field star contamination. Our analysis shows that both
clusters are now dynamically relaxedComment: 16 pages including 8 tables. 22 figures. Accepted by MNRA
Bilinear generating relations for a family of q-polynomials and generalized basic hypergeometric functions
In this paper, we derive a bilinear q-generating function involving basic analogue of Fox's H-function and a general class of q-hypergeometric polynomials. Applications of the main results are also illustrated
Certain Expansion Formulae Involving a Basic Analogue of Fox’s H-Function
Certain expansion formulae for a basic analogue of the Fox’s H-function have been derived by the applications of the q-Leibniz rule for the Weyl type q-derivatives of a product of two functions. Expansion formulae involving a basic analogue of Meijer’s G-function and MacRobert’s E-function have been derived as special cases of the main results
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