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NEW BOUNDS FOR A PERTURBED GENERALIZED TAYLOR'S FORMULA
Cerone, P.,Dragomir, S.S. The Youngnam Mathematical Society Korea 2001 East Asian mathematical journal Vol.17 No.2
A generalised Taylor series with integral remainder involving a convex combination of the end points of the interval under consideration is investigated. Perturbed generalised Taylor series are bounded in terms of Lebesgue p-norms on $[a,b]^2$ for $f_{\Delta}:[a,b]^2{\rightarrow}\mathbb{R}$ with $f_{\Delta}(t,s)=f(t)-f(s)$.
CERONE, P.,DRAGOMIR, S.S.,ROUMELIOTIS, J. The Honam Mathematical Society 1999 호남수학학술지 Vol.21 No.1
An inequality of Ostrowski type for twice differentiable mappings whose derivatives belong to $L_{1}(a,\;b)$ and applications in Numerical Integration and for special means (logarithmic mean, identric mean, p-logarithmic mean etc...) are given.
ON SOME INEQUALITIES FOR THE EXPECTATION AND VARIANCE
Cerone, P.,Dragomir, S.S. 한국전산응용수학회 2001 The Korean journal of computational & applied math Vol.8 No.2
A variety bounds are obtained for the variance and expectation of a continuous random variable whose p.d.f. is defined over a finite interval. Previous results are shown to be particular cases of the current more general development. AMS Mathematics Subject Classification : 26D15, 65Xxx
Dragomir, S . S .,Roumeliotis, J .,Cerone, P . 호남수학회 1999 호남수학학술지 Vol.21 No.1
An inequality of Ostrowski type far twice differentiable mappings whose derivatives belong to L₁(a, b) and applications in Numerical Integration and for special means (logarithmic mean, identric mean, p-logarithmic mean etc...) are given.
DISCRETE CHEBYCHEV FOR MEANS OF SEQUENCES OF DIFFERENT LENGTHS
Cerone, P.,Dragomir, S.S.,Mills, T.M. The Youngnam Mathematical Society Korea 2005 East Asian mathematical journal Vol.21 No.2
Bounds for discrete Chebychev functionals that involve means of sequences of different lengths are investigated in the current article. Earlier bounds for the Chebychev functional involving sums of sequences of the same lengths are utilised in the current development. Weighted generalised Chebychev functionals are also examined.
Characterization of the LIGO detectors during their sixth science run
Aasi, J,Abadie, J,Abbott, B P,Abbott, R,Abbott, T,Abernathy, M R,Accadia, T,Acernese, F,Adams, C,Adams, T,Adhikari, R X,Affeldt, C,Agathos, M,Aggarwal, N,Aguiar, O D,Ajith, P,Allen, B,Allocca, A,Ceron IOP Publishing 2015 Classical and quantum gravity Vol.32 No.11
<P>In 2009-2010, the Laser Interferometer Gravitational-Wave Observatory (LIGO) operated together with international partners Virgo and GEO600 as a network to search for gravitational waves (GWs) of astrophysical origin. The sensitivity of these detectors was limited by a combination of noise sources inherent to the instrumental design and its environment, often localized in time or frequency, that couple into the GW readout. Here we review the performance of the LIGO instruments during this epoch, the work done to characterize the detectors and their data, and the effect that transient and continuous noise artefacts have on the sensitivity of LIGO to a variety of astrophysical sources.</P>
Abadie, J.,Abbott, B. P.,Abbott, R.,Abbott, T. D.,Abernathy, M.,Accadia, T.,Acernese, F.,Adams, C.,Adhikari, R. X.,Affeldt, C.,Agathos, M.,Agatsuma, K.,Ajith, P.,Allen, B.,Ceron, E. Amador,Amariutei, IOP Publishing 2012 The Astrophysical journal Vol.760 No.1
<P>We present the results of a search for gravitational waves associated with 154 gamma-ray bursts (GRBs) that were detected by satellite-based gamma-ray experiments in 2009-2010, during the sixth LIGO science run and the second and third Virgo science runs. We perform two distinct searches: a modeled search for coalescences of either two neutron stars or a neutron star and black hole, and a search for generic, unmodeled gravitational-wave bursts. We find no evidence for gravitational-wave counterparts, either with any individual GRB in this sample or with the population as a whole. For all GRBs we place lower bounds on the distance to the progenitor, under the optimistic assumption of a gravitational-wave emission energy of 10(-2) M-circle dot c(2) at 150 Hz, with a median limit of 17 Mpc. For short-hard GRBs we place exclusion distances on binary neutron star and neutron-star-black-hole progenitors, using astrophysically motivated priors on the source parameters, with median values of 16 Mpc and 28 Mpc, respectively. These distance limits, while significantly larger than for a search that is not aided by GRB satellite observations, are not large enough to expect a coincidence with a GRB. However, projecting these exclusions to the sensitivities of Advanced LIGO and Virgo, which should begin operation in 2015, we find that the detection of gravitational waves associated with GRBs will become quite possible.</P>
INTEGRAL INEQUALITIES AND APPLICATIONS FOR BOUNDING THE ${\check{C}}EBY{\check{S}}EV$ FUNCTIONAL
Cerone, P.,Dragomir, S.S. The Youngnam Mathematical Society Korea 2007 East Asian mathematical journal Vol.23 No.2
Some inequalities related to the $H{\ddot{o}}lder$ integral inequality and applications for bounding the ${\check{C}}eby{\check{s}}ev$ functional are given.
P. Cerone ..et al. KYUNGPOOK UNIVERSITY 1999 Kyungpook mathematical journal Vol.39 No.2
In this paper we derive a new integral inequality of Ostrowski-Gruss type and apply it to estimate the error bounds for some numerical quadrature rules.