Mathematicshttp://repository.iitgn.ac.in/handle/123456789/5472018-04-22T18:24:25Z2018-04-22T18:24:25ZInformation-sharing and decision-making in networks of radiation detectorsYadav, IndrajeetPahlajani, Chetan D.Tanner, Herbert G.Poulakakis, Ioannishttp://repository.iitgn.ac.in/handle/123456789/34932018-02-28T12:17:20Z2018-02-01T00:00:00ZInformation-sharing and decision-making in networks of radiation detectors
Yadav, Indrajeet; Pahlajani, Chetan D.; Tanner, Herbert G.; Poulakakis, Ioannis
A network of sensors observes a time-inhomo-geneous Poisson signal and within a fixed time interval has to decide between two hypotheses regarding the signal’s intensity. The paper reveals an interplay between network topology, essentially determining the quantity of information available to different sensors, and the quality of individual sensor information as captured by the sensor’s likelihood ratio. Armed with analytic expressions of bounds on the error probabilities associated with the binary hypothesis test regarding the intensity of the observed signal, the insight into the interplay between sensor communication and data quality helps in deciding which sensor is better positioned to make a decision on behalf of the network, and links the analysis to network centrality concepts. The analysis is illustrated on networked radiation detection examples, first in simulation and then on cases utilizing field measurement data available through a U.S. Domestic Nuclear Detection Office (dndo) database.
2018-02-01T00:00:00ZFrobenius number and minimal presentation of certain numerical semigroupsMehta, RanjanaSaha, JoydipSengupta, Indranathhttp://repository.iitgn.ac.in/handle/123456789/34832018-02-25T12:16:54Z2018-02-01T00:00:00ZFrobenius number and minimal presentation of certain numerical semigroups
Mehta, Ranjana; Saha, Joydip; Sengupta, Indranath
Suppose e≥4 be an integer, a=e+1, b>a+(e−3)d, gcd(a,d)=1 and d∤(b−a). Let M={a,a+d,a+2d,…,a+(e−3)d,b,b+d}, which forms a minimal generating set for the numerical semigroup Γe(M), generated by the set M. We calculate the Ap\'{e}ry set and the Frobenius number of Γe(M). We also show that the minimal number of generators for the defining ideal p of the affine monomial curve parametrized by X0=ta, X1=ta+d,…,Xe−3=ta+(e−3)d, Xe−2=tb, Xe−1=tb+d is a bounded function of e.
2018-02-01T00:00:00ZAbel–Tauber process and asymptotic formulasBanerjee, D.Chakraborty, K.Kanemitsu, S.Maji, Bibekanandahttp://repository.iitgn.ac.in/handle/123456789/34722018-02-21T13:07:33Z2018-02-01T00:00:00ZAbel–Tauber process and asymptotic formulas
Banerjee, D.; Chakraborty, K.; Kanemitsu, S.; Maji, Bibekananda
The Abel-Tauber process consists of the Abelian process of forming the Riesz sums and the subsequent Tauberian process of differencing the Riesz sums, an analogue of the integration-differentiation process. In this article, we use the Abel-Tauber process to establish an interesting asymptotic expansion for the Riesz sums of arithmetic functions with best possible error estimate. The novelty of our paper is that we incorporate the Selberg type divisor problem in this process by viewing the contour integral as part of the residual function. The novelty also lies in the uniformity of the error term in the additional parameter which varies according to the cases. Generalization of the famous Selberg Divisor problem to arithmetic progression has been made by Rieger [Zum Teilerproblem von Atle Selberg. Math. Nachr. 30 (1965), 181-192], Marcier [Sums of the form Σ g(n)/f(n). Canad. Math. Bull. 24 (1981), 299-307], Nakaya [On the generalized division problem in arithmetic progressions. Sci. Rep. Kanazawa Univ. 37 (1992), 23-47] and around the same time Nowak [Sums of reciprocals of general divisor functions and the Selberg division problem, Abh. Math. Sem. Univ. Hamburg 61 (1991), 163-173] studied the related subject of reciprocals of an arithmetic function and obtained an asymptotic formula with the Vinogradov-Korobov error estimate with the main term as a finite sum of logarithmic terms. We shall also elucidate the situation surrounding these researches and illustrate our results by rich examples.
2018-02-01T00:00:00ZGeneralized Lambert series, Raabe's integral and a two-parameter generalization of Ramanujan's formula for ζ(2m+1)Dixit, AtulGupta, RajatKumar, RahulMaji, Bibekanandahttp://repository.iitgn.ac.in/handle/123456789/34602018-02-15T09:50:58Z2018-01-01T00:00:00ZGeneralized Lambert series, Raabe's integral and a two-parameter generalization of Ramanujan's formula for ζ(2m+1)
Dixit, Atul; Gupta, Rajat; Kumar, Rahul; Maji, Bibekananda
A comprehensive study of the generalized Lambert series ∑n=1∞nN−2hexp(−anNx)1−exp(−nNx),0<a≤1, x>0, N∈N and h∈Z, is undertaken. Two of the general transformations of this series that we obtain here lead to two-parameter generalizations of Ramanujan's famous formula for ζ(2m+1), m>0 and the transformation formula for logη(z). Numerous important special cases of our transformations are derived. An identity relating ζ(2N+1),ζ(4N+1),⋯,ζ(2Nm+1) is obtained for N odd and m∈N. Certain transcendence results of Zudilin- and Rivoal-type are obtained for odd zeta values and generalized Lambert series. A criterion for transcendence of ζ(2m+1) and a Zudilin-type result on irrationality of Euler's constant γ are also given. New results analogous to those of Ramanujan and Klusch for N even, and a transcendence result involving ζ(2m+1−1N), are obtained.
2018-01-01T00:00:00Z