Although Madhava's Rogaviniscaya commonly referred to as Madhavanidana, is largely based on earlier treatises, it has a stamp of its own, by virtue of its description of new diseases absent from earlier works. For instance, two diseases viz., 1) Sula 2) visphota are recognised as independent entities for the first time by Madhava. The description of the dosic type of Sula more extensive than th...

Inequalities are obtained for quadrature rules in terms of upper and lower bounds of the first derivative of the integrand. Bounds of Ostrowski type quadrature rules are obtained and the classical Iyengar inequality for the trapezoidal rule is recaptured as a special case. Applications to numerical integration are demonstrated.

Variance and Fisher information are ingredients of the Cram er-Rao inequality. Fisher information is regarded as a Riemannian metric on a quantum statistical manifold and we choose monotonicity under coarse graining as the fundamental property. The quadratic cost functions are in a dual relation with the Fisher information quantities and they reduce to the variance in the commuting case. The sc...

A unified approach is presented for establishing a broad class of Cramér-Rao inequalities for the location parameter, including, as special cases, the original inequality of Cramér and Rao, as well as an L version recently established by the authors. The new approach allows for generalized moments and Fisher information measures to be defined by convex functions that are not necessarily homogen...

Inequalities are obtained for weighted integrals in terms of bounds involving the first derivative of the function. Quadrature rules are obtained and the classical Iyengar inequality for the trapezoidal rule is recaptured as a special case when the weight function w (x) ≡ 1. Applications to numerical integration are demonstrated.

In the present work, we show how the generalized Cramér-Rao inequality for the estimation of a parameter, presented in a recent paper, can be extended to the mutidimensional case with general norms on Rn, and to a wider context. As a particular case, we obtain a new multidimensional Cramér-Rao inequality which is saturated by generalized q-Gaussian distributions. We also give another related Cr...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this short note, we give an Iyengar-type inequality involving quadratures in n knots, where n is an arbit...

Multiresolution Decomposition' L. Prasad, S.S. Iyengar, R. Rao Department of Computer Science Louisiana State University R.L. Kashyap School of Electrical Engineering Purdue University Abstract This paper proposes a method of appl ing the idea of multiresolution to the probyem of fault-tolerant integration of abstract sensor estimates when the number of sensors is very lar e and a large number ...