Department of Mathematics

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IIT Jodhpur

We consider the location-scale family of distributions, which contains many standard lifetime distributions. We give conditions under which the largest order statistic of a set of random variables with different/the same location as well as different/the same scale parameters dominates that of another set of random variables with respect to various stochastic orders. Along with general results, we consider important special cases, namely, the Feller–Pareto, generalized Pareto, Burr, exponentiated Weibull, Power generalized Weibull, generalized gamma, Half-normal and Fréchet distributions. © 2017 Elsevier Inc.

World University root node

Journal of Multivariate Analysis

On stochastic comparisons of maximum order statistics from the location-scale family of distributions

In this paper, a novel yet simple, multi-sensor fusion technique realizes in spatial domain is proposed. The core idea is to obtain the local activity features assuming that all the input images are random fields. This local activity feature matrix, which essentially incorporates the local features of the image, is then used to construct the fused image. In the penultimate step of the proposed technique, the homogeneity of the final fused image is verified by the consistency verification process. The performance of the proposed technique is validated subjectively and objectively by extensive experiments on different multi-sensor images. Furthermore, the comparative analysis with state-of-the-art methods confirmed the escalating improvement of the proposed technique. © 2001-2012 IEEE.

IEEE Sensors Journal

Multi-Sensor Fusion Based on Local Activity Measure

Evaporation rate of water is strongly influenced by energy barrier due to molecular collision and heat transfer limitations. The evaporation coefficient, defined as the ratio of experimentally measured evaporation rate to that maximum possible theoretical limit, varies over a conflicting three orders of magnitude. In the present work, a semi-analytical transient heat diffusion model of droplet evaporation is developed considering the effect of change in droplet size due to evaporation from its surface, when the droplet is injected into vacuum. Negligible effect of droplet size reduction due to evaporation on cooling rate is found to be true. However, the evaporation coefficient is found to approach theoretical limit of unity, when the droplet radius is less than that of mean free path of vapor molecules on droplet surface contrary to the reported theoretical predictions. Evaporation coefficient was found to reduce rapidly when the droplet under consideration has a radius larger than the mean free path of evaporating molecules, confirming the molecular collision barrier to evaporation rate. The trend of change in evaporation coefficient with increasing droplet size predicted by the proposed model will facilitate obtaining functional relation of evaporation coefficient with droplet size, and can be used for benchmarking the interaction between multiple droplets during evaporation in vacuum. © 2016 Elsevier B.V.

Department of Mechanical Engineering

Physics Letters, Section A: General, Atomic and Solid State Physics

Evaluation of evaporation coefficient for micro-droplets exposed to low pressure: A semi-analytical approach

In this article we study the existence of at least two positive weak solutions of an nonhomogeneous fourth-order Navier boundary-value problem involving critical exponential growth on a bounded domain in ℝ4, with a parameter λ &gt; 0. We establish upper and lower bounds for λ, which determine multiplicity and non-existence of solutions. © 2017 Texas State University.

Electronic Journal of Differential Equations

Multiple solutions of a fourth-order nonhomogeneous equation with critical growth in ℝ4

In this paper, design, fabrication and measurement of single/dual/triple band absorber based on wire structure is presented. The absorber consists of one/two/three metallic wires for single/dual/triple band absorption. These metallic wires are printed on lossy FR4 sheet backed with metallic plate. The resonant frequency is tuned by changing metallic wire length. The proposed absorbers are polarization insensitive due to four fold rotational symmetry in the design. © 2015 IEEE.

Proceedings of the 2015 International Conference on Microwave and Photonics, ICMAP 2015

Design of wire based single/dual/triple band polarization insensitive metamaterial absorber

ABSTRACT: We introduce some new generalized stochastic orderings (in the spirit of relative ageing) which compare probability distributions with the exponential distribution. These orderings are useful to understand the phenomenon of positive ageing classes and also helpful to guide the practitioners when there are crossing hazard rates and/or crossing mean residual lives. We study some characterizations of these orderings. Inter-relations among these orderings have also been discussed. © 2016 Taylor & Francis Group, LLC.

Fulltext

Communications in Statistics - Theory and Methods

On some generalized orderings: In the spirit of relative ageing

We consider the equation (Formula presented.) in the sense of distribution in (Formula presented.) where (Formula presented.) and (Formula presented.). Then it is known that (Formula presented.) solves (Formula presented.) , for some nonnegative constants (Formula presented.) and (Formula presented.). In this paper, we study the existence of singular solutions to (Formula presented.) in a domain (Formula presented.) , (Formula presented.) is a nonnegative measurable function in some Lebesgue space. If (Formula presented.) in (Formula presented.) , then we find the growth of the nonlinearity (Formula presented.) that determines (Formula presented.) and (Formula presented.) to be (Formula presented.). In case when (Formula presented.) , we will establish regularity results when (Formula presented.) , for some (Formula presented.). This paper extends the work of Soranzo (1997) where the author finds the barrier function in higher dimensions (Formula presented.) with a specific weight function (Formula presented.). Later, we discuss its analogous generalization for the polyharmonic operator. © 2015 Taylor & Francis.

Complex Variables and Elliptic Equations

Isolated singularities of polyharmonic operator in even dimension

Majorization is a key concept in studying the Schur-convex property of a function, which is very useful in the study of stochastic orders. In this paper, some results on Schur-convexity have been developed. We have studied the conditions under which a function φ defined by φ(x)=∑i=1nuig(xi) will be Schur-convex. This fills some gap in the theory of majorization. The results so developed have been used in the case of generalized exponential and gamma distributions. During this, we have also developed some stochastic properties of order statistics. © 2016 Elsevier B.V.

Journal of Computational and Applied Mathematics

Some results on majorization and their applications

Image thresholding is the simple and widely used image segmentation method in automatic image analysis. In this paper, a novel image thresholding technique based on the local image features is proposed. The core idea is to generate a local activity feature matrix assuming given image a random field. The histogram of the local activity feature matrix, which essentially incorporate the local features of the image, is used for threshold selection process. The performance of the proposed technique is validated by extensive experiments on different real images, where the definite advantages are demonstrated subjectively and objectively. Further, the comparisons with existing techniques confirmed the effectiveness of the proposed technique. © 2016 Elsevier GmbH

Optik

Image thresholding based on local activity feature matrix

The percentage of renewable energy sources such as solar, wind power and biomass in the energy mix of India is increasing every year. Solar power variability is an important issue for grid integration of solar photovoltaic power plants. The main objective of this paper is to forecast the power generated in a 5 MW solar PV plant owned by Gujarat Power Corporation Limited (GPCL) at Charanka solar park, Gujarat. Charanka is a location with an average of 320 sunny days in a year. Average solar insolation available here is 5.7-6.0 kWh/m2 per day. Data obtained from 1st March 2014-31st August 2014 is used for analysis purposes. In this paper a two stage procedure is used referred to as GNN (Generalized Neural Network) model. In the primary stage pre-processing is done on the raw data followed by neural network model for forecasting. © 2015 IEEE.