Department of Mathematics

&ldquo;IIT Jodhpur is committed to impart quality education to facilitate the creation of qualified, competent and responsible human resources to meet the emerging technological challenges of the world. It is working towards creating an equitable learning platform that is positive, accessible and effective in the face of the modern societal and scientific advancements.

Flexibility in curriculum, in all its academic programs, encompassing elements of teaching, research, creativity, innovation and entrepreneurship is the most unique feature of IIT Jodhpur. The Department of Science and Technology (DST), under the National Mission on Cyber Physical Systems, has identified IIT Jodhpur as a Technology &amp; Innovation Hub in the area of Augmented Reality and Virtual Reality. The institute has also been nominated as the coordinator for the Jodhpur City and Knowledge Cluster by the Office of Principal Scientific Adviser, Government of India.

The sprawling 852-acre IIT Jodhpur campus is a majestic tribute to the deep-rooted diverse cultural heritage of the region. The campus is an architectural masterpiece, which is slated to become an international exemplar of sustainability with net-zero energy, and advanced water and waste management strategies.&rdquo;

IIT Jodhpur

In this paper, we investigate the dynamics of a non-autonomous dynamical system (X,F) generated by a uniformly convergent sequence of continuous self maps on X. We relate the dynamical behavior of (X,F) with the dynamical behavior of the limiting system (and vice versa). In the process, we relate properties like equicontinuity, minimality, various forms of mixing and sensitivities, dense periodicity and denseness of proximal pairs (cells) for the two systems. We also give examples to investigate the necessity of the conditions imposed. © 2018 Elsevier B.V.

World University root node

Fulltext

Topology and its Applications

On dynamics generated by a uniformly convergent sequence of maps

In this paper, we develop the iteration techniques for Galerkin and collocation methods for linear Volterra integral equations of the second kind with a smooth kernel, using piecewise constant functions. We prove that the convergence rates for every step of iteration improve by order O(h2) for Galerkin method, whereas in collocation method, it is improved by O(h) in infinity norm. We also show that the system to be inverted remains same for every iteration as in the original projection methods. We illustrate our results by numerical examples. © 2017, Korean Society for Computational and Applied Mathematics.

Journal of Applied Mathematics and Computing

Superconvergence results of iterated projection methods for linear Volterra integral equations of second kind

In this paper, we consider the classical finite mixture model, which is an effective tool for modeling lifetime distributions for random samples from heterogeneous populations. We discuss new results on stochastic comparison for two finite mixtures when each of them is drawn from one of the following semiparametric families, i.e., proportional hazards, accelerated lifetime and proportional reversed hazards. © 2018, Sociedad de Estadística e Investigación Operativa.

Test

On stochastic comparisons of finite mixtures for some semiparametric families of distributions

We develop a theory of stochastic orders for the age and the residual (remaining) lifetime for populations of manufactured identical items. The obtained theoretical results can be used by manufacturers or users for the justified decisions with respect to, e.g., the increase or decrease in the production rate or with respect to the necessary maintenance actions. Specifically, we show that if the random age of a population is smaller (resp. larger) in some stochastic sense than the defined equilibrium age, then it is also smaller (resp. larger) than the corresponding residual lifetime with respect to different stochastic orders. We discuss various stochastic comparisons between the random age and the residual lifetime for one or more populations. Some ageing properties of the random age and the residual lifetime have also been studied. © 2017, Sociedad de Estadística e Investigación Operativa.

Stochastic ordering for populations of manufactured items

We investigate the following eigenvalue problem {−div(L(x)|∇u|p−2∇u)=λK(x)|u|p−2uin AR1 R2,u=0on ∂AR1 R2, where AR1 R2:={x∈RN:R1&lt;|x|&lt;R2} (0&lt;R1&lt;R2≤∞), λ&gt;0 is a parameter, the weights L and K are measurable with L positive a.e. in AR1 R2 and K possibly sign-changing in AR1 R2. We prove the existence of the first eigenpair and discuss the regularity and positiveness of eigenfunctions. The asymptotic estimates for u(x) and ∇u(x) as |x|→R1 + or R2 − are also investigated. © 2018 Elsevier Inc.}, author_keywords={Asymptotic behavior; Exterior domain; Maximum principles; Regularity; The first eigenvalue; The weighted p-Laplacian; Variational method}, funding_details={Ministerstvo Školství, Mládeže a TělovýchovyMinisterstvo Školství, Mládeže a Tělovýchovy, MŠMT, LO1506}, funding_details={Grantová Agentura České RepublikyGrantová Agentura České Republiky, GA ČR, 18-032523S}, funding_text_1={P. Drábek and A. Sarkar were partly supported by the Grant Agency of the Czech Republic , project no. 18-032523S . K. Ho and A. Sarkar were supported by the project LO1506 of the Czech Ministry of Education, Youth and Sports .}, funding_text_2={P. Dr?bek and A. Sarkar were partly supported by the Grant Agency of the Czech Republic, project no. 18-032523S. K. Ho and A. Sarkar were supported by the project LO1506 of the Czech Ministry of Education, Youth and Sports.}, references={Agudelo, O., Drábek, P., Anisotropic semipositone quasilinear problems (2017) J. Math. Anal. Appl., 452 (2), pp. 1145-1167; Anoop, T.V., Drábek, P., Sankar, L., Sasi, S., Antimaximum principle in exterior domains (2016) Nonlinear Anal., 130, pp. 241-254; Anoop, T.V., Drábek, P., Sasi, S., Weighted quasilinear eigenvalue problems in exterior domains (2015) Calc. Var. Partial Differential Equations, 53 (3-4), pp. 961-975; Autuori, G., Colasuonno, F., Pucci, P., On the existence of stationary solutions for higher-order p-Kirchhoff problems (2014) Commun. Contemp. Math., 16; Chhetri, M., Drábek, P., Principal eigenvalue of p-Laplacian operator in exterior domain (2014) Results Math., 66 (3-4), pp. 461-468; Colasuonnoa, F., Pucci, P., Varga, C., Multiple solutions for an eigenvalue problem involving p-Laplacian type operators (2012) Nonlinear Anal., 75, pp. 4496-4512; DiBenedetto, E., C1+α local regularity of weak solutions of degenerate elliptic equations (1983) Nonlinear Anal., 7 (8), pp. 827-850; Drábek, P., Kufner, A., Kuliev, K., Half-linear Sturm–Liouville problem with weights: asymptotic behavior of eigenfunctions (2014) Proc. Steklov Inst. Math., 284, pp. 148-154; Drábek, P., Kufner, A., Nicolosi, F., Quasilinear Elliptic Equations with Degenerations and Singularities (1997) De Gruyter Series in Nonlinear Analysis and Applications, 5. , Walter de Gruyter and Co. Berlin; Drábek, P., Kuliev, K., Half-linear Sturm–Liouville problem with weights (2012) Bull. Belg. Math. Soc. Simon Stevin, 19, pp. 107-119; Evans, L.C., Gariepy, R.F., Measure Theory and Fine Properties of Functions (1992), CRC Press; Ho, K., Sim, I., Corrigendum to “Existence and some properties of solutions for degenerate elliptic equations with exponent variable” [Nonlinear Anal. 98 (2014) 146–164] (2015) Nonlinear Anal., 128, pp. 423-426; Kawohl, B., Lucia, M., Prashanth, S., Simplicity of the principal eigenvalue for indefinite quasilinear problems (2007) Adv. Difference Equ., 12 (4), pp. 407-434; Ladyzhenskaya, O.A., Ural'tseva, N.N., Linear and Quasilinear Elliptic Equations (1968), Acad. Press; Le, V., Schmitt, K., On boundary value problems for degenerate quasilinear elliptic equations and inequalities (1998) J. Differential Equations, 144, pp. 170-218; Lê, A., Schmitt, K., Variational eigenvalues of degenerate eigenvalue problems for the weighted p-Laplacian (2005) Adv. Nonlinear Stud., 5 (4), pp. 573-585; Lieberman, G.M., Boundary regularity for solutions of degenerate elliptic equations (1988) Nonlinear Anal., 12 (11), pp. 1203-1219; Mitidieri, E., Pohozaev, S.I., A priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities (2001) Proc. Steklov Inst. Math., Tr. Mat. Inst. Steklova, 234, pp. 1-384. , (in Russian). Translation in; Montefusco, E., Radulescu, V., Nonlinear eigenvalue problems for quasilinear operators on unbounded domains (2001) NoDEA Nonlinear Differential Equations Appl., 8, pp. 481-497; Murthy, V., Stampacchia, G., Boundary value problems for some degenerate-elliptic operators (1968) Ann. Mat. Pura Appl., 80, pp. 1-122; Opic, B., Kufner, A., Hardy-Type Inequalities (1990) Pitman Research Notes in Mathematics Series, 279. , Longman Scientific and Technical Harlow; Perera, K., Pucci, P., Varga, C., An existence result for a class of quasilinear elliptic eigenvalue problems in unbounded domains (2014) NoDEA Nonlinear Differential Equations Appl., 21 (3), pp. 441-451; Pucci, P., Serrin, J., The strong maximum principle revisited (2004) J. Differential Equations, 196 (1), pp. 1-66; Wang, Y.-Z., Li, H.-Q., Lower bound estimates for the first eigenvalue of the weighted p-Laplacian on smooth metric measure spaces (2016) Differential Geom. Appl., 45, pp. 23-42}, correspondence_address1={Sarkar, A.; NTIS, Technická 8, Czech Republic; email: sarkara@ntis.zcu.cz}, publisher={Academic Press Inc.}, issn={0022247X}, language={English}, abbrev_source_title={J. Math. Anal. Appl.}, document_type={Article}, source={Scopus},

Journal of Mathematical Analysis and Applications

On the eigenvalue problem involving the weighted p-Laplacian in radially symmetric domains

The work presents an inventive, simple and implementable design approach to enhance the bandwidth of conventional Salisbury Screen Microwave Absorber (SSMA). Theoretically, the maximum fractional bandwidth of SSMA for FR4 substrate with an optimum sheet resistivity of 308 Ω/sq for –10 dB reflection is nearly 42.1%. In comparison, the bandwidth for square patch based SSMA is 59.7% with the same thickness. The design comprises square patches of SSMA placed periodically on a metal sheet. The square patches consist of an FR4 substrate and a 200 Ω/sq resistive sheet. A single reflection null is observed in the SSMA due to λ/4 resonance whereas in the proposed absorber an additional resonant mode is introduced due to coupling between the nearby patches. The simultaneous overlapping of the λ/4 mode and the additional coupling mode results in bandwidth extension. The close agreement between the simulation and measurement data is observed. © 2018, Electromagnetics Academy. All Rights reserved.

Progress in Electromagnetics Research Letters

Design and characterization of square patch Salisbury screen microwave absorber

We synthesized zinc titanate nanopowder in different crystal structures by varying calcination temperature and time and phase evolution is qualitatively investigated using reference intensity ratio (RIR) approach. The electronic properties showed 2.9 eV as indirect band transition, and 3.59 ± 0.02 eV as direct band transition for the highest temperature annealed rhombohedral ZnTiO3 and cubic spinel Zn2TiO4 zinc titanate materials. The intermediate temperature annealed (∼850 °C) material consists of ZnTiO3, Zn2TiO4, and Zn2Ti3O8 zinc titanate nanopowder, showing similar two electronic transitions. Zinc titanate with dominant rhombohedral phase ZnTiO3 (900 °C annealed) and dominant Zn2Ti3O8 phase (750 °C annealed) are used to synthesize mesoporous electrodes for integrating the ZnS passivated CdS quantum dots. Finally, Cu2S counter electrode is integrated with polysulfide electrolyte to realize 1 cm2 area quantum dot sensitized solar cells (QDSSCs). QDSSCs with dominant ZnTiO3 phase are showing lower photovoltaic performance (short circuit current 0.76 mA/cm2, open circuit voltage 0.55 V) with respect to that of dominant Zn2Ti3O8 phase with 2.2 mA/cm2 short circuit current and 0.69 V open circuit voltage, respectively. The observed difference is attributed to differences in electronic and morphological properties of the synthesized zinc titanate powders. © 2018 Elsevier Ltd

Department of Physics

Solar Energy

Nanostructured zinc titanate wide band gap semiconductor as a photoelectrode material for quantum dot sensitized solar cells

Modal analysis of the Reynolds-Orr energy equation for a miscible viscosity stratified slippery channel flow is deliberated. The main aim is to extend the earlier work of Ghosh et al. (Phys. Fluid, Vol. 26, 014107 (2014)) to discusses the instability mechanism, which has not been investigated so far. The generalized equation governing the average rate of change of disturbance kinetic energy is evaluated after solving the Orr-Sommerfeld boundary value problem. The analysis includes viscosity perturbation and slip boundary condition. Maximum growth rate curves for two-dimensional disturbances reconfirm the existence of new unstable modes at low Reynolds numbers. Stabilizing and destabilizing effects of wall velocity slip are found depending on parameter regime. The physical mechanism responsible for the dual role of the wall slip is brought to light by estimating the alteration of kinetic energy due to the production and dissipation of energy originating from various factors inside the perturbed flow. Slip boundary condition at the wall affects the base flow as well as perturbations. Our numerical calculations here show how the wall velocity slip gives impact on each energy terms. The results ensure that, the new unstable mode is occurred due to the overlap of velocity and viscosity disturbance vortices. Stability characteristics of this overlap instability are ruled by the energy sourcing from the Reynolds stress and the viscosity perturbation gradient effect. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Instability mechanism for miscible two-fluid channel flow with wall slip

Image fusion is capable of processing multiple heterogeneous images acquired by single or multi-sensor imaging systems for an improved interpretation of the targeted object or scene. A diversity of applications have benefited from the fusion of multi-sensor images through a more reliable and comprehensive fused result. Likewise, numerous approaches to fuse multi-sensor images have been proposed and published in literature. However, due to a lack of benchmark resources and commonly accepted assessment measures, it is hard to identify the significance of new image fusion algorithms and implementations. This paper reviews and categorizes recent algorithms for image fusion and performance assessment based on reported comparative results. We recommend using non-parametric statistical tests to verify the performance of the pixel-level fusion algorithms. Furthermore, a comprehensive evaluation of 40 fusion algorithms from recently published results is conducted to demonstrate the significance of these algorithms in terms of statistical analyses within their respective applications. Although the results of these performance tests are limited by available data sets, baseline algorithms, and selected assessment metrics; it is a critical step for comparative image fusion research. This paper aims to advance image fusion development by creating a complete inventory of state-of-the-art image fusion techniques and advocating statistical comparison tests to avoid unnecessary duplication of development efforts. Establishing a benchmark study for image fusion is critical for performance comparisons of contemporary methods. © 2017 Elsevier B.V.

Information Fusion

Fusing synergistic information from multi-sensor images: An overview from implementation to performance assessment

We investigate the Fredholm alternative for the p-Laplacian in an exterior domain which is the complement of the closed unit ball in RN (N≥2). By employing techniques of Calculus of Variations we obtain the multiplicity of solutions. The striking difference between our case and the entire space case is also discussed. © 2018 Elsevier Ltd