Department of Mathematics

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The q-gradient is the generalization of the gradient based on the q-derivative. The q-version of the steepest descent method for unconstrained multiobjective optimization problems is constructed and recovered to the classical one as q equals 1. In this method, the search process moves step by step from global at the beginning to particularly neighborhood at last. This method does not depend upon a starting point. The proposed algorithm for finding critical points is verified in the numerical examples. © 2020 the Author(s), licensee AIMS Press.

World University root node

AIMS Mathematics

On Q-steepest descent method for unconstrained multiobjective optimization problems

The instability mechanism based on the Coriolis force, especially on a rapidly rotating portable device handling shear-thinning fluids such as blood, is of utmost importance for eventual detection of diseases by mixing with suitable reagents. Motivated by this proposition, this study renders a modal stability analysis of shear-thinning fluids in a rotating microchannel modeled by the Carreau rheological law. When a microchannel is engraved with a rotating compact disk-based device, the centrifugal force acts as the driving force that actuates the flow and the Coriolis force enhances the mixing process in a significantly short span by destabilizing the flow. An Orr-Sommerfeld-Squire analysis is performed to explore the role of these forces on the linear stability of a rotating shear-thinning flow. Reported results on shear-thinning flow with streamwise disturbances indicate that the critical Reynolds number for the flow transition with viscosity perturbation is nearly half of that of the critical value for the same without viscosity perturbation. In sharp contrast, the present analysis considering spanwise disturbances reveals that the critical Reynolds numbers with and without viscosity perturbation remain virtually unaltered under rotational effects. However, the viscosity variation has no significant influence on the Coriolis force-based instability. Numerical results confirm that a momentous destabilization is possible with the use of the Coriolis force via generating secondary flow inside the channel. Interestingly, the roll cells corresponding to the instabilities at lower time constants exhibit the existence of two distinct vortices, and the center of the stronger one is essentially settled toward the unstable "stratified" region. Moreover, for a higher value of the time constant, only one vortex occupies the entire channel. This, in turn, may turn out to be of fundamental importance in realizing new instability regimes facilitating efficient mixing in rotationally actuated fluidic devices deployed for biochemical analysis and medical diagnostics. © 2020 Author(s).

Fulltext

Physics of Fluids

Coriolis force-based instability of a shear-thinning microchannel flow

Relative ageing describes how one system ages with respect to another. The ageing faster orders are used to compare the relative ageing of two systems. Here, we study ageing faster orders in the hazard and reversed hazard rates. We provide some sufficient conditions for one coherent system to dominate another with respect to ageing faster orders. Further, we investigate whether the active redundancy at the component level is more effective than that at the system level with respect to ageing faster orders, for a coherent system. Furthermore, a used coherent system and a coherent system made out of used components are compared with respect to ageing faster orders. © Applied Probability Trust 2020.

Advances in Applied Probability

On relative ageing of coherent systems with dependent identically distributed components

In this paper, a new approach for zero-watermarking has been proposed based on log-polar mapping, all phase biorthogonal sine transform and singular value decomposition. The core idea is to produce a zero watermark to protect the copyright of the image. For this purpose, the host image is transformed into the log-polar domain followed by the all phase biorthogonal sine transform (APBST). The transformed coefficients are then divided into nonoverlapping blocks and some blocks are selected based on secret key. These blocks are finally used to formulate a reference matrix which is utilized to generate a zero watermark for the host image. A detailed experimental analysis is conducted to demonstrate the feasibility of the proposed algorithm against various image/signal processing distortions. © 2020, Springer Nature Singapore Pte Ltd.

Advances in Intelligent Systems and Computing

A Reference Based Secure and Robust Zero Watermarking System

Reconstructing an indoor scene and generating a layout/floor plan in 3D or 2D is a widely known problem. Quite a few algorithms have been proposed in the literature recently. However, most of the existing methods either use RGB-D images, thus requiring a depth camera, or depend on panoramic photos with the assumption that there is little to no occlusion in the rooms. In this work, we proposed generation of layout using an RGB image captured using a simple mobile phone camera. We take advantage of Simultaneous Localization and Mapping (SLAM) to assess the 3D transformations required for layout generation. SLAM technology is built-in in recent mobile libraries such as ARCore by Google. Hence, the proposed method is fast and efficient, while giving the user freedom to generate layout by simply taking a few conventional photos, rather than relying on specialized depth hardware or occlusion-free panoramic photos. © 2020 IEEE.

Department of Computer Science & Engineering

Proceedings - 2020 IEEE 6th International Conference on Multimedia Big Data, BigMM 2020

LayART: Generating indoor layout using ARCore Transformations

In this article, a Jacobi spectral Galerkin method is developed for weakly singular Volterra integral equations of the second kind. To obtain the superconvergence results, we transform the domain of integration of Volterra integral equation to the standard interval [ - 1 , 1 ] using variable transformation and function transformation. We obtain the convergence rates both in infinity and weighted L2-norm. We prove that the Jacobi spectral iterated Galerkin method shows improvement over the Jacobi spectral Galerkin method. We improve these results further by considering the Jacobi spectral iterated multi-Galerkin method. Theoretical results are justified by the numerical results. © 2019, Springer Nature Switzerland AG.

Mediterranean Journal of Mathematics

Error Analysis of Jacobi Spectral Galerkin and Multi-Galerkin Methods for Weakly Singular Volterra Integral Equations

In this paper we establish the existence of multiple solutions for a class of hamiltonian system with subcritical growth. Here, we use variational method to get multiplicity of solutions using the Lusternik–Schnirelmann category of Ω ¯ in itself. © 2020, Springer-Verlag GmbH Austria, part of Springer Nature.

Monatshefte fur Mathematik

Existence and multiplicity of solutions for a class of Hamiltonian systems

In this work, we study the higher order Kirchhoff type Choquard equation (KC) involving a critical exponential non-linearity and singular weights. We prove the existence of solution to (KC) using Mountain pass Lemma in light of Moser–Trudinger and singular Adams–Moser inequalities. In the second part of the paper, using the Nehari manifold technique and minimization over its suitable subsets, we prove the existence of at least two solutions to the Kirchhoff type Choquard equation (Pλ,M) involving convex–concave type non-linearity. © 2020 Elsevier Ltd

Nonlinear Analysis, Theory, Methods and Applications

Polyharmonic Kirchhoff problems involving exponential non-linearity of Choquard type with singular weights

In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear approximation of all objective functions as well as constraint functions. The sub-problem at every iteration of the sequence has feasible solution. A non-differentiable penalty function is used to deal with constraint violations. A descent sequence is generated which converges to a critical point under the Mangasarian–Fromovitz constraint qualification along with some other mild assumptions. The method is compared with a selection of existing methods on a suitable set of test problems. © 2020, Korean Society for Informatics and Computational Applied Mathematics.

Journal of Applied Mathematics and Computing

A Sequential Quadratic Programming Method for Constrained Multi-objective Optimization Problems

In this paper, we investigate various stochastic orderings for series and parallel systems with independent and heterogeneous components having lifetimes following the proportional odds model. We also investigate comparisons between a system with heterogeneous components and that with homogeneous components. This paper also studies relative ageing orders for two systems in the framework of components having lifetimes following the proportional odds model. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group.