Search results for: Amit Kumar Gautam

Authors: Gaurav Kumar, Rakesh Kumar Bajaj

Abstract:

The applicability of Net Present Value (NPV) in an investment project is becoming more and more popular in the field of engineering economics. The classical NPV methodology involves only the precise and accurate data of the investment project. In the present communication, we give a new mathematical model for NPV which uses the concept of intuitionistic fuzzy set theory. The proposed model is based on triangular intuitionistic fuzzy number, which may be known as Intuitionistic Fuzzy Net Present Value (IFNPV). The model has been applied to an example and the results are presented.

Keywords: Net Present Value, Intuitionistic Fuzzy Set, Investment Projects.

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Authors: Sanjay Kumar Awasthi, Sunil Kumar Bajpai, Surendra Kumar Pandey, Ajay Utiye

Abstract:

The effect of gamma irradiation on micro-hardness of polymer blends of poly (ethyl methacrylate)(PEMA) and poly (ethylene oxide) (PEO) has been investigated to detect the radiation induced crosslinking. The blend system comprises a noncrystallizable polymer, PEMA and a crystallizable polymer, PEO. On irradiation, the overall hardness of the blend specimens for different dose levels infers occurrence of a crosslinking process. The radiation-induced crosslinking was greater for blends having lower concentration of PEO. However, increase in radiation dose causes softening of blend system due to radiation induced scissioning of the chains

Keywords: Microhardness, Radiation induced crosslinking, Solution cast technique, Vicker's hardness number.

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Authors: Devinder Singh, Arbind Kumar, Rajneesh Kumar

Abstract:

The general solution of the equations for a homogeneous isotropic microstretch thermo elastic medium with mass diffusion for two dimensional problems is obtained due to normal and tangential forces. The Integral transform technique is used to obtain the components of displacements, microrotation, stress and mass concentration, temperature change and mass concentration. A particular case of interest is deduced from the present investigation.

Keywords: Normal and tangential force, Microstretch, thermoelastic, The Integral transform technique.

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Authors: Anil Kumar, C. Nagaraja Kumar

Abstract:

The position and momentum space information entropies of hydrogen atom are exactly evaluated. Using isospectral Hamiltonian approach, a family of isospectral potentials is constructed having same energy eigenvalues as that of the original potential. The information entropy content is obtained in position space as well as in momentum space. It is shown that the information entropy content in each level can be re-arranged as a function of deformation parameter.

Keywords: Information Entropy, BBM inequality, Isospectral Potential.

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Authors: Pankaj Gupta, Amit Kumar Srivastava, Nitesh Pandey

Abstract:

This article explores the domain of generative design in order to enhance the development of robot designs for innovative and efficient maintenance approaches for tall buildings. This study aims to optimize the design of robotic hands by focusing on minimizing mass and volume while ensuring they can withstand the specified pressure with equal strength. The research procedure is structured and systematic. The purpose of optimization is to enhance the efficiency of the robot and reduce the manufacturing expenses. The project seeks to investigate the application of generative design in order to optimize products. Autodesk Fusion 360 offers the capability to immediately apply the generative design functionality to the solid model. The effort involved creating a solid model of the Smart Glass Cleaning Robot and optimizing one of its components, the Hand, using generative techniques. The article has thoroughly examined the designs, outcomes, and procedure. These loads serve as a benchmark for creating designs that can endure the necessary level of pressure and preserve their structural integrity. The efficacy of the generative design process is contingent upon the selection of materials, as different materials possess distinct physical attributes. The study utilizes five different materials, namely Steel, Stainless Steel, Titanium, Aluminum, and CFRP (Carbon Fiber Reinforced Polymer), in order to investigate a range of design possibilities.

Keywords: Generative design, mass and volume optimization, material strength analysis, generative design, smart glass cleaning robot.

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Authors: Indradip Banerjee, Souvik Bhattacharyya, Gautam Sanyal

Abstract:

In this paper, an approach is presented to investigate the performance of Pixel Factor Mapping (PFM) and Extended PMM (Pixel Mapping Method) through the qualitative and quantitative approach. These methods are tested against a number of well-known image similarity metrics and statistical distribution techniques. The PFM has been performed in spatial domain as well as frequency domain and the Extended PMM has also been performed in spatial domain through large set of images available in the internet.

Keywords: Qualitative, quantitative, PFM, EXTENDED PMM.

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Authors: Mayank Kumar, D B Mahesh Kumar, Ashwin S Kumar, N K Srinath

Abstract:

In this era of technology, fueled by the pervasive usage of the internet, security is a prime concern. The number of new attacks by the so-called “bots", which are automated programs, is increasing at an alarming rate. They are most likely to attack online registration systems. Technology, called “CAPTCHA" (Completely Automated Public Turing test to tell Computers and Humans Apart) do exist, which can differentiate between automated programs and humans and prevent replay attacks. Traditionally CAPTCHA-s have been implemented with the challenge involved in recognizing textual images and reproducing the same. We propose an approach where the visual challenge has to be read out from which randomly selected keywords are used to verify the correctness of spoken text and in turn detect the presence of human. This is supplemented with a speaker recognition system which can identify the speaker also. Thus, this framework fulfills both the objectives – it can determine whether the user is a human or not and if it is a human, it can verify its identity.

Keywords: CAPTCHA, automatic speech recognition, keyword spotting.

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Authors: P. K. Sarkar, Amit Kumar Jain

Abstract:

The demand for Urban transportation is characterised by a large scale temporal and spatial variations which causes heavy congestion inside metro trains in peak hours near Centre Business District (CBD) of the city. The conventional approach to address peak hour congestion, metro trains has been to increase the supply by way of introduction of more trains, increasing the length of the trains, optimising the time table to increase the capacity of the system. However, there is a limitation of supply side measures determined by the design capacity of the systems beyond which any addition in the capacity requires huge capital investments. The demand side interventions are essentially required to actually spread the demand across the time and space. In this study, an attempt has been made to identify the potential Transport Demand Management tools applicable to Urban Rail Transportation systems with a special focus on differential pricing. A conceptual price elasticity model has been developed to analyse the effect of various combinations of peak and nonpeak hoursfares on demands. The elasticity values for peak hour, nonpeak hour and cross elasticity have been assumed from the relevant literature available in the field. The conceptual price elasticity model so developed is based on assumptions which need to be validated with actual values of elasticities for different segments of passengers. Once validated, the model can be used to determine the peak and nonpeak hour fares with an objective to increase overall ridership, revenue, demand levelling and optimal utilisation of assets.

Keywords: Congestion, differential pricing, elasticity, transport demand management, urban transportation.

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Authors: Shashank Gautam

Abstract:

This paper proposes techniques like MT CMOS, POWER GATING, DUAL STACK, GALEOR and LECTOR to reduce the leakage power. A Full Adder has been designed using these techniques and power dissipation is calculated and is compared with general CMOS logic of Full Adder. Simulation results show the validity of the proposed techniques is effective to save power dissipation and to increase the speed of operation of the circuits to a large extent.

Keywords: Low Power, MT CMOS, Galeor, Lector, Power Gating, Dual Stack, Full Adder.

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Authors: S. Samanta, D. Datta, S. S. Gautam

Abstract:

In this paper, quantitative evaluation of ultrasonic Cscan images through estimation of their Fractal Dimension (FD) is discussed. Necessary algorithm for evaluation of FD of any 2-D digitized image is implemented by developing a computer code. For the evaluation purpose several C-scan images of the Kevlar composite impacted by high speed bullet and glass fibre composite having flaw in the form of inclusion is used. This analysis automatically differentiates a C-scan image showing distinct damage zone, from an image that contains no such damage.

Keywords: C-scan, Impact, Fractal Dimension, Kevlar composite and Inclusion Flaw

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Authors: Amit Kumar Bhandary, Prithviraj Gupta, Siddhartha Mukherjee, Mahua Ghosh Chaudhuri, Rajib Dey

Abstract:

Chromite ores are primarily used for extraction of chromium, which is an expensive metal. For low grade chromite ores (containing less than 40% Cr₂O₃), the chromium extraction is not usually economically viable. India possesses huge quantities of low grade chromite reserves. This deposit can be utilized after proper physical beneficiation. Magnetic separation techniques may be useful after reduction for the beneficiation of low grade chromite ore. The sample collected from the sukinda mines is characterized by XRD which shows predominant phases like maghemite, chromite, silica, magnesia and alumina. The raw ore is crushed and ground to below 75 micrometer size. The microstructure of the ore shows that the chromite grains surrounded by a silicate matrix and porosity observed the exposed side of the chromite ore. However, this ore may be utilized in refractory applications. Chromite ores contain Cr₂O₃, FeO, Al₂O₃ and other oxides like Fe-Cr, Mg-Cr have a high tendency to form spinel compounds, which usually show high refractoriness. Initially, the low grade chromite ore (containing 34.8% Cr₂O₃) was reduced at 1200 ⁰C for 80 minutes with 30% coke fines by weight, before being subjected to magnetic separation. The reduction by coke leads to conversion of higher state of iron oxides converted to lower state of iron oxides. The pre-reduced samples are then characterized by XRD. The magnetically inert mass was then reacted with 20% MgO by weight at 1450 ⁰C for 2 hours. The resultant product was then tested for various refractoriness parameters like apparent porosity, slag resistance etc. The results were satisfactory, indicating that the resultant spinel compounds are suitable for refractory applications for elevated temperature processes.

Keywords: Apparent porosity, beneficiation, low grade chromite, refractory, spinel compounds, slag resistance.

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Authors: Sujit Kumar Sardar Manasi Mandal Samit Kumar Majumder

Abstract:

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun and S.Z. Song introduced the notion of intuitionistic fuzzy points. In this paper we find some relations between the intuitionistic fuzzy ideals of a semigroup S and the set of all intuitionistic fuzzy points of S.

Keywords: Semigroup, Regular(intra-regular) semigroup, Intuitionistic fuzzy point, Intuitionistic fuzzy subsemigroup, Intuitionistic fuzzy ideal, Intuitionistic fuzzy interior ideal, Intuitionistic fuzzy semiprime ideal, Intuitionistic fuzzy prime ideal.

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Authors: Amit Chhabra, Gurvinder Singh, Sandeep Singh Waraich, Bhavneet Sidhu, Gaurav Kumar

Abstract:

Decrease in hardware costs and advances in computer networking technologies have led to increased interest in the use of large-scale parallel and distributed computing systems. One of the biggest issues in such systems is the development of effective techniques/algorithms for the distribution of the processes/load of a parallel program on multiple hosts to achieve goal(s) such as minimizing execution time, minimizing communication delays, maximizing resource utilization and maximizing throughput. Substantive research using queuing analysis and assuming job arrivals following a Poisson pattern, have shown that in a multi-host system the probability of one of the hosts being idle while other host has multiple jobs queued up can be very high. Such imbalances in system load suggest that performance can be improved by either transferring jobs from the currently heavily loaded hosts to the lightly loaded ones or distributing load evenly/fairly among the hosts .The algorithms known as load balancing algorithms, helps to achieve the above said goal(s). These algorithms come into two basic categories - static and dynamic. Whereas static load balancing algorithms (SLB) take decisions regarding assignment of tasks to processors based on the average estimated values of process execution times and communication delays at compile time, Dynamic load balancing algorithms (DLB) are adaptive to changing situations and take decisions at run time. The objective of this paper work is to identify qualitative parameters for the comparison of above said algorithms. In future this work can be extended to develop an experimental environment to study these Load balancing algorithms based on comparative parameters quantitatively.

Keywords: SLB, DLB, Host, Algorithm and Load.

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Authors: Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh K. Pandey

Abstract:

The edges of low contrast images are not clearly distinguishable to human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplacian of Gaussian method has been applied on preprocessed image for edge detection. The algorithm has been tested on two test images.

Keywords: Chebyshev polynomials, Fractional order differentiator, Laplacian of Gaussian (LoG) method, Low contrast image.

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Authors: Dileep Kumar Gupta, Rajendra Prasad, Pradeep Kumar, Varun Narayan Mishra, Ajeet Kumar Vishwakarma, Prashant Kumar Srivastava

Abstract:

An approach was evaluated for the retrieval of soil moisture of bare soil surface using bistatic scatterometer data in the angular range of 200 to 700 at VV- and HH- polarization. The microwave data was acquired by specially designed X-band (10 GHz) bistatic scatterometer. The linear regression analysis was done between scattering coefficients and soil moisture content to select the suitable incidence angle for retrieval of soil moisture content. The 250 incidence angle was found more suitable. The support vector regression analysis was used to approximate the function described by the input output relationship between the scattering coefficient and corresponding measured values of the soil moisture content. The performance of support vector regression algorithm was evaluated by comparing the observed and the estimated soil moisture content by statistical performance indices %Bias, root mean squared error (RMSE) and Nash-Sutcliffe Efficiency (NSE). The values of %Bias, root mean squared error (RMSE) and Nash-Sutcliffe Efficiency (NSE) were found 2.9451, 1.0986 and 0.9214 respectively at HHpolarization. At VV- polarization, the values of %Bias, root mean squared error (RMSE) and Nash-Sutcliffe Efficiency (NSE) were found 3.6186, 0.9373 and 0.9428 respectively.

Keywords: Bistatic scatterometer, soil moisture, support vector regression, RMSE, %Bias, NSE.

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Authors: Parvinder S. Sandhu, Iqbaldeep Kaur, Amit Verma, Inderpreet Kaur, Birinderjit S. Kalyan

Abstract:

This work is a proposed model of CMOS for which the algorithm has been created and then the performance evaluation of this proposition has been done. In this context, another commonly used model called ZSTT (Zero Switching Time Transient) model is chosen to compare all the vital features and the results for the Proposed Equivalent CMOS are promising. In the end, the excerpts of the created algorithm are also included

Keywords: Dual Capacitor Model, ZSTT, CMOS, SPICEMacro-Model.

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Authors: Ashwani Kumar, Jitender Kumar

Abstract:

In this paper, an optimal power flow based approach has been applied for multi-transactions deregulated environment for ATC determination with SVC and STATCOM. The main contribution of the paper is (i) OPF based approach for evaluation of ATC with multi-transactions, (ii) ATC enhancement with FACTS devices viz. SVC and STATCOM for intact and line contingency cases, (iii) Impact of ZIP load on ATC determination and comparison of ATC obtained with SVC and STATCOM. The results have been determined for intact and line contingency cases taking simultaneous as well as single transaction cases for IEEE 24 bus RTS.

Keywords: Available transfer capability, FACTS devices, line contingency, multi-transactions, ZIP load model.

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Authors: Tarun Kumar Naiya, Biswajit Singha, Ashim Kumar Bhattacharya, Sudip Kumar Das

Abstract:

Fuller’s earth is a fine-grained, naturally occurring substance that has a substantial ability to adsorb impurities. In the present study Fuller’s earth has been characterized and used for the removal of Pb(II) from aqueous solution. The effect of various physicochemical parameters such as pH, adsorbent dosage and shaking time on adsorption were studied. The result of the equilibrium studies showed that the solution pH was the key factor affecting the adsorption. The optimum pH for adsorption was 5. Kinetics data for the adsorption of Pb(II) was best described by pseudo-second order model. The effective diffusion co-efficient for Pb(II) adsorption was of the order of 10-8 m2/s. The adsorption data for metal adsorption can be well described by Langmuir adsorption isotherm. The maximum uptake of metal was 103.3 mg/g of adsorbent. Mass transfer analysis was also carried out for the adsorption process. The values of mass transfer coefficients obtained from the study indicate that the velocity of the adsorbate transport from bulk to the solid phase was quite fast. The mean sorption energy calculated from Dubinin-Radushkevich isotherm indicated that the metal adsorption process was chemical in nature. 

Keywords: Fuller's earth, Pseudo second order, Mass Transfer co-efficient, Langmuir

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Authors: Vinod Kumar, Navin Kumar, Surjit Angra, Prince Sharma

Abstract:

This paper presents the design analysis of saddle support of a horizontal pressure vessel. Since saddle have the vital role to support the pressure vessel and to maintain its stability, it should be designed in such a way that it can afford the vessel load and internal pressure of the vessel due to liquid contained in the vessel. A model of horizontal pressure vessel and saddle support is created in ANSYS. Stresses are calculated using mathematical approach and ANSYS software. The analysis reveals the zone of high localized stress at the junction part of the pressure vessel and saddle support due to operating conditions. The results obtained by both the methods are compared with allowable stress value for safe designing.

Keywords: ANSYS, Pressure Vessel, Saddle, Support.

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Authors: Tanuj Kumar, Rakesh Kumar Bajaj

Abstract:

In the present paper, we analyze the vague reliability of k-out-of-n : G system (particularly, series and parallel system) with independent and non-identically distributed components, where the reliability of the components are unknown. The reliability of each component has been estimated using statistical confidence interval approach. Then we converted these statistical confidence interval into triangular intuitionistic fuzzy numbers. Based on these triangular intuitionistic fuzzy numbers, the reliability of the k-out-of-n : G system has been calculated. Further, in order to implement the proposed methodology and to analyze the results of k-out-of-n : G system, a numerical example has been provided.

Keywords: Vague set, vague reliability, triangular intuitionistic fuzzy number, k-out-of-n : G system, series and parallel system.

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Authors: Sumit Kumar, Sunil Kumar, Chandan Deep Singh

Abstract:

This paper presents modeling and simulation of flexible robot in an underwater environment. The underwater environment completely contrasts with ground or space environment. The robot in an underwater situation is subjected to various dynamic forces like buoyancy forces, hydrostatic and hydrodynamic forces. The underwater robot is modeled as Rayleigh beam. The developed model further allows estimating the deflection of tip in two directions. The complete dynamics of the underwater robot is analyzed, which is the main focus of this investigation. The control of robot trajectory is not discussed in this paper. Simulation is performed using Symbol Shakti software.

Keywords: Bond graph modeling, dynamics. modeling, Rayleigh beam, underwater robot.

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Authors: Parvinder S. Sandhu, Iqbaldeep Kaur, Amit Verma, Samriti Jindal, Inderpreet Kaur, Shilpi Kumari

Abstract:

Face Recognition is a field of multidimensional applications. A lot of work has been done, extensively on the most of details related to face recognition. This idea of face recognition using PCA is one of them. In this paper the PCA features for Feature extraction are used and matching is done for the face under consideration with the test image using Eigen face coefficients. The crux of the work lies in optimizing Euclidean distance and paving the way to test the same algorithm using Matlab which is an efficient tool having powerful user interface along with simplicity in representing complex images.

Keywords: Eigen Face, Multidimensional, Matching, PCA.

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Authors: Ambuj Kumar, Sunil Kumar Singh, Shrikant Singh

Abstract:

Sweep frequency response analysis has been turning out a powerful tool for investigation of mechanical as well as electrical integration of transformers. In this paper various aspect of practical application of SFRA has been studied. Open circuit and short circuit measurement were done on different phases of high voltage and low voltage winding. A case study was presented for the transformer of rating 31.5 MVA for various frequency ranges. A clear picture was presented for sub- frequency ranges for HV as well as LV winding. The main motive of work is to investigate high voltage short circuit response. The theoretical concept about SFRA responses is validated with expert system software results.

Keywords: Frequency deviation, OCT & SCT, SFRA, Transformer winding.

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Authors: Jatinder Kumar, Vinod Kumar

Abstract:

Ultrasonic machining (USM) is a non-traditional machining process being widely used for commercial machining of brittle and fragile materials such as glass, ceramics and semiconductor materials. However, USM could be a viable alternative for machining a tough material such as titanium; and this aspect needs to be explored through experimental research. This investigation is focused on exploring the use of ultrasonic machining for commercial machining of pure titanium (ASTM Grade-I) and evaluation of tool wear rate (TWR) under controlled experimental conditions. The optimal settings of parameters are determined through experiments planned, conducted and analyzed using Taguchi method. In all, the paper focuses on parametric optimization of ultrasonic machining of pure titanium metal with TWR as response, and validation of the optimized value of TWR by conducting confirmatory experiments.

Keywords: Ultrasonic machining, titanium, tool wear rate

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Authors: Z.A. Jaffery, Vinay Kumar Chandna, Sunil Kumar Chaudhary

Abstract:

This paper present a MATLAB-SIMULINK model of a single phase 2.5 KVA, 240V RMS controlled PV VSI (Photovoltaic Voltage Source Inverter) inverter using IGBTs (Insulated Gate Bipolar Transistor). The behavior of output voltage, output current, and the total harmonic distortion (THD), with the variation in input dc blocking capacitor (Cdc), for linear and non-linear load has been analyzed. The values of Cdc as suggested by the other authors in their papers are not clearly defined and it poses difficulty in selecting the proper value. As the dc power stored in Cdc, (generally placed parallel with battery) is used as input to the VSI inverter. The simulation results shows the variation in the output voltage and current with different values of Cdc for linear and non-linear load connected at the output side of PV VSI inverter and suggest the selection of suitable value of Cdc.

Keywords: DC Blocking capacitor, IGBTs, PV VSI, THD.

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Authors: S. Meikandasivam, D. Vijayakumar, Rajesh Kumar Nema, Shailendra Kumar Jain

Abstract:

This paper investigates the performance of the single TCSC and proposed split TCSC on transmission system where India’s first TCSC project is installed in Kanpur - Ballabhgarh (KB) line to ensure the fine tuning of line reactance by proposed split TCSC in place of existing KB TCSC. A three phase KB transmission system is developed in MATLAB/Simulink (SimPowerSystems) for

1. without any compensation,
2. with fixed capacitor (FC),
3. with FC + existing KB TCSC and
4. with FC + proposed split TCSC

The KB system is analyzed for a step variation of load and performance of the system is investigated with a closed loop reactance control method.

Keywords: Single TCSC, Split TCSC, TCSC Reactance characteristic curve, Power flow analysis, Sensitivity analysis.

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Authors: Souvik Bhattacharyya, Aparajita Khan, Indradip Banerjee, Gautam Sanyal

Abstract:

Steganography is the art and science that hides the information in an appropriate cover carrier like image, text, audio and video media. In this work the authors propose a new image based steganographic method for hiding information within the complex bit planes of the image. After slicing into bit planes the cover image is analyzed to extract the most complex planes in decreasing order based on their bit plane complexity. The complexity function next determines the complex noisy blocks of the chosen bit plane and finally pixel mapping method (PMM) has been used to embed secret bits into those regions of the bit plane. The novel approach of using pixel mapping method (PMM) in bit plane domain adaptively embeds data on most complex regions of image, provides high embedding capacity, better imperceptibility and resistance to steganalysis attack.

Keywords: PMM (Pixel Mapping Method), Bit Plane, Steganography, SSIM, KL-Divergence.

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Authors: Punit Kumar, Niraj Kumar

Abstract:

The influence of transverse surface roughness on EHL characteristics has been investigated numerically using an extensive set of full EHL line contact simulations for shear-thinning lubricants under pure sliding condition. The shear-thinning behavior of lubricant is modeled using Carreau viscosity equation along with Doolittle-Tait equation for lubricant compressibility. The surface roughness is assumed to be sinusoidal and it is present on the stationary surface. It is found that surface roughness causes sharp pressure peaks along with reduction in central and minimum film thickness. With increasing amplitude of surface roughness, the minimum film thickness decreases much more rapidly as compared to the central film thickness.

Keywords: EHL, Carreau, Shear-thinning, Surface Roughness, Amplitude, Wavelength.

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Authors: S. Sendhil Kumar, M. Senthil Kumar

Abstract:

Maintenance and design engineers have great concern for the functioning of rotating machineries due to the vibration phenomenon. Improper functioning in rotating machinery originates from the damage to rolling element bearings. The status of rolling element bearings require advanced technologies to monitor their health status efficiently and effectively. Avoiding vibration during machine running conditions is a complicated process. Vibration simulation should be carried out using suitable sensors/ transducers to recognize the level of damage on bearing during machine operating conditions. Various issues arising in rotating systems are interlinked with bearing faults. This paper presents an approach for fault diagnosis of bearings using neural networks and time/frequencydomain vibration analysis.

Keywords: Bearing vibration, Condition monitoring, Fault diagnosis, Frequency domain.

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Authors: Anuj K. Sharma, Amit Sharma, Kulbhushan Agnihotri

Abstract:

In this work, we propose and analyze a model of Phytoplankton-Zooplankton interaction with harvesting considering that some species are exploited commercially for food. Criteria for local stability, instability and global stability are derived and some threshold harvesting levels are explored to maintain the population at an appropriate equilibrium level even if the species are exploited continuously.Further,biological and bionomic equilibria of the system are obtained and an optimal harvesting policy is also analysed using the Pantryagin’s Maximum Principle.Finally analytical findings are also supported by some numerical simulations.

Keywords: Phytoplankton-Zooplankton, Global stability, Bionomic Equilibrium, Pontrying-Maximum Principal.

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