Search results for: Gaurav Sharma

Authors: Sunil Kamboj, Vipin Saini, Suman Bala, Gaurav Sharma

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The main aim of the present research was to encapsulate mefenamic acid in niosomes andincorporate the prepared niosomes in the carbopol gel base for sustained therapeutic action. Mefenamic acid loaded niosomes were prepared by thin film hydration technique and evaluated for entrapment efficiency, vesicular size and zeta potential. The entrapment efficiency of the prepared niosomes was found to increase with decreasing the HLB values of surfactants and vesicle size was found to increase with increasing the cholesterol concentration. Niosomal vesicles with good entrapment efficiencies were incorporated in carbopol gel base to form the niosomal gel. The prepared niosomal gel was evaluated for pH, viscosity, spreadability, extrudability and skin permeation study across the rat skin. The results of permeation study revealed that the gel formulated with span 60 niosomes sustained the drug release for 12h. Further the in vivo study showed the good inhibition of inflammation by the gel prepared with span 60 niosomes.

Keywords: Mefenamic acid, niosomal gel, nonionic surfactants, sustained release.

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Authors: Janak Raj Sharma, Rajni Sharma

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Based on Traub-s methods for solving nonlinear equation f(x) = 0, we develop two families of third-order methods for solving system of nonlinear equations F(x) = 0. The families include well-known existing methods as special cases. The stability is corroborated by numerical results. Comparison with well-known methods shows that the present methods are robust. These higher order methods may be very useful in the numerical applications requiring high precision in their computations because these methods yield a clear reduction in number of iterations.

Keywords: Nonlinear equations and systems, Newton's method, fixed point iteration, order of convergence.

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

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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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Authors: Sandeep Sharma, Sarabjit Singh, Meenakshi Sharma

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Load balancing is the process of improving the performance of a parallel and distributed system through a redistribution of load among the processors [1] [5]. In this paper we present the performance analysis of various load balancing algorithms based on different parameters, considering two typical load balancing approaches static and dynamic. The analysis indicates that static and dynamic both types of algorithm can have advancements as well as weaknesses over each other. Deciding type of algorithm to be implemented will be based on type of parallel applications to solve. The main purpose of this paper is to help in design of new algorithms in future by studying the behavior of various existing algorithms.

Keywords: Load balancing (LB), workload, distributed systems, Static Load balancing, Dynamic Load Balancing

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Authors: Rishabh Sharma, Renu Vig, Neeraj Sharma

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The main design parameter of WSN (wireless sensor network) is the energy consumption. To compensate this parameter, hierarchical clustering is a technique that assists in extending duration of the networks life by efficiently consuming the energy. This paper focuses on dealing with the WSNs and the FIS (fuzzy interface system) which are deployed to enhance the BEENISH protocol. The node energy, mobility, pause time and density are considered for the selection of CH (cluster head). The simulation outcomes exhibited that the projected system outperforms the traditional system with regard to the energy utilization and number of packets transmitted to sink.

Keywords: Wireless sensor network, sink, sensor node, routing protocol, fuzzy rule, fuzzy inference system.

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Authors: Gaurav Kumar, Rakesh Kumar Bajaj

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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: Anuj Kumar Sharma, Amit Sharma, Kulbhushan Agnihotri

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In this paper, a delayed plankton-nutrient interaction model consisting of phytoplankton, zooplankton and dissolved nutrient is considered. It is assumed that some species of phytoplankton releases toxin (known as toxin producing phytoplankton (TPP)) which is harmful for zooplankton growth and this toxin releasing process follows a discrete time variation. Using delay as bifurcation parameter, the stability of interior equilibrium point is investigated and it is shown that time delay can destabilize the otherwise stable non-zero equilibrium state by inducing Hopf-bifurcation when it crosses a certain threshold value. Explicit results are derived for stability and direction of the bifurcating periodic solution by using normal form theory and center manifold arguments. Finally, outcomes of the system are validated through numerical simulations.

Keywords: Plankton, Time delay, Hopf-bifurcation, Normal form theory, Center manifold theorem.

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Authors: A. A. Sharma, B. J. N. Sharma

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This paper deals with the study of reflection and transmission characteristics of acoustic waves at the interface of a semiconductor half-space and elastic solid. The amplitude ratios (reflection and transmission coefficients) of reflected and transmitted waves to that of incident wave varying with the incident angles have been examined for the case of quasi-longitudinal wave. The special cases of normal and grazing incidence have also been derived with the help of Gauss elimination method. The mathematical model consisting of governing partial differential equations of motion and charge carriers’ diffusion of n-type semiconductors and elastic solid has been solved both analytically and numerically in the study. The numerical computations of reflection and transmission coefficients has been carried out by using MATLAB programming software for silicon (Si) semiconductor and copper elastic solid. The computer simulated results have been plotted graphically for Si semiconductors. The study may be useful in semiconductors, geology, and seismology in addition to surface acoustic wave (SAW) devices.

Keywords: Quasilongitudinal, reflection and transmission, semiconductors, acoustics.

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Authors: Gaurav Upadhyay, Nand Kishore, Prashant Ranjan, V. S. Tripathi, Shivesh Tripathi

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A frequency reconfigurable multiband antenna for intelligent transportation system (ITS) applications is proposed in this paper. A PIN-diode is used for reconfigurability. Centre frequencies are 1.38, 1.98, 2.89, 3.86, and 4.34 GHz in “ON” state of Diode and 1.56, 2.16, 2.88, 3.91 and 4.45 GHz in “OFF” state. Achieved maximum bandwidth is 18%. The maximum gain of the proposed antenna is 2.7 dBi in “ON” state and 3.95 dBi in “OFF” state of the diode. The antenna is simulated, fabricated, and tested in the lab. Measured and simulated results are in good confirmation.

Keywords: ITS, multiband antenna, PIN-diode, reconfigurable.

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Authors: Sameru Sharma, Sanjay Sharma, Derick Engles

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Multiple-input multiple-output (MIMO) systems are widely in use to improve quality, reliability of wireless transmission and increase the spectral efficiency. However in MIMO systems, multiple copies of data are received after experiencing various channel effects. The limitations on account of complexity due to number of antennas in case of conventional decoding techniques have been looked into. Accordingly we propose a modified sphere decoder (MSD-1) algorithm with lower complexity and give rise to system with high spectral efficiency. With the aim to increase signal diversity we apply rotated quadrature amplitude modulation (QAM) constellation in multi dimensional space. Finally, we propose a new architecture involving space time trellis code (STTC) concatenated with space time block code (STBC) using MSD-1 at the receiver for improving system performance. The system gains have been verified with channel state information (CSI) errors.

Keywords: Channel State Information , Diversity, Multi-Antenna, Rotated Constellation, Space Time Codes.

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Authors: Gaurav Kumar, Dharmbir Prasad, Rudra Pratap Singh

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In the current work, adaptive extended Kalman filter (AEKF) is presented for solution of ground radar based ballistic missile (BM) tracking problem in re-entry phase with unknown ballistic coefficient. The estimation of trajectory of any BM in re-entry phase is extremely difficult, because of highly non-linear motion of BM. The estimation accuracy of AEKF has been tested for a typical test target tracking problem adopted from literature. Further, the approach of AEKF is compared with extended Kalman filter (EKF). The simulation result indicates the superiority of the AEKF in solving joint parameter and state estimation problems.

Keywords: Adaptive, AEKF, ballistic missile, EKF, re-entry phase, target tracking.

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Authors: Ayush Chugh, Gaurav Gupta

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Today’s technology is heavily dependent on web applications. Web applications are being accepted by users at a very rapid pace. These have made our work efficient. These include webmail, online retail sale, online gaming, wikis, departure and arrival of trains and flights and list is very long. These are developed in different languages like PHP, Python, C#, ASP.NET and many more by using scripts such as HTML and JavaScript. Attackers develop tools and techniques to exploit web applications and legitimate websites. This has led to rise of web application security; which can be broadly classified into Declarative Security and Program Security. The most common attacks on the applications are by SQL Injection and XSS which give access to unauthorized users who totally damage or destroy the system. This paper presents a detailed literature description and analysis on Web Application Security, examples of attacks and steps to mitigate the vulnerabilities.

Keywords: Attacks, Injection, JavaScript, SQL, Vulnerability, XSS.

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Authors: Meenakshi Mahajan, Arun Sharma, Navendu Sharma

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Increasing use of cell phone as a medium of human interaction is playing a vital role in solving riddles of crime as well. A young girl went missing from her home late in the evening in the month of August, 2008 when her enraged relatives and villagers physically assaulted and chased her fiancée who often frequented her home. Two years later, her mother lodged a complaint against the relatives and the villagers alleging that after abduction her daughter was either sold or killed as she had failed to trace her. On investigation, a rusted cell phone with partial visible IMEI number, clothes, bangles, human skeleton etc. recovered from abandoned well in the month of May, 2011 were examined in the lab. All hopes pinned on identity of cell phone, for only linking evidence to fix the scene of occurrence supported by call detail record (CDR) and to dispel doubts about mode of sudden disappearance or death as DNA technology did not help in establishing identity of the deceased. The conventional scientific methods were used without success and international mobile equipment identification number of the cell phone could be generated by using statistical analysis followed by online verification. 

Keywords: Call detail record, Luhn algorithm, stereomicroscope.

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Authors: Gaurav Shinde, Sai Charan Gongiguntla, Prajwal Shirur, Ahmed Hambaba

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Health issues are significantly increasing, putting a substantial strain on healthcare services. This has accelerated the integration of machine learning in healthcare, particularly following the COVID-19 pandemic. The utilization of machine learning in healthcare has grown significantly. We introduce DeClEx, a pipeline which ensures that data mirrors real-world settings by incorporating gaussian noise and blur and employing autoencoders to learn intermediate feature representations. Subsequently, our convolutional neural network, paired with spatial attention, provides comparable accuracy to state-of-the-art pre-trained models while achieving a threefold improvement in training speed. Furthermore, we provide interpretable results using explainable AI techniques. We integrate denoising and deblurring, classification and explainability in a single pipeline called DeClEx.

Keywords: Machine learning, healthcare, classification, explainability.

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Authors: Gaurav Upadhyay, Nand Kishore, Prashant Ranjan, Shivesh Tripathi, V. S. Tripathi

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In this paper, a patch antenna array design is proposed for vehicular communication. The antenna consists of 2-element patch array. The antenna array is operating at multiple frequency bands. The multiband operation is achieved by use of slots at proper locations at the patch. The array is made reconfigurable by use of two PIN-diodes. The antenna is simulated and measured in four states of diodes i.e. ON-ON, ON-OFF, OFF-ON, and OFF-OFF. In ON-ON state of diodes, the resonant frequencies are 4.62-4.96, 6.50-6.75, 6.90-7.01, 7.34-8.22, 8.89-9.09 GHz. In ON-OFF state of diodes, the measured resonant frequencies are 4.63-4.93, 6.50-6.70 and 7.81-7.91 GHz. In OFF-ON states of diodes the resonant frequencies are 1.24-1.46, 3.40-3.75, 5.07-5.25 and 6.90-7.20 GHz and in the OFF-OFF state of diodes 4.49-4.75 and 5.61-5.98 GHz. The maximum bandwidth of the proposed antenna is 16.29%. The peak gain of the antenna is 3.4 dB at 5.9 GHz, which makes it suitable for vehicular communication.

Keywords: Antenna, array, reconfigurable, vehicular.

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Authors: Shreyash Sinai Kunde, Siddhang Tendulkar, Shiv Prakash Gupta, Gaurav Kumar, Suresh Mikkili

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One of the major power quality concerns in modern times is the problem of current harmonics. The current harmonics is caused due to the increase in non-linear loads which is largely dominated by power electronics devices. The Shunt active filtering is one of the best solutions for mitigating current harmonics. This paper describes a fuzzy logic controller based (FLC) based three Phase Shunt active Filter to achieve low current harmonic distortion (THD) and Reactive power compensation. The performance of fuzzy logic controller is analysed under both balanced sinusoidal and unbalanced sinusoidal source condition. The above controller serves the purpose of maintaining DC Capacitor Voltage constant. The proposed shunt active filter uses hysteresis current controller for current control of IGBT based PWM inverter. The simulation results of model in Simulink MATLAB reveals satisfying results.

Keywords: Shunt active filter, Current harmonics, Fuzzy logic controller, Hysteresis current controller.

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Authors: Harshit Mehrotra, Gaurav Agrawal, M.C. Srivastava

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Computerized lip reading has been one of the most actively researched areas of computer vision in recent past because of its crime fighting potential and invariance to acoustic environment. However, several factors like fast speech, bad pronunciation, poor illumination, movement of face, moustaches and beards make lip reading difficult. In present work, we propose a solution for automatic lip contour tracking and recognizing letters of English language spoken by speakers using the information available from lip movements. Level set method is used for tracking lip contour using a contour velocity model and a feature vector of lip movements is then obtained. Character recognition is performed using modified k nearest neighbor algorithm which assigns more weight to nearer neighbors. The proposed system has been found to have accuracy of 73.3% for character recognition with speaker lip movements as the only input and without using any speech recognition system in parallel. The approach used in this work is found to significantly solve the purpose of lip reading when size of database is small.

Keywords: Contour Velocity Model, Lip Contour Tracking, LipReading, Visual Character Recognition.

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Authors: Sushil Kumar Swar, Sanjay Kumar Sharma, Hari Krishan Sharma, Sushil Kumar

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The seriously damaged structures during earthquakes show the need and importance of design of reinforced concrete structures with high ductility. Reinforced concrete beam-column joints have an important function in all structures. Under seismic excitation, the beam column joint region is subjected to horizontal and vertical shear forces whose magnitude is many times higher than the adjacent beam and column. Strength and ductility of structures depends mainly on proper detailing of the reinforcement in beamcolumn joints and the old structures were found ductility deficient. DSP materials are obtained by using high quantities of super plasticizers and high volumes of micro silica. In the case of High Performance Densified Small Particle Concrete (HPDSPC), since concrete is dense even at the micro-structure level, tensile strain would be much higher than that of the conventional SFRC, SIFCON & SIMCON. This in turn will improve cracking behaviour, ductility and energy absorption capacity of composites in addition to durability. The fine fibers used in our mix are 0.3mm diameter and 10 mm which can be easily placed with high percentage. These fibers easily transfer stresses and act as a composite concrete unit to take up extremely high loads with high compressive strength. HPDSPC placed in the beam column joints helps in safety of human life due to prolonged failure.

Keywords: High Performance Densified Small Particle Concrete (HPDSPC), Steel Fıber Reinforced Concrete (SFRC), Slurry Infiltrated Concrete (SIFCON), Slurry Infiltrated Mat Concrete (SIMCON).

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Authors: R. Sharma, S. Kumar, C. Sharma

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A number of toxic chlorophenolic compounds are formed during pulp bleaching. The nature and concentration of these chlorophenolic compounds largely depends upon the amount and nature of bleaching chemicals used. These compounds are highly recalcitrant and difficult to remove but are partially removed by the biochemical treatment processes adopted by the paper industry. Identification and estimation of these chlorophenolic compounds has been carried out in the primary and secondary clarified effluents from the paper mill by GCMS. Twenty-six chorophenolic compounds have been identified and estimated in paper mill waste waters. Electrochemical treatment is an efficient method for oxidation of pollutants and has successfully been used to treat textile and oil waste water. Electrochemical treatment using less expensive anode material, stainless steel electrodes has been tried to study their removal. The electrochemical assembly comprised a DC power supply, a magnetic stirrer and stainless steel (316 L) electrode. The optimization of operating conditions has been carried out and treatment has been performed under optimized treatment conditions. Results indicate that 68.7% and 83.8% of cholorphenolic compounds are removed during 2 h of electrochemical treatment from primary and secondary clarified effluent respectively. Further, there is a reduction of 65.1, 60 and 92.6% of COD, AOX and color, respectively for primary clarified and 83.8%, 75.9% and 96.8% of COD, AOX and color, respectively for secondary clarified effluent. EC treatment has also been found to increase significantly the biodegradability index of wastewater because of conversion of non- biodegradable fraction into biodegradable fraction. Thus, electrochemical treatment is an efficient method for the degradation of cholorophenolic compounds, removal of color, AOX and other recalcitrant organic matter present in paper mill waste water.

Keywords: Chlorophenolics, effluent, electrochemical treatment, wastewater.

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Authors: Rajkumar Verma, Bhu Dev Sharma

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In the present communication, the existing measures of fuzzy entropy are reviewed. A generalized parametric exponential fuzzy entropy is defined.Our study of the four essential and some other properties of the proposed measure, clearly establishes the validity of the measure as an entropy.

Keywords: fuzzy sets, fuzzy entropy, exponential entropy, exponential fuzzy entropy.

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Authors: Gaurav Kumar, Rakesh Kumar Bajaj

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The primary objective of the paper is to propose a new method for solving assignment problem under uncertain situation. In the classical assignment problem (AP), z_pqdenotes the cost for assigning the qth job to the pth person which is deterministic in nature. Here in some uncertain situation, we have assigned a cost in the form of composite relative degree F_pq instead of  and this replaced cost is in the maximization form. In this paper, it has been solved and validated by the two proposed algorithms, a new mathematical formulation of IVIF assignment problem has been presented where the cost has been considered to be an IVIFN and the membership of elements in the set can be explained by positive and negative evidences. To determine the composite relative degree of similarity of IVIFS the concept of similarity measure and the score function is used for validating the solution which is obtained by Composite relative similarity degree method. Further, hypothetical numeric illusion is conducted to clarify the method’s effectiveness and feasibility developed in the study. Finally, conclusion and suggestion for future work are also proposed.

Keywords: Assignment problem, Interval-valued Intuitionistic Fuzzy Sets, Similarity Measures, score function.

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Authors: Sourabh Jain, Sukhvir Singh Jain, Gaurav V. Jain

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Intelligent Transportation System is an integrated application of communication, control and monitoring and display process technologies for developing a user–friendly transportation system for urban areas in developing countries. In fact, the development of a country and the progress of its transportation system are complementary to each other. Urban traffic has been growing vigorously due to population growth as well as escalation of vehicle ownership causing congestion, delays, pollution, accidents, high-energy consumption and low productivity of resources. The development and management of urban transport in developing countries like India however, is at tryout stage with very few accumulations. Under the umbrella of ITS, urban corridor management strategy have proven to be one of the most successful system in accomplishing these objectives. The present study interprets and figures out the performance of the 27.4 km long Urban Bus route having six intersections, five flyovers and 29 bus stops that covers significant area of the city by causality analysis. Performance interpretations incorporate Passenger Boarding and Alighting, Dwell time, Distance between Bus Stops and Total trip time taken by bus on selected urban route.

Keywords: Congestion, Dwell time, delay, passengers boarding alighting, travel time.

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Authors: Gaurav

Abstract:

Sexuality remains a personal or a private matter of discussion in the Indian society and generally discussed among the same age group or gender. Complete absence of the sex education has caused serious implications for the students with disabilities in Indian society. There are widespread perceptions that student with disabilities are ‘asexual’, ‘unattractive’ and therefore cannot be considered sexually desirable. Such perceptions continue to reinforce the other perceptions that student with disabilities are somehow incapable of being in an intimate relationship in the life and therefore they do not need any learning related to the sex education. We need to understand that if a student has a disability, it does not mean that student have no emotional feelings, hormones and sexual desires like any other student without disability. Sexuality is an integral part of every human life and should not be seen as matter of shame and guilt. Unfortunately, the concept of the sex education is misunderstood in itself. Instead of realizing the crucial importance of sex education for the students with disabilities or non-disabilities, it is often considered mainly as an education about ‘how to have sexual intercourse’. One needs to understand that it is not just about sexual conduct but also about the gender and sexual identity, self-esteem, self protection and acceptance of self. This research paper examined issues and debates around the sex education, particularly in context of the students with disabilities in India and focuses on how students with disabilities themselves see the need of sex (health) education. To understand their perceptions, descriptive survey method was used. It was found that most of the students among respondent were comfortable and felt it as a strong need for such orientation during their schooling. The paper emphasizes that sex education is a need of the time and further a necessity. Hence it is important for our education system to implement it for the complete well being of the students with disabilities.

Keywords: Disabilities, identity, sexuality, sex education.

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Authors: Ashish Goswami, Rakesh Sharma

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In this paper, LDPC Codes based on defected fullerene graphs have been generated. And it is found that the codes generated are fast in encoding and better in terms of error performance on AWGN Channel.

Keywords: LDPC Codes, Fullerene Graphs, Defected Fullerene Graphs.

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Authors: Sachin Kumar, Y. K. Gupta, J. R. Sharma

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In the present article, a new class of solutions of Einstein field equations is investigated for a spherically symmetric space-time when the source of gravitation is a perfect fluid. All the solutions have been derived by making some suitable arrangements in the field equations. The solutions so obtained have been seen to describe Schwarzschild interior solutions. Most of the solutions are subjected to the reality conditions. As far as the authors are aware the solutions are new.

Keywords: Einstein's equations, General Relativity, PerfectFluid, Spherical symmetric.

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Authors: Shashank Gautam, Pramod Sharma

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In present era, development of digital circuits, signal processors and other integrated circuits, magnitude comparators are challenged by large area and more power consumption. Comparator is most basic circuit that performs comparison. This paper presents a technique to design a two bit comparator which consumes less area and power. DSCH and MICROWIND version 3 are used to design the schematic and design the layout of the schematic, observe the performance parameters at different nanometer technologies respectively.

Keywords: Chip design, consumed power, layout area, two bit comparator.

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Authors: K. K. Sharma, A. C. Katoch

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We investigate nonfactorizable contributions to D → ¤Ç¤Ç decay modes. We perform isospin analysis of the nonfactorizable contributions to these decays. Obtaining the factorizable contributions from spectator-quark diagrams using = 3 C N , we determine nonfactorizable amplitudes for these decays and predict their branching ratios.

Keywords: Mesons, Branching Ratios, Decay Amplitudes, Heavy Flavor Mesons, Nonfactorizable Contributions, Weak Decays.

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Authors: Manisha Dubey, Gaurav Gupta, Anoop Arya

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The demand for power supply increases day by day in developing countries like India henceforth demand of reactive power support in the form of ancillary services provider also has been increased. The multi-line and multi-type Flexible alternating current transmission system (FACTS) controllers are playing a vital role to regulate power flow through the transmission line. Unified power flow controller and interline power flow controller can be utilized to control reactive power flow through the transmission line. In a restructured power system, the demand of such controller is being popular due to their inherent capability. The transmission pricing by using reactive power cost allocation through modified matrix methodology has been proposed. The FACTS technologies have quite costly assembly, so it is very useful to apportion the expenses throughout the restructured electricity industry. Therefore, in this work, after embedding the FACTS devices into load flow, the impact on the costs allocated to users in fraction to the transmission framework utilization has been analyzed. From the obtained results, it is clear that the total cost recovery is enhanced towards the Reactive Power flow through the different transmission line for 5 bus test system. The fair pricing policy towards reactive power can be achieved by the proposed method incorporating FACTS controller towards cost recovery of the transmission network.

Keywords: Inter line power flow controller, Transmission Pricing, Unified power flow controller, cost allocation.

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Authors: Divya Sharma

Abstract:

Nic Pizzolatto’s True Detective offers profound mythological and philosophical ramblings for audiences with literary sensibilities. An American Sothern Gothic with its Bayon landscape of the Gulf Coast of Louisiana, where two detectives Rustin Cohle and Martin Hart begin investigating the isolated murder of Dora Lange, only to discover an entrenched network of perversion and corruption, offers an existential outlook. The proposed research paper shall attempt to investigate the pervasive themes of gothic and existentialism in the music of the first season of the series.

Keywords: Existentialism, Gothic, Music, Mythology, Philosophy.

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Authors: M. R. Yadav, A. K. Sharma, B. S. Thakur

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The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to support our work.

Keywords: Cyclic contraction, rational cyclic contraction, best proximity point and complete metric space.

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