Search results for: Suman Singh

Authors: S. Suman, G. N. Singh

Abstract:

The present manuscript addresses the estimation procedure of population parameter using Poisson probability distribution when characteristic under study possesses a rare sensitive attribute. The generalized form of unrelated randomized response model is suggested in order to acquire the truthful responses from respondents. The resultant estimators have been proposed for two situations when the information on an unrelated rare non-sensitive characteristic is known as well as unknown. The properties of the proposed estimators are derived, and the measure of confidentiality of respondent is also suggested for respondents. Empirical studies are carried out in the support of discussed theory.

Keywords: Poisson distribution, randomized response model, rare sensitive attribute, non-sensitive attribute

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Authors: S. Suman, G. N. Singh

Abstract:

This research work is an effort to analyse the consequences of scrambled response technique to estimate the current population mean in two-occasion successive sampling when the characteristic of interest is sensitive in nature. The generalized estimation procedures have been proposed using sensitive auxiliary variables under additive and multiplicative scramble models. The properties of resultant estimators have been deeply examined. Simulation, as well as empirical studies, are carried out to evaluate the performances of the proposed estimators with respect to other competent estimators. The results of our studies suggest that the proposed estimation procedures are highly effective under the presence of non-response situation. The result of this study also suggests that additive scrambled response model is a better choice in the perspective of cost of the survey and privacy of the respondents.

Keywords: scrambled response, sensitive characteristic, successive sampling, optimum replacement strategy

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Authors: Jaspreet Singh, Gurvinder Singh, Prabhsimran Singh, Rajinder Singh, Prithvipal Singh, Karanjeet Singh Kahlon, Ravinder Singh Sawhney

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Morphological evaluation of Indian languages is one of the burgeoning fields in the area of Natural Language Processing (NLP). The evaluation of a language is an eminent task in the era of information retrieval and text mining. The extraction and classification of knowledge from text can be exploited for sentiment analysis and morphological evaluation. This study coalesce morphological evaluation and sentiment analysis for the task of classification of farmer suicide cases reported in Punjab state of India. The pre-processing of Punjabi text involves morphological evaluation and normalization of Punjabi word tokens followed by the training of proposed model using deep learning classification on Punjabi language text extracted from online Punjabi news reports. The class-wise accuracies of sentiment prediction for four negatively oriented classes of farmer suicide cases are 93.85%, 88.53%, 83.3%, and 95.45% respectively. The overall accuracy of sentiment classification obtained using proposed framework on 275 Punjabi text documents is found to be 90.29%.

Keywords: deep neural network, farmer suicides, morphological processing, punjabi text, sentiment analysis

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Authors: Jagbir Singh Kadyan, C. A. Suman Kadyan

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The researchers attempts to establish whether a relationship exists between the social activities undertaken & the funds that has been spent by the selected corporate organisations. Corporate listed on the (NSE) National Stock Exchange of India, under different categories shall be selected as a sample for the purpose of this study. The researches shall also study the dynamics of corporate social responsibility funding, financing & management of corporate social responsibility funds by the above selected organisations in the Indian context. The rationale behind selecting & undertaking specific corporate social responsibility activities shall be analysed & interpreted to discover the real drivers of corporate social responsibility. Besides above, an attempt shall further make an effort to understand & analyse the nature of impact on the selected corporate organisations on its overall performances due to the activities undertaken under their specific corporate social responsibility programs.

Keywords: corporate social responsibility, organisational performance, national stock exchange, sustainability, society, health, education, sanitation, environment

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Authors: Suman Singh, Myungho Lee, Insik Park, Yangjai Shin, Youn Suk Lee

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Active antimicrobial films prepared by incorporating AgSiO2, AgZn, and AgZ at 1%, 3%, 5%, 10% (w/w) into polypropylene (PP) matrix. Complete thermal, structural, mechanical and functional characterization were carried out of all formulations and determined the antimicrobial efficiency and returnable antimicrobial efficiency according to the Japanese Industrial Standard method. The morphology of the films showed agglomerates of particles in the composites. The active formulation had decreased elongation compared to the pure PP sample. Thermal analyses indicated that the active formulation compositions had increased thermal stability. The films showed 50% antimicrobial properties after the fifth wash against the tested microorganisms, presenting better activity against Gram negative organisms than Gram positive ones. These findings suggest that PP films with AgSiO2, AgZn, and AgZ particles could provide a significant contribution to the quality and safety of seafood in the distribution chain.

Keywords: antimicrobial film, properties and characterization, returnable packaging, sea food

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Authors: Navneetinder Singh, Harprabhjot Singh, Harpreet Singh, Supreet Singh

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Many materials are known to mankind that is widely used for synthesis of corrosion resistant hydrophobic coatings. In the current work, novel hydrophobic composite was synthesized by mixing polytetrafluoroethylene (PTFE) and 20 weight% ceria particles followed by sintering. This composite had same hydrophobic behavior as PTFE. Moreover, composite showed better scratch resistance than virgin PTFE. Pits of plasma sprayed Ni₃Al coating were exploited to hold PTFE composite on the substrate as Superni-75 alloy surface through sintering process. Plasma sprayed surface showed good adhesion with the composite coating during scratch test. Potentiodynamic corrosion test showed 100 fold decreases in corrosion rate of coated sample this may be attributed to inert and hydrophobic nature of PTFE and ceria.

Keywords: polytetrafluoroethylene, PTFE, ceria, coating, corrosion

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Authors: Gurmeet Singh Cheema, Navjotinder Singh, Gurjinder Singh, Amardeep Singh

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Aluminium and its alloys play have excellent corrosion resistant properties, ease of fabrication and high specific strength to weight ratio. In this investigation an attempt has been made to study the effect of different post weld heat treatment methods on the mechanical and metallurgical properties of TIG welded joints of the commercial aluminium alloy. Three different methods of post weld heat treatments are, solution heat treatment, artificial aged and combination of solution heat treatment and artificial aging are given to TIG welded aluminium joints. Mechanical and metallurgical properties of as welded and post weld treated joints of the aluminium alloys was examined.

Keywords: aluminium alloys, TIG welding, post weld heat treatment

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Authors: Jasbinder Singh, Harjit Pal Singh, S. A. Khan

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The work, in this paper, presents the comparison of encoded speech signals by different VoIP narrow-band and wide-band codecs for different modulation schemes. The simulation results indicate that codec has an impact on the speech quality and also effected by modulation schemes.

Keywords: VoIP, coders, modulations, BER, MOS

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Authors: Prayas Sharma

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This paper proposed a generalized class of estimators, an exponential class of estimators based on the adaption of Sharma and Singh (2015) and Solanki and Singh (2013), and a simple difference estimator for estimating unknown population mean in the case of Poisson distributed population in simple random sampling without replacement. The expressions for mean square errors of the proposed classes of estimators are derived from the first order of approximation. It is shown that the adapted version of Solanki and Singh (2013), the exponential class of estimator, is always more efficient than the usual estimator, ratio, product, exponential ratio, and exponential product type estimators and equally efficient to simple difference estimator. Moreover, the adapted version of Sharma and Singh's (2015) estimator is always more efficient than all the estimators available in the literature. In addition, theoretical findings are supported by an empirical study to show the superiority of the constructed estimators over others with an application to earthquake data of Turkey.

Keywords: auxiliary attribute, point bi-serial, mean square error, simple random sampling, Poisson distribution

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Authors: Riya Mishra, Trayambak Tiwari, Anju Lata Singh, I. L. Singh, Tara Singh

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Decrement in vigilance task performance echoes impediment in effortful attention; here attention fluctuated in the realm of external and internal milieu of a person. To examine this fluctuation across time period, we employed two experiments of vigilance task with variation in thought probing rate, which was embedded in the task. The thought probe varies in terms of <2 minute per thought probe and <4 minute per thought probe during vigilance task. A 2x4 repeated measure factorial design was used. 15 individuals participated in this study with an age range of 20-26 years. It was found that thought probing rate has a negative trend with vigilance task performance whereas the subjective measures of mind-wandering have a positive relation with thought probe rate.

Keywords: criterion response, mental status, mind-wandering, thought probe, vigilance

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Authors: Gurpreet Singh, Hazoor Singh, Buta Singh Sidhu

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In the current investigation plasma spray technique was used for depositing hydroxyapatite (HA) and HA – silicon oxide (SiO2) coatings on 316L SS substrate. In HA-SiO2 coating, 20 wt% SiO2 was mixed with HA. The feedstock and coatings were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM)/energy-dispersive X-ray spectroscopy (EDX) analyses. The corrosion resistance of the uncoated, HA coated and HA + 20 wt% SiO2 coated 316L SS was investigated by electrochemical corrosion testing in simulated human body fluid (Ringer’s solution). The influence of SiO2 (20 wt%) on corrosion resistance was determined. After the corrosion testing, the samples were analyzed by XRD and SEM/EDX analyses. The addition of SiO2 reduces the crystallinity of the coating. The corrosion resistance of the 316L SS was found to increase after the deposition of the HA + 20 wt% SiO2 and HA coatings.

Keywords: HA, SiO2, corrosion, Ringer’s solution, 316L SS

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Authors: Gurjinder Singh Randhawa, Jonny Garg, Sukhraj Singh, Gurmeet Singh Cheema

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A major problem related to the use of rotavator is wear of rotavator blades due to abrasion by soil hard particles, as it seriously affects tillage quality and agricultural production economy. The objective of this study was to increase the wear resistance by covering the rotavator blades with two different hard facing electrodes. These blades are generally produced from low carbon or low alloy steel. During the field work i.e. preparing land for the cultivation these blades are subjected to severe wear conditions. Comparative wear tests on a regular rotavator blade and two kinds of hardfacing with electrodes were conducted in the field. These two different hardfacing electrodes, which are designated HARD ALLOY-400 and HARD ALLOY-650, were used for hardfacing. The wear rate in the field tests was found to be significantly different statistically. When the cost is taken into consideration; HARD ALLOY-650 and HARD ALLOY-400 have been found to be the best hardfacing electrodes.

Keywords: hardfacing, rotavator blades, hard alloy-400, abrasive wear

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Authors: Sandeep Singh Sandhu, Karanvir Singh Ghuman, Parminder Singh Saini

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The aim of the present investigation was to study the effect of ultrasonic vibration on the cladding of the AISI 308 on the mild steel plates using the shielded metal arc welding (SMAW). Ultrasonic vibrations were applied to molten austenitic stainless steel during the welding process. Due to acoustically induced cavitations and streaming there is a complete mixture of the clad metal and the base metal. It was revealed that cladding of AISI 308 over mild steel along with ultrasonic vibrations result in uniform and finer grain structures. The effect of the vibration on the dilution, mechanical properties and metallographic studies were also studied. It was found that the welding done using the ultrasonic vibration has the less dilution and CVN value for the vibrated sample was also high.

Keywords: surfacing, ultrasonic vibrations, mechanical properties, shielded metal arc welding

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Authors: Aarushi Agarwal, Tara Singh, Anju Lata Singh, Trayambak Tiwari, Indramani Lal Singh

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The existing interdependent relationship between attention and consciousness has been put to debate since long. To testify the nature, dual-task paradigm has been used to simultaneously manipulate awareness and attention. With central discrimination task which is attentional demanding, participants also perform simple discrimination task in the periphery in near absence of attention. Individual-based analysis of performance accuracy in single and dual condition showed and above chance level performance i.e. more than 80%. In order to widen the understanding of extent of discrimination carried in near absence of attention, natural image and its geometric equivalent shape were presented in the periphery; synthetic objects accounted to lower level of performance than natural objects in dual condition. The gaze plot and heatmap indicate that peripheral performance do not necessarily involve saccade every time, verifying the discrimination in the periphery was in near absence of attention. Thus our studies show an interdependent nature of attention and awareness.

Keywords: attention, awareness, dual task paradigm, natural and geometric images

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Authors: Balkar Singh, Gurpreet Singh, Vivek Aggarwal, Sehijpal Singh

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The present research focused to improve the machinability of Hastelloy C-276 at different machining speeds such as 31, 55, and 79 m/min. The use of CO2 gas and Minimum quantity lubrication (MQL) was applied as coolant and lubrication purposes to enhance the machinability of the superalloy. The output in the form of surface roughness (S.R) and heat generation was monitored under dry, MQL, and MQL-CO2-cooled conditions. The Design of the Experiment was prepared using MINITAB software utilizing Taguchi L-27 orthogonal arrays followed by ANOVA analysis for finding the impact of input variables on output responses. At different speeds and lubrication conditions, different behavioral patterns for Surface Roughness and the temperature was observed. ANOVA analysis depicted that the cooling environment impacted the S.R. majorly (50%) followed by cutting speed (29.84%), feed rate (5.09%), and least through depth of cut (4.95%). On the other side, the temperature was greatly influenced by cutting speed (69.12%), Cryo-MQL (8.09%), feed rate (7.59%), and depth of cut (6.20%). Experimental results revealed that Cryo-MQL cooling enhanced the Surface roughness by 12% compared to MQL condition.

Keywords: Hastelloy C-276, minimum quantity lubrication, olive oil, cryogenic Cooling (CO2)

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Authors: Geeta Kasana, Kulbir Singh, Satvinder Singh

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In this paper, a steganographic scheme for digital images using Integer Wavelet Transform (IWT) is proposed. The cover image is decomposed into wavelet sub bands using IWT. Each of the subband is divided into blocks of equal size and secret data is embedded into the largest and smallest pixel values of each block of the subband. Visual quality of stego images is acceptable as PSNR between cover image and stego is above 40 dB, imperceptibility is maintained. Experimental results show better tradeoff between capacity and visual perceptivity compared to the existing algorithms. Maximum possible error analysis is evaluated for each of the wavelet subbands of an image.

Keywords: DWT, IWT, MSE, PSNR

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Authors: Deepak Nathiya1, Ramesh Roop Rai, Pratima Singh1, Preeti Raj1, Supriya Suman, Balvir Singh Tomar

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Background: Sarcopenia is a catabolic state in liver cirrhosis (LC), accelerated with a breakdown of skeletal muscle to release amino acids which adversely affects survival, health-related quality of life, and response to any underlying disease. The primary objective of the study was to investigate the long-term effect of branched-chain amino acids (BCAA) supplementations on parameters associated with improved prognosis in sarcopenic patients with LC, as well as to evaluate its impact on cirrhotic-related events. Methods: We carried out a 24 week, single-center, randomized, open-label, controlled, two cohort parallel-group intervention trial comparing the efficacy of BCAA against lactoalbumin (L-ALB) on 106 sarcopenic liver cirrhotics. The BCAA (intervention) group was treated with 7.2 g BCAA per whereas, the lactoalbumin group was also given 6.3 g of L-Albumin. The primary outcome was to assess the impact of BCAA on parameters of sarcopenia: muscle mass, muscle strength, and physical performance. The secondary outcomes were to study combined survival and maintenance of liver function changes in laboratory and clinical markers in the duration of six months. Results: Treatment with BCAA leads to significant improvement in sarcopenic parameters: muscle strength, muscle function, and muscle mass. The total cirrhotic-related complications and cumulative event-free survival occurred fewer in the BCAA group than in the L-ALB group. Prognostic markers also improved significantly in the study. Conclusion: The current clinical trial demonstrated that long-term BCAAs supplementation improved sarcopenia and prognostic markers in patients with advanced liver cirrhosis.

Keywords: sarcopenia, liver cirrhosis, BCAA, quality of life

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Authors: Gurpreet Singh, Hazoor Singh, Kulbir Singh Sandhu

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Friction Stir Welding Process emerged as promising solid-state welding and eliminates various welding defects like cracks and porosity in joining of dissimilar aluminum alloys. In the present research, Friction Stir Welding (FSW) is carried out on dissimilar aluminum alloys 2000 series and 6000 series this combination of alloys are highly used in automobile and aerospace industry due to their good strength to weight ratio, mechanical, and corrosion properties. The joints characterized by applying various destructive and non-destructive tests. Three critical welding parameters were considered i.e. Tool Rotation speed, Transverse speed, and Tool Geometry. The effective range of tool rotation speed from 1200-1800 rpm and transverse speed from 60-240 mm/min and tool geometry was studied. The two-different difficult to weld alloys were successfully welded. All the samples showed different microstructure with different set of welding parameters. It has been revealed with microstructure scans that grain refinement plays a crucial role in mechanical properties.

Keywords: aluminum alloys, friction stir welding, mechanical properties, microstructure

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Authors: Gurinder Singh, Kulbir Singh

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Digital multimedia contents such as image, video, and audio can be tampered easily due to the availability of powerful editing softwares. Multimedia forensics is devoted to analyze these contents by using various digital forensic techniques in order to validate their authenticity. Digital image forensics is dedicated to investigate the reliability of digital images by analyzing the integrity of data and by reconstructing the historical information of an image related to its acquisition phase. In this paper, a survey is carried out on the forgery detection by considering the most recent and promising digital image forensic techniques.

Keywords: Computer Forensics, Multimedia Forensics, Image Ballistics, Camera Source Identification, Forgery Detection

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Authors: Kanchan Singh, Sheo Kumar Singh

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The fundamental problem of subspace coding is to explore the maximum possible cardinality Aq(n, d, k) of a set of k-dimensional subspaces of an n-dimensional vector space over Fq such that the subspace distance satisfies ds(W1, W2) ≥ d for any two distinct subspaces W1, W2 in this set. In this paper, we construct a new class of constant dimension codes (CDCs) by generalizing the coset construction and combining it with CDCs derived from parallel linkage construction and coset construction with an aim to improve the new lower bounds of Aq(n, d, k). We found a remarkable improvement in some of the lower bounds of Aq(n, d, k).

Keywords: constant dimension codes, rank metric codes, coset construction, parallel linkage construction

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Authors: Buta Singh Sidhu, Sukhpal Singh Chatha, Hazoor Singh Sidhu

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In the present investigation, 75Cr3C2-25NiCr coating was deposited on T91 boiler tube steel substrate by high velocity oxy-fuel (HVOF) process to enhance high-temperature corrosion resistance. High-temperature performance of bare, as well as HVOF-coated steel specimens was evaluated for 1500 h under cyclic conditions in the platen superheater zone coal-fired boiler, where the temperature was around 900 °C. Experiments were carried out for 15 cycles each of 100 h duration followed by 1 h cooling at ambient temperature. The performance of the bare and coated specimens was assessed via metal thickness loss corresponding to the corrosion scale formation and the depth of internal corrosion attack. 75Cr3C2-25NiCr coating deposited on T91 steel imparted better hot corrosion resistance than the uncoated steel. Inferior resistance of bare T91 steel is attributed to the formation of pores and loosely bounded oxide scale rich in Fe2O3.

Keywords: 75Cr3C2-25NiCr, HVOF process, boiler steel, coal fired boilers

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Sartaj Singh, Amar Singh, Ashok Sharma, Sandeep Kaur

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With upcoming threats in a digital world, we need to work continuously in the area of security in all aspects, from hardware to software as well as data modelling. The rise in social media activities and hunger for data by various entities leads to cybercrime and more attack on the privacy and security of persons. Cryptography has always been employed to avoid access to important data by using many processes. Symmetric key and asymmetric key cryptography have been used for keeping data secrets at rest as well in transmission mode. Various cryptosystems have evolved from time to time to make the data more secure. In this research article, we are studying various cryptosystems in asymmetric cryptography and their application with usefulness, and much emphasis is given to Elliptic curve cryptography involving algebraic mathematics.

Keywords: cryptography, symmetric key cryptography, asymmetric key cryptography

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Authors: Davinder Singh, Jaimal Singh Khamba, Tarun Nanda

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Growth of the Indian economy has accelerated to 8% and efforts are on to further propel it to 10%. Undoubtedly, all the segments of the economy, viz. agriculture, industry and services have to improve their contribution to the economy. Growth of Micro-small and medium enterprises (MSMEs) is a sine qua non for the growth of industry, exports and other segments of the economy. Furthermore, promotion of entrepreneurship is also vital for sustenance and upward movement of the current growth trajectory of the economy. The MSME sector acts as a catalyst in upholding and encouraging the creation of the innovative spirit and entrepreneurship in the economy, thereby helping in laying the foundation for rapid industrial development. In this competitive world, they need to be able to confront the increasing competition from developed and emerging economies and to plug into the new market opportunities.

Keywords: characteristics, management, MSMEs, technology infrastructure

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Authors: Gurmeet Singh Cheema, Gurjinder Singh, Amardeep Singh Kang

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Aluminium alloy 6061 is a medium to high strength heat-treatable alloy which has very good corrosion resistance and very good weldability. Friction Stir Welding was developed and this technique has attracted considerable interest from the aerospace and automotive industries since it is able to produce defect free joints particularly for light metals i.e aluminum alloy and magnesium alloy. In the friction stir welding process, welding parameters such as tool rotational speed, welding speed and tool shoulder diameter play a major role in deciding the weld quality. In this research work, an attempt has been made to understand the effect of tool rotational speed, welding speed and tool shoulder diameter on friction stir welded AA6061 aluminium alloy joints. Statistical tool such as central composite design is used to develop the mathematical relationships. The mathematical model was developed to predict mechanical properties of friction stir welded aluminium alloy joints at the 95% confidence level.

Keywords: aluminium alloy, friction stir welding, central composite design, mathematical relationship

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Authors: V. Singh, S. Singh, S. S. Garewal

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Metal matrix composites with aluminum as the matrix material have been heralded as the next great development in advanced engineering materials. Aluminum metal matrix composites (AMMC) refer to the class of light weight high performance material systems. Properties of AMMCs can be tailored to the demands of different industrial applications by suitable combinations of matrix, reinforcement and processing route. AMMC finds its application in automotive, aerospace, defense, sports and structural areas. This paper presents an overview of AMMC material systems on aspects relating to processing, types and applications with case studies.

Keywords: aluminum metal matrix composites, applications of aluminum metal matrix composites, lighting material processing of aluminum metal matrix composites

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Authors: Vivek Kumar Singh, Tripti Singh

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An ad hoc wireless network consists of mobile networks which creates an underlying architecture for communication without the help of traditional fixed-position routers. Ad-hoc On-demand Distance Vector (AODV) is a routing protocol used for Mobile Ad hoc Network (MANET). Nevertheless, the architecture must maintain communication routes although the hosts are mobile and they have limited transmission range. There are different protocols for handling the routing in the mobile environment. Routing protocols used in fixed infrastructure networks cannot be efficiently used for mobile ad-hoc networks, so that MANET requires different protocols. This paper presents the performance analysis of the routing protocols used various parameter-patterns with Two-ray model.

Keywords: AODV, packet transmission rate, pause time, ZRP, QualNet 6.1

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Authors: Amit Prakash Singh, Shyamli Singh, Chavi Srivastav

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This paper presents the idea of Internet of Thing (IoT) for the infrastructure of smart cities. Internet of Thing has been visualized as a communication prototype that incorporates myriad of digital services. The various component of the smart cities shall be implemented using microprocessor, microcontroller, sensors for network communication and protocols. IoT enabled systems have been devised to support the smart city vision, of which aim is to exploit the currently available precocious communication technologies to support the value-added services for function of the city. Due to volume, variety, and velocity of data, it requires analysis using Big Data concept. This paper presented the various techniques used to analyze big data using machine learning.

Keywords: IoT, smart city, embedded systems, sustainable environment

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Authors: Sukhveer Singh, Sandeep Singh

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A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: uncertain transportation problem, efficient solution, ranking function, fuzzy transportation problem

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