Search results for: Manoj Pandey

Authors: Manoj Kumar Dutta

Abstract:

Wavelength division multiplexing (WDM) technology is the most promising technology for the proper utilization of huge raw bandwidth provided by an optical fiber. One of the key problems in implementing the all-optical WDM network is the packet contention. This problem can be solved by several different techniques. In time domain approach the packet contention can be reduced by incorporating fiber delay lines (FDLs) as optical buffer in the switch architecture. Different types of buffering architectures are reported in literatures. In the present paper a comparative performance analysis of three most popular FDL architectures are presented in order to obtain the best contention resolution performance. The analysis is further extended to consider the effect of different fiber non-linearities on the network performance.

Keywords: WDM network, contention resolution, optical buffering, non-linearity, throughput

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Authors: Froogh Shooshtaryzadeh, Pramod Pandey

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The present study investigates place and manner harmony in typically developing (TD) children and children with phonological disorder (PD) who are acquiring Farsi as their first language. Five TD and five PD children are examined regarding their place and manner harmony patterns. Data is collected through a Picture-Naming Task using 132 pictures of different items designed to elicit the production of 132 different words. The examination of the data has indicated some similarities and differences in harmony patterns in PD and TD children. Moreover, the results of this study on the place and manner harmony have illustrated some differences with the results of the preceding studies on languages other than Farsi. The results of this study are discussed and compared with results from other studies. Optimality Theory is employed to explain some of the findings of this study.

Keywords: place harmony, manner harmony, phonological development, Farsi

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Authors: Chander Shekhar, Manoj Kumar

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The present research paper is based on the explorations and excavations of Buddhist sites of the Indian state Haryana. It is a small state in north India. Earlier it was part of greater Punjab. Haryana has a very rich ancient history right from the Stone Age. It is known as the cradle of civilization. During the Buddha period, Haryana was very prosperous. Buddha also visited this region during the travel of the northwest province of British India. In this research work, the authors describe the Buddhist trail in Haryana and the tangible heritage of Buddhism, which were built in the respect and memory of the Buddha's journey like Stupa, Monasteries, Pillar, sculptures, etc. Several stupas like Chaneti Stupa, Thanesar Stupa, Agroha stupa, Adibadri, Katrawali, Assandh Stupa, and many monasteries were come into light during the excavation and exploration in Haryana as well as a lot of Buddhist sculptures also found.

Keywords: archaeology, Buddhism, exploration, excavations, stupa

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Authors: M. V. Manoj Kumar, Likewin Thomas, Annappa

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Process mining research discipline bridges the gap between data mining and business process modeling and analysis, it offers the process-centric and end-to-end methods/techniques for analyzing information of real-world process detailed in operational event-logs. In this paper, we have proposed a notation called trace logo for graphically representing control-flow perspective (order of execution of activities) of process. A trace logo consists of a stack of activity names at each position, sizes of the activity name indicates their frequency in the traces and the total height of the activity depicts the information content of the position. A trace logo created from a set of aligned traces generated using Multiple Trace Alignment technique.

Keywords: consensus trace, process mining, multiple trace alignment, trace logo

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Authors: Deepali Lal, Sudha Summerwar, Jyoutsna Pandey

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The resistance of pesticide by the pest is an important matter of concern.The pesticide of plant origin having nontoxic biodegradable and environmentally friendly qualities. The frequent spraying of toxic chemicals is developing resistance to the pesticide. Leaf powder of the plants like Argimone mexicana and Calotropis procera is prepared, Different doses of these plant extracts are given to the Fourth in star stages of Helicoverpa armigera through feeding methods, to find their efficacy the experimental findings will be put under analysis using various parameters. The effect on paritrophic membrane is also studied.

Keywords: distillation plant, acetone, alcohol, pipette, castor leaves, grams pods, larvae of helicoverpa armigera, plant extract, vails, jars, cotton

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Authors: Avadhesh Yadav, Balram Manoj Kumar

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A solar powered air heating system using parabolic trough collector was experimentally investigated. In this experimental setup, the reflected solar radiations were focused on absorber tube which was placed at focal length of the parabolic trough. In this setup, air was used as working fluid which collects the heat from absorber tube. To enhance the performance of parabolic trough, collector with different type of reflectors were used. It was observed for aluminum sheet maximum temperature is 52.3ºC, which 24.22% more than steel sheet as reflector and 8.5% more than aluminum foil as reflector, also efficiency by using Aluminum sheet as reflector compared to steel sheet as reflector is 61.18% more. Efficiency by using aluminum sheet as reflector compared to aluminum foil as reflector is 18.98% more.

Keywords: parabolic trough collector, reflectors, air flow rates, solar power, aluminum sheet

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Authors: Abhishek Jha, Manoj Kumar

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This paper proposes a new type of two wheels differential type odometry to estimate the next position and orientation of mobile robots. The proposed odometry is composed for two independent wheels with respective encoders. The two wheels rotate independently, and the change is determined by the difference in the velocity of the two wheels. Angular velocities of the two wheels are measured by rotary encoders. A mathematical model is proposed for the mobile robots to precisely move towards the goal. Using measured values of the two encoders, the current displacement vector of a mobile robot is calculated by kinematics of the mathematical model. Using the displacement vector, the next position and orientation of the mobile robot are estimated by proposed odometry. Result of simulator experiment by the developed odometry is shown.

Keywords: mobile robot, odometry, unicycle, differential type, encoders, infrared range sensors, kinematic model

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Authors: Amit Kumar Patel, M. C. Bhambri, Damini Thawait, Srishti Pandey

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The experiment was carried out at Raipur during rainy season of 2012. The experiment revealed that the performance of Dubraj was comparatively better than that of badshah bhog, Vishnu bhog and bisni. The number of grains panicle-1, number of filled grains panicle-1 were comparable in Dubraj and badshah bhog. Among the different nutrient, application of 80:50:40 kg N:P2O5:K2O ha-1(50% Inorganic+50% Organic) gave better performance in all the above characters. It is revealed that the variety Dubraj fertilized with 80:50:40 kg N:P2O5:K2O ha-1(50% Inorganic+50% Organic) gave the good yield attributing characters along with highest yield.

Keywords: scented rice, organic manures, chemical fertilizers, yield, varieties

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Authors: Priyesh Kumar Pandey, Zakir Husain, R. K. Jarial

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Condition monitoring and diagnostic is important for testing of power transformer in order to estimate the remnant life. Concentration of furan content in transformer oil can be a promising indirect measurement of the aging of transformer insulation. The oil gets contaminated mainly due to ageing. The present paper introduces adaptive neuro fuzzy technique to correlate furanic compounds obtained by high performance liquid chromatography (HPLC) test and remnant life of the power transformer. The results are obtained by conducting HPLC test at TIFAC-CORE lab, NIT Hamirpur on thirteen power transformer oil samples taken from Himachal State Electricity Board, India.

Keywords: adaptive neuro fuzzy technique, furan compounds, remnant life, transformer oil

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Authors: N. Das, N. Samanta, L. Pandey, C. Roy Chaudhuri

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Early diagnosis of infection like Hep-B virus in blood is important for low cost medical treatment. For this purpose, it is desirable to develop a point of care device which should be able to detect trace quantities of the target molecule in blood. In this paper, we report a nanoporous silicon oxide sensor which is capable of detecting down to 1fM concentration of Hep-B surface antigen in blood without the requirement of any centrifuge or pre-concentration. This has been made possible by the presence of resonant peak in the sensitivity characteristics. This peak is observed to be dependent only on the concentration of the specific antigen and not on the interfering species in blood serum. The occurrence of opposite impedance change within the pores and at the bottom of the pore is responsible for this effect. An electronic interface has also been designed to provide a display of the virus concentration.

Keywords: impedance spectroscopy, ultrasensitive detection in blood, peak frequency, electronic interface

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Authors: R. C. Sharma, Rishabh Bansal, Prajwal Menon, Manoj K. Sharma

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Silicon-air battery is highly promising for electric vehicles due to its high theoretical energy density (8470 Whkg⁻¹) and its discharge products are non-toxic. For the first time, pure silicon and germanium powders are used as anode material. Nickel wire meshes embedded with charcoal and manganese dioxide powder as cathode and concentrated potassium hydroxide is used as electrolyte. Voltage-time curves have been presented in this study for pure silicon and germanium powder and 5% and 10% germanium with silicon powder. Silicon powder cell assembly gives a stable voltage of 0.88 V for ~20 minutes while Si-Ge provides cell voltage of 0.80-0.76 V for ~10-12 minutes, and pure germanium cell provides cell voltage 0.80-0.76 V for ~30 minutes. The cell voltage is higher for concentrated (10%) sodium hydroxide solution (1.08 V) and it is stable for ~40 minutes. A sharp decrease in cell voltage beyond 40 min may be due to rapid corrosion.

Keywords: Silicon-air battery, Germanium-air battery, voltage-time curve, open circuit voltage, Anodic corrosion

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Authors: Ramnath Narhete, Saket Pandey, Puran Gour

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This paper presents of dual-band planner antenna with a compact radiator for 2.4/5.2/5.8 proposed by optimizing its resonant frequency, Bandwidth of operation and radiation frequency using the genetic algorithm. The antenna consists L-shaped and E-shaped radiating element to generate two resonant modes for dual band operation. The above techniques have been successfully used in many applications. Dual band antenna with the compact radiator for 2.4/5.2/5.8 GHz WLAN application design and radiator size only width 8mm and a length is 11.3 mm. The antenna can we used for various application in the field of communication. Genetic algorithm will be used to design the antenna and impedance matching network.

Keywords: genetic algorithm, dual-band E, dual-band L, WLAN, compact radiator

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Authors: Kapil Pandey, Vishnu Goyal

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Spatial and temporal data analysis is very well known in the field of satellite image processing. When spatial data are correlated with time, series analysis it gives the significant results in change detection studies. In this paper the GIS and Remote sensing techniques has been used to find the change detection using time series satellite imagery of Uttarakhand state during the years of 1990-2010. Natural vegetation, urban area, forest cover etc. were chosen as main landuse classes to study. Landuse/ landcover classes within several years were prepared using satellite images. Maximum likelihood supervised classification technique was adopted in this work and finally landuse change index has been generated and graphical models were used to present the changes.

Keywords: GIS, landuse/landcover, spatial and temporal data, remote sensing

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Authors: Manoj Kumar, Preeti Goel

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National Capital Region of India is one of the most populous urban agglomerations in the world. This region has residents from all the parts of India, and their shopping behaviors are quite different. The region also has the substantial population of people from other countries. Due to high purchasing power of a large number of people, NCR is one the major markets for luxury fashion brands. Marketers of luxury fashion brands keep on adding innovative features to their products to attract the buyers. This research is an attempt to understand the major factors which impact the brand selection for these brands and other buying decisions like purchasing time and location. The research is based on primary data collected from potential buyers of luxury fashion brands and the people involved in the marketing of these brands in various roles. The research has tried to identify the relative strength of various factors on the shopping behavior for these brands.

Keywords: luxury brands, fashion, shopping, National Capital Region (NCR)

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Authors: Bhupinder Kaur, O. P. Pandey

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An automobile industry is using variety of materials for better comfort and utility. The present work describes the details of failure analysis done for windshield glass of a four-wheeler class. The failure occurred in two different models of the heavy duty class of four wheelers, which analysed separately. The company reported that the failure has occurred only in their rear windshield when vehicles parked under shade for several days. These glasses were characterised by dilatometer, differential thermal analyzer, and X-ray diffraction. The glasses were further investigated under scanning electron microscope with energy dispersive X-ray spectroscopy and X-ray dot mapping. The microstructural analysis of the glasses done at the surface as well as at the fractured area indicates that carbon as an impurity got segregated as banded structure throughout the glass. Since carbon absorbs higher heat, it causes thermal mismatch to the entire glass system, and glass shattered down. In this work, the details of sequential analysis done to predict the cause of failure are present.

Keywords: failure, windshield, thermal mismatch, carbon

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Authors: Naragain Phumchusri, Krisada Roekdethawesab, Manoj Lohatepanont

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Overbooking is an approach of selling more goods or services than available capacities because sellers anticipate that some buyers will not show-up or may cancel their bookings. At present, many airlines deploy overbooking strategy in order to deal with the uncertainty of their customers. Particularly, some airlines sell more cargo capacity than what they have available to freight forwarders with beliefs that some of them will cancel later. In this paper, we propose methods to find the optimal overbooking level of volume and weight for air cargo in order to minimize the total cost, containing cost of spoilage and cost of offloaded. Cancellations of volume and weight are jointly random variables with a known joint distribution. Heuristic approaches applying the idea of weight and volume independency is considered to find an appropriate answer to the full problem. Computational experiments are used to explore the performance of approaches presented in this paper, as compared to a naïve method under different scenarios.

Keywords: air cargo overbooking, offloading capacity, optimal overbooking level, revenue management, spoilage capacity

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Authors: Manoj Kumar, Rajesh Kumar

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With the favourable geographical conditions at Indian-subcontinent, it is suitable for flourishing renewable energy. Increasing amount of dependence on coal and other conventional sources is driving the world into pollution and depletion of resources. This paper presents the statistics of energy consumption and energy generation in Indian Sub-continent, which notifies us with the increasing energy demands surpassing energy generation. With the aggrandizement in demand for energy, usage of coal has increased, since the major portion of energy production in India is from thermal power plants. The increase in usage of thermal power plants causes pollution and depletion of reserves; hence, a paradigm shift to renewable sources is inevitable. In this work, the capacity and potential of renewable sources in India are analyzed. Based on the analysis of this work, future potential of these sources is estimated.

Keywords: depletion of reserves, energy consumption and generation, emmissions, global warming, renewable sources

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Authors: Aarnav Singh, Jayesh Ghatate, Tarush Pandey

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Non-Governmental Organizations (NGOs) play a crucial role in addressing societal challenges, relying heavily on financial transactions to fund their impactful initiatives. However, traditional financial systems can be cumbersome and lack transparency, hindering the efficiency and trustworthiness of NGO operations. The Ethereum main-net, while pioneering the decentralized finance landscape, grapples with inherent scalability challenges, restricting its transaction throughput to a range of 15-45 transactions per second (TPS). This limitation poses substantial obstacles for NGOs engaging in swift and dynamic financial transactions critical to their operational efficiency. This research is a comprehensive exploration of the intricacies of these scalability challenges and delves into the design and implementation of a purpose-built blockchain system explicitly crafted to surmount these constraints.

Keywords: non-governmental organizations, decentralized system, zero knowledge Ethereum virtual machine, decentralized application

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Authors: Samba Raju, Chiluveru, Manoj Tripathy

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Intelligibility is an essential characteristic of a speech signal, which is used to help in the understanding of information in speech signal. Background noise in the environment can deteriorate the intelligibility of a recorded speech. In this paper, we presented a simple variance subtracted - variable level discrete wavelet transform, which improve the intelligibility of speech. The proposed algorithm does not require an explicit estimation of noise, i.e., prior knowledge of the noise; hence, it is easy to implement, and it reduces the computational burden. The proposed algorithm decides a separate decomposition level for each frame based on signal dominant and dominant noise criteria. The performance of the proposed algorithm is evaluated with speech intelligibility measure (STOI), and results obtained are compared with Universal Discrete Wavelet Transform (DWT) thresholding and Minimum Mean Square Error (MMSE) methods. The experimental results revealed that the proposed scheme outperformed competing methods

Keywords: discrete wavelet transform, speech intelligibility, STOI, standard deviation

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Authors: Prateek Singh, Arun Kumar Pandey, C. Raghu Kumar, M. R. Rath, A. S. Reddy

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Drum scrubber is widely used equipment in the washing of Iron ore. The purpose of the scrubber is to release the adhered fine clayey particles from the iron-bearing particles. Presently, the iron ore wash plants in the Eastern region of India consist of the scrubber, double deck screen followed by screw classifier as the main unit operations. Hence, scrubber performance efficiency has a huge impact on the downstream product quality. This paper illustrates the effect of scrubber feed % solids on scrubber performance and alumina distribution on downstream equipment. Further, it was established that scrubber performance efficiency could be defined as the ratio of the adhered particles (-0.15mm) released from scrubber feed during scrubbing operation with respect to the maximum possible release of -0.15mm (%) particles.

Keywords: scrubber, adhered particles, feed % solids, efficiency

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Authors: Chaudhuri Manoj Kumar Swain, Susmita Das

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This paper explores a detailed procedure of predicting a path loss (PL) model and its application in estimating the coverage probability in a WiMAX network. For this a hybrid approach is followed in predicting an empirical PL model of a 2.65 GHz WiMAX network deployed in a suburban environment. Data collection, statistical analysis, and regression analysis are the phases of operations incorporated in this approach and the importance of each of these phases has been discussed properly. The procedure of collecting data such as received signal strength indicator (RSSI) through experimental set up is demonstrated. From the collected data set, empirical PL and RSSI models are predicted with regression technique. Furthermore, with the aid of the predicted PL model, essential parameters such as PL exponent as well as the coverage probability of the network are evaluated. This research work may assist in the process of deployment and optimisation of any cellular network significantly.

Keywords: WiMAX, RSSI, path loss, coverage probability, regression analysis

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Authors: M. V. Manoj Kumar, Likewin Thomas, Annappa

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Process mining provides methods and techniques for analyzing event logs recorded in modern information systems that support real-world operations. While analyzing an event-log, state-of-the-art techniques available in process mining believe that the operational process as a static entity (stationary). This is not often the case due to the possibility of occurrence of a phenomenon called concept drift. During the period of execution, the process can experience concept drift and can evolve with respect to any of its associated perspectives exhibiting various patterns-of-change with a different pace. Work presented in this paper discusses the main aspects to consider while addressing concept drift phenomenon and proposes a method for detecting and localizing the sudden concept drifts in control-flow perspective of the process by using features extracted by processing the traces in the process log. Our experimental results are promising in the direction of efficiently detecting and localizing concept drift in the context of process mining research discipline.

Keywords: abrupt drift, concept drift, sudden drift, control-flow perspective, detection and localization, process mining

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Authors: Arvind Kumar, Manoj Kumar, Dattatraya H. Nagaraj, Amanpreet Singh, Jayanthi Prattapati

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In recent years, the use of renewable energy resources instead of pollutant fossil fuels and other forms has increased. Photovoltaic generation is becoming increasingly important as a renewable resource since it does not cause in fuel costs, pollution, maintenance, and emitting noise compared with other alternatives used in power applications. In this paper, Perturb and Observe and Incremental Conductance methods are used to improve energy conversion efficiency under different environmental conditions. PI controllers are used to control easily DC-link voltage, active and reactive currents. The whole system is simulated under standard climatic conditions (1000 W/m2, 250C) in MATLAB and the irradiance is varied from 1000 W/m2 to 300 W/m2. The use of PI controller makes it easy to directly control the power of the grid connected PV system. Finally the validity of the system will be verified through the simulations in MATLAB/Simulink environment.

Keywords: incremental conductance algorithm, modeling of PV panel, perturb and observe algorithm, photovoltaic system and simulation results

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Authors: Anil Kumar Pandey

Abstract:

Power plane noise is the most significant source of signal integrity (SI) issues in a high-speed digital design. In this paper, power integrity (PI) analysis of multiple power planes in a power delivery system of a 12-layer high-speed FPGA board is presented. All 10 power planes of HSD board are analyzed separately by using 3D Electromagnetic based PI solver, then the transient simulation is performed on combined PI data of all planes along with voltage regulator modules (VRMs) and 70 current drawing chips to get the board level power noise coupling on different high-speed signals. De-coupling capacitors are placed between power planes and ground to reduce power noise coupling with signals.

Keywords: power integrity, power-aware signal integrity analysis, electromagnetic simulation, channel simulation

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Authors: Manoj Reghu, Prabhu Rajagopal, C. V. Krishnamurthy, Krishnan Balasubramaniam

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A thorough understanding of guided ultrasonic wave behavior in structures is essential for the application of existing Non Destructive Evaluation (NDE) technologies, as well as for the development of new methods. However, the analysis of guided wave phenomena is challenging because of their complex dispersive and multimodal nature. Although numerical solution procedures have proven to be very useful in this regard, the increasing complexity of features and defects to be considered, as well as the desire to improve the accuracy of inspection often imposes a large computational cost. Hybrid models that combine numerical solutions for wave scattering with faster alternative methods for wave propagation have long been considered as a solution to this problem. However usually such models require modification of the base code of the solution procedure. Here we aim to develop Generic Hybrid models that can be directly applied to any two different solution procedures. With this goal in mind, a Numerical Hybrid model and an Analytical-Numerical Hybrid model has been developed. The concept and implementation of these Hybrid models are discussed in this paper.

Keywords: guided ultrasonic waves, Finite Element Method (FEM), Hybrid model

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Authors: Javeed Akhtar, R. K. Pandey, Z. R. Azaz Ahmad Azad

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For the purpose of making different uses of food material for the development of extruded foods are produced using single and twin extruders. Extrusion cooking is a useful and economical tool for processing of novel food. This high temperature, short time processing technology causes chemical and physical changes that alter the nutritional and physical quality of the product. Extrusion processing of food ingredients characteristically depends on associating process conditions that influence the product qualities. The process parameters are optimized for extrusion of food material in order to obtain the maximum nutritive value by inactivating the anti-nutritional factors. The processing conditions such as moisture content, temperature and time are controlled to avoid over heating or under heating which otherwise would result in a product of lower nutritional quality.

Keywords: extrusion processing, single and twin extruder, operating condition of extruders and extruded novel foods, food and agricultural engineering

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Authors: Prabhu Thangaraju, Manoj Deepak, A. Sivakumar

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Removal of inter vertebral disc along with spinal fusion has many disadvantages such as causing stress fractures. If it is possible regenerate the spine it would be possible avoid the complications of the surgery and achieve better results. Our study involves the use of mesenchymal stem cells in regenerating the discs. Our study involved 10 patients who presented with degenerative disc disease between 2008-2011 in our hospital. After adequate pre-operative check prepared mesenchymal stem cells were injected into the disc spaces. These patients were subjected to conservative therapy for a minimum of six weeks before they were accepted into the study. They were followed up regularly for a minimum of 2years with serial radiographs and MRI. 8 out of the 10 patients had completed reduction in the pain. The T2 weighted MRI images in 9 out of the 10 patients showed a bright signal compared the previous Images which indicated that there was improvement in the hydration levels. From the case study of 10 patients who were subjected to mesenchymal cell therapy in our hospital, we can conclude that the use of mesenchymal cells in treatment of intervertebral disc degeneration in a safe and effective option.

Keywords: mesenchymal stem cells, intervertebral disc, the spine, disc degeneration

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Authors: G. K. Pandey, D. Ramadasu, I. Banerjee, V. Vinod, G. Padmakumar, V. Prakash, K. K. Rajan

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Detailed thermal hydraulic investigations are very essential for safe and reliable functioning of liquid metal cooled fast breeder reactors. These investigations are further more important for components with complex profile, since there is no direct correlation available in literature to evaluate the hydraulic characteristics of such components directly. In those cases available correlations for similar profile or geometries may lead to significant uncertainty in the outcome. Hence experimental approach can be adopted to evaluate these hydraulic characteristics more precisely for better prediction in reactor core components. Prototype Fast Breeder Reactor (PFBR), a sodium cooled pool type reactor is under advanced stage of construction at Kalpakkam, India. Several components of this reactor core require hydraulic investigation before its usage in the reactor. These hydraulic investigations on full scale models, carried out by experimental approaches using water as simulant fluid are discussed in the paper.

Keywords: fast breeder reactor, cavitation, pressure drop, reactor components

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Authors: Sanjay Upadhyay, Om Prakash Pandey

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Hydrogen has been promoted as an alternative source of energy, which is renewable, cost-effective, and nature-friendly. Hydrogen evolution reaction (HER) can be used for mass production of hydrogen at a very low cost through electrochemical water splitting. An active and efficient electrocatalyst is required to perform this reaction. Till date, platinum (Pt) is a stable and efficient electrocatalyst towards HER. But its high cost and low abundance hiders its large scale uses. Molybdenum carbide having a similar electronic structure to platinum can be a great alternative to costly platinum. In this study, pure phase molybdenum carbide (Mo₂C) has been synthesized in a single step. Synthesis temperature and holding time have been optimized to obtain pure phases of Mo₂C. The surface, structural and morphological properties of as-synthesized compounds have been studied. The HER activity of as-synthesized compounds has been explored in detail.

Keywords: capacitance, hydrogen fuel, molybdenum carbide, nanoparticles

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Authors: Manju Pandey, Nilay Khare, S. C. Shrivastava

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This paper is the final in a series, which has defined two new classes of aggregation operators for triangular and trapezoidal fuzzy numbers based on the geometrical characteristics of their fuzzy membership functions. In the present paper, a new aggregation operator for trapezoidal fuzzy numbers has been defined. The new operator is based on the geometric mean of the membership lines to the left and right of the maximum possibility interval. The operator is defined and the analytical relationships have been derived. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TrFN aggregates have also been computed.

Keywords: LR fuzzy number, interval fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, apex angle, left apex angle, right apex angle, aggregation operator, arithmetic and geometric mean

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