Search results for: M. Naveen Krishna

Authors: R. A. Jamdade, Rokade A. C., Deshpande V. Y.

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The freshwater fish fauna of Kudali River, a northern right bank tributary of the Krishna River Western Ghats of India was studied. It is one of the smallest tributary of Krishna river and never been explored for fish fauna assessment. It extends over 23 Kms having 22 fish species belonging to 15 genera and 7 families, of these 3 species are endemic to Western Ghats, 2 are globaly endangered and 2 near to be threatened. Downstream the Kudal locality, the river is under the influence of anthropogenic activities and over fishing, where conservation action plans are needed to be undertaken for conservation of endangered and near to be threatened fish fauna.

Keywords: freshwater, fish, fauna, western Ghats, anthropogenic activity, conservation

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Authors: M. Kishore Kumar

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The ancient Vedas and Upanishads are a treasure of knowledge gifted to the world by India. The four Vedas, a conglomerate of Hindu scriptures, contain many principles of modern management at organisation as well as at individual levels. It lays down the duties of a King and ministers as well as its citizens and cites values for leadership. Bhagawadgita (or ‘Gita’ in short), popularly cited as Pancham (Fifth) Veda, is stated to be sermoned about 5000 years ago by Lord Krishna. In the midst of the Kurukshetra battle, Gitopadesh was given various aspects such as dharma (duties), karma (action), stithaprajna (stable mind), nishkama (detachment from results) and ethics. Arjun was steered to victory by Lord Krishna as his charioteer, and the 700-odd-verse holy text Bhagawadgita can become a valuable guide for all of us to achieve success in business management. Many parallels exist between modern-day management theories and principles enshrined in Vedic texts.

Keywords: goal, motivation, leadership, mind, management

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Authors: Shashank Gupta, Iteash Agarwal, Vijayalaxmi Mogiligidda, Rajesh Kumar Krishnan, Sruthi Chennuri, Deepika Aggarwal, Anwesha Hoodati, Sheroy Cooper, Ranjan, Mohammad Bilal Sheik, Bhavya K. M., Manasa Hegde, M. Naveen Krishna, Amit Kumar Chauhan, Mallikarjun Korrapati, Sumit Singh, J. B. Singh, Sunil Sud, Sunil Gupta, Sidhartha Pant, Sankar, Neha Agrawal, Ashish Ranjan, Piyush Mohapatra, Roopak T., Arsh Ahmad, Nanjunda M., Dilip Singh

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Major research interests on quantum key distribution (QKD) are primarily focussed on increasing 1. point-to-point transmission distance (1000 Km), 2. secure key rate (Mbps), 3. security of quantum layer (device-independence). It is great to push the boundaries on these fronts, but these isolated approaches are neither scalable nor cost-effective due to the requirements of specialised hardware and different infrastructure. Current and future QKD network requires addressing different sets of challenges apart from distance, key rate, and quantum security. In this regard, we present ChaQra -a sub-quantum network with core features as 1) Crypto agility (integration in the already deployed telecommunication fibres), 2) Software defined networking (SDN paradigm for routing different nodes), 3) reliability (addressing denial-of-service with hybrid quantum safe cryptography), 4) upgradability (modules upgradation based on scientific and technological advancements), 5) Beyond QKD (using QKD network for distributed computing, multi-party computation etc). Our results demonstrate a clear path to create and accelerate quantum secure Indian subcontinent under the national quantum mission.

Keywords: quantum network, quantum key distribution, quantum security, quantum information

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Authors: Krishna Mohana Rao Gurram, R. Padmini, P. Vamsi Krishna

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As a part of extensive research for ecologically safe and operator friendly cutting fluids, this paper presents the experimental investigations on the performance of eco-friendly vegetable oil based nanofluids in turning operation. In order to assess the quality of nano cutting fluids used during machining, cutting temperatures, cutting forces and surface roughness under constant cutting conditions are measured. The influence of two types of nanofluids prepared from nano boric acid and CNT particles mixed separately with coconut oil, on machining performance during turning operation is examined. Comparative analysis of the results obtained is done under dry and lubricant environments. Results obtained using cutting fluids prepared from vegetable oil based nanofluids are encouraging and more pronouncing by the application of CCCNT at machining zone. The extent of improvement in reduction of cutting temperatures, main cutting force, tool wear and surface roughness is tracked to be 13%, 37.5%, 44% and 40% respectively by the application of CCCNT compared to dry machining.

Keywords: nanoparticles, vegetable oil, machining, MQL, surface roughness

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Authors: Naveen Porika, Snigdho Majumdar, Niraj Sethi

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Water, food and energy securities are emerging as increasingly important and vital issues for India and the world. Hyderabad urban agglomeration (HUA), the capital city of Andhra Pradesh State in India, is the sixth largest city has a population of about 8.2 million. The Musi River, which is a tributary of Krishna river flows from west to east right through the heart of Hyderabad, about 80% of the water used by people is released back as sewage, which flows back into Musi every day with detrimental effects on the environment and people downstream of the city. The average daily sewage generated in Hyderabad city is 950 MLD, however, treatment capacity exists only for 541 Million Liters per Day (MLD) but only 407 MLD of sewage is treated. As a result, 543 MLD of sewage daily flows into Musi river. Hyderabad’s current estimated water demand stands at 320 Million Gallons per Day (MGD). However, its installed capacity is merely 270 MGD; by 2020 estimated demand will grow to 400 MGD. There is huge gap between current supply and demand, and this is likely to widen by 2021. Developing new fresh water sources is a challenge for Hyderabad, as the fresh water sources are few and far from the City (about 150-200 km) and requires excessive pumping. The constraints presented above make the conventional alternatives for supply augmentation unsustainable and unattractive .One such dependable and captive source of easily available water is the treated sewage. With proper treatment, water of desired quality can be recovered from the waste water (sewage) for recycle and reuse. Hyderabad Amberpet sewage treatment of capacity 339 MLD is Asia’s largest sewage treatment plant. Tertiary sewage treatment Standard basic engineering modules of 30 MLD,60 MLD, 120MLD & 180 MLD for sewage treatment plants has been developed which are utilized for developing Sewage Reclamation & Reuse model in Asia’s largest sewage treatment plant. This paper will focus on Hyderabad Water Supply & Demand, Sewage Generation & Treatment, Technical aspects of Tertiary Sewage Treatment and Utilization of developed standard modules for reclamation & reuse of treated sewage to overcome the deficit of 130 MGD as projected by 2021.

Keywords: water reclamation, reuse, Andhra Pradesh, hyderabad, musi river, sewage, demand and supply, recycle, Amberpet, 339 MLD, engineering modules, tertiary treatment

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Authors: K. C. Gayithri, S. K. Naveen Kumar

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ZnO is one of the most important semiconductor materials, non toxic, biocompatible, antibacterial properties for research and it is used in many biomedical applications. MnxZn1-xO nano thin films were prepared by a spin coating sol-gel method on silicon substrate. The structural, optical, electrical properties of Mn Doped ZnO are studied by using X-rd, FESEM, UV-Visible spectrophotometer. The X-rd reveals that the sample shows hexagonal wurtzits structure. Surface morphology and thickness of the sample are characterized by field emission scanning electron microscopy. Absorption and transmission spectra are studied by UV-Visible spectrophotometer. The electrical properties are measured by TCR meter.

Keywords: transition metals, Mn doped ZnO, Sol-gel, x-ray diffraction

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Authors: Neha Asthana, Vishal Krishna Prasad

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Collaborative planning and forecasting are the innovative and systematic approaches towards productive integration and assimilation of data synergized into information. The changing and variable market dynamics have persuaded global business chains to incorporate collaborative planning and forecasting as an imperative tool. Thus, it is essential for the supply chains to constantly improvise, update its nature, and mould as per changing global environment.

Keywords: information transfer, forecasting, optimization, supply chain management

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Authors: Hare Krishna Nigam

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In this paper, for the first time, (E,q)(C,2) product summability method is introduced and two quite new results on degree of approximation of the function f belonging to Lip (alpha,r)class and W(L(r), xi(t)) class by (E,q)(C,2) product means of Fourier series, has been obtained.

Keywords: Degree of approximation, (E, q)(C, 2) means, Fourier series, Lebesgue integral, Lip (alpha, r)class, W(L(r), xi(t))class of functions

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Authors: R. Naveen, E. Vanitha, S. Gayathri

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The use of Sandwich composite materials in aerospace and civil infrastructure application has been increasing especially due to their enormously low weight that leads to a reduction in the total weight and fuel consumption, high flexural and transverse shear stiffness, and corrosion resistance. The essential properties of sandwich materials vary according to the application area of the structure. The objectives of this study are to identify the mechanical behaviour and failure mechanisms of sandwich structures made of bamboo, V- board and metal (Aluminium as face sheet and Foam as Core material). The three-point bending test and UTM (Universal testing machine) experimental tests are done for three specimens for each type of sandwich composites. From the experiment results of three sandwich composites, bamboo shows high Young’s modulus of elasticity and low density.

Keywords: bamboo sandwich composite, metal sandwich composite, sandwich composite, v-board sandwich composite

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Authors: Sandeep Kumar, Naveen Gupta

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The propagation of the Non-Gaussian laser beam results in strong self-focusing as compare to the Gaussian laser beam, which helps to achieve a prerequisite of the plasma-based electron, Terahertz generation, and higher harmonic generations. The theoretical investigation on the evolution of non-Gaussian laser beam through the collisional plasma with ramped density has been presented. The non-uniform irradiance over the cross-section of the laser beam results in redistribution of the carriers that modifies the optical response of the plasma in such a way that the plasma behaves like a converging lens to the laser beam. The formulation is based on finding a semi-analytical solution of the nonlinear Schrodinger wave equation (NLSE) with the help of variational theory. It has been observed that the decentred parameter ‘q’ of laser and wavenumber of ripples of medium contribute to providing the required conditions for the improvement of self-focusing.

Keywords: non-Gaussian beam, collisional plasma, variational theory, self-focusing

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Authors: R. Rishi Jain, S. V. Viswanath, R. Naveen Vasanthan

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Generally all the IC engines, alternators, air conditioner compressors, oil pumps and coolant pumps are driven by a crankshaft utilizing V-belt drivers. An increase in the number of idle pulleys results in the increase of frictional power. Further, components like idler and belt tensioner are also needed to run the belt drive which adds to the frictional power. The aspiration of this paper is to minimize the friction power by introducing a new system that could combine all the accessories in one shaft within a single casing. This is conceptualized to minimize the friction power, service and maintenance cost, space and also time. The validation of this work can be executed through a simpler drive transmitting power from the crank shaft.

Keywords: single drive, idler pulley, belt tensioner, friction power, casing, space and cost

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Authors: D. Rama Krishna, Y. Pandu Rangaiah

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This paper presents the design of multiband reconfigurable antenna using PIN diodes for four iterations and all the four iterations have been validated by measuring return loss and pattern measurements of developed prototype antenna. The simulated and experimental data have demonstrated the concepts of a multiband reconfigurable antenna by switching OFF and ON of PIN diodes for multiple band frequencies. The technique has taken the advantage of a different number of radiating lengths with the use of PIN diode switches, each configuration resonating at multiband frequencies.

Keywords: frequency reconfigurable, meandered line multiband antenna, PIN diode, multiband frequencies

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Authors: Rakesh Krishna, Abhishek Poddar

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The paper discusses the work carried out on the implementation of control techniques like Digital Pulse Width Modulation (PWM) and Digital Pulse Fired control(PFC). These techniques are often used in devices like inverters, battery chargers, DC-to-DC converters can also be implemented on household devices like heaters. The advantage being the control and improved life span of device. In case of batteries using these techniques are known to increase the life span of battery in mobiles and other hand-held devices. 8051 microcontroller is used to implement these methods.Thyristors are used for switching operations.

Keywords: PWM, SVM, PFC, bidirectional inverters, snubber

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Authors: Mukesh Kumar, Onkar Singh, Naveen Kumar, Amar Deep

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The waste cooking oil is taken as feedstock for biodiesel production. For this research, waste cooking oil is collected from many hotels and restaurants, and then biodiesel is prepared for experimentation purpose. The prepared biodiesel is mixed with mineral diesel in the proportion of 10%, 20%, and 30% to perform tests on a diesel engine. The experimental analysis is carried out at different load conditions to analyze the impact of the blending ratio on the performance and emission parameters. When the blending proportion of biodiesel is increased, then the highest pressure reduces due to the fall in the calorific value of the blended mixture. Experimental analysis shows a promising decrease in nitrogen oxides (NOx). A mixture of 20% biodiesel and mineral diesel is the best negotiation, mixing ratio, and beyond that, a remarkable reduction in the outcome of the performance has been observed.

Keywords: alternative sources, diesel engine, emissions, performance

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Authors: G. V. Siva Krishna Rao, B. Srinivasa Rao

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The main aim of the paper is to implement a technique using distributed generation in distribution systems to reduce the distribution system losses and to improve voltage profiles. The fuzzy logic technique is used to select the proper location of DG and an analytical method is proposed to calculate the size of DG unit at any power factor. The optimal sizes of DG units are compared with optimal sizes obtained using the genetic algorithm. The suggested method is programmed under Matlab software and is tested on IEEE 33 bus system and the results are presented.

Keywords: DG Units, sizing of DG units, analytical methods, optimum size

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Authors: Shri Krishna Mishra, Badri Yadav

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India is a democratic country requires creative dynamic citizen for its development. And it will be possible only when school produce creative prosperous students. In this aspect, researcher find out that curricular and other curricular activities of Ramkrishna Mission School is unique up to some extent because it gives emphasis on value education and holistic development of students. It giving the emphasis on self-realization, standing on their own feet and community work. Most of the teacher of this school are competent to organize classrooms and manage the behavior of their students so, outcome of this school is very effective and impressive to other school.

Keywords: Ramakrishna Mission School, analysis of curricular, other curricular activities of R. M. School, teachers

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Authors: Nelvin Joseph, K. Krishna Milan Rao, Praveen Dwarakanath

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The explosive growth of Smart phones around the world has led to the shift of the primary engagement tool for entertainment from traditional consoles and music players to an all integrated device. Augmented Reality is the next big shift in bringing in a new dimension to the play. The paper explores the construct and working of the community engine in Delta T – an Augmented Reality game that allows users to evolve rules in the game basis collective bargaining mirroring democracy even in a gaming world.

Keywords: augmented reality, artificial neural networks, mobile application, human computer interaction, community engine

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Authors: S. Naveen, V. Sivasubramanian

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A modeling theory is proposed to consider the vaporization of LNG during its contact with water following its release from an underwater source. The spillage of LNG underwater can lead to a decrease in the surface temperature of water and subsequent freezing. This can in turn affect the heat flux distribution from the released LNG onto the water surrounding it. The available models predict the rate of vaporization considering the surface of contact as a solid wall, and considering the entire phenomena as a solid-liquid operation. This assumption greatly under-predicted the overall heat transfer on LNG water interface. The vaporization flux would first decrease during the film boiling, followed by an increase during the transition boiling and a steady decrease during the nucleate boiling. A superheat theory is introduced to enhance the accuracy in the prediction of the heat transfer between LNG and water. The work suggests that considering the superheat theory can greatly enhance the prediction of LNG vaporization on underwater releases and also help improve the study of overall thermodynamics.

Keywords: evaporation rate, heat transfer, LNG vaporization, underwater LNG release

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Authors: Annapureddy Srikant Reddy, Atthanti Mahendra, Samala Chinni Krishna, N. Neelima

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In our present world, we are generating a lot of data and we, need a specific device to store all these data. Generally, we store data in pen drives, hard drives, etc. Sometimes we may loss the data due to the corruption of devices. To overcome all these issues, we implemented a cloud space for storing the data, and it provides more security to the data. We can access the data with just using the internet from anywhere in the world. We implemented all these with the java using Net beans IDE. Once user uploads the data, he does not have any rights to change the data. Users uploaded files are stored in the cloud with the file name as system time and the directory will be created with some random words. Cloud accepts the data only if the size of the file is less than 2MB.

Keywords: cloud space, AES, FTP, NetBeans IDE

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Authors: Jiwan Kumar, Pooja, Sandeep Negi, Anjum Rouf, Amit Kumar, Naveen Lakra

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In modern times where, health issues are increasing day by day, breast cancer is also one of them, which is very crucial and really important to find in the early stages. Doctors can use this model in order to tell their patients whether a cancer is not harmful (benign) or harmful (malignant). We have used the knowledge of machine learning in order to produce the model. we have used algorithms like Logistic Regression, Random forest, support Vector Classifier, Bayesian Network and Radial Basis Function. We tried to use the data of crucial parts and show them the results in pictures in order to make it easier for doctors. By doing this, we're making ML better at finding breast cancer, which can lead to saving more lives and better health care.

Keywords: Bayesian network, radial basis function, ensemble learning, understandable, data making better, random forest, logistic regression, breast cancer

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Authors: Perumalla Naveen Kumar

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Global Positioning System (GPS) is used for civilian and military user positioning applications. The accuracy of GPS is degrading mainly because of ionospheric error. It is very important to analyze the effects of ionosphere on the performance of satellite systems especially in the low latitude regions. These variations depend on the Total Electron Content (TEC) in the ionosphere. To investigate the variations in the atmosphere, a mini satellite known as YOUTHSAT is launched by India. This is the outcome of the collaboration between India and USSR. One of the YOUTHSAT Indian payload is RaBIT (Radio Beacon for Ionospheric Tomography). In this paper, YOUTHSAT RaBIT payload data for the three typical days of 2011 are considered. The analysis is carried out for four Indian stations. The variations of Slant TEC, elevation angle and azimuth angles are analyzed with respect to local time. The obtained results are encouraging.

Keywords: Global Positioning System (GPS), Total Electron Content (TEC), YOUTHSAT, Radio Beacon for Ionospheric Tomography (RaBIT)

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Authors: Ram Sharan Mehta, Naveen Kumar Pandey, Binod Kumar Deo

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Quality of Life (QOL) is an important component in the evaluation of the well-being of People Living with AIDS (PLWA). This study assessed the effectiveness of education intervention programme in improving the QOL of PLWA on ART attaining the ART-clinics at B. P. Koirala Institute of Health Sciences (BPKIHS), Nepal. A pre-experimental research design was used to conduct the study among the PLWA on ART at BPKIHS from June to August 2013 involving 60 PLWA on pre-test randomly. The mean age of the respondents was 36.70 ± 9.92, and majority of them (80%) were of age group of 25-50 years and Male (56.7%). After education intervention programme there is significant change in the QOL in all the four domains i.e. Physical (p=0.008), Psychological (p=0.019), Social (p=0.046) and Environmental (p=0.032) using student t-test at 0.05 level of significance. There is significant (p= 0.016) difference in the mean QOL scores of pre-test and post-test. High QOL scores in post-test after education intervention programme may reflective of the effectiveness of planned education interventions programme.

Keywords: telephone, AIDS, health service, Nepal

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Authors: Y. Sunita Rani, Y. Hari Krishna, M. V. Ramana Murthy, K. Sudhaker Reddy

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This article studied effects of radiation and chemical reaction on MHD casson fluoid flow past a Permeable Stretching Sheet in a Porous Medium. Suitable transformations are considered to transform the governing partial differential equations as ordinary ones and then solved by the numerical procedures like Runge- Kutta – Fehlberg shooting technique method. The effects of various governing parameters, on the velocity, temperature and concentration are displayed through graphs and discussed numerically.

Keywords: MHD, Casson fluid, porous medium, permeable stretching sheet

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Authors: Vidyadhar Suram, D. Chamundeeswari, Umamaheswara Rao, Krishna Mohan Chinnala

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Peltophorum pterocarpum known as copper pod belongs to the family Fabaceae, native to tropical south-eastern asia and a popularly ornamental tree grown around the world. In traditional medicine it is used as an astringent to cure or relieve intestinal disorders after pain at childbirth, sprains, bruises and swelling or as a lotion for eye troubles, muscular pains and sores. It is also used for gargles and tooth powders. Medcinally; it has proven to possess various pharmacological activities. The powdered root part of Peltophorum pterocarpum (250gr) were extracted exhaustively using different solvents and phytochemical investigations has shown the presence of various secondary metabolites like alkaloids, flavanoids, tannins, saponins, proteins, glycosides, steriods, and volatile.

Keywords: antibacterialactivity, fabaceae, peltophorum pterocarpum, isocoumari, alkaloids

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Authors: K. N. Seetharamu, Naveen Teggi, Kiranakumar Dhavalagi, Narayana Kamath

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A method of temperature calculations is developed to study the conditions leading to hot spot occurrence on multicore chips. A physical model which has salient features of multicore chips is incorporated for the analysis. The model consists of active and background cell laid out in a checkered pattern, and this pattern repeats itself in each fine grain active cells. The die has three layers i) body ii) buried oxide layer iii) wiring layer, stacked one above the other with heat source placed at the interface between wiring and buried oxide layer. With this model we propose analytical method to calculate the target hotspot temperature, heat flow to top and bottom layers of the die and thermal resistance components at each granularity level, assuming appropriate values of die dimensions and parameters. Finally we attempt to find an easier method for the calculation of the target hotspot temperature using graph.

Keywords: checkered pattern, granularity level, heat conduction, multicore chips, target hotspot temperature

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Authors: B. Suraj Aravind, M. H. M. Krishna Prasad

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There exist emerging applications of data streams that require association rule mining, such as network traffic monitoring, web click streams analysis, sensor data, data from satellites etc. Data streams typically arrive continuously in high speed with huge amount and changing data distribution. This raises new issues that need to be considered when developing association rule mining techniques for stream data. This paper proposes to introduce an improved data stream association rule mining algorithm by eliminating the limitation of resources. For this, the concept of cloud computing is used. Inclusion of this may lead to additional unknown problems which needs further research.

Keywords: data stream, association rule mining, cloud computing, frequent itemsets

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Authors: Dilip K. Prasad, C. Krishna Prasath, Deepu Rajan, Lily Rachmawati, Eshan Rajabally, Chai Quek

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This paper discusses the technical challenges in maritime image processing and machine vision problems for video streams generated by cameras. Even well documented problems of horizon detection and registration of frames in a video are very challenging in maritime scenarios. More advanced problems of background subtraction and object detection in video streams are very challenging. Challenges arising from the dynamic nature of the background, unavailability of static cues, presence of small objects at distant backgrounds, illumination effects, all contribute to the challenges as discussed here.

Keywords: autonomous maritime vehicle, object detection, situation awareness, tracking

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Authors: Sandeep Kumar, Naveen Gupta

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Terahertz (THz) generation has been investigated by beating two cosh-Gaussian laser beams of the same amplitude but different wavenumbers and frequencies through rippled collisionless plasma. The ponderomotive force is operative which is induced due to the intensity gradient of the laser beam over the cross-section area of the wavefront. The electrons evacuate towards a low-intensity regime, which modifies the dielectric function of the medium and results in cross focusing of cosh-Gaussian laser beams. The evolution of spot size of laser beams has been studied by solving nonlinear Schrodinger wave equation (NLSE) with variational technique. The laser beams impart oscillations to electrons which are enhanced with ripple density. The nonlinear oscillatory motion of electrons gives rise to a nonlinear current density driving THz radiation. It has been observed that the periodicity of the ripple density helps to enhance the THz radiation.

Keywords: rippled collisionless plasma, cosh-gaussian laser beam, ponderomotive force, variational technique, nonlinear current density

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Authors: Ankit Tyagi, Reet Kamal Tiwari, Naveen James

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In India, landslides are the most frequently occurring disaster in the regions of the Himalayas and the Western Ghats. The steep slopes and land use in these areas are quite apprehensive. In the recent past, many landslide hazard zonation (LHZ) works have been carried out in the Himalayas. However, the preparation of LHZ maps considering temporal factors such as seismic ground shaking, seismic amplification at surface level, and rainfall are limited. Hence this study presents a comprehensive use of the multi-criteria decision-making (MCDM) method in landslide risk assessment. In this research, we conducted both geospatial and geotechnical analysis to minimize the danger of landslides. Geospatial analysis is performed using high-resolution satellite data to produce landslide causative factors which were given weightage using the MCDM method. The geotechnical analysis includes a slope stability check, which was done to determine the potential landslide slope. The landslide risk map can provide useful information which helps people to understand the risk of living in an area.

Keywords: landslide hazard zonation, PHA, AHP, GIS

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Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

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The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation

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