Search results for: Prakash Verma

Authors: S. Arun Prakash, V. Malathi, M. S. Mani Rajan

Abstract:

The analytical bright two soliton solution of the 3- coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two-soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.

Keywords: Optical soliton, soliton interaction, soliton switching, WDM.

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Authors: Madiajagan Muthaiyan, Neha Goel, Deepti Sunder Prakash

Abstract:

This paper discusses about an intelligent system to be installed in ambulances providing professional support to the paramedics on board. A video conferencing device over mobile 4G services enables specialists virtually attending the patient being transferred to the hospital. The data centre holds detailed databases on the patients past medical history and hospitals with the specialists. It also hosts various software modules that compute the shortest traffic –less path to the closest hospital with the required facilities, on inputting the symptoms of the patient, on a real time basis.

Keywords: 4G mobile services, cloud computing, data centre, intelligent system, optimization, real time traffic reporting, SaaS, video conferencing.

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Authors: P.S.Prakash, S.Selvan

Abstract:

Packet switched data network like Internet, which has traditionally supported throughput sensitive applications such as email and file transfer, is increasingly supporting delay-sensitive multimedia applications such as interactive video. These delaysensitive applications would often rather sacrifice some throughput for better delay. Unfortunately, the current packet switched network does not offer choices, but instead provides monolithic best-effort service to all applications. This paper evaluates Class Based Queuing (CBQ), Coordinated Earliest Deadline First (CEDF), Weighted Switch Deficit Round Robin (WSDRR) and RED-Boston scheduling schemes that is sensitive to delay bound expectations for variety of real time applications and an enhancement of WSDRR is proposed.

Keywords: QoS, Delay-sensitive, Queuing delay, Scheduling

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Authors: Rakesh Kumar, Piush Verma, Yaduvir Singh

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A mobile ad hoc network (MANET) is a self configuring network, without any centralized control. The topology of this network is not always defined. The main objective of this paper is to introduce the fundamental concepts of MANETs to the researchers and practitioners, who are involved in the work in the area of modeling and simulation of MANETs. This paper begins with an overview of mobile ad hoc networks. Then it proceeds with the overview of routing protocols used in the MANETS, their properties and simulation methods. A brief tabular comparison between the routing protocols is also given in this paper considering different routing protocol parameters. This paper introduces a new routing scheme developed by the use of evolutionary algorithms (EA) and analytical hierarchy process (AHP) which will be used for getting the optimized output of MANET. In this paper cryptographic technique, ceaser cipher is also employed for making the optimized route secure.

Keywords: AHP, AODV, Cryptography, EA, MANET, Optimized output.

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Authors: Praveen Saraswat, Vipin Kumar Verma, Rudraman Singh

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The unsteady transient free convection flow of an incompressible dissipative viscous fluid between parallel plates at different distances have been investigated under porous medium. Due to presence of heat flux under the influence of uniform transverse magnetic field the velocity distribution and the temperature distribution, is shown graphically. Since exact solution is not possible so we find parametrical solution by perturbation technique. The result is shown in graph for different parameters. We notice that heat generation effects fluid velocity keeping in which of free convection which cools.

Keywords: Transient, Convection, MHD, Viscous, Porous.

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Authors: Tao Qu, Chandra Prakash, Vikas Tomar

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The interfaces between organic and inorganic phases in natural materials have been shown to be a key factor contributing to their high performance. This work analyzes crack propagation in a 2-ply laminate subjected to uniaxial tensile mode-I crack propagation loading that has laminate properties derived based on biological material constituents (marine exoskeleton- chitin and calcite). Interfaces in such laminates are explicitly modeled based on earlier molecular simulations performed by authors. Extended finite element method and cohesive zone modeling based simulations coupled with theoretical analysis are used to analyze crack propagation. Analyses explicitly quantify the effect that interface mechanical property variation has on the delamination as well as the transverse crack propagation in examined 2-ply laminates.

Keywords: Chitin, composites, interfaces, fracture.

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Authors: Ajay Verma, Nitin Seth

Abstract:

In this era of competitiveness, there is a growing need for supply chains also to become competitive enough to handle pressures like varying customer’s expectations, low cost high quality products to be delivered at the minimum time and the most important is throat cutting competition at world wide scale. In the recent years, supply chain competitiveness has been, therefore, accepted as one of the most important philosophies in the supply chain literature and researchers have tried to identify variables of supply chain competitiveness. This paper highlights some of the concepts of supply chain competitiveness and tries to identify select variables on the basis of literature review. Further, the paper tries to highlight the importance of the identified variables in the achievement of supply chain competitiveness. The aim is to explore the concept and to motivate researchers to further investigate the unexplored areas of this important subject domain.

Keywords: Supply Chain Competitiveness, Demand Management, Integration, Inventory Management, Flexibility, Information Technology.

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Authors: G. N. Sekhar, P. G. Siddheshwar, G. Jayalatha, R. Prakash

Abstract:

The problem of thermal convection in temperature and magnetic field sensitive Newtonian ferromagnetic liquid is studied in the presence of uniform vertical magnetic field and throughflow. Using a combination of Galerkin and shooting techniques the critical eigenvalues are obtained for stationary mode. The effect of Prandtl number (Pr > 1) on onset is insignificant and nonlinearity of non-buoyancy magnetic parameter M3 is found to have no influence on the onset of ferroconvection. The magnetic buoyancy number, M1 and variable viscosity parameter, V have destabilizing influences on the system. The effect of throughflow Peclet number, Pe is to delay the onset of ferroconvection and this effect is independent of the direction of flow.

Keywords: Ferroconvection, throughflow, temperature dependent viscosity, magnetic field dependent viscosity.

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Authors: R. Prakash, B. Meenakshipriya, R. Kumaravelan

Abstract:

This paper presents modeling and simulation of Grid Connected Photovoltaic (PV) system by using improved mathematical model. The model is used to study different parameter variations and effects on the PV array including operating temperature and solar irradiation level. In this paper stepped P&O algorithm is proposed for MPPT control. This algorithm will identify the suitable duty ratio in which the DC-DC converter should be operated to maximize the power output. Photo voltaic array with proposed stepped P&O-MPPT controller can operate in the maximum power point for the whole range of solar data (irradiance and temperature).

Keywords: Photovoltaic (PV), Maximum Power Point Tracking (MPPT), Boost converter, Stepped Perturb & Observe method (Stepped P&O).

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Authors: Vivek Bharti, Inderpreet Kaur, Saurabh Verma, Renu Gangwar, Hari Kumar Singh

Abstract:

This work presents a dual-band Coplanar Waveguide (CPW) fed rectangular patch antenna designed for applications in Industrial, Scientific, and Medical (ISM) Band sensing. Fabricated on a cost-effective FR-4 substrate with specific dimensions, the antenna incorporates a rectangular slot and a copper patch, optimized through simulation to achieve desired characteristics, particularly focusing on the reflection coefficient. A unique feature is introduced through the integration of copper cells forming a Partially Reflecting Surface (PRS) to feed the antenna. Dual-band functionality is achieved, covering frequencies of 1.28 GHz-1.3 GHz and 4.9 GHz-5.2 GHz, catering to diverse communication needs within these frequency ranges. The addition of a superstrate enhances the antenna’s gain, resulting in 4.5 dBi at 1.28 GHz-1.3 GHz and 6.5 dBi at 4.9 GHz-5.2 GHz, with an efficiency of 58%.

Keywords: ISM, Coplanar waveguide fed, superstrate, circularly polarized.

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Authors: Gouri Prakash

Abstract:

One of the common problems encountered in software engineering is addressing and responding to the changing nature of requirements. While several approaches have been devised to address this issue, ranging from instilling resistance to changing requirements in order to mitigate impact to project schedules, to developing an agile mindset towards requirements, the approach discussed in this paper is one of conceptualizing the delta in requirement and modeling it, in order to plan a response to it. To provide some context here, change is first formally identified and categorized as either formal change or informal change. While agile methodology facilitates informal change, the approach discussed in this paper seeks to develop the idea of facilitating formal change. To collect, document meta-requirements that represent the phenomena of change would be a pro-active measure towards building a realistic cognition of the requirements entity that can further be harnessed in the software engineering process.

Keywords: Change Management, Agile methodology, Metarequirements

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Authors: B. J. Sandesh, Saurabha Jirgi, S. Vidya, Prakash Eljer, Gowri Srinivasa

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In this paper, we propose a framework to help users to search and retrieve the portions in the lecture video of their interest. This is achieved by temporally segmenting and indexing the lecture video using the topic keywords. We use transcribed text from the video and documents relevant to the video topic extracted from the web for this purpose. The keywords for indexing are found by applying the non-negative matrix factorization (NMF) topic modeling techniques on the web documents. Our proposed technique first creates indices on the transcribed documents using the topic keywords, and these are mapped to the video to find the start and end time of the portions of the video for a particular topic. This time information is stored in the index table along with the topic keyword which is used to retrieve the specific portions of the video for the query provided by the users.

Keywords: Video indexing and retrieval, lecture videos, content based video search, multimodal indexing.

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Authors: Arun Jacob, Leena R., Krishnakumar T.S., Jose Prakash M.

Abstract:

Effective cooling of electronic equipment has emerged as a challenging and constraining problem of the new century. In the present work the feasibility and effectiveness of jet impingement cooling on electronics were investigated numerically and experimentally. Studies have been conducted to see the effect of the geometrical parameters such as jet diameter (D), jet to target spacing (Z) and ratio of jet spacing to jet diameter (Z/D) on the heat transfer characteristics. The values of Reynolds numbers considered are in the range 7000 to 42000. The results obtained from the numerical studies are validated by conducting experiments. From the studies it is found that the optimum value of Z/D ratio is 5. For a given Reynolds number, the Nusselt number increases by about 28% if the diameter of the nozzle is increased from 1mm to 2mm. Correlations are proposed for Nusselt number in terms of Reynolds number and these are valid for air as the cooling medium.

Keywords: CFD, heat transfer coefficient, Nusselt number, ratio of jet diameter to jet spacing (Z/D), Reynolds number, turbulence model.

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Authors: Jay Prakash Singh

Abstract:

The aim of the present paper is to study properties of Quasi conformally flat LP-Sasakian manifolds with a coefficient α. In this paper, we prove that a Quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α is an η−Einstein and in a quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α if the scalar curvature tensor is constant then M is of constant curvature.

Keywords: LP-Sasakian manifolds, coefficient α, quasi conformal curvature tensor, concircular vector field, torse forming vector field, η-Einstein manifold.

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Authors: Anjushi Verma, Tirthankar Gayen

Abstract:

Although, reliability is an important attribute of quality, especially for mission critical systems, yet, there does not exist any versatile model even today for the reliability assessment of component-based software. The existing Black Box models are found to make various assumptions which may not always be realistic and may be quite contrary to the actual behaviour of software. They focus on observing the manner in which the system behaves without considering the structure of the system, the components composing the system, their interconnections, dependencies, usage frequencies, etc.As a result, the entropy (uncertainty) in assessment using these models is much high.Though, there are some models based on operation profile yet sometimes it becomes extremely difficult to obtain the exact operation profile concerned with a given operation. This paper discusses the drawbacks, deficiencies and limitations of Black Box approaches from the perspective of various authors and finally proposes a conceptual model for the reliability assessment of software.

Keywords: Black Box, faults, failure, software reliability.

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Authors: Kesari Verma, Aniruddha S. Thoke, Pritam Singh

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Automatic face detection is a complex problem in image processing. Many methods exist to solve this problem such as template matching, Fisher Linear Discriminate, Neural Networks, SVM, and MRC. Success has been achieved with each method to varying degrees and complexities. In proposed algorithm we used upright, frontal faces for single gray scale images with decent resolution and under good lighting condition. In the field of face recognition technique the single face is matched with single face from the training dataset. The author proposed a neural network based face detection algorithm from the photographs as well as if any test data appears it check from the online scanned training dataset. Experimental result shows that the algorithm detected up to 95% accuracy for any image.

Keywords: Face Detection, Face Recognition, NN Approach, PCA Algorithm.

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Authors: Priyanka R. Oberoi, Chandra B. Maurya, Prakash A. Mahanwar

Abstract:

Ionizing radiation can cause a drastic change in the physical and chemical properties of the material exposed. Numerous medical devices are sterilized by ionizing radiation. In the current research paper, an attempt was made to develop precise and inexpensive polymeric film dosimeter which can be used for controlling radiation dosage. Polymeric film containing (pH sensitive dye) indicator dye Bromophenol blue (BPB) was casted to check the effect of Gamma radiation on its optical and physical properties. The film was exposed to gamma radiation at 4 kGy/hr in the range of 0 to 300 kGy at an interval of 50 kGy. Release of vinyl acetate from an emulsion on high radiation reacts with the BPB fading the color of the film from blue to light blue and then finally colorless, indicating a change in pH from basic to acidic form. The change was characterized by using CIE l*a*b*, ultra-violet spectroscopy and FT-IR respectively.

Keywords: Bromophenol blue, dosimeter, gamma radiation, polymer.

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Authors: N. P. Yadav, Deepti Verma

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This paper focuses on the mathematical modeling for solidification of Al alloy in a cube mold cavity to study the solidification behavior of casting process. The parametric investigation of solidification process inside the cavity was performed by using computational solidification/melting model coupled with Volume of fluid (VOF) model. The implicit filling algorithm is used in this study to understand the overall process from the filling stage to solidification in a model metal casting process. The model is validated with past studied at same conditions. The solidification process is analyzed by including the effect of pouring velocity as well as natural convection from the wall and geometry of the cavity. These studies show the possibility of various defects during solidification process.

Keywords: Buoyancy driven flow, natural convection driven flow, residual flow, secondary flow, volume of fluid.

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Authors: Bhavana Prakash Shrivastava, Kavita Khare

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This paper presents a synthesis and simulation of proposed enhanced buffer. The design provides advantages of both buffer and bufferless network for that two cross bar switches are used. The concept of virtual channel (VC) is eliminated from the previous design by using an efficient flow-control scheme that uses the storage already present in pipelined channels in place of explicit input VCBs. This can be addressed by providing enhanced buffers on the bufferless link and creating two virtual networks. With this approach, VCBs act as distributed FIFO buffers. Without VCBs or VCs, deadlock prevention is achieved by duplicating physical channels. An enhanced buffer provides a function of hand shaking by providing a ready valid handshake signal and two bit storage. Through this design the power is reduced to 15.65% and delay is reduced to 97.88% with respect to virtual channel router.

Keywords: Enhanced buffer, Gate delay, NOC, VCs, VCB.

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Authors: Prakash Persad, Kelvin Loutan, Jr., Trichelle Seepersad

Abstract:

The Finite Element Method is commonly used in the analysis of flexible manipulators to predict elastic displacements and develop joint control schemes for reducing positioning error. In order to preserve simplicity, regular geometries, ideal joints and connections are assumed. This paper presents the dynamic FE analysis of a 4- degrees of freedom open chain manipulator, intended for striking a curved 3D surface percussion musical instrument. This was done utilizing the new MultiBody Dynamics Module in COMSOL, capable of modeling the elastic behavior of a body undergoing rigid body type motion.

Keywords: Dynamic modeling, Entertainment robots, Finite element method, Flexible robot manipulators, Multibody dynamics, Musical robots.

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Authors: P. S. Prakash, S. Selvan

Abstract:

QoS Routing aims to find paths between senders and receivers satisfying the QoS requirements of the application which efficiently using the network resources and underlying routing algorithm to be able to find low-cost paths that satisfy given QoS constraints. The problem of finding least-cost routing is known to be NP-hard or complete and some algorithms have been proposed to find a near optimal solution. But these heuristics or algorithms either impose relationships among the link metrics to reduce the complexity of the problem which may limit the general applicability of the heuristic, or are too costly in terms of execution time to be applicable to large networks. In this paper, we concentrate an algorithm that finds a near-optimal solution fast and we named this algorithm as optimized Delay Constrained Routing (ODCR), which uses an adaptive path weight function together with an additional constraint imposed on the path cost, to restrict search space and hence ODCR finds near optimal solution in much quicker time.

Keywords: QoS, Delay, Routing, Optimization.

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Authors: Ajay Verma, Nitin Seth

Abstract:

In this era of competitiveness, there is a growing need for supply chains also to become competitive enough to handle pressures like varying customer’s expectations, low cost high quality products to be delivered at the minimum time and the most important is throat cutting competition at world wide scale. In the recent years, supply chain competitiveness has been, therefore, accepted as one of the most important philosophies in the supply chain literature. Various researchers and practitioners have tried to identify and implement strategies in supply chains which can bring competitiveness in the supply chains i.e. supply chain competitiveness. The purpose of this paper is to suggest select strategies for supply chain competitiveness in the Indian manufacturing sector using an integrated approach of literature review and exploratory interviews with eminent professionals from the supply chain area in various industries, academia and research. The aim of the paper is to highlight the important area of competitiveness in the supply chain and to suggest recommendations to the industry and managers of manufacturing sector.

Keywords: Competitiveness, Supply Chain Competitiveness, Collaboration, Coordination, Cooperation.

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Authors: K. Saharan, M.V. R. K. Sarma, A. S. Roesti, A. Prakash, B. N. Johri, M. Aragno, V. S. Bisaria, V. Sahai

Abstract:

Chemically defined Schlegel-s medium was modified to improve production of cell growth and other metabolites that are produced by fluorescent pseudomonad R62 strain. The modified medium does not require pH control as pH changes are kept within ± 0.2 units of the initial pH 7.1 during fermentation. The siderophore production was optimized for the fluorescent pseudomonad strain in the modified medium containing 1% glycerol as a major carbon source supplemented with 0.05% succinic acid and 0.5% Ltryptophan. Indole-3 acetic acid (IAA) production was higher when L-tryptophan was used at 0.5%. The 2,4- diacetylphloroglucinol (DAPG) was higher with amended three trace elements in medium. The optimized medium produced 2.28 g/l of dry cell mass and 900 mg/l of siderophore at the end of 36 h cultivation, while the production levels of IAA and DAPG were 65 mg/l and 81 mg/l respectively at the end of 48 h cultivation.

Keywords: Fluorescent pseudomonad, Fermentation, Metabolites production, PGPR.

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Authors: Arun Goel, D. V. S. Verma, Sanjeev Sangwan

Abstract:

Present study was aimed to develop a discharge measuring device for irrigation and laboratory channels. Experiments were conducted on sharp edged constricted flow meters having four types of width constrictions namely 2:1, 1.5:1, 1:1 and 90o in the direction of flow. These devices were made of MS sheets and installed separately in a rectangular flume. All these four devices were tested under free and submerged flow conditions. Eight different discharges varying from 2 lit/sec to 30 lit/sec were passed through each device. In total around 500 observations of upstream and downstream depths were taken in the present work. For each discharge, free submerged and critical submergence under different flow conditions were noted and plotted. Once the upstream and downstream depths of flow over any of the device are known, the discharge can be easily calculated with the help of the curves developed for free and submerged flow conditions. The device having contraction 2:1 is the most efficient one as it allows maximum critical submergence.

Keywords: Flowrate, flowmeter, open channels, submergence.

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Authors: K. L. Verma

Abstract:

Analysis for the propagation of elastic waves in arbitrary anisotropic plates is investigated, commencing with a formal analysis of waves in a layered plate of an arbitrary anisotropic media, the dispersion relations of elastic waves are obtained by invoking continuity at the interface and boundary of conditions on the surfaces of layered plate. The obtained solutions can be used for material systems of higher symmetry such as monoclinic, orthotropic, transversely isotropic, cubic, and isotropic as it is contained implicitly in the analysis. The cases of free layered plate and layered half space are considered separately. Some special cases have also been deduced and discussed. Finally numerical solution of the frequency equations for an aluminum epoxy is carried out, and the dispersion curves for the few lower modes are presented. The results obtained theoretically have been verified numerically and illustrated graphically.

Keywords: Anisotropic, layered, dispersion, elastic waves, frequency equations.

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Authors: K. Prakash Vel, Lif Miriam Hamouda

Abstract:

Consumer behaviour analysis represents an important field of study in marketing. Particularly strategy development for marketing and communications will be more focused and effective when marketers have an understanding of the motivations, behaviour and psychology of consumers. While materialism has been found to be one of the important elements in consumer behaviour, compulsive consumption represents another aspect that has recently attracted more attention. This is because of the growing prevalence of dysfunctional buying that has raised concern in consumer societies. Present studies and analyses on origins and motivations of compulsive buying have mainly focused on either individual factors or groups of related factors and hence a need for a holistic view exists. This paper provides a comprehensive perspective on compulsive consumption and establishes relevant propositions keeping the family life cycle stages as a reference for the incidence of chronic consumer states and their influence on compulsive consumption.

Keywords: Chronic consumer states, compulsive consumption, family life cycle

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Authors: R.Sukesh Kumar, Abhisek Verma, Jasprit Singh

Abstract:

In this work a novel approach for color image segmentation using higher order entropy as a textural feature for determination of thresholds over a two dimensional image histogram is discussed. A similar approach is applied to achieve multi-level thresholding in both grayscale and color images. The paper discusses two methods of color image segmentation using RGB space as the standard processing space. The threshold for segmentation is decided by the maximization of conditional entropy in the two dimensional histogram of the color image separated into three grayscale images of R, G and B. The features are first developed independently for the three ( R, G, B ) spaces, and combined to get different color component segmentation. By considering local maxima instead of the maximum of conditional entropy yields multiple thresholds for the same image which forms the basis for multilevel thresholding.

Keywords: conditional entropy, multi-level thresholding, segmentation, two dimensional image histogram

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Authors: Prakash G L, Thejaswini M, S H Manjula, K R Venugopal, L M Patnaik

Abstract:

Computing and maintaining network structures for efficient data aggregation incurs high overhead for dynamic events where the set of nodes sensing an event changes with time. Moreover, structured approaches are sensitive to the waiting time that is used by nodes to wait for packets from their children before forwarding the packet to the sink. An optimal routing and data aggregation scheme for wireless sensor networks is proposed in this paper. We propose Tree on DAG (ToD), a semistructured approach that uses Dynamic Forwarding on an implicitly constructed structure composed of multiple shortest path trees to support network scalability. The key principle behind ToD is that adjacent nodes in a graph will have low stretch in one of these trees in ToD, thus resulting in early aggregation of packets. Based on simulations on a 2,000-node Mica2- based network, we conclude that efficient aggregation in large-scale networks can be achieved by our semistructured approach.

Keywords: Aggregation, Packet Merging, Query Processing.

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Authors: Kaliyaperumal Anandavel, Raghu V. Prakash, Antonio Davis

Abstract:

This paper presents the influence of preloading on a) the contact tractions, b) slip levels and c) stresses at the dovetail blade-disc interface of an aero-engine through a three-dimensional (3D) finite element (FE) modeling and analysis. The preloading is applied by an interference fit at the dovetail interface and the bulk loading is applied through the rotational speed of rotor. Preloading at the dovetail interface reduces the peak contact pressure developed due to bulk loading up to 35%, and reduces the peak contact pressure and stress difference between top and bottom contact edges. Increasing the level of preloading reduces the cyclic stress amplitude at the interface up to certain values of preload and as a consequence, an improvement in fatigue life could be expected. Fretting damage, due to vibration and wind milling effect during engine ground condition, can be minimized by preloading the dovetail interface.

Keywords: Dovetail interface, Preload, Interference fit, ContactStress, Fretting Fatigue.

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Authors: Surinder Deswal, D. V. S. Verma

Abstract:

Aeration by a plunging water jet is an energetically attractive way to effect oxygen-transfer than conventional oxygenation systems. In the present study, a new type of conical shaped plunging aeration device is fabricated to generate hollow inclined ined plunging jets (jet plunge angle of π/3 ) to investigate its oxygen transfer capacity. The results suggest that the volumetric oxygen-transfer coefficient and oxygen-transfer efficiency of the conical plunging jet aerator are competitive with other types of aeration systems. Relationships of volumetric oxygen-transfer coefficient with jet power per unit volume and jet parameters are also proposed. The suggested relationships predict the volumetric oxygentransfer coefficient within a scatter of ± 15% . Further, the application of Support Vector Machines on the experimental data revealed its utility in the prediction of volumetric oxygen-transfer coefficient and development of conical plunging jet aerators.

Keywords: Conical plunging jet, oxygen-transfer efficiency, support vector machines, volumetric oxygen-transfer coefficient.

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