Search results for: G. S. V. Radha Krishna Rao
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 179

Search results for: G. S. V. Radha Krishna Rao

179 Query Optimization Techniques for XML Databases

Authors: Su Cheng Haw, G. S. V. Radha Krishna Rao

Abstract:

Over the past few years, XML (eXtensible Mark-up Language) has emerged as the standard for information representation and data exchange over the Internet. This paper provides a kick-start for new researches venturing in XML databases field. We survey the storage representation for XML document, review the XML query processing and optimization techniques with respect to the particular storage instance. Various optimization technologies have been developed to solve the query retrieval and updating problems. Towards the later year, most researchers proposed hybrid optimization techniques. Hybrid system opens the possibility of covering each technology-s weakness by its strengths. This paper reviews the advantages and limitations of optimization techniques.

Keywords: indexing, labeling scheme, query optimization, XML storage.

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178 On Properties of Generalized Bi-Γ-Ideals of Γ-Semirings

Authors: Teerayut Chomchuen, Aiyared Iampan

Abstract:

The notion of Γ-semirings was introduced by Murali Krishna Rao as a generalization of the notion of Γ-rings as well as of semirings. We have known that the notion of Γ-semirings is a generalization of the notion of semirings. In this paper, extending Kaushik, Moin and Khan’s work, we generalize the notion of generalized bi-Γ-ideals of Γ-semirings and investigate some related properties of generalized bi-Γ-ideals.

Keywords: Γ-semiring, bi-Γ-ideal, generalized bi-Γ-ideal.

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177 Using Rao-Blackwellised Particle Filter Track 3D Arm Motion based on Hierarchical Limb Model

Authors: XueSong Yu, JiaFeng Liu, XiangLong Tang, JianHua Huang

Abstract:

For improving the efficiency of human 3D tracking, we present an algorithm to track 3D Arm Motion. First, the Hierarchy Limb Model (HLM) is proposed based on the human 3D skeleton model. Second, via graph decomposition, the arm motion state space, modeled by HLM, can be discomposed into two low dimension subspaces: root nodes and leaf nodes. Finally, Rao-Blackwellised Particle Filter is used to estimate the 3D arm motion. The result of experiment shows that our algorithm can advance the computation efficiency.

Keywords: Hierarchy Limb Model; Rao-Blackwellised Particle Filter; 3D tracking

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176 Performance Assessment of Carbon Nano Tube Based Cutting Fluid in Machining Process

Authors: Alluru Gopala Krishna, Thella Babu Rao

Abstract:

In machining, there is always a problem with heat generation and friction produced during the process as they consequently affect tool wear and surface finish. An instant heat transfer mechanism could protect the cutting tool edge and enhance the tool life by cooling the cutting edge of the tool. In the present work, carbon nanotube (CNT) based nano-cutting fluid is proposed for machining a hard-to-cut material. Tool wear and surface roughness are considered for the evaluation of the nano-cutting fluid in turning process. The performance of nanocoolant is assessed against the conventional coolant and dry machining conditions and it is observed that the proposed nanocoolant has produced better performance than the conventional coolant.

Keywords: CNT based nanocoolant, turning, tool wear, surface roughness.

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175 The Next Frontier for Mobile Based Augmented Reality: An Evaluation of AR Uptake in India

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

Abstract:

Augmented and Virtual Realties is quickly becoming a hotbed of activity with millions of dollars being spent on R & D and companies such as Google and Microsoft rushing to stake their claim. Augmented reality (AR) is however marching ahead due to the spread of the ideal AR device – the smartphone. Despite its potential, there remains a deep digital divide between the Developed and Developing Countries. The Technological Acceptance Model (TAM) and Hofstede cultural dimensions also predict the behaviour intention to uptake AR in India will be large. This paper takes a quantified approach by collecting 340 survey responses to AR scenarios and analyzing them through statistics. The Survey responses show that the Intention to Use, Perceived Usefulness and Perceived Enjoyment dimensions are high among the urban population in India. This along with the exponential smartphone indicates that India is on the cusp of a boom in the AR sector.

Keywords: Mobile augmented reality, technology acceptance model, Hofstede, cultural dimensions, India.

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174 Surface Roughness Optimization in End Milling Operation with Damper Inserted End Milling Cutters

Authors: Krishna Mohana Rao, G. Ravi Kumar, P. Sowmya

Abstract:

This paper presents a study of the Taguchi design application to optimize surface quality in damper inserted end milling operation. Maintaining good surface quality usually involves additional manufacturing cost or loss of productivity. The Taguchi design is an efficient and effective experimental method in which a response variable can be optimized, given various factors, using fewer resources than a factorial design. This Study included spindle speed, feed rate, and depth of cut as control factors, usage of different tools in the same specification, which introduced tool condition and dimensional variability. An orthogonal array of L9(3^4)was used; ANOVA analyses were carried out to identify the significant factors affecting surface roughness, and the optimal cutting combination was determined by seeking the best surface roughness (response) and signal-to-noise ratio. Finally, confirmation tests verified that the Taguchi design was successful in optimizing milling parameters for surface roughness.

Keywords: ANOVA, Damper, End Milling, Optimization, Surface roughness, Taguchi design.

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173 Performance Analysis of CATR Reflector with Super Hybrid Modulated Segmented Exponential Serrated Edges

Authors: T. Venkata Rama Krishna, P. Siddaiah, B. Prabhakara Rao

Abstract:

This paper presented a theoretical and numerical investigation of the Compact Antenna Test Range (CATR) equipped with Super Hybrid Modulated Segmented Exponential Serrations (SHMSES). The investigation was based on diffraction theory and, more specifically, the Fresnel diffraction formulation. The CATR provides uniform illumination within the Fresnel region to test antenna. Application of serrated edges has been shown to be a good method to control diffraction at the edges of the reflectors. However, in order to get some insight into the positive effect of serrated edges a less rigorous analysis technique known as Physical Optics (PO) may be used. Ripple free and enhanced quiet zone width are observed for specific values of width and height modulation factors per serrations. The performance of SHMSE serrated reflector is evaluated in order to observe the effects of edge diffraction on the test zone fields.

Keywords: Fresnel region, quiet zone, physical optics, ripples, serrations.

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172 Novel Rao-Blackwellized Particle Filter for Mobile Robot SLAM Using Monocular Vision

Authors: Maohai Li, Bingrong Hong, Zesu Cai, Ronghua Luo

Abstract:

This paper presents the novel Rao-Blackwellised particle filter (RBPF) for mobile robot simultaneous localization and mapping (SLAM) using monocular vision. The particle filter is combined with unscented Kalman filter (UKF) to extending the path posterior by sampling new poses that integrate the current observation which drastically reduces the uncertainty about the robot pose. The landmark position estimation and update is also implemented through UKF. Furthermore, the number of resampling steps is determined adaptively, which seriously reduces the particle depletion problem, and introducing the evolution strategies (ES) for avoiding particle impoverishment. The 3D natural point landmarks are structured with matching Scale Invariant Feature Transform (SIFT) feature pairs. The matching for multi-dimension SIFT features is implemented with a KD-Tree in the time cost of O(log2 N). Experiment results on real robot in our indoor environment show the advantages of our methods over previous approaches.

Keywords: Mobile robot, simultaneous localization and mapping, Rao-Blackwellised particle filter, evolution strategies, scale invariant feature transform.

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171 Jeffrey's Prior for Unknown Sinusoidal Noise Model via Cramer-Rao Lower Bound

Authors: Samuel A. Phillips, Emmanuel A. Ayanlowo, Rasaki O. Olanrewaju, Olayode Fatoki

Abstract:

This paper employs the Jeffrey's prior technique in the process of estimating the periodograms and frequency of sinusoidal model for unknown noisy time variants or oscillating events (data) in a Bayesian setting. The non-informative Jeffrey's prior was adopted for the posterior trigonometric function of the sinusoidal model such that Cramer-Rao Lower Bound (CRLB) inference was used in carving-out the minimum variance needed to curb the invariance structure effect for unknown noisy time observational and repeated circular patterns. An average monthly oscillating temperature series measured in degree Celsius (0C) from 1901 to 2014 was subjected to the posterior solution of the unknown noisy events of the sinusoidal model via Markov Chain Monte Carlo (MCMC). It was not only deduced that two minutes period is required before completing a cycle of changing temperature from one particular degree Celsius to another but also that the sinusoidal model via the CRLB-Jeffrey's prior for unknown noisy events produced a miniature posterior Maximum A Posteriori (MAP) compare to a known noisy events.

Keywords: Cramer-Rao Lower Bound (CRLB), Jeffrey's prior, Sinusoidal, Maximum A Posteriori (MAP), Markov Chain Monte Carlo (MCMC), Periodograms.

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170 Transient Enhanced LDO Voltage Regulator with Improved Feed Forward Path Compensation

Authors: Suresh Alapati, Sreehari Rao Patri, K. S. R. Krishna Prasad

Abstract:

Anultra-low power capacitor less low-dropout voltage regulator with improved transient response using gain enhanced feed forward path compensation is presented in this paper. It is based on a cascade of a voltage amplifier and a transconductor stage in the feed forward path with regular error amplifier to form a composite gainenhanced feed forward stage. It broadens the gain bandwidth and thus improves the transient response without substantial increase in power consumption. The proposed LDO, designed for a maximum output current of 100 mA in UMC 180 nm, requires a quiescent current of 69 )A. An undershot of 153.79mV for a load current changes from 0mA to 100mA and an overshoot of 196.24mV for current change of 100mA to 0mA. The settling time is approximately 1.1 )s for the output voltage undershooting case. The load regulation is of 2.77 )V/mA at load current of 100mA. Reference voltage is generated by using an accurate band gap reference circuit of 0.8V.The costly features of SOC such as total chip area and power consumption is drastically reduced by the use of only a total compensation capacitance of 6pF while consuming power consumption of 0.096 mW.

Keywords: Capacitor-less LDO, frequency compensation, Transient response, latch, self-biased differential amplifier.

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169 Noise Estimation for Speech Enhancement in Non-Stationary Environments-A New Method

Authors: Ch.V.Rama Rao, Gowthami., Harsha., Rajkumar., M.B.Rama Murthy, K.Srinivasa Rao, K.AnithaSheela

Abstract:

This paper presents a new method for estimating the nonstationary noise power spectral density given a noisy signal. The method is based on averaging the noisy speech power spectrum using time and frequency dependent smoothing factors. These factors are adjusted based on signal-presence probability in individual frequency bins. Signal presence is determined by computing the ratio of the noisy speech power spectrum to its local minimum, which is updated continuously by averaging past values of the noisy speech power spectra with a look-ahead factor. This method adapts very quickly to highly non-stationary noise environments. The proposed method achieves significant improvements over a system that uses voice activity detector (VAD) in noise estimation.

Keywords: Noise estimation, Non-stationary noise, Speechenhancement.

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168 Identification of LTI Autonomous All Pole System Using Eigenvector Algorithm

Authors: Sudipta Majumdar

Abstract:

This paper presents a method for identification of a linear time invariant (LTI) autonomous all pole system using singular value decomposition. The novelty of this paper is two fold: First, MUSIC algorithm for estimating complex frequencies from real measurements is proposed. Secondly, using the proposed algorithm, we can identify the coefficients of differential equation that determines the LTI system by switching off our input signal. For this purpose, we need only to switch off the input, apply our complex MUSIC algorithm and determine the coefficients as symmetric polynomials in the complex frequencies. This method can be applied to unstable system and has higher resolution as compared to time series solution when, noisy data are used. The classical performance bound, Cramer Rao bound (CRB), has been used as a basis for performance comparison of the proposed method for multiple poles estimation in noisy exponential signal.

Keywords: MUSIC algorithm, Cramer Rao bound, frequency estimation.

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167 The Accuracy of the Flight Derivative Estimates Derived from Flight Data

Authors: Jung-hoon Lee, Eung Tai Kim, Byung-hee Chang, In-hee Hwang, Dae-sung Lee

Abstract:

The accuracy of estimated stability and control derivatives of a light aircraft from flight test data were evaluated. The light aircraft, named ChangGong-91, is the first certified aircraft from the Korean government. The output error method, which is a maximum likelihood estimation technique and considers measurement noise only, was used to analyze the aircraft responses measures. The multi-step control inputs were applied in order to excite the short period mode for the longitudinal and Dutch-roll mode for the lateral-directional motion. The estimated stability/control derivatives of Chan Gong-91 were analyzed for the assessment of handling qualities comparing them with those of similar aircraft. The accuracy of the flight derivative estimates derived from flight test measurement was examined in engineering judgment, scatter and Cramer-Rao bound, which turned out to be satisfactory with minor defects..

Keywords: Light Aircraft, Flight Test, Accuracy, Engineering Judgment, Scatter, Cramer-Rao Bound

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166 Estimation of Aquifer Properties Using Pumping Tests: Case Study of Pydibhimavaram Industrial Area, Srikakulam, India

Authors: G. Venkata Rao, P. Kalpana, R. Srinivasa Rao

Abstract:

Adequate and reliable estimates of aquifer parameters are of utmost importance for proper management of vital groundwater resources. At present scenario, the ground water is polluted because of industrial waste disposed over the land and the contaminants are transported in the aquifer from one area to another area, which is depending on the characteristics of the aquifer and contaminants. To know the contaminant transport, the accurate estimation of aquifer properties is highly needed. Conventionally, these properties are estimated through pumping tests carried out on water wells. The occurrence and movement of ground water in the aquifer are characteristically defined by the aquifer parameters. The pumping (aquifer) test is the standard technique for estimating various hydraulic properties of aquifer systems, viz., transmissivity (T), hydraulic conductivity (K), storage coefficient (S) etc., for which the graphical method is widely used. The study area for conducting pumping test is Pydibheemavaram Industrial area near the coastal belt of Srikulam, AP, India. The main objective of the present work is to estimate the aquifer properties for developing contaminant transport model for the study area.

Keywords: Aquifer, contaminant transport, hydraulic conductivity, industrial waste, pumping test.

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165 General Purpose Graphic Processing Units Based Real Time Video Tracking System

Authors: Mallikarjuna Rao Gundavarapu, Ch. Mallikarjuna Rao, K. Anuradha Bai

Abstract:

Real Time Video Tracking is a challenging task for computing professionals. The performance of video tracking techniques is greatly affected by background detection and elimination process. Local regions of the image frame contain vital information of background and foreground. However, pixel-level processing of local regions consumes a good amount of computational time and memory space by traditional approaches. In our approach we have explored the concurrent computational ability of General Purpose Graphic Processing Units (GPGPU) to address this problem. The Gaussian Mixture Model (GMM) with adaptive weighted kernels is used for detecting the background. The weights of the kernel are influenced by local regions and are updated by inter-frame variations of these corresponding regions. The proposed system has been tested with GPU devices such as GeForce GTX 280, GeForce GTX 280 and Quadro K2000. The results are encouraging with maximum speed up 10X compared to sequential approach.

Keywords: Connected components, Embrace threads, Local weighted kernel, Structuring element.

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164 Characteristic Study on Conventional and Soliton Based Transmission System

Authors: Bhupeshwaran Mani, S. Radha, A. Jawahar, A. Sivasubramanian

Abstract:

Here, we study the characteristic feature of conventional (ON-OFF keying) and soliton based transmission system. We consider 20Gbps transmission system implemented with Conventional Single Mode Fiber (C-SMF) to examine the role of Gaussian pulse which is the characteristic of conventional propagation and Hyperbolic-secant pulse which is the characteristic of soliton propagation in it. We note the influence of these pulses with respect to different dispersion lengths and soliton period in conventional and soliton system respectively and evaluate the system performance in terms of Quality factor. From the analysis, we could prove that the soliton pulse has the consistent performance even for long distance without dispersion compensation than the conventional system as it is robust to dispersion. For the length of transmission of 200Km, soliton system yielded Q of 33.958 while the conventional system totally exhausted with Q=0.

Keywords: Soliton, dispersion length, Soliton period, Return-tozero (RZ), Q-factor.

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163 Transformerless AC-DC Converter

Authors: Saisundar. S., I Made Darmayuda, Zhou Jun, Krishna Mainali, Simon Ng Sheung Yan, Eran Ofek

Abstract:

This paper compares the recent transformerless ACDC power converter architectures and provides an assessment of each. A prototype of one of the transformerless AC-DC converter architecture is also presented depicting the feasibility of a small form factor, power supply design. In this paper component selection guidelines to achieve high efficiency AC-DC power conversion are also discussed.

Keywords: AC-DC converter, digitally controlled, switched mode power supply, transformerless.

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162 Collaborative Planning and Forecasting

Authors: Neha Asthana, Vishal Krishna Prasad

Abstract:

Collaborative Planning and Forecasting is an innovative and systematic approach 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.

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161 Anti-Homomorphism in Fuzzy Ideals

Authors: K. Chandrasekhara Rao, V. Swaminathan

Abstract:

The anti-homomorphic image of fuzzy ideals, fuzzy ideals of near-rings and anti ideals are discussed in this note. A necessary and sufficient condition has been established for near-ring anti ideal to be characteristic.

Keywords: Fuzzy Ideals, Anti fuzzy subgroup, Anti fuzzy ideals, Anti homomorphism, Lower α level cut.

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160 Formation Control of Mobile Robots

Authors: Krishna S. Raghuwaiya, Shonal Singh, Jito Vanualailai

Abstract:

In this paper, we study the formation control problem for car-like mobile robots. A team of nonholonomic mobile robots navigate in a terrain with obstacles, while maintaining a desired formation, using a leader-following strategy. A set of artificial potential field functions is proposed using the direct Lyapunov method for the avoidance of obstacles and attraction to their designated targets. The effectiveness of the proposed control laws to verify the feasibility of the model is demonstrated through computer simulations

Keywords: Control, Formation, Lyapunov, Nonholonomic

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159 Compliance Modelling and Optimization of Kerf during WEDM of Al7075/SiCP Metal Matrix Composite

Authors: Thella Babu Rao, A. Gopala Krishna

Abstract:

This investigation presents the formulation of kerf (width of slit) and optimal control parameter settings of wire electrochemical discharge machining which results minimum possible kerf while machining Al7075/SiCp MMCs. WEDM is proved its efficiency and effectiveness to cut the hard ceramic reinforced MMCs within the permissible budget. Among the distinct performance measures of WEDM process, kerf is an important performance characteristic which determines the dimensional accuracy of the machined component while producing high precision components. The lack of available of the machinability information such advanced MMCs result the more experimentation in the manufacturing industries. Therefore, extensive experimental investigations are essential to provide the database of effect of various control parameters on the kerf while machining such advanced MMCs in WEDM. Literature reviled the significance some of the electrical parameters which are prominent on kerf for machining distinct conventional materials. However, the significance of reinforced particulate size and volume fraction on kerf is highlighted in this work while machining MMCs along with the machining parameters of pulse-on time, pulse-off time and wire tension. Usually, the dimensional tolerances of machined components are decided at the design stage and a machinist pay attention to produce the required dimensional tolerances by setting appropriate machining control variables. However, it is highly difficult to determine the optimal machining settings for such advanced materials on the shop floor. Therefore, in the view of precision of cut, kerf (cutting width) is considered as the measure of performance for the model. It was found from the literature that, the machining conditions of higher fractions of large size SiCp resulting less kerf where as high values of pulse-on time result in a high kerf. A response surface model is used to predict the relative significance of various control variables on kerf. Consequently, a powerful artificial intelligence called genetic algorithms (GA) is used to determine the best combination of the control variable settings. In the next step the conformation test was conducted for the optimal parameter settings and found good agreement between the GA kerf and measured kerf. Hence, it is clearly reveal that the effectiveness and accuracy of the developed model and program to analyze the kerf and to determine its optimal process parameters. The results obtained in this work states that, the resulted optimized parameters are capable of machining the Al7075/SiCp MMCs more efficiently and with better dimensional accuracy.

Keywords: Al7075SiCP MMC, kerf, WEDM, optimization.

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158 Trajectory Tracking Using Artificial Potential Fields

Authors: Krishna S. Raghuwaiya, Shonal Singh, Jito Vanualailai

Abstract:

In this paper, the trajectory tracking problem for carlike mobile robots have been studied. The system comprises of a leader and a follower robot. The purpose is to control the follower so that the leader-s trajectory is tracked with arbitrary desired clearance to avoid inter-robot collision while navigating in a terrain with obstacles. A set of artificial potential field functions is proposed using the Direct Method of Lyapunov for the avoidance of obstacles and attraction to their designated targets. Simulation results prove the efficiency of our control technique.

Keywords: Control, Trajectory Tracking, Lyapunov.

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157 Optimal Placement of Processors based on Effective Communication Load

Authors: A. R. Aswatha, T. Basavaraju, N. Bhaskara Rao

Abstract:

This paper presents a new technique for the optimum placement of processors to minimize the total effective communication load under multi-processor communication dominated environment. This is achieved by placing heavily loaded processors near each other and lightly loaded ones far away from one another in the physical grid locations. The results are mathematically proved for the Algorithms are described.

Keywords: Ascending Sort Index Vector, EffectiveCommunication Load, Effective Distance Matrix, OptimalPlacement, Sorting Order.

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156 Using Data Clustering in Oral Medicine

Authors: Fahad Shahbaz Khan, Rao Muhammad Anwer, Olof Torgersson

Abstract:

The vast amount of information hidden in huge databases has created tremendous interests in the field of data mining. This paper examines the possibility of using data clustering techniques in oral medicine to identify functional relationships between different attributes and classification of similar patient examinations. Commonly used data clustering algorithms have been reviewed and as a result several interesting results have been gathered.

Keywords: Oral Medicine, Cluto, Data Clustering, Data Mining.

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155 Determinants of Investment in Fixed Assets in Electric Power Industry - An Econometric Analysis

Authors: S. L. Tulasi Devi, R. N. Rao

Abstract:

This paper focuses attention on specific aspects of entrepreneurial decisions relating to investment, both in the total fixed investments and plant & machinery (separately). Demand and financial factors, internal and external, are considered in the investment analysis. Finally the influence of determinants of fixed investment and investment plans are examined in Electric Power industry in India.

Keywords: Determinants, Electric Power Industry, Fixed Assets, Econometric Analysis.

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154 (T1, T2)*- Semi Star Generalized Locally Closed Sets

Authors: M. Sundararaman, K. Chandrasekhara Rao

Abstract:

The aim of this paper is to continue the study of (T1, T2)-semi star generalized closed sets by introducing the concepts of (T1, T2)-semi star generalized locally closed sets and study their basic properties in bitopological spaces.

Keywords: (T1, T2)*-semi star generalized locally closed sets, T1T2-semi star generalized closed sets.

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153 Challenges in Video Based Object Detection in Maritime Scenario Using Computer Vision

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

Abstract:

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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152 Data Mining in Oral Medicine Using Decision Trees

Authors: Fahad Shahbaz Khan, Rao Muhammad Anwer, Olof Torgersson, Göran Falkman

Abstract:

Data mining has been used very frequently to extract hidden information from large databases. This paper suggests the use of decision trees for continuously extracting the clinical reasoning in the form of medical expert-s actions that is inherent in large number of EMRs (Electronic Medical records). In this way the extracted data could be used to teach students of oral medicine a number of orderly processes for dealing with patients who represent with different problems within the practice context over time.

Keywords: Data mining, Oral Medicine, Decision Trees, WEKA.

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151 On Optimum Stratification

Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

Abstract:

In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: Auxiliary variable, Dynamic programming technique, Nonlinear programming problem, Optimum stratification, Uniform distribution.

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150 A Quadratic Approach for Generating Pythagorean Triples

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

Abstract:

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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