Search results for: the suspended string equation
1256 The Finite Difference Scheme for the Suspended String Equation with the Nonlinear External Forces
Authors: Jaipong Kasemsuwan
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This paper presents the finite difference scheme and the numerical simulation of suspended string. The vibration solutions when the various external forces are taken into account are obtained and compared with the solutions without external force. In addition, we also investigate how the external forces and their powers and coefficients affect the amplitude of vibration.
Keywords: Nonlinear external forces, Numerical simulation, Suspended string equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15061255 The Finite Difference Scheme for the Suspended String Equation with the Nonlinear Damping Term
Authors: Jaipong Kasemsuwan
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A numerical solution of the initial boundary value problem of the suspended string vibrating equation with the particular nonlinear damping term based on the finite difference scheme is presented in this paper. The investigation of how the second and third power terms of the nonlinear term affect the vibration characteristic. We compare the vibration amplitude as a result of the third power nonlinear damping with the second power obtained from previous report provided that the same initial shape and initial velocities are assumed. The comparison results show that the vibration amplitude is inversely proportional to the coefficient of the damping term for the third power nonlinear damping case, while the vibration amplitude is proportional to the coefficient of the damping term in the second power nonlinear damping case.Keywords: Finite-difference method, the nonlinear damped equation, the numerical simulation, the suspended string equation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14511254 Automata-Based String Analysis for Detecting Malware in Android Programs
Authors: Assad Maalouf, Lunjin Lu, James Lynott
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We design and implement a precise model of string operations using finite state machine transformers and state transformers to approximate the values string variables can take throughout the execution of the program.We use our model to analyze Android program string variables. Our experimental results show that our string analysis is very efficient at detecting the contextual effect of string operations on the string variables. Our model proved to be very useful when it came to verifying statements about the string variables of the program.Keywords: Abstract interpretation, android, static analysis, string analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7261253 Improving Taint Analysis of Android Applications Using Finite State Machines
Authors: Assad Maalouf, Lunjin Lu, James Lynott
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We present a taint analysis that can automatically detect when string operations result in a string that is free of taints, where all the tainted patterns have been removed. This is an improvement on the conservative behavior of previous taint analyzers, where a string operation on a tainted string always leads to a tainted string unless the operation is manually marked as a sanitizer. The taint analysis is built on top of a string analysis that uses finite state automata to approximate the sets of values that string variables can take during the execution of a program. The proposed approach has been implemented as an extension of FlowDroid and experimental results show that the resulting taint analyzer is much more precise than the original FlowDroid.Keywords: Android, static analysis, string analysis, taint analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6621252 RB-Matcher: String Matching Technique
Authors: Rajender Singh Chillar, Barjesh Kochar
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All Text processing systems allow their users to search a pattern of string from a given text. String matching is fundamental to database and text processing applications. Every text editor must contain a mechanism to search the current document for arbitrary strings. Spelling checkers scan an input text for words in the dictionary and reject any strings that do not match. We store our information in data bases so that later on we can retrieve the same and this retrieval can be done by using various string matching algorithms. This paper is describing a new string matching algorithm for various applications. A new algorithm has been designed with the help of Rabin Karp Matcher, to improve string matching process.Keywords: Algorithm, Complexity, Matching-patterns, Pattern, Rabin-Karp, String, text-processing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17651251 Techniques Used in String Matching for Network Security
Authors: Jamuna Bhandari
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String matching also known as pattern matching is one of primary concept for network security. In this area the effectiveness and efficiency of string matching algorithms is important for applications in network security such as network intrusion detection, virus detection, signature matching and web content filtering system. This paper presents brief review on some of string matching techniques used for network security.
Keywords: Filtering, honeypot, network telescope, pattern, string, signature.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27011250 A Practical Distributed String Matching Algorithm Architecture and Implementation
Authors: Bi Kun, Gu Nai-jie, Tu Kun, Liu Xiao-hu, Liu Gang
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Traditional parallel single string matching algorithms are always based on PRAM computation model. Those algorithms concentrate on the cost optimal design and the theoretical speed. Based on the distributed string matching algorithm proposed by CHEN, a practical distributed string matching algorithm architecture is proposed in this paper. And also an improved single string matching algorithm based on a variant Boyer-Moore algorithm is presented. We implement our algorithm on the above architecture and the experiments prove that it is really practical and efficient on distributed memory machine. Its computation complexity is O(n/p + m), where n is the length of the text, and m is the length of the pattern, and p is the number of the processors.Keywords: Boyer-Moore algorithm, distributed algorithm, parallel string matching, string matching.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21881249 A New Edit Distance Method for Finding Similarity in Dna Sequence
Authors: Patsaraporn Somboonsak, Mud-Armeen Munlin
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The P-Bigram method is a string comparison methods base on an internal two characters-based similarity measure. The edit distance between two strings is the minimal number of elementary editing operations required to transform one string into the other. The elementary editing operations include deletion, insertion, substitution two characters. In this paper, we address the P-Bigram method to sole the similarity problem in DNA sequence. This method provided an efficient algorithm that locates all minimum operation in a string. We have been implemented algorithm and found that our program calculated that smaller distance than one string. We develop PBigram edit distance and show that edit distance or the similarity and implementation using dynamic programming. The performance of the proposed approach is evaluated using number edit and percentage similarity measures.Keywords: Edit distance, String Matching, String Similarity
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 33161248 String Matching using Inverted Lists
Authors: Chouvalit Khancome, Veera Boonjing
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This paper proposes a new solution to string matching problem. This solution constructs an inverted list representing a string pattern to be searched for. It then uses a new algorithm to process an input string in a single pass. The preprocessing phase takes 1) time complexity O(m) 2) space complexity O(1) where m is the length of pattern. The searching phase time complexity takes 1) O(m+α ) in average case 2) O(n/m) in the best case and 3) O(n) in the worst case, where α is the number of comparing leading to mismatch and n is the length of input text.
Keywords: String matching, inverted list, inverted index, pattern, algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15551247 Distributed Splay Suffix Arrays: A New Structure for Distributed String Search
Authors: Tu Kun, Gu Nai-jie, Bi Kun, Liu Gang, Dong Wan-li
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As a structure for processing string problem, suffix array is certainly widely-known and extensively-studied. But if the string access pattern follows the “90/10" rule, suffix array can not take advantage of the fact that we often find something that we have just found. Although the splay tree is an efficient data structure for small documents when the access pattern follows the “90/10" rule, it requires many structures and an excessive amount of pointer manipulations for efficiently processing and searching large documents. In this paper, we propose a new and conceptually powerful data structure, called splay suffix arrays (SSA), for string search. This data structure combines the features of splay tree and suffix arrays into a new approach which is suitable to implementation on both conventional and clustered computers.Keywords: suffix arrays, splay tree, string search, distributedalgorithm
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17761246 Data Quality Enhancement with String Length Distribution
Authors: Qi Xiu, Hiromu Hota, Yohsuke Ishii, Takuya Oda
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Recently, collectable manufacturing data are rapidly increasing. On the other hand, mega recall is getting serious as a social problem. Under such circumstances, there are increasing needs for preventing mega recalls by defect analysis such as root cause analysis and abnormal detection utilizing manufacturing data. However, the time to classify strings in manufacturing data by traditional method is too long to meet requirement of quick defect analysis. Therefore, we present String Length Distribution Classification method (SLDC) to correctly classify strings in a short time. This method learns character features, especially string length distribution from Product ID, Machine ID in BOM and asset list. By applying the proposal to strings in actual manufacturing data, we verified that the classification time of strings can be reduced by 80%. As a result, it can be estimated that the requirement of quick defect analysis can be fulfilled.Keywords: Data quality, feature selection, probability distribution, string classification, string length.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13281245 String Searching in Dispersed Files using MDS Convolutional Codes
Authors: A. S. Poornima, R. Aparna, B. B. Amberker, Prashant Koulgi
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In this paper, we propose use of convolutional codes for file dispersal. The proposed method is comparable in complexity to the information Dispersal Algorithm proposed by M.Rabin and for particular choices of (non-binary) convolutional codes, is almost as efficient as that algorithm in terms of controlling expansion in the total storage. Further, our proposed dispersal method allows string search.Keywords: Convolutional codes, File dispersal, Filereconstruction, Information Dispersal Algorithm, String search.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12781244 Optimization of Human Comfort Reaction for Suspended Cabin Tractor Semitrailer Drivers
Authors: L.A.Kumaraswamidhas, P.Velmurugan, K.Sankaranarayanasamy
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This work has been conducted to study on comfort level of drivers of suspended cabin tractor semitrailer. Some drivers suffer from low back pain caused by vibration. The practical significance of applying suspended cabin type of tractor semi trailer was tested at different road conditions, different speed as well as different load conditions for comfortable driver seat interface (x, y, z ) and the process parameters have been prioritized using Taguchi-s L27 orthogonal array. Genetic Algorithm (GA) is used to optimize the human comfort vibration of suspended cabin tractor semitrailer drivers. The practical significance of applying GA to human comfort to reaction of suspended cabin tractor semitrailer has been validated by means of computing the deviation between predicted and experimentally obtained human comfort to vibration. The optimized acceleration data indicate a little uncomfortable ride for suspended cabin tractor semitrailer.
Keywords: Genetic Algorithm, Ride Comfort, Taguchi Method, Tractor Semitrailer
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25581243 Workspace Analysis of 6–6 Cable-Suspended Parallel Robots
Authors: Arian Bahrami, Amir Teimourian
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In this paper, the effect of the moving platform size on the workspace volume of 6–6 cable-suspended parallel robots is investigated in details for different geometric configurations and orientations of the moving platform. The obtained hints can be used as a rule of thumb in designing this type of robot.Keywords: Cable-suspended parallel robot, system analysis and design, workspace analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11561242 The Performance of the Character-Access on the Checking Phase in String Searching Algorithms
Authors: Mahmoud M. Mhashi
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A new algorithm called Character-Comparison to Character-Access (CCCA) is developed to test the effect of both: 1) converting character-comparison and number-comparison into character-access and 2) the starting point of checking on the performance of the checking operation in string searching. An experiment is performed; the results are compared with five algorithms, namely, Naive, BM, Inf_Suf_Pref, Raita, and Circle. With the CCCA algorithm, the results suggest that the evaluation criteria of the average number of comparisons are improved up to 74.0%. Furthermore, the results suggest that the clock time required by the other algorithms is improved in range from 28% to 68% by the new CCCA algorithmKeywords: Pattern matching, string searching, charactercomparison, character-access, and checking.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13071241 Using ε Value in Describe Regular Languages by Using Finite Automata, Operation on Languages and the Changing Algorithm Implementation
Authors: Abdulmajid Mukhtar Afat
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This paper aims at introducing nondeterministic finite automata with ε value which is used to perform some operations on languages. a program is created to implement the algorithm that converts nondeterministic finite automata with ε value (ε-NFA) to deterministic finite automata (DFA).The program is written in c++ programming language. The program inputs are FA 5-tuples from text file and then classifies it into either DFA/NFA or ε -NFA. For DFA, the program will get the string w and decide whether it is accepted or rejected. The tracking path for an accepted string is saved by the program. In case of NFA or ε-NFA automation, the program changes the automation to DFA to enable tracking and to decide if the string w exists in the regular language or not.
Keywords: Finite automata, DFA, NFA, ε-NFA, Eclose, operations on languages.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8371240 Approximation Algorithm for the Shortest Approximate Common Superstring Problem
Authors: A.S. Rebaï, M. Elloumi
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The Shortest Approximate Common Superstring (SACS) problem is : Given a set of strings f={w1, w2, ... , wn}, where no wi is an approximate substring of wj, i ≠ j, find a shortest string Sa, such that, every string of f is an approximate substring of Sa. When the number of the strings n>2, the SACS problem becomes NP-complete. In this paper, we present a greedy approximation SACS algorithm. Our algorithm is a 1/2-approximation for the SACS problem. It is of complexity O(n2*(l2+log(n))) in computing time, where n is the number of the strings and l is the length of a string. Our SACS algorithm is based on computation of the Length of the Approximate Longest Overlap (LALO).Keywords: Shortest approximate common superstring, approximation algorithms, strings overlaps, complexities.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15051239 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t
Authors: Ahmet Tekcan, Betül Gezer, Osman Bizim
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Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.
Keywords: Pell equation, Diophantine equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23861238 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4
Authors: Armend Sh. Shabani
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Let D ≠ 1 be a positive non-square integer. In this paper are given the proofs for two conjectures related to Pell-s equation x2 -Dy2 = ± 4, proposed by A. Tekcan.Keywords: Pell's equation, solutions of Pell's equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12361237 Prognostic and Diagnostic Modes of Mathematical Model for the Pre-operation of Suspended Sediment Transport model in Estuaries and Coastal areas
Authors: Worachat Wannawong, Chaiwat Ekkawatpanit, Sanit Wongsa
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Both prognostic and diagnostic modes of a 3D baroclinic model in hydrodynamic and sediment transport models of the Princeton Ocean Model (POM) were conducted to separate prognose and diagnose effects of different hydrodynamic factors on transport of suspended sediment discharged from the rivers to the Gulf of Thailand (GoT). Both transport modes of suspended sediment distribution in the GoT were numerically simulated. It could be concluded that the suspended sediment discharged from the rivers around the GoT. Most of sediments in estuaries and coastal areas are deposited outside the GoT under the condition of wind-driven current, and very small amount of the sediments of them are transported faraway. On the basis of wind forcing, sediments from the lower GoT to the upper GoT are mainly transported south-northwestward and also continuously moved north-southwestward. An obvious 3D characteristic of suspended sediment transport is produced in the wind-driven current residual circulation condition. In this study, the transport patterns at the third layer are generally consistent with the typhoon-induced strong currents in two case studies of Typhoon Linda 1997. The case studies presented the prognostic and diagnostic modes during 00UTC28OCT1997 to 12UTC06NOV1997 in a short period with the current condition for pre-operation of the suspended sediment transport model in estuaries and coastal areas.Keywords: prognostic, diagnostic, baroclinic, sediment transport, estuaries.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15011236 An Analytical Method for Solving General Riccati Equation
Authors: Y. Pala, M. O. Ertas
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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.
Keywords: Riccati Equation, ordinary differential equation, nonlinear differential equation, analytical solution, proper solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20231235 The Pell Equation x2 − Py2 = Q
Authors: Ahmet Tekcan, Arzu Özkoç, Canan Kocapınar, Hatice Alkan
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Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + 1 and Q = k2. In this paper, we consider the integer solutions of the Pell equation x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce some relations on the integer solutions (xn, yn) of it.Keywords: Pell equation, solutions of Pell equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21051234 Increase of Sensitivity in 3D Suspended Polymeric Microfluidic Platform through Lateral Misalignment
Authors: Ehsan Yazdanpanah Moghadam, Muthukumaran Packirisamy
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In the present study, a design of the suspended polymeric microfluidic platform is introduced that is fabricated with three polymeric layers. Changing the microchannel plane to be perpendicular to microcantilever plane, drastically decreases moment of inertia in that direction. In addition, the platform is made of polymer (around five orders of magnitude less compared to silicon). It causes significant increase in the sensitivity of the cantilever deflection. Next, although the dimensions of this platform are constant, by misaligning the embedded microchannels laterally in the suspended microfluidic platform, the sensitivity can be highly increased. The investigation is studied on four fluids including water, seawater, milk, and blood for flow ranges from low rate of 5 to 70 µl/min to obtain the best design with the highest sensitivity. The best design in this study shows the sensitivity increases around 50% for water, seawater, milk, and blood at the flow rate of 70 µl/min by just misaligning the embedded microchannels in the suspended polymeric microfluidic platform.Keywords: Microfluidic, biosensor, MEMS.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8841233 Suspended Matter Model on Alsat-1 Image by MLP Network and Mathematical Morphology: Prototypes by K-Means
Authors: S. Loumi, H. Merrad, F. Alilat, B. Sansal
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In this article, we propose a methodology for the characterization of the suspended matter along Algiers-s bay. An approach by multi layers perceptron (MLP) with training by back propagation of the gradient optimized by the algorithm of Levenberg Marquardt (LM) is used. The accent was put on the choice of the components of the base of training where a comparative study made for four methods: Random and three alternatives of classification by K-Means. The samples are taken from suspended matter image, obtained by analytical model based on polynomial regression by taking account of in situ measurements. The mask which selects the zone of interest (water in our case) was carried out by using a multi spectral classification by ISODATA algorithm. To improve the result of classification, a cleaning of this mask was carried out using the tools of mathematical morphology. The results of this study presented in the forms of curves, tables and of images show the founded good of our methodology.Keywords: Classification K-means, mathematical morphology, neural network MLP, remote sensing, suspended particulate matter
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15221232 The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp
Authors: Ahmet Tekcan, Arzu Özkoç, Hatice Alkan
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In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp.Keywords: Diophantine equation, Pell equation, quadratic form.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12651231 A Comparison of Artificial Neural Networks for Prediction of Suspended Sediment Discharge in River- A Case Study in Malaysia
Authors: M.R. Mustafa, M.H. Isa, R.B. Rezaur
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Prediction of highly non linear behavior of suspended sediment flow in rivers has prime importance in the field of water resources engineering. In this study the predictive performance of two Artificial Neural Networks (ANNs) namely, the Radial Basis Function (RBF) Network and the Multi Layer Feed Forward (MLFF) Network have been compared. Time series data of daily suspended sediment discharge and water discharge at Pari River was used for training and testing the networks. A number of statistical parameters i.e. root mean square error (RMSE), mean absolute error (MAE), coefficient of efficiency (CE) and coefficient of determination (R2) were used for performance evaluation of the models. Both the models produced satisfactory results and showed a good agreement between the predicted and observed data. The RBF network model provided slightly better results than the MLFF network model in predicting suspended sediment discharge.Keywords: ANN, discharge, modeling, prediction, suspendedsediment,
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17231230 Comparative Analysis of Photovoltaic Systems
Authors: Irtaza M. Syed, Kaamran Raahemifar
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This paper presents comparative analysis of photovoltaic systems (PVS) and propose practical techniques to improve operational efficiency of the PVS. The best engineering and construction practices for PVS are identified and field oriented recommendation are made. Comparative analysis of central and string inverter based, as well as 600 and 1000VDC PVS are performed. In addition, direct current (DC) and alternating current (AC) photovoltaic (PV) module based systems are compared. Comparison shows that 1000V DC String Inverters based PVS is the best choice.Keywords: Photovoltaic module, photovoltaic systems, operational efficiency improvement, comparative analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22981229 Nonlinearity and Spectrum Analysis of Drill Strings with Component Mass Unbalance
Authors: F. Abdul Majeed, H. Karki, Y. Abdel Magid, M. Karkoub
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This paper analyses the non linear properties exhibited by a drill string system under various un balanced mass conditions. The drill string is affected by continuous friction in the form of drill bit and well bore hole interactions. This paper proves the origin of limit cycling and increase of non linearity with increase in speed of the drilling in the presence of friction. The spectrum of the frequency response is also studied to detect the presence of vibration abnormalities arising during the drilling process.Keywords: Drill strings, Nonlinear, Spectrum analysis, Unbalanced mass
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17231228 Solution of The KdV Equation with Asymptotic Degeneracy
Authors: Tapas Kumar Sinha, Joseph Mathew
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Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).
Keywords: KdV equation, Asymptotic Degeneracy, Solitons, Inverse Scattering
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16201227 Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method
Authors: Said Laachir, Aziz Laaribi
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The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.
Keywords: Helmholtz equation, Nikiforov-Uvarov method, exact solutions, eigenfunctions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3003