Search results for: Two-phase simplex method.

Authors: El-Said Badr, Mahmoud Moussa, Konstantinos Paparrizos, Nikolaos Samaras, Angelo Sifaleras

Abstract:

There are two major variants of the Simplex Algorithm: the revised method and the standard, or tableau method. Today, all serious implementations are based on the revised method because it is more efficient for sparse linear programming problems. Moreover, there are a number of applications that lead to dense linear problems so our aim in this paper is to present some computational results on parallel implementation of dense Simplex Method. Our implementation is implemented on a SMP cluster using C programming language and the Message Passing Interface MPI. Preliminary computational results on randomly generated dense linear programs support our results.

Keywords: Linear Programming, MPI, Parallel Implementation, Simplex Algorithm.

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Authors: Clio G. Vossou, Ioannis N. Koukoulis, Christopher G. Provatidis

Abstract:

The present work encounters the solution of the defect identification problem with the use of an evolutionary algorithm combined with a simplex method. In more details, a Matlab implementation of Genetic Algorithms is combined with a Simplex method in order to lead to the successful identification of the defect. The influence of the location and the orientation of the depressed ellipsoidal flaw was investigated as well as the use of different amount of static data in the cost function. The results were evaluated according to the ability of the simplex method to locate the global optimum in each test case. In this way, a clear impression regarding the performance of the novel combination of the optimization algorithms, and the influence of the geometrical parameters of the flaw in defect identification problems was obtained.

Keywords: Defect identification, genetic algorithms, optimization.

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Authors: S. H. Nasseri, E. Ardil, A. Yazdani, R. Zaefarian

Abstract:

The fuzzy set theory has been applied in many fields, such as operations research, control theory, and management sciences, etc. In particular, an application of this theory in decision making problems is linear programming problems with fuzzy numbers. In this study, we present a new method for solving fuzzy number linear programming problems, by use of linear ranking function. In fact, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy number linear programming, rankingfunction, simplex method.

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Authors: S.H. Nasseri, E. Ardil

Abstract:

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

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Authors: Prashant P. Bedekar, Sudhir R. Bhide, Vijay S. Kale

Abstract:

Overcurrent (OC) relays are the major protection devices in a distribution system. The operating time of the OC relays are to be coordinated properly to avoid the mal-operation of the backup relays. The OC relay time coordination in ring fed distribution networks is a highly constrained optimization problem which can be stated as a linear programming problem (LPP). The purpose is to find an optimum relay setting to minimize the time of operation of relays and at the same time, to keep the relays properly coordinated to avoid the mal-operation of relays. This paper presents two phase simplex method for optimum time coordination of OC relays. The method is based on the simplex algorithm which is used to find optimum solution of LPP. The method introduces artificial variables to get an initial basic feasible solution (IBFS). Artificial variables are removed using iterative process of first phase which minimizes the auxiliary objective function. The second phase minimizes the original objective function and gives the optimum time coordination of OC relays.

Keywords: Constrained optimization, LPP, Overcurrent relaycoordination, Two-phase simplex method.

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Authors: P. Luangpaiboon, S. Boonhao

Abstract:

This study proposes a multi-response surface optimization problem (MRSOP) for determining the proper choices of a process parameter design (PPD) decision problem in a noisy environment of a grease position process in an electronic industry. The proposed models attempts to maximize dual process responses on the mean of parts between failure on left and right processes. The conventional modified simplex method and its hybridization of the stochastic operator from the hunting search algorithm are applied to determine the proper levels of controllable design parameters affecting the quality performances. A numerical example demonstrates the feasibility of applying the proposed model to the PPD problem via two iterative methods. Its advantages are also discussed. Numerical results demonstrate that the hybridization is superior to the use of the conventional method. In this study, the mean of parts between failure on left and right lines improve by 39.51%, approximately. All experimental data presented in this research have been normalized to disguise actual performance measures as raw data are considered to be confidential.

Keywords: Grease Position Process, Multi-response Surfaces, Modified Simplex Method, Hunting Search Method, Desirability Function Approach.

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Authors: P. N. Korde, P. P. Bedekar

Abstract:

The time coordination of overcurrent relays (OCR) in a power distribution network is of great importance, as it reduces the power outages by avoiding the mal-operation of the backup relays. For this, the optimum value of the time multiplier setting (TMS) of OCRs should be chosen. The problem of determining the optimum value of TMS of OCRs in power distribution networks is formulated as a constrained optimization problem. The objective is to find the optimum value of TMS of OCRs to minimize the time of operation of relays under the constraint of maintaining the coordination of relays. A power distribution network can have a combination of numerical and electromechanical relays. The TMS of numerical relays can be set to any real value (which satisfies the constraints of the problem), whereas the TMS of electromechanical relays can be set in fixed step (0 to 1 in steps of 0.05). The main contribution of this paper is a formulation of the problem as a mixed-integer linear programming (MILP) problem and application of Gomory's cutting plane method to find the optimum value of TMS of OCRs. The TMS of electromechanical relays are taken as integers in the range 1 to 20 in the step of 1, and these values are mapped to 0.05 to 1 in the step of 0.05. The results obtained are compared with those obtained using a simplex method and its variants. It has been shown that the mixed-integer linear programming method outperforms the simplex method (and its variants) in the case of a system having a combination of numerical and electromechanical relays.

Keywords: Backup protection, constrained optimization, Gomory's cutting plane method, mixed-integer linear programming, overcurrent relay coordination, simplex method.

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Authors: Seksan Chunothaisawat, Pongchanun Luangpaiboon

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There are two common types of operational research techniques, optimisation and metaheuristic methods. The latter may be defined as a sequential process that intelligently performs the exploration and exploitation adopted by natural intelligence and strong inspiration to form several iterative searches. An aim is to effectively determine near optimal solutions in a solution space. In this work, a type of metaheuristics called Ant Colonies Optimisation, ACO, inspired by a foraging behaviour of ants was adapted to find optimal solutions of eight non-linear continuous mathematical models. Under a consideration of a solution space in a specified region on each model, sub-solutions may contain global or multiple local optimum. Moreover, the algorithm has several common parameters; number of ants, moves, and iterations, which act as the algorithm-s driver. A series of computational experiments for initialising parameters were conducted through methods of Rigid Simplex, RS, and Modified Simplex, MSM. Experimental results were analysed in terms of the best so far solutions, mean and standard deviation. Finally, they stated a recommendation of proper level settings of ACO parameters for all eight functions. These parameter settings can be applied as a guideline for future uses of ACO. This is to promote an ease of use of ACO in real industrial processes. It was found that the results obtained from MSM were pretty similar to those gained from RS. However, if these results with noise standard deviations of 1 and 3 are compared, MSM will reach optimal solutions more efficiently than RS, in terms of speed of convergence.

Keywords: Ant colony optimisation, metaheuristics, modified simplex, non-linear, rigid simplex.

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Authors: Victor A. Naumenko, Yuriy A. Tyulenev, Alla A. Kushch

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The objective of current issue was to develop a model of testicular herpes simplex virus (HSV) type I infection for assessment of viral effect on fertility. 56 male mice were inoculated intraperitoneally with different concentrations of HSV on 8 day post partum. It was revealed that the optimal dose was 100 plaque forming units per mice as it provided testicular infection in 100% of survivors. HSV proteins were detected both in somatic and germ cells (spermatogonia, spermatocytes, spermatides). Although DNA load in testis was descending from 3 to 28 days post infection only 12.5% of infected males had offspring after mating with uninfected females comparing to 87.5% in control (p=0.012). These results are the first direct evidence for HSV impact in male sterility. Prepuberal mice appeared to be a suitable model for investigation of pathogenesis of virus-associated fertility disorders.

Keywords: Herpes simplex virus type I, male fertility, prepuberal mice, spermatogenesis.

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Authors: Sasadhar Bera, Indrajit Mukherjee

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Ant colony optimization (ACO) and its variants are applied extensively to resolve various continuous optimization problems. As per the various diversification and intensification schemes of ACO for continuous function optimization, researchers generally consider components of multidimensional state space to generate the new search point(s). However, diversifying to a new search space by updating only components of the multidimensional vector may not ensure that the new point is at a significant distance from the current solution. If a minimum distance is not ensured during diversification, then there is always a possibility that the search will end up with reaching only local optimum. Therefore, to overcome such situations, a Mahalanobis distance-based diversification with Nelder-Mead simplex-based search scheme for each ant is proposed for the ACO strategy. A comparative computational run results, based on nine nonlinear standard test problems, confirms that the performance of ACO is improved significantly with the integration of the proposed schemes in the ACO.

Keywords: Ant Colony Optimization, Diversification Scheme, Intensification, Mahalanobis Distance, Nelder-Mead Simplex.

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Authors: M. Pandi, K. Premalatha

Abstract:

The DNA microarray technology concurrently monitors the expression levels of thousands of genes during significant biological processes and across the related samples. The better understanding of functional genomics is obtained by extracting the patterns hidden in gene expression data. It is handled by clustering which reveals natural structures and identify interesting patterns in the underlying data. In the proposed work clustering gene expression data is done through an Advanced Nelder Mead (ANM) algorithm. Nelder Mead (NM) method is a method designed for optimization process. In Nelder Mead method, the vertices of a triangle are considered as the solutions. Many operations are performed on this triangle to obtain a better result. In the proposed work, the operations like reflection and expansion is eliminated and a new operation called spread-out is introduced. The spread-out operation will increase the global search area and thus provides a better result on optimization. The spread-out operation will give three points and the best among these three points will be used to replace the worst point. The experiment results are analyzed with optimization benchmark test functions and gene expression benchmark datasets. The results show that ANM outperforms NM in both benchmarks.

Keywords: Spread out, simplex, multi-minima, fitness function, optimization, search area, monocyte, solution, genomes.

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Authors: P. Luangpaiboon

Abstract:

Various intelligences and inspirations have been adopted into the iterative searching process called as meta-heuristics. They intelligently perform the exploration and exploitation in the solution domain space aiming to efficiently seek near optimal solutions. In this work, the bee algorithm, inspired by the natural foraging behaviour of honey bees, was adapted to find the near optimal solutions of the transportation management system, dynamic multi-zone dispatching. This problem prepares for an uncertainty and changing customers- demand. In striving to remain competitive, transportation system should therefore be flexible in order to cope with the changes of customers- demand in terms of in-bound and outbound goods and technological innovations. To remain higher service level but lower cost management via the minimal imbalance scenario, the rearrangement penalty of the area, in each zone, including time periods are also included. However, the performance of the algorithm depends on the appropriate parameters- setting and need to be determined and analysed before its implementation. BEE parameters are determined through the linear constrained response surface optimisation or LCRSOM and weighted centroid modified simplex methods or WCMSM. Experimental results were analysed in terms of best solutions found so far, mean and standard deviation on the imbalance values including the convergence of the solutions obtained. It was found that the results obtained from the LCRSOM were better than those using the WCMSM. However, the average execution time of experimental run using the LCRSOM was longer than those using the WCMSM. Finally a recommendation of proper level settings of BEE parameters for some selected problem sizes is given as a guideline for future applications.

Keywords: Meta-heuristic, Bee Algorithm, Dynamic Multi-Zone Dispatching, Linear Constrained Response SurfaceOptimisation Method, Weighted Centroid Modified Simplex Method

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Authors: Bruno Félix, André Vasconcelos, José Tribolet

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Nowadays increasingly the population makes use of Information Technology (IT). As such, in recent year the Portuguese government increased its focus on using the IT for improving people-s life and began to develop a set of measures to enable the modernization of the Public Administration, and so reducing the gap between Public Administration and citizens.Thus the Portuguese Government launched the Simplex Program. However these SIMPLEX eGov measures, which have been implemented over the years, present a serious challenge: how to forecast its impact on existing Information Systems Architecture (ISA). Thus, this research is focus in addressing the problem of automating the evaluation of the actual impact of implementation an eGovSimplification and Modernization measures in the Information Systems Architecture. To realize the evaluation we proposes a Framework, which is supported by some key concepts as: Quality Factors, ISA modeling, Multicriteria Approach, Polarity Profile and Quality Metrics

Keywords: Information System Architecture, Evaluation, eGov Simplification measure, Multicriteria Evaluation

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Authors: F. Tafnout, E. Belut, B. Oesterlé, J.R. Fontaine

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As a part of the development of a numerical method of close capture exhausts systems for machining devices, a test rig recreating a situation similar to a grinding operation, but in a perfectly controlled environment, is used. The properties of the obtained spray of solid particles are initially characterized using particle tracking velocimetry (PTV), in order to obtain input and validation parameters for numerical simulations. The dispersion of a tracer gas (SF6) emitted simultaneously with the particle jet is then studied experimentally, as the dispersion of such a gas is representative of that of finer particles, whose aerodynamic response time is negligible. Finally, complete modeling of the test rig is achieved to allow comparison with experimental results and thus to progress towards validation of the models used to describe a twophase flow generated by machining operation.

Keywords: Pollutants, capture, tracer gas, SF6, PTV, numericalmodeling.

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Authors: Timothée Bligny, Clément Codron, Antoine Estruch, Nicolas Girodet, Clément Ginet

Abstract:

Collateralized Debt Obligations are not as widely used nowadays as they were before 2007 Subprime crisis. Nonetheless there remains an enthralling challenge to optimize cash flows associated with synthetic CDOs. A Gaussian-based model is used here in which default correlation and unconditional probabilities of default are highlighted. Then numerous simulations are performed based on this model for different scenarios in order to evaluate the associated cash flows given a specific number of defaults at different periods of time. Cash flows are not solely calculated on a single bought or sold tranche but rather on a combination of bought and sold tranches. With some assumptions, the simplex algorithm gives a way to find the maximum cash flow according to correlation of defaults and maturities. The used Gaussian model is not realistic in crisis situations. Besides present system does not handle buying or selling a portion of a tranche but only the whole tranche. However the work provides the investor with relevant elements on how to know what and when to buy and sell.

Keywords: Synthetic Collateralized Debt Obligation (CDO), Credit Default Swap (CDS), Cash Flow Optimization, Probability of Default, Default Correlation, Strategies, Simulation, Simplex.

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Authors: Waqar Haque, Pai Qi

Abstract:

The speculative locking (SL) protocol extends the twophase locking (2PL) protocol to allow for parallelism among conflicting transactions. The adaptive speculative locking (ASL) protocol provided further enhancements and outperformed SL protocols under most conditions. Neither of these protocols consider the impact of network latency on the performance of the distributed database systems. We have studied the performance of ASL protocol taking into account the communication overhead. The results indicate that though system load can counter network latency, it can still become a bottleneck in many situations. The impact of latency on performance depends on many factors including the system resources. A flexible discrete event simulator was used as the testbed for this study.

Keywords: concurrency control, distributed database systems, speculative locking

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Authors: Mahmood Reza Rahimi, Hajir Karimi

Abstract:

Downward turbulent bubbly flows in pipes were modeled using computational fluid dynamics tools. The Hydrodynamics, phase distribution and turbulent structure of twophase air-water flow in a 57.15 mm diameter and 3.06 m length vertical pipe was modeled by using the 3-D Eulerian-Eulerian multiphase flow approach. Void fraction, liquid velocity and turbulent fluctuations profiles were calculated and compared against experimental data. CFD results are in good agreement with experimental data.

Keywords: CFD, Bubbly flow, Vertical pipe, Population balance modeling, Gas void fraction, Liquid velocity, Normal turbulent stresses.

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Authors: Mehrnoush Shamsfard, Maryam Sadr Mousavi

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Extracting thematic (semantic) roles is one of the major steps in representing text meaning. It refers to finding the semantic relations between a predicate and syntactic constituents in a sentence. In this paper we present a rule-based approach to extract semantic roles from Persian sentences. The system exploits a twophase architecture to (1) identify the arguments and (2) label them for each predicate. For the first phase we developed a rule based shallow parser to chunk Persian sentences and for the second phase we developed a knowledge-based system to assign 16 selected thematic roles to the chunks. The experimental results of testing each phase are shown at the end of the paper.

Keywords: Natural Language Processing, Semantic RoleLabeling, Shallow parsing, Thematic Roles.

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Authors: Inta Volodko, Valentina Koliskina

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Linear stability analysis of wake-shear layers in twophase shallow flows is performed in the present paper. Twodimensional shallow water equations are used in the analysis. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. The stability calculations are performed for different values of the particle loading parameter and two other parameters which characterize the velocity ratio and the velocity deficit. The results show that the particle loading parameter has a stabilizing effect on the flow while the increase in the velocity ratio or in the velocity deficit destabilizes the flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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Authors: Mingyu Zhong, Yi Xie

Abstract:

Results in one field necessarily give insight into the others, and all have much potential for scientific and technological application. The Hadamard-transform technique once been applied to the spectrometry also has its use in the SNR Enhancement of OTDR. In this report, a new set of code (Simplex-codes) is discussed and where the addition gain of SNR come from is implied.

Keywords: Hadamard-transform, matrixes, averaging, opticaltime-domain reflectometry (OTDR).

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Authors: Abdolamir Nekoubin

Abstract:

The objective of this paper is to analyze the performance of a double-sided axial flux permanent magnet brushless DC (AFPM BLDC) motor with two-phase winding. To study the motor operation, a mathematical dynamic model has been proposed for motor, which became the basis for simulations that were performed using MATLAB/SIMULINK software package. The results of simulations were presented in form of the waveforms of selected quantities and the electromechanical characteristics performed by the motor. The calculation results show that the two-phase motor version develops smooth torque and reaches high efficiency. The twophase motor can be applied where more smooth torque is required. Finally a study on the influence of switching angle on motor performance shows that when advance switching technique is used, the motor operates with the highest efficiency.

Keywords: brushless DC motor, inverter, switching angle.

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Authors: Joel V. Madison, Hans E. Kimmel

Abstract:

Saturated two-phase fluid flows are often subject to pressure induced oscillations. Due to compressibility the vapor bubbles act as a spring with an asymmetric non-linear characteristic. The volume of the vapor bubbles increases or decreases differently if the pressure fluctuations are compressing or expanding; consequently, compressing pressure fluctuations in a two-phase pipe flow cause less displacement in the direction of the pipe flow than expanding pressure fluctuations. The displacement depends on the ratio of liquid to vapor, the ratio of pressure fluctuations over average pressure and on the exciting frequency of the pressure fluctuations. In addition, pressure fluctuations in saturated vapor bubbles cause condensation and evaporation within the bubbles and change periodically the ratio between liquid to vapor, and influence the dynamical parameters for the oscillation. The oscillations are conforming to an isenthalpic process at constant enthalpy with no heat transfer and no exchange of work. The paper describes the governing non-linear equation for twophase fluid oscillations with condensation and evaporation, and presents steady state approximate solutions for free and for pressure induced oscillations. Resonance criteria and stability are discussed.

Keywords: condensation, evaporation, non-linear oscillations, pressure induced, two-phase flow

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Authors: Elangeshwaran Pathmanathan, Rosdiazli Ibrahim, Vijanth Sagayan Asirvadam

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This paper aims to develop a NOx emission model of an acid gas incinerator using Nelder-Mead least squares support vector regression (LS-SVR). Malaysia DOE is actively imposing the Clean Air Regulation to mandate the installation of analytical instrumentation known as Continuous Emission Monitoring System (CEMS) to report emission level online to DOE . As a hardware based analyzer, CEMS is expensive, maintenance intensive and often unreliable. Therefore, software predictive technique is often preferred and considered as a feasible alternative to replace the CEMS for regulatory compliance. The LS-SVR model is built based on the emissions from an acid gas incinerator that operates in a LNG Complex. Simulated Annealing (SA) is first used to determine the initial hyperparameters which are then further optimized based on the performance of the model using Nelder-Mead simplex algorithm. The LS-SVR model is shown to outperform a benchmark model based on backpropagation neural networks (BPNN) in both training and testing data.

Keywords: artificial neural networks, industrial pollution, predictive algorithms, support vector machines

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Authors: Nor Hayati Ibrahim, Yaakob B. Che Man, Chin Ping Tan, Nor Aini Idris

Abstract:

Interaction effects of xanthan gum (XG), carboxymethyl cellulose (CMC), and locust bean gum (LBG) on the flow properties of oil-in-water emulsions were investigated by a mixture design experiment. Blends of XG, CMC and LBG were prepared according to an augmented simplex-centroid mixture design (10 points) and used at 0.5% (wt/wt) in the emulsion formulations. An appropriate mathematical model was fitted to express each response as a function of the proportions of the blend components that are able to empirically predict the response to any blend of combination of the components. The synergistic interaction effect of the ternary XG:CMC:LBG blends at approximately 33-67% XG levels was shown to be much stronger than that of the binary XG:LBG blend at 50% XG level (p < 0.05). Nevertheless, an antagonistic interaction effect became significant as CMC level in blends was more than 33% (p < 0.05). Yield stress and apparent viscosity (at 10 s-1) responses were successfully fitted with a special quartic model while flow behaviour index and consistency coefficient were fitted with a full quartic model (R2 adjusted ≥ 0.90). This study found that a mixture design approach could serve as a valuable tool in better elucidating and predicting the interaction effects beyond the conventional twocomponent blends.

Keywords: O/W emulsions, flow behavior, polysaccharideinteraction, mixture design.

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Authors: Zhengsheng Wang, Jing Qi, Chuntao Liu, Yuanjun Li

Abstract:

The harmonic Arnoldi method can be used to find interior eigenpairs of large matrices. However, it has been shown that this method may converge erratically and even may fail to do so. In this paper, we present a new method for computing interior eigenpairs of large nonsymmetric matrices, which is called weighted harmonic Arnoldi method. The implementation of the method has been tested by numerical examples, the results show that the method converges fast and works with high accuracy.

Keywords: Harmonic Arnoldi method, weighted harmonic Arnoldi method, eigenpair, interior eigenproblem, non symmetric matrix.

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Authors: Jin Sup Kim, Woo Young Jung, Minho Kwon

Abstract:

In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Keywords: Dynamic, α-Method, P-Method, PC α-Method, Newmark method.

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Authors: Imran Khan Pathan, Anil Bhandari, Peeyush K. Sharma, Rakesh K. Patel, Suresh Purohit

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Floating tablets of Marichyadi Vati were developed with an aim to prolong its gastric residence time and increase the bioavailability of drug. Rapid gastrointestinal transit could result in incomplete drug release from the drug delivery system above the absorption zone leading to diminished efficacy of the administered dose. The tablets were prepared by wet granulation technique, using HPMC E50 LV act as Matrixing agent, Carbopol as floating enhancer, microcrystalline cellulose as binder, Sodium bi carbonate as effervescent agent with other excipients. The simplex lattice design was used for selection of variables for tablets formulation. Formulation was optimized on the basis of floating time and in vitro drug release. The results showed that the floating lag time for optimized formulation was found to be 61 second with about 97.32 % of total drug release within 3 hours. The vitro release profiles of drug from the formulation could be best expressed zero order with highest linearity r² = 0.9943. It was concluded that the gastroretentive drug delivery system can be developed for Marichyadi Vati containing Piperine to increase the residence time of the drug in the stomach and thereby increasing bioavailability.

Keywords: Piperine, Marichyadi Vati, Gastroretentive drug delivery, Floating tablet.

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Authors: Seemaa Diwedi

Abstract:

The study area receives a wide variety of wastes generated by municipalities and the industries like paints and pigments, metal processing industries, thermal power plants electroprocessing industries etc. The Physico-chemical and structural investigation of water from river Pandu indicated high level of chlorides and calcium which made the water unsuitable for human use. Algae like Cyclotella fumida, Asterionella Formosa, Cladophora glomerata, Pediastrum simplex, Scenedesmus bijuga, Cladophora glomerata were the dominant pollution tolerant species recorded under these conditions. The sensitive and less abundant species of algae included Spirogyra sps., Merismopedia sps. The predominance colonies of Zygnema sps, Phormidium sps, Mycrocystis aeruginosa, Merismopedia minima, Pandorina morum, seems to correlate with high organic contents of Pandu river water. This study assumes significance as some algae can be used as bioindicators of water pollution and algal floral of a municipal drain carrying waste effluents from industrial area Kanpur and discharge them into the river Pandu flowing onto southern outskirts of Kanpur city.

Keywords: Kanpur, North India, Physico-chemical, Pollution, River Pandu.

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Authors: J.S.C. Prentice

Abstract:

The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: RK1GL2X3, RK1GL2, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, local error, global error.

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Authors: Mohammed Salem Alzahrani

Abstract:

In this paper the optimality of the solution of an existing real word assignment problem known as the seat assignment problem using Seat Assignment Method (SAM) is discussed. SAM is the newly driven method from three existing methods, Hungarian Method, Northwest Corner Method and Least Cost Method in a special way that produces the easiness & fairness among all methods that solve the seat assignment problem.

Keywords: Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM), A Real Word Assignment Problem.

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