Search results for: numerical investigations

Authors: Sukru Merey, Caglar Sinayuc

Abstract:

Gas hydrate deposits which are found in deep ocean sediments and in permafrost regions are supposed to be a fossil fuel reserve for the future. The Black Sea is also considered rich in terms of gas hydrates. It abundantly contains gas hydrates as methane (CH₄~80 to 99.9%) source. In this study, by using the literature, seismic and other data of the Black Sea such as salinity, porosity of the sediments, common gas type, temperature distribution and pressure gradient, the optimum gas production method for the Black Sea gas hydrates was selected as mainly depressurization method. Numerical simulations were run to analyze gas production from gas hydrate deposited in turbidites in the Black Sea by depressurization.

Keywords: Black Sea hydrates, depressurization, turbidites, HydrateResSim.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1331

Authors: Mehrdad Abkenari, Alireza Rezaei, Naghmeh Pournayeb

Abstract:

There have recently been many studies and investments in developed and developing countries regarding the possibility of recycling construction waste, which are still ongoing. Since the term 'construction waste' covers a vast spectrum of materials in constructing buildings, roads and etc., many investigations are required to measure their technical performance in use as well as their time and place of use. Concrete is among the major and fundamental materials used in current construction industry. Along with the rise of population in developing countries, it is desperately required to meet the people's primary need in construction industry and on the other hand, dispose existing wastes for reducing the amount of environmental pollutants. Restrictions of natural resources and environmental pollution are the most important problems encountered by civil engineers. Reusing construction waste is an important and economic approach that not only assists the preservation of environment but also, provides us with primary raw materials. In line with consistent municipal development in disposal and reuse of construction waste, several approaches including, management of construction waste and materials, materials recycling and innovation and new inventions in materials have been predicted. This article has accordingly attempted to study the activities related to recycling of construction wastes and then, stated the economic, quantitative, qualitative and environmental results obtained.

Keywords: Civil engineering, environment, recycling, construction waste.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2874

Authors: S.M. Lee, J.H. Koo, J.H. Park, S.C. Won

Abstract:

In this paper, we propose synchronization of an array of nonlinear systems with time delays. The array of systems is decomposed into isolated systems to establish appropriate Lyapunov¬Krasovskii functional. Using the Lyapunov-Krasovskii functional, a sufficient condition for the synchronization is derived in terms of LMIs(Linear Matrix Inequalities). Delayed feedback control gains are obtained by solving the sufficient condition. Numerical examples are given to show the validity the proposed method.

Keywords: Synchronization, Delay, Lyapunov method, LMI.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1421

Authors: Hsuan-Ku Liu

Abstract:

In this paper, the American exchange option (AEO) valuation problem is modelled as a free boundary problem. The critical stock price for an AEO is satisfied an integral equation implicitly. When the remaining time is large enough, an asymptotic formula is provided for pricing an AEO. The numerical results reveal that our asymptotic pricing formula is robust and accurate for the long-term AEO.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1597

Authors: S. W. Lo, S.-H. Lu, Y. H. Guo, L.-C. Hsu

Abstract:

In this paper a novel design of aerostatic thrust bearing is proposed and is analyzed numerically. The capillary restrictor and bearing disk are made of elastomer like silicone and PU. The viscoelasticity of elastomer helps the capillary expand for more air flux and at the same time, allows conicity of the bearing surface to form when the air pressure is enhanced. Therefore the bearing has the better ability of passive compensation. In the present example, as compared with the typical model, the new designs can nearly double the load capability and offer four times static stiffness.

Keywords: Aerostatic, bearing, elastomer, static stiffness.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1907

Authors: Chao Wang, Ting-Zhu Huang Chen Jia

Abstract:

In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.

Keywords: Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Error estimation, P-matrix, M-matrix.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1710

Authors: Alexey V. Klyuev, Valery P. Samarin, Viktor F. Klyuev, Andrey V. Klyuev

Abstract:

A power measurement algorithm of the input mix components of the noise signal and pulse interference is considered. The algorithm efficiency analysis has been carried out for different interference-to-signal ratio. Algorithm performance features have been explored by numerical experiment results.

Keywords: Noise signal, pulse interference, signal power, spectrum width, detection.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1451

Authors: Lina Yan, Shiheng Wang, Ke Wang

Abstract:

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS).

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1885

Authors: Osama A. Terfas, Abdusalam A. Alaktiwi

Abstract:

Pressure vessels are usually operating at temperatures where the conditions of linear elastic fracture mechanics are no longer met because massive plasticity precedes crack propagation. In this work the development of a surface crack in a pressure vessel subject to bending and tension under elastic-plastic fracture mechanics conditions was investigated. Finite element analysis was used to evaluate the hydrostatic stress, the J-integral and crack growth for semi-elliptical surface-breaking cracks. The results showed non-uniform stress triaxiality and crack driving force around the crack front at large deformation levels. Different ductile crack extensions were observed which emphasis the dependent of ductile tearing on crack geometry and type of loading. In bending the crack grew only beneath the surface, and growth was suppressed at the deepest segment. This contrasts to tension where the crack breaks through the thickness with uniform growth along the entire crack front except at the free surface. Current investigations showed that the crack growth developed under linear elastic fracture mechanics conditions will no longer be applicable under ductile tearing scenarios.

Keywords: Bending, ductile tearing, fracture toughness, stress triaxiality, tension.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2650

Authors: Abhisek Sarkar, Abhimanyu Gaur

Abstract:

In this report we have discussed the theoretical aspects of the flow transformation, occurring through a series of bifurcations. The parameters and their continuous diversion, the intermittent bursts in the transition zone, variation of velocity and pressure with time, effect of roughness in turbulent zone, and changes in friction factor and head loss coefficient as a function of Reynolds number for a transverse flow across a cylinder have been discussed. An analysis of the variation in the wake length with Reynolds number was done in FORTRAN.

Keywords: Attractor, Bifurcation, Energy cascade, Energy spectra, Intermittence, Vortex stretching.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1845

Authors: Zarina Bibi, I., Khairil Iskandar, O.

Abstract:

In this paper, parallelism in the solution of Ordinary Differential Equations (ODEs) to increase the computational speed is studied. The focus is the development of parallel algorithm of the two point Block Backward Differentiation Formulas (PBBDF) that can take advantage of the parallel architecture in computer technology. Parallelism is obtained by using Message Passing Interface (MPI). Numerical results are given to validate the efficiency of the PBBDF implementation as compared to the sequential implementation.

Keywords: Ordinary differential equations, parallel.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1642

Authors: M. S. Mahmoud

Abstract:

This study was conducted to evaluate the manganese removal from aqueous solution using Banana peels activated carbon (BPAC). Batch experiments have been carried out to determine the influence of parameters such as pH, biosorbent dose, initial metal ion concentrations and contact times on the biosorption process. From these investigations, a significant increase in percentage removal of manganese 97.4% is observed at pH value 5.0, biosorbent dose 0.8 g, initial concentration 20 ppm, temperature 25 ± 2°C, stirring rate 200 rpm and contact time 2h. The equilibrium concentration and the adsorption capacity at equilibrium of the experimental results were fitted to the Langmuir and Freundlich isotherm models; the Langmuir isotherm was found to well represent the measured adsorption data implying BPAC had heterogeneous surface. A raw groundwater samples were collected from Baharmos groundwater treatment plant network at Embaba and Manshiet Elkanater City/District-Giza, Egypt, for treatment at the best conditions that reached at first phase by BPAC. The treatment with BPAC could reduce iron and manganese value of raw groundwater by 91.4% and 97.1%, respectively and the effect of the treatment process on the microbiological properties of groundwater sample showed decrease of total bacterial count either at 22°C or at 37°C to 85.7% and 82.4%, respectively. Also, BPAC was characterized using SEM and FTIR spectroscopy.

Keywords: Biosorption, banana peels, isothermal models, manganese.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3228

Authors: M. Tohidi, J. Yang, C. Baniotopoulos

Abstract:

Progressive collapse of buildings typically occurs  when abnormal loading conditions cause local damages, which leads  to a chain reaction of failure and ultimately catastrophic collapse. The  tie force (TF) method is one of the main design approaches for  progressive collapse. As the TF method is a simplified method, further  investigations on the reliability of the method is necessary. This study  aims to develop an improved TF method to design the cross wall  structures for progressive collapse. To this end, the pullout behavior of  strands in grout was firstly analyzed; and then, by considering the tie  force-slip relationship in the friction stage together with the catenary  action mechanism, a comprehensive analytical method was developed.  The reliability of this approach is verified by the experimental results  of concrete block pullout tests and full scale floor-to-floor joints tests  undertaken by Portland Cement Association (PCA). Discrepancies in  the tie force between the analytical results and codified specifications  have suggested the deficiency of TF method, hence an improved  model based on the analytical results has been proposed to address this  concern.

 

Keywords: Cross wall, progressive collapse, ties force method, catenary, analytical.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3663

Authors: C. Sinescu, M. Negrutiu, M. Romînu, C. Haiduc, E. Petrescu, M. Leretter, A.G. Podoleanu

Abstract:

Optical Coherence Tomography (OCT) combined with the Confocal Microscopy, as a noninvasive method, permits the determinations of materials defects in the ceramic layers depth. For this study 256 anterior and posterior metal and integral ceramic fixed partial dentures were used, made with Empress (Ivoclar), Wollceram and CAD/CAM (Wieland) technology. For each investigate area 350 slices were obtain and a 3D reconstruction was perform from each stuck. The Optical Coherent Tomography, as a noninvasive method, can be used as a control technique in integral ceramic technology, before placing those fixed partial dentures in the oral cavity. The purpose of this study is to evaluate the capability of En face Optical Coherence Tomography (OCT) combined with a fluorescent method in detection and analysis of possible material defects in metalceramic and integral ceramic fixed partial dentures. As a conclusion, it is important to have a non invasive method to investigate fixed partial prostheses before their insertion in the oral cavity in order to satisfy the high stress requirements and the esthetic function.

Keywords: Ceramic Fixed Partial Dentures, Material Defects, En face Optical Coherence Tomography, Fluorescence.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1466

Authors: Harald Rojacz, Markus Varga, Horst Winkelmann

Abstract:

Within this work High Temperature Single Impact Studies were performed to evaluate deformation mechanisms at different energy and momentum levels. To show the influence of different microstructures and hardness levels and their response to single impacts four different materials were tested at various temperatures up to 700°C. One carbide reinforced NiCrBSi based Metal Matrix Composite and three different steels were tested. The aim of this work is to determine critical energies for fracture appearance and the materials response at different energy and momenta levels. Critical impact loadings were examined at elevated temperatures to limit operating conditions in impact dominated regimes at elevated temperatures. The investigations on the mechanisms were performed using different means of microscopy at the surface and in metallographic cross sections. Results indicate temperature dependence of the occurrence of cracks in hardphase rich materials, such as Metal Matrix Composites High Speed Steels and the influence of different impact momenta at constant energies on the deformation of different steels.

Keywords: Deformation, High Temperature, Metal Matrix Composite, Single Impact Test, Steel.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1984

Authors: Fauzi Jarushi, S. AlKaabim, Paul Cosentino

Abstract:

The Standard Penetration Test (SPT) is the most common in situ test for soil investigations. On the other hand, the Cone Penetration Test (CPT) is considered one of the best investigation tools. Due to the fast and accurate results that can be obtained it complaints the SPT in many applications like field explorations, design parameters, and quality control assessments. Many soil index and engineering properties have been correlated to both of SPT and CPT. Various foundation design methods were developed based on the outcome of these tests. Therefore it is vital to correlate these tests to each other so that either one of the tests can be used in the absence of the other, especially for preliminary evaluation and design purposes. The primary purpose of this study was to investigate the relationships between the SPT and CPT for different type of sandy soils in Florida. Data for this research were collected from number of projects sponsored by the Florida Department of Transportation (FDOT), six sites served as the subject of SPT-CPT correlations. The correlations were established between the cone resistance (qc), sleeve friction (fs) and the uncorrected SPT blow counts (N) for various soils. A positive linear relationship was found between qc, fs and N for various sandy soils. In general, qc versus N showed higher correlation coefficients than fs versus N. qc/N ratios were developed for different soil types and compared to literature values, the results of this research revealed higher ratios than literature values.

Keywords: In situ tests, Correlation, SPT, CPT.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16530

Authors: Vladimir S. Timofeev

Abstract:

In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: Characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2236

Authors: M. A. Tayfun, M. A. Alkhalidi

Abstract:

The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is reexamined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: Ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2074

Authors: S. Gómez, G. Sánchez, J. Zarama, M. Castañeda Ramos, J. Escoto Alcántar, J. Torres, A. Núñez, S. Santana, F. Nájera, J. A. Lopez

Abstract:

This paper shows in detail the mathematical model of direct and inverse kinematics for a robot manipulator (welding type) with four degrees of freedom. Using the D-H parameters, screw theory, numerical, geometric and interpolation methods, the theoretical and practical values of the position of robot were determined using an optimized algorithm for inverse kinematics obtaining the values of the particular joints in order to determine the virtual paths in a relatively short time.

Keywords: Kinematics, degree of freedom, optimization, robot manipulator.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6052

Authors: Jafar Biazar, Behzad Ghanbari

Abstract:

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1568

Authors: Ou Xie, Zhenyu Zhao

Abstract:

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.

Keywords: Ill-posed problem, Unknown source, Poisson equation, Tikhonov regularization method, Discrepancy principle

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1424

Authors: Grigorios N. Beligiannis, Georgios A. Tsirogiannis, Panayotis E. Pintelas

Abstract:

In this contribution, a way to enhance the performance of the classic Genetic Algorithm is proposed. The idea of restarting a Genetic Algorithm is applied in order to obtain better knowledge of the solution space of the problem. A new operator of 'insertion' is introduced so as to exploit (utilize) the information that has already been collected before the restarting procedure. Finally, numerical experiments comparing the performance of the classic Genetic Algorithm and the Genetic Algorithm with restartings, for some well known test functions, are given.

Keywords: Genetic Algorithms, Restartings, Search space exploration, Search space exploitation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2113

Authors: Tae H. Lee, J.H. Park, S.M. Lee, H.Y. Jung

Abstract:

This paper addresses functional projective lag synchronization of Lorenz system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. For this purpose, an adaptive control law is proposed to make the states of two identical Lorenz systems asymptotically synchronize up. Based on Lyapunov stability theory, a novel criterion is given for asymptotical stability of the null solution of an error dynamics. Finally, some numerical examples are provided to show the effectiveness of our results.

Keywords: Adaptive function projective synchronization, Chaotic system, Lag synchronization, Lyapunov method

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1582

Authors: Xiaoshu Lu, Martti Viljanen

Abstract:

A new analytical model is developed which provides close-formed solutions for both transient indoor and envelope temperature changes in buildings. Time-dependent boundary temperature is presented as Fourier series which can approximate real weather conditions. The final close-formed solutions are simple, concise, and comprehensive. The model was compared with numerical results and good accuracy was obtained. The model can be used as design and control guidelines in engineering applications for analysing mechanical heat transfer properties for buildings.

Keywords: Analytical model, heat transfer, whole building.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2020

Authors: Benedek Kovacs, Janos Toth

Abstract:

Solutions are proposed for the central problem of estimating the reaction rate coefficients in homogeneous kinetics. The first is based upon the fact that the right hand side of a kinetic differential equation is linear in the rate constants, whereas the second one uses the technique of neural networks. This second one is discussed deeply and its advantages, disadvantages and conditions of applicability are analyzed in the mirror of the first one. Numerical analysis carried out on practical models using simulated data, and our programs written in Mathematica.

Keywords: Neural networks, parameter estimation, linear regression, kinetic models, reaction rate coefficients.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1965

Authors: N. Kumaresan, J. Kavikumar, M. Kumudthaa, Kuru Ratnavelu

Abstract:

In this paper, solution of fuzzy differential equation under general differentiability is obtained by genetic programming (GP). The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.

Keywords: Fuzzy differential equation, Generalized differentiability, Genetic programming and H-difference.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2218

Authors: Chai Mingming, Li Lei, Lu Xiaoxia

Abstract:

In this paper, the mechanism of stratified liquids’ mixing in a cylinder is investigated. It is focused on the effects of Rayleigh-Taylor Instability (RTI) and rotation of the cylinder on liquid interface mixing. For miscible liquids, Planar Laser Induced Fluorescence (PLIF) technique is applied to record the concentration field for one liquid. Intensity of Segregation (IOS) is used to describe the mixing status. For immiscible liquids, High Speed Camera is adopted to record the development of the interface. The experiment of RTI indicates that it plays a great role in the mixing process, and meanwhile the large-scale mixing is triggered, and subsequently the span of the stripes decreases, showing that the mesoscale mixing is coming into being. The rotation experiments show that the spin-down process has a great role in liquid mixing, during which the upper liquid falls down rapidly along the wall and crashes into the lower liquid. During this process, a lot of interface instabilities are excited. Liquids mix rapidly in the spin-down process. It can be concluded that no matter what ways have been adopted to speed up liquid mixing, the fundamental reason is the interface instabilities which increase the area of the interface between liquids and increase the relative velocity of the two liquids.

Keywords: Interface instability, liquid mixing, Rayleigh-Taylor Instability, spin-down process, spin-up process.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 904

Authors: Osama Yusuf Ababneh

Abstract:

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2936

Authors: Yan Shuang Zhang, Taehan Lee, Byung Ho Jeong

Abstract:

A DEA model can generally evaluate the performance using multiple inputs and outputs for the same period. However, it is hard to avoid the production lead time phenomenon some times, such as long-term project or marketing activity. A couple of models have been suggested to capture this time lag issue in the context of DEA. This paper develops a dual-MPO model to deal with time lag effect in evaluating efficiency. A numerical example is also given to show that the proposed model can be used to get efficiency and reference set of inefficient DMUs and to obtain projected target value of input attributes for inefficient DMUs to be efficient.

Keywords: DEA, efficiency, time lag, dual problem.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1790

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.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1529