]>
2014
12
4
83
New Implementation of Reproducing Kernel Hilbert Space Method for Solving a Class of Third-order Differential Equations
New Implementation of Reproducing Kernel Hilbert Space Method for Solving a Class of Third-order Differential Equations
en
en
In this paper, we apply the new implementation of reproducing kernel Hilbert space method to give the
approximate solution to some third-order boundaryvalue problems with variable coefficients. In this
method, the analytical solution is expressed in the form of a series. At the end, two examples are given to
illustrate implementation, accuracy and effectiveness of the method.
253
262
Eslam
Moradi
Aasadolla
Yusefi
Abolfazl
Abdollahzadeh
Elham
Tila
Reproducing kernel Hilbert space method
Boundary value problems
Third-order differential equations
Approximatesolution.
Article.1.pdf
[
[1]
F. Geng, M. Cui, A reproducing kernel method for solving nonlocal fractional boundary value problems, Appl. Math. Letters , 25 (2012), 818-823
##[2]
F. Geng, S. Qian, Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers, Appl. Math. Letters , 26 (2013), 998-1004
##[3]
H. Du, M. Cui, Approximate solution of the Fredholm integral equation of the first kind in a reproducing kernel space, Appl. Math. Letters , 21 (2008), 617-623
##[4]
H. Du, M. Cui , Representation of the exact solution and stability analysis on the Fredholm integral equation of the first kind in a reproducing kernel space, Appl. Math. Comp. , 182 (2006), 1608-1614
##[5]
L. Yang, J. Shen, Y. Wang , The reproducing kernel method for solving the system of linear Volterra integral equations with variable coefficients, J. Comp. Appl. Math , 236 (2012), 2398-2405
##[6]
Z. Chen, W. Jiang , The exact solution of a class of Volterra integral equation with weakly singular kernel, Appl. Math. Comp. , 217 (2011), 7515-7519
##[7]
Z. Chen, Y. Lin , The exact solution of a class of linear integral equation with weakly singular kernel, J. Math. Anal. Appl., 344 (2008), 726-736
##[8]
W. Jiang, M. Cui , The exact solution and stability analysis for integral equation of third or frist kind with singular kernel, Appl. Math. Comp. , 202 (2008), 666-674
##[9]
F. Geng, Solving integral equation of the third kind in the reproducing kernel space, Bulltein Iranian Math. Society , 38 (2011), 543-551
##[10]
M. Cui, Z. Deng , On the best operator of interpolation, J. Math. Numerica.Sinica. , 8(2) (1986), 209-216
##[11]
M. Cui, F. Geng, Solving singular two-point boundary value problem in reproducing kernel space, J. Comp. Appl. Math., 205 (2007), 6-15
##[12]
W. Wang, M. Cui, Bo Han, A new method for solving a class of singular two-point boundary value problems , Appl. Math. Comp. , 206 (2008), 721-727
##[13]
F. Geng, M. Cui , Solving singular nonlinear two-point boundary value problems in the reproducing kernel space, J. of the Korean Math. Society, 45 (3) (2008), 631-644
##[14]
F. Geng, M. Cui , Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space, Appl. Math. Comp., 192 (2007), 389-398
##[15]
W. Jiang, M. Cui, Y. Lin, Anti-periodic solutions for Rayleigh-type equations via the reproducing kernel Hilbert space method, Commun Nonlinear SciNumerSimulat , 15 (2010), 1754-1758
##[16]
E. Babolian, Sh. Javadi, E. Moradi, RKM for the Numerical Solution of Bratu’s Initial Value Problem , submitted on December 27, (2013)
##[17]
F. Geng, Iterative reproducing kernel method for a beam equation with third-order nonlinear boundary conditions, Mathematical Sciences , (2012)
##[18]
B. Wu, X. Li, Application of reproducing kernel method to third order three-point boundary value problems, Appl. Math. Comp., 217 (2010), 3425-3428
##[19]
F. Geng, M. Cui, Solving a nonlinear system of second order boundary value problems, J. Math. Anal. Appl. , 327 (2007), 1167-1181
##[20]
Gh. Akram, H. Rehman, Solution of fifth order boundary value problems in reproducing kernel space, Middle-East Journal of Scientific Research , 10(2) (2011), 191-195
##[21]
M. Mohammadi, R. Mokhtari, Solving the generalized regularized long wave equation on the basis of a reproducing kernel space , J. Comp. Appl. Math. , 235 (2011), 4003-4014
##[22]
M. Cui, Y. Lin, Nonlinear numerical analysis in reproducing kernel Hilbert space, Nova Science Publisher, New York (2009)
##[23]
M. Rabbani, New Homotopy Perturbation Method to Solve Non-Linear Problems , Journal of mathematics and computer Science , 7 (2013), 272-275
##[24]
M. Saravi, A. Nikkar, M. Hermann, J. Vahidi, R. Ahari, A New Modified Approach for solving seven-order Sawada-Kotara equations, Journal of mathematics and computer Science , 6 (2013), 230-237
##[25]
S. Gh. Hosseini, S. M. Hosseini, M. Heydari, M. Amini, The analytical solution of singularly perturbed boundary value problems, Journal of mathematics and computer science , 10 (2014), 7-22
]
Forecasting Number of Students Applicant for Courses by Artificial Neural Networks
Forecasting Number of Students Applicant for Courses by Artificial Neural Networks
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en
Forecasting the number of students who are going to take a special course in next semester in Computer Engineering field at Payam Noor University is the subject. To do this, many neural network structures have been tested with MATLAB software by existing data and were compared to real data, networks like feedforward backpropagation 3 and 4-layared, RBF network, etc. To achieve a network with optimum structure, various parameters and criteria like MAE, MSE and MSEREG, have been examined. At last, a 3-layered feedback neural network in the form of 20-n-1 was chosen for this problem. Comparing experiential results with real data, it is shown that the obtained model can effectively forecast enrolments of students. So it can be used for forecasting tasks especially when a forecast with high accuracy is needed.
263
270
Jafar
Pouramini
Artificial Neural Network
RBF network
Elman network
Hopfield network
Forecasting
Article.2.pdf
[
[1]
Saeed Ayat, Zabihollah Ahmad Pour, Comparison between artificial neural network learning algorithms for prediction of student average considering effective factors in Learning and educational progress, Journal of mathematics and computer science , 8 (2014), 215-225
##[2]
Ali Ghezelbash, Predicting changes in stock index and gold prices to neural network approach, The Journal of mathematics and computer science , 4(2) (2012), 227-236
##[3]
Mahnaz Bagheri , The bankruptcy prediction in Tehran share holding using neural and it’s comparision with logistic regression, The Journal of mathematics and computer science , 5(3) (2012), 219-228
##[4]
Mehdi Sotoudeh, Elahe Farshad, Application of neural network for forecasting gas price in America, The Journal of mathematics and computer science , 4(2) (2012), 216-226
##[5]
Mehdi Sotoudeh, Elahe Farshad , Application of neural network for forecasting gas price in America, Journal of mathematics and computer science , 4(2) (2012), 216-226
##[6]
k. Abhishek, M. P. Singh, S. Ghosh, A. Anand, Weather forecasting model using artificial neural network, procedia technology, 4 (2012), 311-318
##[7]
M. Qi, G. P. Zhang, An Investigation of model selection criteria for neural network time series forecasting, european journal of operational research, 132 (2001), 666-680
##[8]
Ufuk Yolcu, Erol Egrioglu, Cagdas H. Aladag , A new linear & nonlinear artificial neural network model for time series forecasting, Decision Support Systems, 54 (2013), 1340-1347
##[9]
Juan Peralta Donate, Paulo Cortez, Germán Gutiérrez Sánchez, Araceli Sanchis de Miguel, Time series forecasting using a weighted cross-validation evolutionary artificial neural network ensemble, Neurocomputing, 109 (2013), 27-32
##[10]
I. Kaastra, M. Boyd, Designing a neural network for forecasting financial and economic time series, neurocomputing, 10 (1996), 215-236
##[11]
E. Azoff, Neural network time series forecasting of financial markets, John Wiley & Sons, (1994)
]
Error Detection Mechanism Based on Bch Decoder and Root Finding of Polynomial Over Finite Fields
Error Detection Mechanism Based on Bch Decoder and Root Finding of Polynomial Over Finite Fields
en
en
Error Correction Code is very important in modern communication systems. BCH (Bose, Chaudhuri, and Hocqunghem) codes are being widely used in variety communication and storage systems. In this paper the construction and decoding BCH codes which are based on finite field arithmetic is introduced and also an improved algorithm for finding roots of polynomials over finite fields is proposed. This makes possible significant speed up of the decoding process of BCH codes.
271
281
Saeideh
Nabipour
Javad
Javidan
Gholamreza Zare
Fatin
Error Correction Code
BCH code
root-finding polynomial
Chien Search
BRS algorithm.
Article.3.pdf
[
[1]
S. Lin, D. J. Costello, Error control coding: fundamentals and applications, Prentice-Hall Inc., (2004)
##[2]
R. T. Chien, B. D. Cunningham, I. B. Oldham, Hybrid methods for finding roots of a polynomial with application to BCH decoding, IEEE Transactions on Information Theory, 15(2) (1969. ), 329-335
##[3]
T.-K. Truong, J.-H. Jeng, I. S. Reed, Fast algorithm for computing the roots of error locator polynomials up to degree 11 in Reed-Solomon decoders, IEEE Transactions on Communications, 49(5) (2001), 779-783
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C. Paar, Optimized arithmetic for Reed–Solomon encoders, in Proc. IEEE Int. Symp. Inf. Theory, Ulm, Germany, Jun.–Jul., (1997), 250-250
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O. Ore, On a special class of polynomials, Trans. Am. Math. Soc., 35 (1933), 559-584
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S. Lin, D. J. Constello, Error Control coding, Englewood Cliffs, NJ:Prentice-Hall (1983)
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A. Hocquenghem, Codes correcteurs d’erreurs, Chiffres, 2 (1959), 147-56
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R. E. Blahut, Algebraic Codes for Data Transmission, U.K.: Cambridge Univ. Press, Cambridge (2003)
##[9]
Y.-M. Lin et al., A 26.9K 314.5 Mb/s Soft (32400, 32208) BCH Decoder Chip for DVB-S2 System, IEEE J. Solid- State Circuits, 45(11) (2010), 2330-2340
##[10]
C.-C. Chu, Y.-M. Lin, C.-H. Yang, H.-C. Chang, A fully parallel BCH codec with double error correcting capability for NOR flash applications, in Proc. IEEE Int. Conf. Acoust. Speech, Signal Process, (2012), 1605-1608
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Dr. M. H. L. Chen, D. Fredmon, R. W. Donaldson, Performance enhancment using Forward error correction on Power line Communication channels , m IEEE Trans. on Power Del. , vol 9. no. 2 (1994)
##[12]
L. Biard, D. Noguet , Reed Solomon Codes for Low Power Communication, Journal of Communications, 3(2) (2008), 13-21
]
Some New Mutation Operators for Genetic Data Clustering
Some New Mutation Operators for Genetic Data Clustering
en
en
Genetic algorithm is one of evolutionary algorithms which have been used widely to solve many problems such as data clustering. There are lots of genetic data clustering algorithms which have worked on fitness function to improve the accuracy of algorithm in evaluation of generated chromosomes and have used simple and all purpose crossover and mutation operators such as one point crossover and random change mutation. Mutation process randomly modifies the gene values at selected locations to increase genetic diversity, by forcing the algorithm to search areas other than the current area. Simple non heuristic mutations such as random change mutation increase genetic diversity but they also increase execution time and decrease fitness of population. In this paper we introduce some new heuristic mutation operators for genetic data clustering. Experimental results show that all of proposed mutation operators creates better offspring than random change mutation and increases the fitness of population.
282
294
Gholam Hasan
Mohebpour
Arash Ghorbannia
Delavar
Data mining
data clustering
genetic algorithm
mutation operator
partitioning
Article.4.pdf
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[1]
John H. Holland, Adaptation in Natural and Artificial Systems, the University of Michigan Press, (1975)
##[2]
Jong De, A. Kenneth , An Analysis of the Behavior of a Class of Genetic Adaptive Systems, Doctoral thesis, Dept. Computer and Communication Sciences, University of Michigan, Ann Arbor (1975)
##[3]
D. E. Goldberg, Genetic Algorithm in Search, Optimization and Machine Learning, Addison –Wesley, New York (1989)
##[4]
Yongguo Liu, Xindong Wu, Yidong Shen , Automatic clustering using genetic algorithms, Applied Mathematics and Computation , 218 (2011), 1267-1279
##[5]
Hong He, YonghongTan, A two-stage genetic algorithm for automatic clustering, Neurocomputing, 81 (2012), 49-59
##[6]
L. E. Agustin-Blas, S. Salcedo-Sanz, S. Jimenez-Fernandez , L. Carro-Calvo, J. Del Ser, J. A. Portilla-Figueras, A new grouping genetic algorithm for clustering problems, Expert Systems with Applications, 39 (2012), 9695-9703
##[7]
Dongxia Chang, Yao Zhao, Changwen Zheng, Xianda Zhang , A genetic clustering algorithm using a message-based similarity measure, Expert Systems with Applications , 39 (2012), 2194-2202
##[8]
Amin Aalaei, Hamed Fazlollahtabar, Iraj Mahdavi, Nezam Mahdavi-Amiri, Mohammad Hassan Yahyanejad, A genetic algorithm for a creativity matrix cubic space clustering, A case study in Mazandaran Gas Company, Applied Soft Computing , 13 (2013), 1661-1673
##[9]
Jose A. Castellanos-Garzon, Fernando Diaz, An evolutionary computational model applied to cluster analysis of DNA microarray data, Expert Systems with Applications , 40 (2013), 2575-2591
##[10]
Riccardo Poli, W. B. Langdon, Genetic programming with one-point crossover, In P. K. Chawdhry, R. Roy, and R. K. Pant, editors, Second On-line World Conference on Soft Computing in Engineering Design and Manufacturing, Springer-Verlag London, (1997), 23-27
##[11]
, http://repository.seasr.org/Datasets/UCI/arff/ , , ()
##[12]
R. Maghsoudi , A. Ghorbannia Delavar, S. Hoseyny, R. Asgari, Y. Heidari, Representing the New Model for Improving K-Means Clustering Algorithm based on Genetic Algorithm , The Journal of Mathematics and Computer Science , 2(2) (2011), 329-336
]
Fixed Points of Nonexpansive Mappings in Banach Spaces
Fixed Points of Nonexpansive Mappings in Banach Spaces
en
en
In this paper we study the approximation of common fixed points of a finite family of nonexpansive
mappings in uniformly smooth Banach spaces. Also we show that the convergence of the proposed
algorithm can be proved under some types of control conditions.
295
303
F.
Golkar
A.
Dianatifar
A. M.
Aminpour
M.
Sadeghi
Nonexpansive mapping
Strong convergence
Common fixed point
Uniformly smooth Banach space.
Article.5.pdf
[
[1]
H. K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl., 659–678 (2000)
##[2]
H. K. Xu , Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. , 298 (2004), 279-291
##[3]
K. Goebel, S. Reich, Uniform Convexity, Nonexpansive mappings and Hyperbolic Geometry, Dekker (1984)
##[4]
S. Atsushiba, W. Takahashi , Strong convergence theorems for a finite family of nonexpansive mappings and applications, Indian J. Math. , 41 (1999), 435-453
##[5]
Sh. Banerjee, B. S. Choudhury, Weak and strong convergence theorems of a new iterative process with errors for common fixed points of a finite families of asymptotically nonexpansive mappings in the intermediate sense in Banach spaces, TJMCS, 11 (2014), 79-85
##[6]
S. S. Chang, Some problems and results in the study of nonlinear analysis, Nonlinear Anal. , 33 (1997), 4197-4208
##[7]
T. Suzuki, Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals , J. Math. Anal. Appl., 305 (2005), 227-239
##[8]
Y. Yao, A general iterative method for a finite family of nonexpansive mappings , Nonlinear Anal., 66 (2007), 2676-2687
]
Experimental Estimation of Number of Clusters Based on Cluster Quality
Experimental Estimation of Number of Clusters Based on Cluster Quality
en
en
Text Clustering is a text mining technique which divides the given set of text documents into significant clusters. It is used for organizing a huge number of text documents into a well-organized form. In the majority of the clustering algorithms, the number of clusters must be specified apriori, which is a drawback of these algorithms. The aim of this paper is to show experimentally how to determine the number of clusters based on cluster quality. Since partitional clustering algorithms are well-suited for clustering large document datasets, we have confined our analysis to a partitional clustering algorithm.
304
315
G. Hannah
Grace
Kalyani
Desikan
clusters
cluster quality
CLUTO
entropy
purity.
Article.6.pdf
[
[1]
Jiawei Han, Micheline Kamber, Jian Pei , Data Mining Concepts and Techniques, second edition Morgan Kaufmann Publishers, ISBN 13: 978-1-55860-901-3. ()
##[2]
Pankaj Jajoo , Document clustering, IIT Kharagpur, Thesis (2008)
##[3]
A. K. Jain, M. N. Murty, P. J. Flynn, Data Clustering: A Review, ACM Computing Surveys, Vol.31, No.3, September (1999)
##[4]
Ying Zhao, George Karypis, Empirical and Theoretical Comparisons of Selected Criterion Functions for Document Clustering, supported by NSF ACI-0133464, CCR-9972519, EIA-9986042, ACI-9982274, and by Army HPC Research Center. (2004)
##[5]
K. P. Soman, Shyam Diwakar, V. Ajay, Insight Into Data Mining: Theory and Practice, by Prentice Hall of India Private Limited , ISBN-81-203-2897-3. ( 2006 )
##[6]
Satya Chaitanya Sripada, Dr. M. Sreenivasa Rao, Comparison of purity and entropy of k-means clustering and fuzzy c means clustering, Indian journal of computer science and engineering; Vol 2 no.3 June , ISSN:0976-5166. (2011)
##[7]
Tim Van de Cruys, Mining for meaning: the extraction of lexico-semantic knowledge from text, Dissertation, Evaluation of cluster quality, chapter 6 , University of Groningen (2010)
##[8]
Anna Huang, Similarity measures for Text Document Clustering, University of Waikato, Hamilton, New Zealand, NZCSRSC 2008, Christ Church, New Zealand (2008)
##[9]
CLUTO-A Clustering Toolkit, , http://glaros.dtc.umn.edu/gkhome/views/cluto, ()
]
Improving the Key Agreement Protocol Security Based on Hadamard Matrices
Improving the Key Agreement Protocol Security Based on Hadamard Matrices
en
en
In this paper, the security of key agreement protocol based on Sylvester Hadamard matrices proposed by Chang-hui Choe and Moon Ho Lee has been improved. Applying new changes, the weakness of their protocol was introduced and its security was increased. In short, new symmetric key agreement protocol will be suitable for insecure communication when two users want to share a common secret key with the low computing power.
316
319
Ali
Zaghian
Mohammad Jafar
Hashemi
Ahmad
Majlesi
Encryption
Security
Sylvester Hadamard Matrices
Key agreement.
Article.7.pdf
[
[1]
W. Stallings, Cryptography and Network Security principels and practice, 5th ed., (2011)
##[2]
W. Diffie, M. Hellman, New directions in cryptography, IEEE Trans.Inf. Theory, 22 (1976), 644-654
##[3]
Behrouz A. Forouzan, Cryptography and Network Security, 2nd Edition, McGraw-Hill Education Pvt. Ltd. (2010)
##[4]
C.-h. Choe, M. H. Lee, Key agreement protocol using Sylvester Hadamard matrices, Journal of Communication and networks, 13 (2011), 1435-1443
##[5]
K. J. Horadam, Hadamard Matrices, Princeton university Press , (2007)
##[6]
K. J. Horadam, P. Udaya, Cocyclic Hadamard codes, IEEE Trans.Inf. Theory, 46 (2000), 1545-1550
]
Mathematical Analysis of Soil-structure Interaction Including Kinematic and Inertial Interaction Effects
Mathematical Analysis of Soil-structure Interaction Including Kinematic and Inertial Interaction Effects
en
en
In this research, both kinematic interaction (KI) and inertial interaction (II) effects of soil-structure
interaction (SSI) on inelastic seismic demands of structures are investigated. Site effect is also considered
only by applying ground motions recorded at site classes D and E (as defined in NEHRP[1] and
FEMA-440 [2]) that on them SSI effect is considerable. Carrying out a parametric study, the structure and
underlying soil are modeled as a Single Degree Of Freedom (SDOF) structure with elasto-plastic behavior
and a mathematical simplified 3DOF system, based on the concept of Cone Models, respectively. Also
the foundation is considered as a rigid cylinder embedded in the soil with different embedment ratios.
Then the whole soil-structure systems are analyzed under 30 ground motion recorded at site classes D and
E and a comprehensive parametric study is performed for a wide range of non-dimensional parameters
defining SSI problem. Results indicated that ignoring SSI causes considerable and in some cases un-conservative
differences in seismic demands of structures. In the case of embedded foundation, it is observed
that rocking input motion due to KI plays the main role and increase the structural demands especially in
deep foundation embedment and slender buildings located on soft soils.
Consequently, comparing the results with and without inclusion of SSI effects reveals that both II and
KI effects of SSI play an important role in analyses or design procedures and ignoring them may cause
un-conservative results in cases of deep embedded foundation and slender structures.
320
336
Leila
Khanmohammadi
Javad Vaseghi
Amiri
Mohammad Reza
Davoodi
Mohammad Ali
Ghannad
soil-structure interaction
cone model
foundation embedment
kinematic interaction (KI)
Inertial interaction (II)
Strength reduction factor
ductility demand
Elastic and inelastic seismic demands
Article.8.pdf
[
[1]
BSSC, NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, FEMA-450, Washington (2003)
##[2]
FEMA-440, Improvement of nonlinear static seismic procedures, ATC-55 Draft, Washington (2005)
##[3]
A. S. Veletsos, J. W. Meek, Dynamic Behavior Building-Foundation Systems, Earthquake Engineering and Structural Dynamic, 34 (1974), 121-138
##[4]
A. S. Veletsos, V. V. D Nair, Seismic Interaction of Soil on Hysteretic foundation, Journal of Structural Division (ASCE), 101 (1975), 109-129
##[5]
J. P. Wolf , Dynamic Soil-structure Interaction, Prentice Hall , New Jersey (1985)
##[6]
J. Aviles, L. E. Perez-Rocha, Diagrams of Effective Periods and Damping of Soil-structure Systems, Journal of Geotechnical and Geo-environmental Engineering, 125 (1999), 711-715
##[7]
J. Bielak, Dynamic Response of Non-linear Building-foundation Systems, Earthquake Engineering and Structural Dynamic, 6 (1978), 17-30
##[8]
J. Aviles, L. E. Perez-Rocha, Soil-structure Interaction in Yielding Systems, Earthquake Engineering and Structural Dynamic, 32 (2003), 1749-1771
##[9]
J. Aviles, L. E. Perez-Rocha, Design Concepts for Yielding Structures on Flexible Foundation, Engineering Structure, 27 (2005), 443-454
##[10]
Y. O. Beredugo, M. Novak, Coupled horizontal and rocking vibration of embedded footings, Canadian Geotechnical Journal, 9(4) (1972), 477-497
##[11]
F. Elsabee, E. Kausel, J. M. Roesset, Dynamic stiffness of embedded foundations, Proceedings of the ASCE Second Annual Engineering Mechanics Division Specialty Conference, North Carolina, (1977), 40-43
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J. P. Morray, Kinematic interaction problem of embedded circular foundations, M.Sc. Thesis, Department of Civil Engineering, Massachusetts Institute of Technology (1975)
##[13]
J. E. Luco, H. L. Wong, M. D. Trifunac, A note on the dynamic response of rigid embedded foundations, Earthquake Engineering and Structural Dynamics, 4(2) (1975), 119-127
##[14]
J. Bielak, Dynamic behavior of structures with embedded foundations, Earthquake Engineering and Structural Dynamics, 3(3) (1975), 259-274
##[15]
E. Kausel, R. V. Whitman, J. P. Morray, F. Elsabee, The spring method for embedded foundations, Nuclear Engineering and Design, 48 (1978), 377-392
##[16]
J. Aviles, L. Perez-Rocha, Effects of foundation embedment during building–soil interaction, Earthquake Engineering and Structural Dynamics, 27(12) (1998), 1523-1540
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I. Takewaki, N. Takeda, K. Uetani , Fast practical evaluation of soil–structure interaction of embedded structures, Soil Dynamics and Earthquake Engineering, 23(3) (2003), 13-20
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A. S. Veletsos, B. Verbic, Dynamics of elastic and yielding structure–foundation systems, Proceedings of Fifth World Conference on Earthquake Engineering, Rome, Italy, (1973), 2610-2613
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J. Bielak, Dynamic response of non-linear building–foundation systems, Earthquake Engineering and Structural Dynamics , 6(1) (1978), 17-30
##[20]
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J. P. Wolf, Foundation Vibration Analysis using Simple Physical Models, Prentice-Hall: Englewood Cliffs, NJ (1994)
##[23]
S. L. Kramer, Geotechnical Earthquake Engineering, Prentice-Hall: Englewood Cliffs, NJ (1996)
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A. S. Veletsos, Dynamic of structure-foundation systems, In: Hal WJ, editor, Structural and Geotechnical Mechanics, Prentice- Hall: Englewood Cliffs, NJ. A Volume Honoring N.M. Newmark, (1977), 333-361
##[25]
M. A. Ghannad, A study on the effect of soil-structure interaction on the dynamic properties of structures using simplified methods, Ph.D. thesis. Japan, Nagoya University (1998)
##[26]
J. W. Meek, J. P. Wolf, Cone models for embedded foundation, Journal of Geotechnical Engineering Division (ASCE), 120(1) (1994), 60-80
##[27]
ATC-3-06, Applied Technology Council , Tentative provisions for the development of seismic regulations for buildings, California (1978)
]