2016
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SPATIOTEMPORAL DYNAMIC OF TOXIN PRODUCING PHYTOPLANKTON (TPP)ZOOPLANKTON INTERACTION
2
2
The present paper deals with a toxin producing phytoplankton (TPP)zooplankton interaction in spatial environment in thecontext of phytoplankton bloom. In the absence of diffusion the stability of the given system in terms of coexistence and hopf bifurcation has been discussed. After that TPPzooplankton interaction is considered in spatiotemporal domain by assuming self diffusion in both population. It has been obtained that in the presence of diffusion given system becomes unstable (Turing instability) under certain conditions. Moreover, by applying the normal form theory and the center manifold reduction for partial differential equations (PDEs), the explicit algorithm determining the direction ofHopf bifurcations and the stability of bifurcating periodic solutions is derived. Finally, numericalsimulations supporting the theoretical analysis are also included.
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189
197


A. K.
Sharma
Department of Mathematics, DAV College Jagraon, India
Department of Mathematics, DAV College Jagraon,
Iran


A.
Sharma
Department of Applied Sciences, DAV Institute of Engineering and Technology,
Jalandhar, India
Department of Applied Sciences, DAV Institute
Iran


K.
Agnihotri
Department of Applied Sciences, SBSSTC, Ferozpur, India.
Department of Applied Sciences, SBSSTC, Ferozpur,
Iran
Toxin producing phytoplankton
zooplankton
Hopf Bifurcation
Turing instability
Normal Form
Center manifold theorem
[E. Beltrami, T.O. Carroll, Modelling the role of viral diseases in recurrent phytoplankton blooms, J. ##Math. Biol. 32 (1994) 857863. ##J. Chattopadhyay, R.R. Sarkar, S. Mandal, Toxinproducing plankton may act as a biological control ##for planktonic bloomsfield study and mathematical modelling, J. Theor. Biol. 215 (2002) 333344. ##J. Chattopadhyay, R.R. Sarkar, A. El Abdllaoui, A delay differential equation model on harmful algal ##blooms in the presence of toxic substances, IMA J. Math. Appl. Med. Biol. 19, (2002) 137161. ##S. Roy, S. Alam, J. Chattopadhyay, Competitive effects of toxinproducing phytoplankton on overall ##plankton populations in the Bay of Bengal, Bull. Math. Biol. 68(8) 2006 23032320. ##S. Roy, S. Bhattacharya, P. Das, J. Chattopadhyay, Interaction among nontoxic phytoplankton, toxic ##phytoplankton and zooplankton inferences from field observations, J. Biol. Phys. 33(1) (2007) 117. ##D.A., Siegel, Jr.D.J. McGillicuddy, E.A. Fields, Mesoscale eddies, satellite altimetry and new produc ##tion in the Sargasso sea, J. Geophys. Res. 104, (1999) 1335913379. ##L. Matthews, J. Brindley, Patchiness in plankton populations, Dyn. Stab. Syst. 12 (1997) 3959. ##J.W. Pitchford, J. Brindley, Prey patchiness, predator survival and fish recruitment, Bull. Math. Biol. ##(2007) 527546. ##S. Roy, Spatial interaction among nontoxic phytoplankton, toxic phytoplankton, and zooplankton: ##emergence in space and time, J. Biol. Phys. 34, (2008) 459474. ##B. Mukhopadhyay, R. Bhattacharyya, Modelling phytoplankton allelopathy in a nutrientplankton ##model with spatial heterogeneity, Ecological modelling 198 (2006) 163173. ##C. Tiana, L. Zhang, Z. guilin, Pattern formation for a model of plankton allelopathy with cross ##diffusion, Journal of the Franklin Institute 348 (2011) 19471964. ##B.D. Hassard, N.D. Kazarinoff, Y.H. Wan., Theory and Applications of Hopf bifurcation, Cambridge, ##Cambridge University Press, 1981. ##S. Pal, S. Chatterjee, J. Chattopadhyay, Role of toxin and nutrient for the occurrence and termination ##of plankton bloomresults drawn from field observations and a mathematical model, J. Biosystem ##(2007) 87100. ##S. Chakarborty, S. Roy, J. Chattopadhyay, Nutrientlimiting toxin producing and the dynamics of ##two phytoplankton in culture media: A mathematical model, J. Ecological Modelling 213 (2) (2008) ##R. R. Sarkar, J. Chattopadhyay, Occurence of planktonic blooms under environmental fluctuations ##and its possible control mechanismmathematical models and experimental observations, J.Theor. ##Biol. 224 (2003) 501516. ##J. Ives, Possible mechanism underlying copepod grazing responses to levels of toxicity in red tide ##dinoflagellates, J. Exp. Mar. Biol. Ecol. 112 (1987) 131145. ##E. Buskey, C. Hyatt, Effects of Texas (USA) brown tide alga on planktonic grazers, Mar. Ecol. Prog. ##Ser. 126 (1995) 285292. ##A. Sharma, A. K. Sharma, K. Agnihotri, The dynamic of planktonnutrient interaction with discrete ##delay, Applied Mathematics and Computation, 231 (2014) 503515. ##K. Das, S. Ray, Effect of delay on nutrient cycling in phytoplanktonzooplankton interactions in ##estuarine system, Ecol. model. 215 (2008) 6976. ##N.K. Thakur, R.K. Upadhyay, S.N. Raw, Instabilities and Patterns in ZooplanktonPhytoplankton ##Dynamics: Effect of Spatial Heterogeneity, ICMMSC, 283 (2012)229236. ##]
EFFICIENCY MEASUREMENT OF NDEA WITH INTERVAL DATA
2
2
Data envelopment analysis (DEA) is a nonparametric technique for evaluation of relative efficiency of decision making units described by multiple inputs and outputs. It is based on solving linear programming problems. Since 1978 when basic DEA model was introduced many its modifications were formulated. Among them are two or multistage models with serial or parallel structure often called network DEA models that are widely discussed in professional community in the last years. The exact known inputs and outputs are required in these DEA models. However, in the real world, the concern is systems with interval (bounded) data. When we incorporate such interval data into multistage DEA models, the resulting DEA model becomes a nonlinear programming problem. In this study, we suggest an approach to measure the efficiency of series and parallel systems with interval data that preserves the linearity of DEA model. Also, the interval DEA models are proposed to measure the lower and upper bounds of the efficiency of each DMU with interval data.
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199
210


S.
Keikha Javan
Department of Mathematics, Zabol Branch, Islamic Azad University, Zabol, Iran
Department of Mathematics, Zabol Branch,
Iran


M.
RostamyMalkhalifeh
Department of Mathematics, Science and Research Branch, Islamic Azad University,
Tehran, Iran
Department of Mathematics, Science and Research
Iran
DEA
Network DEA
Interval Data
divisional efficiency
overall efficiency
[Ashrafi, A. Jaafer, A.B. (2011). Efficiency Measurement of Series and Parallel Production Systems with Interval Data By Data Envelopment Analysis, Australian Journal of Basic and Applied Sciences, 5(11): 14351443. ##Beasley, J. (1995). Determining teaching and research efficiencies. Journal of the Operational Research Society, 46, 441–452. ##Charnes, A., Cooper, W. W., & Rhodes, E. (1978) Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444. ##Cook, W. D., & Seiford, L. M. (2009).Data envelopment analysis (DEA) – Thirty years on. European Journal of Operational Research, 192, 1–17. ##Da Cruz, N. F. Carvalho, P. & Marques, R. C. (2013). Disentangling the cost efficiency of jointly provided water and wastewater services. Utilities Policy, 24, 70–77. ##Emrouznejad, A., Parker, B. R., & Tavares, G. (2008). Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA. SocioEconomic Planning Sciences, 42, 151–157. ##Fure, R., Grabowski, R., Grosskopf, S., & Kraft, S. (1997). Efficiency of a fixed but allocable input: A nonparametric approach. Economics Letters, 56, 187–193. ##Kao, C., & Lin, P. H. (2011). Qualitative factors in data envelopment analysis: A fuzzy number approach. European Journal of Operational Research, 211, 586–593. ##Kao, C., & Lin, P. H. (2012).Efficiency of parallel production systems with fuzzy data. Fuzzy Sets and Systems, 198, 83–98. ##Liu, J. S., Lu, L. Y. Y., Lu, W. M., & Lin, B. J. Y. (2013a). A survey of DEA applications. Omega, 41, 893–902. ##Liu, J. S., Lu, L. Y. Y., Lu, W. M., & Lin, B. J. Y. (2013b). Data envelopment analysis 1978–2010: A citationbased literature survey. Omega, 41, 3–15 ##Matthews, K. (2013). Risk management and managerial efficiency in Chinese banks: A network DEA framework. Omega, 41, 207–215. ##Rogge, N., & Jaeger, S. (2012).Evaluating the efficiency of municipalities in collecting and processing municipal solid waste: A shared input DEAmodel. Waste Management, 32, 1968–1978. ##Seiford, L. M. (1996). Data envelopment analysis: The evolution of the state of the art (1978–1995). Journal of Productivity Analysis, 7, 99–138. ##Tsutsui, M., & Goto, M. (2009). A multidivision efficiency evaluation of U.S. electric power companies using a weighted slacksbased measure. SocioEconomic Planning Sciences, 43, 201–208. ##Zhou, P., Ang, B. W., & Poh, K. L. (2008). A survey of data envelopment analysis in energy and environmental studies. European Journal of Operational Research, 189, 1–18. ##]
APPLICATION OF THE RANDOM MATRIX THEORY ON THE CROSSCORRELATION OF STOCK PRICES
2
2
The analysis of crosscorrelations is extensively applied for understanding of interconnections in stock markets. Variety of methods are used in order to search stock crosscorrelations including the Random Matrix Theory (RMT), the Principal Component Analysis (PCA) and the Hierachical Structures.
In this work, we analyze crosscrrelations between price fluctuations of 20 company stocks of Iran by using RMT. We find the eigenvalues and eigenvectors of the matrices of the crosscorrelations related to these stocks.
The results show some eigenvalues do not fall within the bounds of RMT eigenvalues, that indicate the correlations of stocks in usual and critical flucatutions.
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211
219


F.
Sotoude Vanoliya
Department of Statistics, University of Mazandaran, Iran
Department of Statistics, University of Mazandaran
Iran


A.
Pourdarvish Heydari
Department of Statistics, University of Mazandaran, Iran
Department of Statistics, University of Mazandaran
Iran
Random Matrix Theory
CrossCorrelation
Eigenvalue and eigenvector
NUMERICAL SOLUTION OF DELAY INTEGRAL EQUATIONS BY USING BLOCK PULSE FUNCTIONS ARISES IN BIOLOGICAL SCIENCES
2
2
This article proposes a direct method for solving three types of integral equations with time delay. By using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. Numerical examples shows that the proposed scheme have a suitable degree of accuracy.
1

221
231


M.
Nouri
Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran,
Iran
Department of Mathematics, South Tehran Branch,
Iran


K.
Maleknejad
Department of Mathematics, Iran University of Science and Technology, Narmak,
Tehran, Iran
Department of Mathematics, Iran University
Iran
Block pulse functions
Delay operational matrix.Block pulse functions
Operational matrix
Integral equations with time delay
Delay operational matrix
NUMERICAL ANALYSIS OF THE CASIMIR EFFECT DUE TO A SCALAR FIELD
2
2
In this paper, we study the Casimir effect of a scalar field with Dirichlet boundary condition in some certain topologies. By numerical analysis we show that Casimir energy is a shapedependent quantity. We also obtain the phase transition in different topologies in which the Casimir force changes from attractive to repulsive or vice versa. eararqr
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233
241


A.
Ghaffari
Department of Physics, Islamic Azad University, Central Tehran Branch, PO. Code
1416894351, Iran.
Department of Physics, Islamic Azad University,
Iran


M. R.
Tanhayi
Department of Physics, Islamic Azad University, Central Tehran Branch, PO. Code
1416894351, Iran.
Department of Physics, Islamic Azad University,
Iran
APPLICATION OF THE BELLMAN AND ZADEH'S PRINCIPLE FOR IDENTIFYING THE FUZZY DECISION IN A NETWORK WITH INTERMEDIATE STORAGE
2
2
In most of the reallife applications we deal with the problem of transporting some special fruits, as banana, which has particular production and distribution processes. In this paper we restrict our attention to formulating and solving a new bicriterion problem on a network in which in addition to minimizing the traversing costs, admissibility of the quality level of fruits is a main objective. However, the fruits are possibly stored at some intermediate node for practical purposes. We call the new model the best shipping pattern problem with intermediate storage. Here, it is assumed that both arc costs and times are crisp numbers. The main contribution of this model is an actual interpretation of the given fuzzy trapezoidal number, as the quality of delivered commodities. Since the presented problem has a fuzzy structure, the Bellman and Zadeh's maxmin criterion can be used to treat it as a crisp singleobjective problem, which is easily solvable. An illustrative example is solved, to explain the presented details.
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243
252


Mohammad
Rahimian
Department of Mathematics, Islamic Azad University, MasjedSoleiman Branch,
MasjedSoleiman, Iran
Department of Mathematics, Islamic Azad University
Iran


Esmaiel
Keshavarz
Department of Mathematics, Islamic Azad University, Sirjan Branch, Sirjan, Iran;
Department of Mathematics, Islamic Azad University
Iran


Hamid
Hassasi
Faculty of Management Sciences, Islamic Azad University, Central Tehran Branch,
Tehran, Iran
Faculty of Management Sciences, Islamic Azad
Iran
multiple criterion optimization
best shipping pattern
Fuzzy number
BellmanZadeh's principle
GENERALIZATION OF TITCHMARSH'S THEOREM FOR THE GENERALIZED FOURIERBESSEL TRANSFORM
2
2
In this paper, using a generalized translation operator, we prove theestimates for the generalized FourierBessel transform in the space L2 on certainclasses of functions.
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253
260


S.
El ouadih
Department of Mathematics, Faculty of Sciences A¨ın Chock,University Hassan II,
Casablanca, Morocco;
Department of Mathematics, Faculty of Sciences
Iran


R.
Daher
Department of Mathematics, Faculty of Sciences A¨ın Chock,University Hassan II,
Casablanca, Morocco
Department of Mathematics, Faculty of Sciences
Iran


M.
El hamma
Department of Mathematics, Faculty of Sciences A¨ın Chock,University Hassan II,
Casablanca, Morocco.
Department of Mathematics, Faculty of Sciences
Iran
singular dierential operator
generalized translation operatorsingular dierential operator
generalized FourierBessel transform
generalized translation operator
[R. F. Al Subaie and M. A. Mourou, The continuous wavelet transform for a Bessel type ##operator on the half line, Mathematics and Statistics 1(4): 196203, 2013. ##V. A. Abilov and F. V. Abilova, Approximation of functions by FourierBessel sums, Izv. ##Vyssh. Uchebn. Zaved., Mat., No. 8, 39 (2001). ##V.S.Vladimirov, Equations of mathematical physics, Marcel Dekker, New York,1971,Nauka, ##Moscow,1976. ##B.M.Levitan, Expansion in Fourier series and integrals over Bessel functions, Uspekhi ##Math.Nauk, 6,No.2,102143,1951. ##Titchmarsh.EC , Introduction to the theory of Fourier integrals . Claredon , oxford, 1948, ##Komkniga.Moxow.2005. ##R. F. Al Subaie and M. A. Mourou, Transmutation operators associated with a Bessel type ##operator on the half line and certain of their applications, Tamsii. oxf. J. Inf. Math. Scien 29 ##(3) (2013), pp. 329349. ##A.G.Sveshnikov,A.N.Bogolyubov and V.V.Kratsov, Lectures on mathematical physics, ##Nauka, Moscow,2004)[in Russian]. ##Platonov.SS, The Fourier transform of function satisfying the Lipshitz condition on rank 1 ##symetric spaces , Siberian Math.J.46(2) (2005), 11081118.##]