]>
2016
16
1
129
Equitable Associate Fuzzy Graph of a Fuzzy Graph
Equitable Associate Fuzzy Graph of a Fuzzy Graph
en
en
Let \(G= (V, \sigma, \mu)\) be a fuzzy graph. Let \(H\) be the graph constructed from \(G\) as follows \(V(H) =V(G)\),
two points \(u\) and \(v\) are adjacent in \(H\) if and only if \(u\) and \(v\) are adjacent and degree fuzzy equitable in
\(G\). \(H\) is called the adjacency inherent fuzzy equitable graph of \(G\) or fuzzy equitable associate graph
of \(G\) and is denoted by \(e^{ef}(G)\). In this paper we introduced the concept of fuzzy equitable associate
graph and obtain some interesting results for this new parameter in fuzzy equitable associate graph.
1
7
M.
Rani
K. M.
Dharmalingam
Fuzzy equitable dominating set
fuzzy equitable associate graph
pre-e-fuzzy equitable graph
degree equitable fuzzy graph.
Article.1.pdf
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[1]
E. J. Cockayne, S. T. Hedetniemi, Towards a theory of domination in graphs, Networks, (1977), 247-261
##[2]
K. M. Dharmalingam, M. Rani, Equitable Domination in Fuzzy Graphs, Int. J. Pure Appl. Math., 94 (2014), 661-667
##[3]
Kuppusamy Markandan Dharmalingam, Equitable Associate Graph of a Graph, Bull. Int. Math. Virtual Inst., 2 (2012), 109-116
##[4]
J. N Mordeson, P. S Nair, Fuzzy graphs and Fuzzy Hyper graphs, Physica Verlag, Heidelberg, (1998), Second edition , (2001)
##[5]
A. Nagoor Gani, V. T. Chandra Sekaran, Domination in Fuzzy Graph, Adv. Fuzzy Sets Syst., 1 (2006), 17-26
##[6]
A. Nagoor Gani, P. Vadivel, Contribution to the theory of Domination, Independence and Irredundance in Fuzzy graph, Bull. Pure Appl. Sci. Sect. E Math. Stat., 28 (2009), 179-187
##[7]
A. Rosenfeld, Fuzzy graphs, in, L. A. Zadeh, K. S. Fu, M. Shimura (Eds), Fuzzy sets and their Applications to congnitive and Decision Processes, Academic Press, New York, (1975), 77-95
##[8]
E. Sampath Kumar, L. Puspalatha, Strong, weak domination and domination balance in a graph , Discrete Math., 161 (1996), 235-242
##[9]
A. Somasundaram, S. Somasundaram, Domination in Fuzzy Graphs-I, Elsevier Science, 19 (1998), 787-791
##[10]
V. Swaminathan, K. M. Dharmalingam, Degree Equitable Domination on Graphs, Kragujevac J. Math., 35 (2011), 191-197
##[11]
Z. Tahmasbzadehbaee, N. D. Soner, D. A. Mojdeh, Neighborhood number in Graphs, J Math. Comput. Sci., 5 (2012), 265-270
]
Coloring the Dth Power of The Cartesian Product of Two Cycles and Two Paths
Coloring the Dth Power of The Cartesian Product of Two Cycles and Two Paths
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en
The \(d^{th}\) power graph \(G^d\) is defined on the vertex set of a graph \(G\) in such a way that distinct
vertices with distance at most \(d\) in \(G\) are joined by an edge. In this paper the chromatic number of
the \(d^{th}\) power of the Cartesian product \(C_m\square C_n\) of two cycles is studied and some of the exact value
of \(\chi((C_m\square C_n)^d)\) with conditions are determined. Also the chromatic number of the \(d^{th}\) power of
grid \(P_m\square P_n\) with some conditions are determined and the exact value of \(\chi((P_m\square P_n)^d)\) for \(n = 2, 3\)
is obtained.
8
17
Elham Sharifi
Yazdi
Chromatic number
power graphs
distance \(d\) coloring
Cartesian product of cycles
Cartesian product of paths.
Article.2.pdf
[
[1]
S. H. Chiang, J. H. Jan, On L(d,1)-labeling of Cartesian product of a cycle and a path, Discrete Appl. Math., 156 (2008), 2867-2881
##[2]
Z. Dvořák, D. Král, P. Nejedlý, R. Škrekovski , Coloring squares of planar graphs with girth six, J. Combin., 29 (2008), 838-849
##[3]
R. E. Jamison, G. L. Matthews, Distance k colorings of Hamming graphs, In proceedings of the thirty seventh southeastern International Conference on combinatorics, Graph Theory and Computing, 183 (2006), 193-202
##[4]
F. Kramer, H. Kramer, A survey on the distance colouring of graphs, Discrete Math., 308 (2008), 422-426
##[5]
K. W. Lih, W. Wan, Coloring the square of an outerplanar graph, Taiwanese J. Math., 10 (2006), 1015-1023
##[6]
M. Molloy, M. R. Salavatipour, A bound on the chromatic number of the square of a planar graph, J. Combin. Theory Ser. B,, 94 (2005), 189-213
##[7]
K. Selvakumar, S. Nithya, \(d_2\)-coloring of a graph, J. Math. Comput. Sci., 3 (2011), 102-111
##[8]
E. Sopena, J. Wu, Coloring the square of the Cartesian product of two cycles, Discrete Math., 310 (2010), 2327-2333
]
Bcwsn- a Dynamic Load Balancing Algorithm for Decrease Congestion Cost in Wireless Sensor Network
Bcwsn- a Dynamic Load Balancing Algorithm for Decrease Congestion Cost in Wireless Sensor Network
en
en
Lifetime network is one of the important needs in wireless sensor networks. Case studies show that
network increased lifetime possible by spending costs. The cost of congestion is one of those cases.
The cost of back pressuring and blocking the rout with timer is obtained in the difference literature.
We will be given a dynamic balancing algorithm by BCWSN to reduce congestion. By integration
of certain parameters in this the proposed method we have achieved the objective function. To
achieve a dynamic balance in the network, with the help of this function and provides the detection
threshold and assign the proper id, we have proposed strategies to choose the receiver and sender
nodes. Finally, we could with reducing the processing time in the BCWSN proposed method increase
network lifetime as compared to the previous.
18
25
Arash
Rahbari
Arash Ghorbannia
Delavar
Wireless Sensor network
BCWSN algorithm
load balancing
congestion cost.
Article.3.pdf
[
[1]
M. I. Akbas, D. Turgut, Lightweight routing with dynamic interests in wireless sensor and actor networks, Ad Hoc Networks, 11 (2013), 2313-2328
##[2]
K. Akkaya, M. Younis, Energy and QoS aware routing for wireless sensor networks , Cluster Comput., 8 (2005), 179-188
##[3]
J. N. Al-Karaki, A. E. Kamal, Routing techniques in wireless sensor networks: a survey, IEEE Wireless Commun., 11 (2004), 6-28
##[4]
M. Amadeo, A. Molinaro, G. Ruggeri, E-CHANET: Routing,forwarding and transport in Information- Centric multihop wireless networks, Comput. Commun., 36 (2013), 792-803
##[5]
O. Banimelhem, S. Khasawneh, GMCAR: Grid-based multipath with congestion avoidance routing protocolin wireless sensor networks, Ad Hoc Networks, 10 (2012), 1346-1361
##[6]
F. Castano, A. Rossi, M. Sevaux, N. Velasco, On the use of multiple sinks to extend the lifetime in connected wireless sensor networks , Electron. Notes Discrete Math., 41 (2013), 77-84
##[7]
G. H. Ekbatanifard, R. Monsefi, M. H. Yaghmaee, S. A. Hosseini, Queen-MAC: A quorum-based energy- efficient medium access control protocol for wireless sensor networks, Comput. Networks, 56 (2012), 2221-2236
##[8]
M. Eslami, J. Vahidi, M. Askarzadeh, Designing and Implementing a Distributed Genetic Algorithm for Optimizing Work Modes in Wireless Sensor Network, J. math. comput. sci., 11 (2014), 291-299
##[9]
B. Fateh, M. Govindarasu, Energy minimization by exploiting data redundancy in real-time wireless sensor networks, Ad Hoc Networks, 11 (2013), 1715-1731
##[10]
S. Hedayati, A. Ghorbannia Delavar, The method of GBR optimization by special parameters to decrease energy consumption in WSNs , J. math. comput. sci., 8 (2014), 387-397
##[11]
W. R. Heinzelman, A. Chandrakasan, H. Balakrishnam, Energy-efficient communication protocol for wireless sensor networks, IEEE System Sci., 2 (2000), 1-10
##[12]
R. Kacimi, R. Dhaou, A. L. Beylot, Load balancing techniques for lifetime maximizing in wireless sensor networks, Ad Hoc Networks, 11-8 (2013), 2172-2186
##[13]
J. Kang, Y. Zhang, B. Nath, TARA: Topology-Aware Resource Adaptation to Alleviate Congestion in Sensor Networks, , 18 (2007), 919-931
##[14]
K. S. Lee, S. Oh, C. Kim, A dynamic ID management protocol for CSMA/IC in ad hoc networks , Ad Hoc Networks, 11 (2013), 991-1005
##[15]
C. Y. Lee, L. C. Shiu, F. T. Lin, C. S. Yang, Distributed topology control algorithm on broadcasting in wireless sensor network, J. Network Comput. Appl., 36 (2013), 1186-1195
##[16]
I. A. Modupe, O. O. Olugbara, A. Modupe, Minimizing Energy Consumption in Wireless Ad hoc Networks with Meta heuristics, Procedia Comput. Sci., 19 (2013), 106-115
##[17]
I. H. Peng, Y. W. Chen, Energy consumption bounds analysis and its applications for grid based wireless sensor networks, J. network Comput. Appl., 36 (2013), 444-451
##[18]
A. A. Rezaee, M. H. Yaghmaee, A. M. Rahmani, A. H. Mohajerzadeh, HOCA: Healthcare Aware Optimized Congestion Avoidance and control protocol for wireless sensor networks, J. Network Comput. Appl., 37 (2014), 216-228
##[19]
F. Rouhi, A. Ghorbannia Delavar, S. Hedayati, ETDWSN: A method for energy efficiency increase by combining the index parameters in wireless sensor networks, J. math. comput. sci., 11 (2014), 166-176
##[20]
C. Sergiou, V. Vassiliou, A. Paphitis, Hierarchical Tree Alternative Path (HTAP) algorithm for congestion control in wireless sensor networks, Ad Hoc Networks, 11 (2013), 257-272
##[21]
X. Wang, H. Qian, Research on all-IP communication between wireless sensor networks and IPv6 networks , Comput. Standards & Interfaces, 35 (2013), 403-414
##[22]
F. Yan, A. K. H. Yeung, G. Chen, A numerical study of energy consumption and time efficiency of sensor networks with difrerent structural topologies and routing methods , Commun. Nonlinear Science Numer. Simul., 18-9 (2013), 2515-2526
]
Fixed Points for Quasi Contraction Maps on Complete Metric Spaces
Fixed Points for Quasi Contraction Maps on Complete Metric Spaces
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en
The present paper deals with unique fixed point results for quasi contraction mappings on a
metric space satisfying some generalized inequality conditions in first section and unique common
fixed point result for asymptotically regular mappings of certain type and satisfying a generalized
contraction condition in another section. The results obtained generalize the earlier results of Fisher
(1979), Hardy and Roger (1973) and others in turn.
26
32
A.
Choudhury
T.
Som
Quasi contraction
complete metric space
asymptotically regular
generalized contraction
fixed point.
Article.4.pdf
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[1]
B. Fisher, Quasi contractions on metric spaces, Pro. Amer. Math. Soc., 75 (1979), 321-325
##[2]
K. Goebel, W. A. Kirk, T. N. Shimi, A fixed point theorem in uniformly convex spaces, Bull. Math. Ital., 7 (1973), 67-75
##[3]
D. E. Hardy, T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull., 16 (1973), 201-206
##[4]
G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly, 83 (1976), 261-263
##[5]
R. N. Mukherjee, Common fixed points of some nonlinear mappings, Ind. J. Pure appl. Math., 12 (1981), 930-933
##[6]
B. E. Rhoades, A comparison of various definitions of contractive maps, Trans. Amer. Math. Soc., 226 (1977), 257-290
]
Inflated-parameter Harris Distribution
Inflated-parameter Harris Distribution
en
en
Inflated-parameter Harris distribution is introduced and its properties are studied. A characterization
based on p.g.f is given. The maximum likelihood and moment estimators of the parameters
are found out together with their standard errors. The distribution is seen to be a good fit to a
real life situation concerning the published results of Kerala Public Service Commission.
33
49
E.
Sandhya
T. L.
Abraham
Harris distribution
generalized power series distribution
zero inflated distributions
estimation of parameters.
Article.5.pdf
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L. Minkova, A generalization of the classical distributions, Commun. Stat. Theory Methods, 31 (2002), 871-888
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E. Sandhya, S. Sherly, N. Raju, Harris family of discrete distributions, Some Innovations in Statistics, Special volume in honor of Professor T. S. K Moothathu, University of Kerala, Trivandrum , (2008), 57-72
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S. Beckett, J. Jee, T. Nebue, S. Pompilas, Q. Washington, A. Singh , N. pal, Zero- in ated Poisson (ZIP) distributions, parameters estimation appl. model data natural calamities, , (), -
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]
Jit Scheduling Problem on Flexible Flow Shop with Machine Break Down, Machine Eligibility and Setup Times
Jit Scheduling Problem on Flexible Flow Shop with Machine Break Down, Machine Eligibility and Setup Times
en
en
In this research, the problem of scheduling
flexible
flowshop system with machine breakdown,
machine eligibility, machine-dependent setup time and sequence-dependent setup time to minimizing
total weighted earliness and tardiness is studied. Firstly, the problem is formulated as a Mixed
Integer Linear Programming model. With this mathematic model, small-sized instances are solved
to optimality. The considered problem is too dificult to be optimally solved for large problem sizes,
and hence two metaheuristics algorithms namely genetic algorithm (GA) and imperialist competitive
algorithm (ICA) are proposed to afford large-sized instances. Due to the sensitivity of the proposed
algorithms to parameter's values, the taguchi method as an optimization technique to widespread
tune different parameters of applied algorithms is employed to improve solutions authenticity. These
proposed algorithms were coded and tested on randomly generated examples, then to accredit the
effectiveness of them computational results are examined in terms of relative percentage deviation.
Moreover, some sensitive analyses are executed for comparing the performance of algorithms in
various conditions. The computational evaluations expressly confirm the high performance of the
proposed genetic algorithm against imperialist competitive algorithm for related scheduling problem.
50
68
N.
Kangarloo
J.
Rezaeian
X.
Khosrawi
mixed integer linear programming
genetic algorithm
imperialist competitive algorithm
Flexible flowshop
taguchi.
Article.6.pdf
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[1]
A. Allahverdi, T. C. Ng, T. C. E. Cheng, M. Y. Kovalyov, A survey of scheduling problems with setup times or costs, European Journal of Operational Research, 187 (2008), 985-1032
##[2]
T. S. Arthanari, K. G. Ramamurthy, An extension of two machines sequencing problem, Operation search, 8 (1971), 10-22
##[3]
E. Atashpaz Gargari, C. Lucas, Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition, IEEE Congress on Evolutionary Computation, Singapore, (2007), 4661-4667
##[4]
J. Behnamian, S. M. T. Fatemi Ghomi, Hybrid flowshop scheduling with machine and resource-dependent processing times, Applied Mathematical Modeling, 35 (2011), 1107-1123
##[5]
J. Behnamian, S. M. T. Fatemi Ghomi, M. Zandieh, A multi-phase covering Pareto-optimal front method to multi-objective scheduling in a realistic hybrid flowshop using a hybrid metaheuristic, Expert Systems with Applications, 36 (2009), 11057-11069
##[6]
J. Behnamian, S. M. T. Fatemi Ghomi, M. Zandieh, Development of a hybrid metaheuristic to minimize earliness and tardiness in a hybrid flowshop with sequence-dependent setup times, International Journal of Production Research, 48 (2010), 1415-1438
##[7]
A. Bellanger, S. Hanafi, C. Wilbaut, Three-stage hybrid- flowshop model for cross-docking, Computers & Operations Research, 40 (2013), 1109-1121
##[8]
V. Botta-Genoulaz, Hybrid flowshop scheduling with precedence constraints and time lags to minimize maximum lateness, International Journal of Production Economics, 64 (2000), 101-111
##[9]
H. S. Choi, J. S. Kim, D. H. Lee, Real-time Scheduling for Reentrant Hybrid Flow Shops: a Decision Tree Based Mechanism and Its Application to a TFT-LCD Line, Expert Systems with Applications, 38 (2011), 3514-3521
##[10]
O. Engin, A. Döyen, A new approach to solve hybrid flowshop scheduling problems by artificial immune systemv, Future Generation Computer Systems, 20 (2004), 1083-1095
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E. Figielska, A genetic algorithm and a simulated annealing algorithm combined with column generation technique for solving the problem of scheduling in the hybrid flowshop with additional resources, Computers & Industrial Engineering, 56 (2009), 142-151
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E. Figielska, A heuristic for scheduling in a two-stage hybrid flowshop with renewable resources shared among the stages, European Journal of Operational Research, 236 (2014), 433-444
##[13]
M. Gholami, M. Zandieh, An immune algorithm for scheduling a hybrid flowshop with sequence- dependent setup times and machines with random breakdowns, International Journal of Production Research, 47 (2009), 6999-7027
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D. E. Goldberg , Genetic algorithms in search, optimization, and machine learning, Reading, MA: Addison-Wesley (1989)
##[15]
J. N. D. Gupta, K. Krüger, V. Lauff, F. Werner, Y. N. Sotskov, Heuristics for hybrid flow shops with controllable processing times and assignable due dates, Computers & Operations Research. , 29 (2002), 1417-1439
##[16]
M. Heydari, E. Mohammadi, A fuzzy heuristic algorithm for the flow shop scheduling problem, The Journal of Mathematics and Computer Science, 4 (2010), 349-354
##[17]
Y. Honghong, W. Zhiming, The application of Adaptive Genetic Algorithms in FMS dynamic rescheduling, International Journal of Computer Integrated Manufacturing, 16 (2003), 1-382
##[18]
A. Janiaka, E. Kozanb, M. Lichtensteina, C. Oguzc, Metaheuristic approaches to the hybrid flowshop scheduling problem with a cost-related criterion, International Journal of Production Economics, 105 (2007), 407-424
##[19]
Z. Jin, Z. Yang, T. Ito, Metaheuristic algorithms for the multistage hybrid flowshop scheduling problem, International Journal of Production Economics, 100 (2006), 322-334
##[20]
J. Jungwattanakit, M. Reodecha, M. P. Chaovalitwongse, F. Werner, A comparison of scheduling algorithms for flexible flowshop problems with unrelated parallel machines, setup times, and dual criteria, Computer & Operation Research, 36 (2009), 358-378
##[21]
S. Khalouli, F. Ghedjati, A. Hamzaoui, A meta-heuristic approach to solve a JIT scheduling problem in hybrid flow shop, Engineering Applications of Artificial Intelligence, 23 (2010), 765-771
##[22]
H. R. Kia, H. Davoudpour, M. Zandieh , Scheduling a dynamic flexible flow line with sequence-dependent setup times: a simulation analysis, International Journal of Production Research, 48 (2010), 4019-4042
##[23]
F. S. C. Lam, B. C. Lin, C. Sriskandarajah, H. Yan, Scheduling to minimize product design time using a genetic algorithm, International Journal of Production Research, 37 (1999), 1369-1386
##[24]
R. Logendran, S. Carson, E. Hanson, Group scheduling in flexible flowshops, International Journal of Production Economics, 96 (2005), 143-155
##[25]
O. Moursli, Y. Pochet, A branch-and-bound algorithm for the hybrid flowshop, International Journal of Production Economics , 64 (2000), 113-125
##[26]
A. Naderi, M. Zandieh, A. Khaleghi Ghoshe Balagh, V. Roshanaei, An improved simulated annealing for hybrid flowshops with sequence-dependent setup and transportation times to minimize total completion time and total tardiness , Expert Systems with Applications, 36 (2008), 9625-9633
##[27]
T. Nishi, Y. Hiranaka, M. Inuiguchi, Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness, Computers & Operations Research, 37 (2010), 189-198
##[28]
Q. K. Pan, L. Wang, J. Q. Li, J. H. Duan, A novel discrete artificial bee colony algorithm for the hybrid flowshop scheduling problem with makespan minimization, Omega, 45 (2014), 42-56
##[29]
C. R. Reeves, Genetic algorithms for the operations researcher, INFORMS Journal on Computing, 9 (1997), 231-250
##[30]
R. Ruiz, C. Maroto, A genetic algorithm for hybrid flowshops with sequence dependent setup times and machine eligibility, European Journal of Operational Research, 169 (2006), 781-800
##[31]
M. S. Salvador, A solution to a special case of flowshop scheduling problems, In: Elmaghraby SE, editor, Symposium of the theory of scheduling and its applications, New York: Springer, (1973), 83-91
##[32]
H. Seidgar, M. Ezzati, M. kiani, R. Tavakoli-Moghaddam, An Efficient Genetic Algorithm for Two- stage Hybrid Flow Shop Scheduling with Preemption and Sequence Dependent Setup Time, Journal of Mathematics and Computer Science, 6 (2013), 251-259
##[33]
L. Su, A hybrid two-stage flowshop with limited waiting time constraints, Computers & Industrial Engineering, 44 (2003), 409-424
##[34]
L. Tang, W. Liu, J. Liu, A neural network model and algorithm for the hybrid flowshop scheduling problem in a dynamic environment , Journal of Intelligent Manufacturing, 16 (2005), 361-370
##[35]
L. Tang, H. Xuan, J. Liu, A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time, Computers & Operations Research, 33 (2006), 3344-3359
##[36]
S. Vob, A. Witt, Hybrid flowshop scheduling as a multi-mode multi-project scheduling problem with batching requirements, International Journal of Production Economics, 105 (2007), 445-458
##[37]
X. Wang, L. Tang, A tabu search heuristic for the hybrid flowshop scheduling with finite intermediate buffers, Computers & Operations Research, 36 (2009), 907-918
##[38]
J. Xie, X. Wang, Complexity and algorithms for two-stage flexible flowshop scheduling with availability constraints, Computer and Mathematics with Application, 50 (10-12) (2005), 1629-1638
##[39]
Y. Yang, S. Kreipl, M. Pinedo, Heuristics for minimizing total weighted tardiness in flexible flowshop, Journal of Scheduling, 3 (2000), 71-88
##[40]
V. Yaurima, L. Burtseva, A. Tchernykh, Hybrid flowshop with unrelated machines, sequence-dependent setup time, availability constraints and limited buffers, Computers & Industrial Engineering, 56 (2009), 1452-1463
##[41]
M. Zandieh, S. M. T. Fatemi Ghomi, S. M. Moattar Husseini, An immune algorithm approach to hybrid flow shops scheduling with sequence-dependent setup times, Journal of Applied Mathematics and Computation, 180 (2006), 111-127
]
Completeness and Compact Generation in Partially Ordered Sets
Completeness and Compact Generation in Partially Ordered Sets
en
en
In this paper we introduce a notion of density in posets in a more general fashion. We also
introduce completeness in posets and study compact generation in posets based on such completeness
and density.
69
76
A.
Vaezi
V.
Kharat
U-density
U-complete poset
U-compactly generated poset
U-regular interval.
Article.7.pdf
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G. Birkhoff, Lattice Theory, American Mathematical Society, New York (1940)
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A. Björner, On complements in lattices of finite length, Discrete Math., 36 (1981), 325-326
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##[10]
M. Stern, Semimodular lattices: Theory and Applications, Cambridge University Press, Cambridge (1999)
]
The Heun Equation and Generalized Sl(2) Algebra
The Heun Equation and Generalized Sl(2) Algebra
en
en
In this paper, first we introduce the Heun equation. In order to solve such equation we show the
generators of generalized \(sl(2)\). Second, we arrange the Heun equation in terms of new operators
formed of generalized \(sl(2)\) generators and it's commutator relation. Here, instead of \(J^+(r), J^-(r)\) and
\(J^0\) we use the \(P^+(r), P^-(r)\) and \(P^0(r)\) as operators of generalized sl(2) algebra. This correspondence
gives us opportunity to arrange the parameters \(\alpha\) and \(\beta\) in \(P^0(r)\). Also, the commutator of such
operators leads us to have generalized \(sl(2)\) algebra. Also, we obtain the Casimir operators and
show that it corresponds to \(P^+, P^-\) and some constants. These operators lead to deform the
structure of generalized \(sl(2)\) algebra in the Heun equation. Finally, we investigate the condition for
exactly and quasi-exactly solvable system with constraint on the corresponding operators \(P^+\) and \(P^-\).
77
80
J.
Sadeghi
A.
Vaezi
F.
Larijani
Heun equation
generalized \(sl(2)\) algebra
commutative relation.
Article.8.pdf
[
[1]
A. Decarreau, M. C. Dumont-Lepage, P. Maroni, A. Robert, A. Ronveaux, Formes canoniques des equations confluentes de l'equation de Heun, Ann. Soc. Sci. Bruxelles, 92 (1978), 53-78
##[2]
A. Decarreau, P. Maroni, A. Robert, Sur les equations confluentes de l'equation de Heun, Ann. Soc. Sci. Bruxelles, 92 (1978), 151-189
##[3]
B. D. B. Figueiredo, On some solutions to generalized spheroidal wave equations and applications, J. Phys. A, 35 (2002), 2877-2906
##[4]
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Intra Regular and Interior Ideal in \(\Gamma- Ag^*\)-groupoids
Intra Regular and Interior Ideal in \(\Gamma- Ag^*\)-groupoids
en
en
Non-associative algebraic structures are of interest to consider for their remarkable properties.
In this paper, we generalize the \(AG^*\)-groupoids to \(\Gamma-AG^*\)-groupoids and study their algebraic
properties. Among other results, it is shown that every \(\Gamma-AG^*\)-groupoid is left alternative and a
\(\Gamma-AG^*\)-groupoid having a left cancellative element is a \(T^1-\Gamma-AG^*\)-groupoid, a \(a\Gamma-AG^*\)-groupoid
\(S\) is a \(\Gamma\)-intra-regular if \(S\Gamma a = S\) holds for all \(a \in S\), let \(S\) be a \(\Gamma\)-intra-regular of \(\Gamma-AG^*\)-groupoid
then B is a right \(\Gamma\)-ideal of \(S\) if \(B\Gamma S = B\), if S is a \(\Gamma\)-intra-regular of \(\Gamma-AG^*\)-groupoid then
\((S\Gamma B)\Gamma S = B\), where \(B\) is a \(\Gamma\)-interior ideal of \(S\), in an \(\Gamma\)-intra-regular of \(\Gamma-AG^*\)-groupoid \(S\) if \(A\)
is a \(\Gamma\)-interior ideal of \(S\) then \(A\) is a \(\Gamma\)-bi-ideal of \(S\), in an \(\Gamma\)-intra-regular of \(\Gamma-AG^*\)-groupoid \(S\)
if \(A\) is a \(\Gamma\)-interior ideal of \(S\) then \(A\) is a \(\Gamma(1, 2)\)-ideal of \(S\).
81
87
A. R.
Shabani
H.
Rasouli
\(\Gamma-AG\)-groupoid
\(\Gamma-AG^*\)-groupoid
\(T^1-\Gamma-AG\)-groupoid
\(\Gamma\)-left alternative
\(\Gamma\)-left cancellative
\(\Gamma\)-3-band
\(\Gamma\)-interior ideal
\(\Gamma\)-intra-regular
\(\Gamma\)-bi-ideal
\(\Gamma(1، 2)\)-ideal.
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]
The Combined Laplace-homotopy Analysis Method for Partial Differential Equations
The Combined Laplace-homotopy Analysis Method for Partial Differential Equations
en
en
In this paper, the Laplace transform homotopy analysis method (LHAM) is employed to obtain
approximate analytical solutions of the linear and nonlinear differential equations. This method
is a combined form of the Laplace transform method and the homotopy analysis method. The
proposed scheme finds the solutions without any discretization or restrictive assumptions and is free
from round-off errors and therefore, reduces the numerical computations to a great extent. Some
illustrative examples are presented and the numerical results show that the solutions of the LHAM
are in good agreement with those obtained by exact solution.
88
102
Javad
Vahidi
Homotopy analysis method
Laplace transform method
partial differential equation.
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Numerical Solutions for Linear Fractional Differential Equations of Order \(1 < \alpha< 2\) Using Finite Difference Method (ffdm)
Numerical Solutions for Linear Fractional Differential Equations of Order \(1 < \alpha< 2\) Using Finite Difference Method (ffdm)
en
en
The major goal of this paper is to find accurate solutions for linear fractional differential equations
of order \(1 < \alpha < 2\) . Hence, it is necessary to carry out this goal by preparing a new method called
Fractional Finite Difference Method (FFDM). However, this method depends on several important
topics and definitions such as Caputo's definition as a definition of fractional derivative, Finite
Difference Formulas in three types (Forward, Central and Backward) for approximating the second
and third derivatives and Composite Trapezoidal Rule for approximating the integral term in the
Caputo's definition. In this paper, the numerical solutions of linear fractional differential equations
using FFDM will be discussed and illustrated. The purposed problem is to construct a method
to find accurate approximate solutions for linear fractional differential equations. The efficiency of
FFDM will be illustrated by solving some problems of linear fractional differential equations of order
\(1 < \alpha< 2\).
103
111
Ramzi B.
Albadarneh
Iqbal M.
Batiha
Mohammad
Zurigat
Finite difference formulas
composite trapezoidal rule
numerical solutions
linear fractional differential equation.
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Constraint Fuzzy Sequential Pattern Mining with TOPSIS Method
Constraint Fuzzy Sequential Pattern Mining with TOPSIS Method
en
en
To maintain profitability, many companies consider effective customer relationship management
(CRM) to be one of the critical factors for success. The central objective of CRM is to maximize the
lifetime value of a customer to a company and find positive customers. One of the methods that help
this is sequential pattern mining. Sequential pattern mining is to discover all sub-sequences that are
frequent. The classical sequential pattern mining algorithms do not allow processing of numerical
data and require preprocessing of these data into a binary representation, which necessarily leads
to a loss of information. Fuzzy sets are used to overcome this problem. In present fuzzy sequential
pattern mining algorithms, there isn't any matter of itemset time and sequences are only found
based on sequence of happening. In this paper, a novel algorithm about fuzzy sequential pattern
mining is proposed with the time-gap constraints confine the time interval between two adjacent
elements to a reasonable period while the sliding time window constraint permits elements of a pattern to span a set of transactions within a user-specified window and a fuzzy membership function is
considered. Therefore, loss of useful sequences is prevented in the search process. The proposed algorithm searches for a goal sequence within the defined fuzzy sliding window and fuzzy gap functions.
112
130
F.
Zabihi
M. M.
Pedram
M.
Ramezan
Fuzzy sequential pattern mining
constraint
fuzzy gap.
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