ORIGINAL_ARTICLE
Maps preserving triple product on rings
Let R and R0 be two unital rings such that R contains a non-trivial idempotent P1. If R is a prime ring, we characterize the form of bijectivemap ' : R ! R0 which satises '(ABP) = '(A)'(B)'(P), for every A;B 2 Rand P 2 fP1; P2g, where P2 := I P1 and I is the unit member of R. It isshown that ' is an isomorphism multiplied by a central element. Finally, wecharacterize the form of ' : R ! R which satises '(P)'(A)'(P) = PAP,for every A 2 R and P 2 fP1; P2g.
https://jmmrc.uk.ac.ir/article_2901_73e9a4973b6ec51a9a39abe5ed111e5c.pdf
2021-10-01
1
8
10.22103/jmmrc.2021.16645.1124
Preserver problem
Ring
Triple product
Non-trivial idempotent
Ali
Taghavi
taghavi@umz.ac.ir
1
Department of Mathematics, Faculty of Mathematical Sciences, University
of Mazandaran, P.O.Box 47416-1468, Babolsar, Iran.
LEAD_AUTHOR
Roja
Hosseinzadeh
ro.hosseinzadeh@umz.ac.ir
2
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O.Box 47416-1468, Babolsar, Iran.
AUTHOR
V. Darvish, N.M. Nazari, H. Rohi, A. Taghavi, Maps preserving $ eta-$product $ AP+eta PA^* $ on $C^*-$algebras, J. Korean Math. Soc. 54 (3), 867-876 (2017).
1
H. Gao, $*-$Jordan-triple multiplicative surjective maps on $B(H)$, J. Math. Anal. Appl. 401, 397-403 (2013).
2
L. Gonga, X. Qi, J. Shao, F. Zhang, Strong (skew) $ xi- $Lie commutativity preserving maps on algebras, Cogent Math. 2(1), 1003175 (2015).
3
C. Jianlian, C. Park, Maps preserving strong skew lie product on factor von Neumann algebras, Acta Math. Scientia. 32(2), 531-538 (2012).
4
P. Li, F. Lu, Nonlinear maps preserving the Jordan triple 1-$*$-product on von Neumann algebras, Complex Anal. Oper. Theory. 11, 109–117 (2017).
5
L. Liu, LG.X. Ji, Maps preserving Product $X^*Y+ YX^*$ on factor von Neumann algebras, Linear Multilinear Algebra. 59(9), 951-955 (2011).
6
W.S. Martindale III, When are multiplicative mappings additive?, Proc. Amer. Math. Soc. 21, 695-698 (1969).
7
L. Moln'{a}r, On isomorphisms of standard operator algebras, Studia Math. 142(3), 295-302 (2000).
8
L. Moln'{a}r, Multiplicative Jordan triple isomorphisms on the self-adjoint elements of von Neumann algebras, Linear Algebra Appl. 419, 586-600 (2006).
9
L. Moln'{a}r, P. '{S}emrl, P., Transformations of the unitary group on a Hilbert space, J. Math. Anal. Appl. 388, 1205-1217 (2012).
10
A. Taghavi, Maps preserving Jordan triple product on the self-adjoint elements of $C^*-$algebras, Asian-European J. Math. 10, No. 2, 1750022(7 pages) (2017). 11, 391-405 (2020).
11
A. Taghavi, M. Razeghi, M. Nouri, V. Darvish, Maps preserving triple product $A^*B + BA^*$ on $*-$algebras, Asian-European J. Math. 12, No. 3, 1950038(13 pages) (2019).
12
A. Taghavi, S. Salehi, Continuous maps preserving Jordan triple products from $mathbb{GL}_1$ to $mathbb{GL}_2$ and $mathbb{GL}_3$, Linear Multilinear Algebra. Published online: 20 Mar (2019).
13
A. Taghavi, S. Salehi, Continuous maps preserving Jordan triple products from $mathbb{GL}_n(mathbb{C})$into $mathbb{C}^*$, Indagationes Mathematicae. 28, 1233-1239 (2017).
14
A. Taghavi, S. Salehi, Continuous maps preserving Jordan triple products from $mathbb{U}_n$ into $mathbb{D}_m$, Indagationes Mathematicae. 30, 157–164 (2019).
15
A. Taghavi, E. Tavakoli, Additivity of maps preserving Jordan triple products on prime $C^*-$algebras, Annals of Functional Analysis. 11, 391-405 (2020).
16
J.H. Zhang, F.J. Zhang, Nonlinear maps preserving Lie products on factor von Neumann algebra, Linear Algebra Appl. 42, 18-30 (2008).
17
ORIGINAL_ARTICLE
An approach to change the topology of a topological space with the help of its closed sets in the presence of grills
The aim of this paper is introduce an approach to convert thetopology of a topological space to another topology(in fact, a coarser topology).For this purpose, considering a closed set P of subsets of a topological space(X; T) and a grill G on the space, we use the closure operator cl associated withT, to define a new Kuratowski closure operator cl_p on X. The operator cl_p induces the desired topology. We then characterize the form of this resultingtopology and also determine its relationship to the initial topology of the space.Some examples are given. Also, using a suitable grill in the method, we converteach topological space to corresponding D-space.
https://jmmrc.uk.ac.ir/article_2902_7dda9000c93d3e33252544448658fc21.pdf
2021-10-01
9
19
10.22103/jmmrc.2021.17094.1132
Kuratowski closure operator
Kuratowski closure axioms
grill
D-topology
D-space
Amin
Talabeigi
talabeigi.amin@gmail.com
1
Department of Mathematics,
Payame Noor University, Tehran, Iran
LEAD_AUTHOR
V. M. Babych,V. O. Pyekhtyeryev, Closed extension topology,Scientific Bulletin of Uzhhorod University:Series of Mathematics and Informatics, Vol. 2, (2015), 7-10.
1
N. Broojerdian, A. Talabeigi, One-point $lambda$-compactification via grills, Iran J Sci Technol Trans Sci., Vol. 41,(2017), 909-912.
2
K. C. Chattopadhyay, W. J. Thron, Extensions of closure spaces,Can. J. Math.,Vol. 29, (1977), 1277-1286.
3
K. C. Chattopadhyay, O. Njastad and W. J. Thron, Merotopic spaces and extensions of closure spaces, Can. J. Math., Vol. 35, (1983), 613-629.
4
G. Choquet, Sur les notions de filtre et grille, Comptes Rendus Acad. Sci. Paris, Vol. 224, (1947), 171-173.
5
A. S. Mashhour, A. A. Allam, F. S. Mahmoud and F. H. Khedr, On supratopological spaces, Indian J. Pure Appl. Math., Vol. 14, (1983), 502-510.
6
A. Talabeigi, On the Tychonoff's type theorem via grills, Bull. Iranian Math. Soc., Vol. 42, No. 1 (2016), 37-41.
7
A. Talabeigi, Extracting some supra topologies from the topology of a topological space using stacks(Accepted in AUT Journal of Mathematics and Computing (AJMC) and to appear). doi: 10.22060/ajmc.2021.19123.1042
8
W. J. Thron, Proximity structures and grills, Math. Ann. Vol. 206, (1973), 35-62.
9
S. Willard, General topology, Addison–Wesley publishing company, 1970.
10
11
ORIGINAL_ARTICLE
A preconditioned Jacobi-type method for solving multi-linear systems
Recently, Zhang et al. [Applied Mathematics Letters 104 (2020) 106287] proposed a preconditioner to improve the convergence speed of three types of Jacobi iterative methods for solving multi-linear systems. In this paper, we consider the Jacobi-type method which works better than the other two ones and apply a new preconditioner. The convergence of proposed preconditioned iterative method is studied. It is shown that the new approach is superior to the recently examined one in the literature. Numerical experiments illustrate the validity of theoretical results and the efficiency of the proposed preconditioner.
https://jmmrc.uk.ac.ir/article_2903_98d19aa45d30b72b66f2f4a51825c2b4.pdf
2021-10-01
21
31
10.22103/jmmrc.2021.16997.1129
Iterative method
multi-linear system
strong $mathcal{M}$-tensor
preconditioning
Mehdi
Najafi-Kalyani
m.najafi.uk@gmail.com
1
Department of Mathematics, Vali-e-Asr University of Rafsanjan, PO Box 518, Rafsanjan, Iran
LEAD_AUTHOR
Fatemeh
P. A. Beik
f.beik@vru.ac.ir
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, PO Box 518, Rafsanjan, Iran
AUTHOR
[1] C. Bu, X. Zhang, J. Zhou, W. Wang, Y. Wei, The inverse, rank and product of tensors, Linear Algebra and Its Applications, vol. 446, (2014) 269{280.
1
[2] D. Liu, W. Li, S.W. Vong, A new preconditioned SOR method for solving multi-linear systems with an M-tensor, Calcolo, vol. 57, no. 2 (2020), DOI: 10.1007/s10092-020-00364-8.
2
[3] D. Liu, W. Li, S.W. Vong, The tensor splitting with application to solve multi-linear systems, Journal of Computational and Applied Mathematics, vol. 330, (2018) 75{94.
3
[4] F.P.A. Beik, M. Naja -Kalyani, J. Khalide, Preconditioned iterative methods for tensor multi-linear systems based on majorization matrix, Preprint, Available online on ResearchGate.
4
[5] J.Y. Shao, A general product of tensors with applications, Linear Algebra and its applications, vol. 439, no. 8 (2013) 2350{2366.
5
[6] K.C. Chang, K. Pearson, T. Zhang, Perron{Frobenius theorem for nonnegative tensors, Communications in Mathematical Sciences, vol. 6, no. 2 (2008) 507{520.
6
[7] L.B. Cui, C. Chen, W. Li, An eigenvalue problem for even order tensors with its applications, Linear and Multilinear Algebra, vol. 64, no. 4 (2016) 602{621.
7
[8] L.B. Cui, M.H. Li, Y. Song, Preconditioned tensor splitting iterations method for solving multi-linear systems, Applied Mathematics Letters, vol. 96, (2019) 89{94.
8
[9] L.B. Cui, W. Li, M.K. Ng, Primitive tensors and directed hypergraphs, Linear Algebra and its Applications, vol. 471, (2015) 96{108.
9
[10] L.B. Cui, X.Q. Zhang, S.L. Wu, A new preconditioner of the tensor splitting iterative method for solving multi-linear systems with M-tensors, Computational and Applied Mathematics, vol. 39, no. 173 (2020), DOI:10.1007/s40314-020-01194-8.
10
[11] L.B. Cui, Y. Song, On the uniqueness of the positive Z-eigenvector for nonnegative tensors, Journal of Computational and Applied Mathematics, vol. 352, (2019) 72{78.
11
[12] L.H. Lim, Singular values and eigenvalues of tensors: a variational approach, In: 1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing; IEEE; (2005) 129{132.
12
[13] L. Qi, Eigenvalues of a real supersymmetric tensor, Journal of Symbolic Computation, vol. 40, no. 6 (2005) 1302{1324.
13
[14] M. Ng, L. Qi, G. Zhou, Finding the largest eigenvalue of a nonnegative tensor, SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 3 (2010) 1090{1099.
14
[15] Q. Yang, Y. Yang, Further results for Perron{Frobenius theorem for nonnegative tensors II, SIAM Journal on Matrix Analysis and Applications, vol. 32, no. 4 (2011) 1236{1250.
15
[16] W. Ding, L. Qi, Y. Wei,M-tensors and nonsingular M-tensors, Linear Algebra and Its Applications, vol. 439, no. 10 (2013) 3264{3278.
16
[17] W. Li, D. Liu, S.W. Vong, Comparison results for splitting iterations for solving multilinear systems, Applied Numerical Mathematics, vol. 134, (2018) 105{121.
17
[18] W. Liu, W. Li, On the inverse of a tensor, Linear Algebra and its Applications, vol.495, (2016) 199{205.
18
[19] Y. Zhang, Q. Liu, Z. Chen, Preconditioned Jacobi type method for solving multi-linear systems with M-tensors, Applied Mathematics Letters, vol. 104, (2020) 106287.
19
ORIGINAL_ARTICLE
An Implication of Fuzzy ANOVA in Vehicle Battery Manufacturing
Analysis of variance (ANOVA) is an important method in exploratory and confirmatory data analysis when explanatory variables are discrete and response variables are continues and independent from each other. The simplest type of ANOVA is one-way analysis of variance for comparison among means of several populations. In this paper, we extend one-way analysis of variance to a case where observed data are non-symmetric triangular or normal fuzzy observations rather than real numbers. Meanwhile, a case study on the car battery length-life is provided on the basis on the proposed method.
https://jmmrc.uk.ac.ir/article_3017_05c35a9b2dd9016cb22b6b6c08d8f09a.pdf
2021-10-01
33
47
10.22103/jmmrc.2021.17325.1137
Fuzzy decision
Non-symmetric fuzzy data
Arithmetic fuzzy numbers
Analysis of variance
Abbas
Parchami
parchami@uk.ac.ir
1
Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
LEAD_AUTHOR
Mashallah
Mashinchi
mashinchi@uk.ac.ir
2
Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
AUTHOR
Cengiz
Kahraman
kahramanc@itu.edu.tr
3
Department of Industrial Engineering, Istanbul Technical University, Macka Istanbul, Turkey
AUTHOR
[1] W.G. Cochran and G.M. Cox, Experimental designs, 2nd edition, Wiley, New York, 1957.
1
[2] A. Cuevas, M. Febrero and R. Fraiman, An ANOVA test for functional data, Comput. Statist. Data Anal. 47 (2004) 111{122.
2
[3] A. Dean and D. Voss, Design and analysis of experiments, Springer-Verlag, New York, 1999.
3
[4] D. Dubois, H. Prade, Fuzzy sets and systems: Theory and application, Academic, New York, 1980.
4
[5] P. Filzmoser and R. Viertl, Testing hypotheses with fuzzy data: the fuzzy p-value , Metrika 59 (2009) 21{29.
5
[6] M.A. Gil, M. Montenegro, G. Gonzalez-Rodriguez, A. Colubi, and M.R. Casals, Boot-strap approach to the multi-sample test of means with imprecise data, Comput. Statist. Data Anal. 51 (2006) 141{162.
6
[7] R.R. Hocking, Methods and applications of linear models: Regression and the analysis of variance, John Wiley & Sons, New York, 1996.
7
[8] A. Kaufmann and M.M. Gupta, Introduction to fuzzy arithmetic: Theory and applications, Van Nastrand, New York, 1985.
8
[9] W.J. Lee, H.Y. Jung, J.H. Yoon and S.H. Choi, Analysis of variance for fuzzy data based on permutation method, International Journal of Fuzzy Logic and Intelligent Systems 17 (2017) 43{50.
9
[10] M. Montenegro, A. Colubi, M.R. Casals and M.A. Gil, Asymptotic and bootstrap techniques for testing the expected value of a fuzzy random variable, Metrika 59 (2004) 31{49.
10
[11] M. Montenegro, G. Gonzalez-Rodriguez, M.A. Gil, A. Colubi and M.R. Casals, Introduction to ANOVA with fuzzy random variables, In: Lopez-Diaz, M., Gil, M.A., Grzegorzewski, P., Hryniewicz, O., Lawry, J. (Eds.), Soft Methodology and random information systems. Springer, (Berlin, 2004) 487{494.
11
[12] D.C. Montgomery, Design and analysis of experiments, Third edition, John Wiley & Sons, New York, 1991.
12
[13] H.T. Nguyen and E.A. Walker, A rst course in fuzzy logic, Third edition, Chapman Hall/CRC, Paris, 2005.
13
[14] M.R. Nourbakhsh, M. Mashinchi and A. Parchami, Analysis of variance based on fuzzy observations, International Journal of Systems Science 44 (2013) 714{726.
14
[15] A. Parchami, R. Ivani, M. Mashinchi and . Kaya, An implication of fuzzy ANOVA:Metal uptake and transport by corn grown on a contaminated soil, Chemometrics and Intelligent Laboratory Systems 164 (2017) 56{63.
15
[16] A. Parchami, M.R. Nourbakhsh and M. Mashinchi, Analysis of variance in uncertain environments, Complex & Intelligent Systems 3 (2017, 189{196.
16
[17] A. Parchami, B. Sadeghpour-Gildeh, M. Nourbakhsh and M. Mashinchi, A new generation of process capability indices based on fuzzy measurements, Journal of Applied Statistics 41 (2014) 1122{1136.
17
[18] A. Parchami, M. Mashinchi and C. Kahraman, A case study on vehicle battery manufacturing using fuzzy analysis of variance, Proceedings of the INFUS 2020 Conference,July 21-23 (Istanbul, 2020), 916{923.
18
[19] M.L. Puri and D.A. Relescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (1986)409{422.
19
[20] M.L. Rizzo, Statistical computing with R, Chapman Hall/CRC, Paris, 2008.
20
[21] S.M. Taheri and M. Are , Testing hypotheses based on fuzzy test statistic, Soft Comput. 13 (2009) 617{625.
21
[22] R. Viertl and F.L. Boca Raton, Statistical methods for non-precise data, CRC Press, Paris, 1996.
22
[23] H.C. Wu, Analysis of variance for fuzzy data, International Journal of Systems Science 38 (2007) 235{246.
23
[24] R. Xu and C. Li, Multidimensional least-squares tting with a fuzzy model, Fuzzy Sets and Systems 119 (2001) 215{223.
24
ORIGINAL_ARTICLE
Perron-Frobenius theory on the higher-rank numerical range for some classes of real matrices
We present an extension of Perron-Frobenius theory to the higher-rank numerical rangeof real matrices. We define a new type of the rank-k numerical radius for real matrices, i.e., thesign-real rank-k numerical radius, and derive some properties of it. In addition, we extend Issos' results on the higher-rank numerical range of nonnegative matrices to real matrices.Finally, we give some examples that are used to illustrate our theoretical results.
https://jmmrc.uk.ac.ir/article_3018_39aaa70d4798a72347b6f524c71dc8b4.pdf
2021-10-01
49
61
10.22103/jmmrc.2021.17564.1147
Sign-real rank-k numerical radius
sign-real spectral radius
Perron-Frobenius theory, signature matrices
higher-rank numerical range
Mostafa
Zangiabadi
zangiabadi1@gmail.com
1
Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran
LEAD_AUTHOR
Hamidreza
Afshin
hamidrezaafshin@yahoo.com
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
AUTHOR
[1] A. Aretaki and J. Maroulas, The higher rank numerical range of nonnegative matrices,Cent. Eur. J. Math., vol. 11, no.3(2013), 435{446.
1
[2] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences,vol. 9, SIAM, Philadelphia, 1994.
2
[3] M.T. Chien and H. Nakazato, Boundary generating curves of the c-numerical range,Linear Algebra Appl., vol. 294, no. 1-3(1999), 67{84.
3
[4] M.D. Choi, D.W. Kribs and K. Zyczkowski, Higher-rank numerical ranges and compression problems, Linear Algebra Appl., vol. 418 no. 2-3(2006), 828{839.
4
[5] M.D. Choi, D.W. Kribs and K. Zyczkowski, Quantum error correcting codes from the compression formalism, Rep. Math. Phys., vol. 58, no. 1(2006), 77{86.
5
[6] G. Frobenius, Uber Matrizen aus nichtnegativen Elementen, Math. Nat. K1., (1912),456{477.
6
[7] R.A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
7
[8] R.A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press,Cambridge, 1991.
8
[9] J.N. Issos, The eld of values of non-negative irreducible matrices, Ph.D. Thesis,Auburn University, 1966.
9
[10] C.K. Li, B.-S. Tam and P.Y. Wu, The numerical range of a nonnegative matrix, Linear Algebra Appl., vol. 350, no. 1-3(2002), 1{23.
10
[11] C.K. Li and H. Schneider, Applications of the Perron{Frobenius theory to population dynamics, J. Math. Biol., vol. 44, no. 5(2002), 250{262.
11
[12] C.K. Li, Y.T. Poon and N.S. Sze, Condition for the higher rank numerical range to be non-empty, Linear Multilinear Algebra, vol. 57, no. 4(2009), 365{368.
12
[13] M.-H. Matcovschi and O. Pastravanu, Perron{Frobenius theorem and invariant sets in linear systems dynamics , in Proceedings of the 15th IEEE Mediterranean Conference on Control and Automation (MED07), Athens, Greece, 2007.
13
[14] H. Mink, Nonnegative Matrices, Wiley, New York, 1988.
14
[15] S.M. Rump., Theorems of Perron-Frobenius type for matrices without sign restrictions,linear Algebra Appl., vol. 266(1997), 1{42.
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[16] S. M. Rump, Conservatism of the Circle Criterion Solution of a Problem posed by A.Megretski, IEEE Trans. Autom. Control, vol. 46, no. 10(2001), 1605{1608.
16
[17] S. M. Rump, conditioned Matrices are componentwise near to singularity, SIAM Rev.,vol. 41, no. 1(1999), 102{112.
17
[18] B. Shafai, J. Chen and M. Kothandaraman, Explicit formulas for stability of nonnegative and Metzlerian matrices, IEEE Transactions on Automatic Control, vol. 42, no. 2(1997),265{270.
18
[19] M. Zangiabadi and H. R. Afshin, A new concept for numerical radius: the sign-real numerical radius, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., vol.76, no. 3(2014), 91{98.
19
[20] M. Zangiabadi and H. R. Afshin, Perron{Frobenius theory on the numerical range for some classes of real matrices, J. Mahani Math. Res. Cent., vol. 2, no. 2(2013), 1{15.
20
ORIGINAL_ARTICLE
Eigenvalues for tridiagonal 3-Toeplitz matrices
In this paper, we study the eigenvalues of real tridiagonal 3-Toeplitz matricesof different order. When the order of a tridiagonal 3-Toeplitz matrix is n = 3k + 2,the eigenvalues were found explicitly. Here, we consider the distribution of eigenvaluesfor a tridiagonal 3-Toeplitz matrix of orders n = 3k and n = 3k + 1. We explain ourmethod by finding roots of a combination of Chebyshev polynomials of the secondkind. This distribution solves the eigenproblem for integer powers of such matrices.
https://jmmrc.uk.ac.ir/article_3019_2240ffcf63fe00d5244dda150b8442bd.pdf
2021-10-01
63
72
10.22103/jmmrc.2021.17349.1138
3-Toeplitz matrix
Chebyshev Polynomials
Eigenvalue
Maryam
Shams Solary
shamssolary@gmail.com
1
Department of Applied Mathematics, Payame Noor University, Po Box 19395-3697 Tehran, Iran.
LEAD_AUTHOR
[1] R. Alvarez-Nodarse, F. Marcellan: On the Favard Theorem and its extensions., J. Comput.Appl. Math. 127 (2001)231{254.
1
[2] R. Alvarez-Nodarse, J. Petronilho, N.R. Quintero, On some tridiagonal k-Toeplitz matrices: Algebraic and analytical aspects. Applications, J. Comput. Appl. Math. 184 (2005) 518{537.
2
[3] D. Bini, V. Pan, Ecient algorithms for the evaluation of the eigenvalues of (block) banded Toeplitz matrices,. Math. Comp., 50 (1988) 431{48.
3
[4] D. Bini and V. Pan, On the Evaluation of the Eigenvalues of a Banded Toeplitz Block Matrix, Tech. Rep. CUCS-024-90, Columbia University, Computer Science Dept., N.Y., 1990.
4
[5] A. Bottcher, S. Grudsky, Spectral Properties of Banded Toeplitz Matrices, SIAM, Philadelphia, 2005.
5
[6] J. P. Boyd, Solving Transcendental Equations: The Chebyshev Polynomial Proxy and Other Numerical Root nders, Perturbation Series, and Oracles (Other Titles in Applied Mathematics), SIAM, 2014.
6
[7] S.N. Chandler-Wilde, M.J.C. Gover, On the application of a generalization of Toeplitz matrices to the numerical solution of integral equations with weakly singular convolution kernels, IMA J. Numer. Anal. 9 (1989) 525{544.
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[8] T. A. Driscoll, N. Hale, L. N. Trefethen, editors, Chebfun Guide, Pafnuty Publications, Oxford, 2014.
8
[9] D. Fasino, S. Serra Capizzano, From Toeplitz matrix sequence to zero distribution of orthogonal polynomials, Contemp. Math. 323 (2003) 329{339.
9
[10] C.M. da Fonseca, The characteristic polynomial of some perturbed tridiagonal kToeplitz matrices, Appl. Math. Sci. (Ruse) 1, 2 (2007) 59{67.
10
[11] J. Gutierrez-Gutierrez, Entries of continuous functions of large Hermitian tridiagonal 2-Toeplitz matrices, Linear Algebra Appl. 439 (2013) 34{54.
11
[12] M.J.C. Gover, S. Barnett, D.C. Hothersall, Sound propagation over inhomogeneous boundaries, in: Internoise 86, Cambridge, MA (1986) 377{382.
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[13] M.J.C. Gover, The eigenproblem of a tridiagonal 2-Toeplitz matrix, Linear Algebra Appl. 197 (1994) 63{78.
13
[14] W. Gautschi, Orthogonal Polynomials in MATLAB: Exercises and Solutions, SIAM, 2016.
14
[15] G. Konig, M. Moldaschl, and W. N. Gansterer, Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations, J. Comput. Appl. Math. 236 (2012) 3696{3703.
15
[16] D. Kulkarni, D. Schmidt, S.-K. Tsui, Eigenvalues of tridiagonal pseudo-Toeplitz matrices, Linear Algebra Appl. 297 (1999) 63{80.
16
[17] F. Marcella'n, J. Petronilho, Orthogonal polynomials and cubic polynomial mappings I, Comm. Anal. Theory Contin. Fractions 8 (2000) 88{116.
17
[18] F. Marcella'n, J. Petronilho, Orthogonal polynomials and cubic polynomial mappings II, Comm. Anal. Theory Contin. Fractions 9 (2001) 11{20.
18
[19] M. Mazza, A. Ratnani, S. Serra-Capizzano, Spectral analysis and spectral symbol for the 2D curl-curl (stabilized) operator with applications to the related iterative solutions, Math. Comp. 88 (2019) 1155{1188.
19
[20] J. Rimas, Explicit expression for powers of tridiagonal 2-Toeplitz matrix of odd order, Linear Algebra Appl. 436 (2012) 3493{3506.
20
[21] M. Shams Solary, Computational properties of pentadiagonal and anti-pentadiagonal block band matrices with perturbed corners, Soft Computing 24 (2020) 301-309.
21
[22] F. Shengjin, A new extracting formula and a new distinguishing means on the one variable cubic equation, Natural Science Journal of Hainan Teachers College 2 (1989) 91{98.
22
ORIGINAL_ARTICLE
Fuzzy, Possibility, Probability, and Generalized Uncertainty Theory in Mathematical Analysis
This presentation outlines from a quantitative point of view, the relationships between probability theory, possibility theory, and generalized uncertainty theory, and the role that fuzzy set theory plays in the context of these theories. Fuzzy sets, possibility, and probability entities are de
ned in terms of a function. In each case, these three functions map the real numbers to the interval [0,1]. However, each of these functions are de
ned with di¤erent properties. There are generalizations associated with these three theories that lead to intervals (sets of connected real numbers bounded by two points) and interval functions (sets of functions that are bounded by known upper and lower functions). An interval or interval function encodes the fact that it is unknown which of the points or functions is the point or function in questions, that is, the numerical value or real-valued function is unknown, it is uncertain. For generalizations given by pairs of numbers or functions, a case is made for a particular type of generalized uncertainty theory, interval-valued probability measures, as a way to unify the generalizations of probability, possibility theory, as well as other generalized probability theories via fuzzy intervals and fuzzy interval functions. This presentation brings a new understanding of quantitative fuzzy set theory, possibility theory, probability theory, and generalized uncertainty and gleans from existing research with the intent to organize and further clarify existing approaches.
https://jmmrc.uk.ac.ir/article_3020_de14f1f1796bbd2c882e1965404f8822.pdf
2021-10-01
73
101
10.22103/jmmrc.2021.18055.1160
Possibility
Probability
Generalized Uncertainty
Weldon
Lodwick
weldon.lodwick@ucdenver.edu
1
Dept. of Mathematical and Statistical Sciences, University of Colorado Denver, Colorado, USA
LEAD_AUTHOR
[1] Archimedes of Siracusa, On the measurement of the circle," In: Thomas L. Heath (editor),The Works of Archimedes, Cambridge University Press, Cambridge, 1897; Dover edition, 1953.
1
[2] Dubois, D. (2005) On the links between probability and possibility theories", Plenary talk at IFSA 2005, Beijing, China.
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[3] Dubois, D. (2010), The role of fuzzy sets in decision sciences: old techniques and new directions," Fuzzy Sets and Systems, 184:1, pp. 3{28.
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[4] Dubois, D. (2014). Uncertainty Theories: A Uni ed View", Plenary talk at FLINS and CBSF III 2014, Jo~ao Pessoa, Brazil.
4
[5] Dubois, D., Kerre, E., Mesiar,R., and Prade, H. (2000). Chapter 10, Fuzzy Interval Analysis", in Didier Dubois and Henri Prade, (editors) Fundamentals of Fuzzy Sets, Kluwer Academic Publishers, Boston.
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[6] Dubois, D., Nguyen, H. T., and Prade, H. (2000). Chapter 7, Possibility Theory, Probability and Fuzzy Sets: Misunderstandings, Bridges and Gaps", in Didier Dubois and Henri Prade, (editors) Fundamentals of Fuzzy Sets, Kluwer Academic Publishers, Boston.
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[7] Dubois, D. and Prade, H. (1982). On several representations of an uncertainty body of evidence", in M. M. Gupta and E. Sanchez, editors. Fuzzy Information and Decision Processes, North-Holland, Amsterdam, pp. 167-181.
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[8] Dubois, D. and Prade, H. (1988). Possibility Theory, Plenum Press, New York.
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[9] Dubois, D. and Prade, H. (1992). When upper probabilities are possibility measures", Fuzzy Sets and Systems,49, pp. 65-74.
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[10] Dubois, D. and Prade H., editors (2000). Fundamentals of Fuzzy Sets. Kluwer Academic Press.
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[11] Dubois, D. and Prade, H. (2009), Formal representations of uncertainty," Chapter 3 in. D. Bouyssou, D. Dubois, H. Prade, Editors, Decision-Making Process, ISTE, London, UK & Wiley, Hoboken, N.J., USA.
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[12] Dubois, D. and Prade, H. (2011). Mathware&Soft Computing Magazine 18:1, December 2011, pp. 18-71.
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[13] Dubois, D., and Prade, H. (2012). Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets." Fuzzy Sets and Systems, 192, pp. 3-24.
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[14] Dubois, D. and Prade, H. (2015). Possibility theory and its applications: Where do we stand?" in Kacprzyk, J. and Pedrycz, W., (editors) Handbook of Computational Intelligence, Springer, pp. 31-60.
14
[15] Ferson, S., Kreinovich, V., Ginzburg, R., Sentz, K., and Myers, D. S., (2003). Constructing Probability Boxes and Dempster-Shafer Structures. Sandia National Laboratories, Technical Report SAND2002-4015, Albuquerque, New Mexico.
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[16] Jamison, K. D., Lodwick, W. A. (2004), Interval-Valued Probability Measures,"UCD/CCM Report No. 213, March 2004.
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[17] Jamison, K. D. and Lodwick, W. A. (2020) A new approach to interval-valued probability measures, A formal method for consolidating the languages of information de ciency: Foundations", Information Sciences, 507, pp. 86-107.
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[18] Kaufmann, A. and Gupta, M. M. (1985) . Introduction to Fuzzy Arithmetic -Theory and Applications, Van Nostrand Reinhold.
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[19] Lodwick, W. A. and Bachman, K., (2005), Solving large scale fuzzy possibilistic optimization problems", Fuzzy Optimization and Decision Making, 4:4, pp. 257-278.
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[20] Lodwick, W. A., and Jenkins, O. (2013), Constrained intervals and interval spaces," Soft Computing, 17: 8, pp. 1393-1402.
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[21] Lodwick, W. A., Neumaier, A. and Newman, F. D., Optimization under uncertainty: Methods and applications in radiation therapy," Proceedings 10th IEEE International Conference on Fuzzy Systems 2001, 3, pp. 1219-1222.
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[22] Lodwick, W. A. and Sales Neto, L. (2021). Flexible and Generalized Uncertainty Optimization. Springer-Verlag.
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[25] Klir, G. J., and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River, New Jersey.
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[26] Moore, R. E., Kearfott R. B. , and Cloud, M. J. (2009). Introduction to Interval Analysis. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA.
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[27] Puri, M. L., and Ralescu, D. (1982). A possibility measure is not a fuzzy measure", Fuzzy Sets and Systems, 7, pp. 311-313.
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[31] Zadeh, L. (1978). Fuzzy sets as a basis for a theory of possibility", Fuzzy Sets and Systems, 1(1), pp. 3-28.
31
ORIGINAL_ARTICLE
On Hierarchical Multiple Imputation Method for Handling Missing Data
In this work we carry out a multiple imputation technique for handling missing observations. We propose an algorithm, which performs a hierarchical multiple imputation using edition rules to impute missing values. We assess our algorithm using a simulation study and a numerical application of our algorithm in dataset of Kerman Chamber of Commerce, Industries, Mines and Agriculture is presented for more illustration.
https://jmmrc.uk.ac.ir/article_3021_45d6f831fa819ce904f73db98a966664.pdf
2021-10-01
103
114
10.22103/jmmrc.2021.17749.1153
Missing Data
Multiple Imputation
Editing Rules
Data Cleaning
Ayyub
Sheikhi
sheikhy.a@uk.ac.ir
1
Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
LEAD_AUTHOR
Alireza
Arabpour
arabpour@uk.ac.ir
2
Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
AUTHOR
Khosravi
Mohsen
khosravi_mm@uk.ac.ir
3
Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
AUTHOR
Mashallah
Mashinchi
mashinchi@uk.ac.ir
4
Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
AUTHOR
Reza
Pourmousa
pourm@uk.ac.ir
5
Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
AUTHOR
Mohsen
Rezapour
mohsenrzp@uk.ac.ir
6
Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
AUTHOR
Mohammad Javad
Roastami
rostami@uk.ac.ir
7
Department of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, Iran. and Kerman Chamber of Commerce, Industries, Mines and Agriculture, Kerman, Iran
AUTHOR
Amin
Abbdollah Nejad
aminabdollahnejad@gmail.com
8
Kerman Chamber of Commerce, Industries, Mines and Agriculture, Kerman, Iran
AUTHOR
Abed
Badakhshan
abidbadakhshan@gmail.com
9
Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
AUTHOR
[1] Charu C Aggarwal and Saket Sathe. Outlier ensembles: An introduction. Springer, 2017.
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[2] Malik Agyemang, Ken Barker, and Rada Alhajj. A comprehensive survey of numeric and symbolic outlier mining techniques. Intelligent Data Analysis, 10(6):521{538, 2006.
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[3] Zohreh Akbari and Rainer Unland. Automated determination of the input parameter of dbscan based on outlier detection. In IFIP International Conference on Arti cial Intelligence Applications and Innovations, pages 280{291. Springer, 2016.
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[4] Krishnan Bhaskaran and Liam Smeeth. What is the di erence between missing completely at random and missing at random? International Journal of Epidemiology, 43(4):1336{1339, 2014.
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[5] Nicole M Butera, Siying Li, Kelly R Evenson, Chongzhi Di, David M Buchner, Michael J LaMonte, Andrea Z LaCroix, and Amy Herring. Hot deck multiple imputation for handling missing accelerometer data. Statistics in Biosciences, 11(2):422{448, 2019.
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[6] S van Buuren and Karin Groothuis-Oudshoorn. mice: Multivariate imputation by chained equations in r. Journal of statistical software, pages 1{68, 2010.
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[7] James R Carpenter, Michael G Kenward, and Ian R White. Sensitivity analysis after multiple imputation under missing at random: a weighting approach. Statistical methods in medical research, 16(3):259{275, 2007.
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[8] Ya Chen, Yongjun Li, Huaqing Wu, and Liang Liang. Data envelopment analysis with missing data: A multiple linear regression analysis approach. International Journal of Information Technology & Decision Making, 13(01):137{153, 2014.
8
[9] Zhangyu Cheng, Chengming Zou, and Jianwei Dong. Outlier detection using isolation forest and local outlier factor. In Proceedings of the conference on research in adaptive and convergent systems, pages 161{168, 2019.
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[10] Tamraparni Dasu and Theodore Johnson. Exploratory data mining and data cleaning. John Wiley & Sons, 2003.
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[11] Ivan P Fellegi and David Holt. A systematic approach to automatic edit and imputation. Journal of the American Statistical Association, 71(353):17{35, 1976.
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[12] Gary Fraser and Ru Yan. Guided multiple imputation of missing data: using a subsample to strengthen the missing-at-random assumption. Epidemiology, pages 246{252, 2007.
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[13] Alex A Freitas. Data mining and knowledge discovery with evolutionary algorithms. Springer Science & Business Media, 2013.
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[14] Salvador Garca, Julian Luengo, and Francisco Herrera. Data preprocessing in data mining. Springer, 2015.
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[15] Benjamin Yael Gravesteijn, Charlie Aletta Sewalt, Esmee Venema, Daan Nieboer, Ewout W Steyerberg, and CENTER-TBI Collaborators. Missing data in prediction research: A ve-step approach for multiple imputation, illustrated in the center-tbi study. Journal of neurotrauma, 38(13):1842{1857, 2021.
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[16] Simon Grund, Oliver Ludtke, and Alexander Robitzsch. Multiple imputation of missing data in multilevel models with the r package mdmb: a exible sequential modeling approach. Behavior Research Methods, pages 1{19, 2021.
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[17] Julie Josse and Francois Husson. Handling missing values in exploratory multivariate data analysis methods. Journal de la Societe Francaise de Statistique, 153(2):79{99, 2012.
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[18] Hyun Kang. The prevention and handling of the missing data. Korean Journal of Anes-thesiology, 64(5):402, 2013.
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[19] Shahidul Islam Khan and Abu Sayed Md Latiful Hoque. Sice: an improved missing data imputation technique. Journal of Big Data, 7(1):1{21, 2020.
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[20] Hang J Kim, Alan F Karr, and Jerome P Reiter. Statistical disclosure limitation in the presence of edit rules. Journal of Ocial Statistics, 31(1):121{138, 2015.
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[21] Sang Kyu Kwak and Jong Hae Kim. Statistical data preparation: management of missing values and outliers. Korean Journal of Anesthesiology, 70(4):407, 2017.
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[22] Roderick JA Little and Donald B Rubin. Statistical analysis with missing data, volume 793. John Wiley & Sons, 2019.
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[23] Daniel McNeish. Missing data methods for arbitrary missingness with small samples. Journal of Applied Statistics, 44(1):24{39, 2017.
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[24] Jared S Murray et al. Multiple imputation: a review of practical and theoretical ndings. Statistical Science, 33(2):142{159, 2018.
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[25] Irfan Pratama, Adhistya Erna Permanasari, Igi Ardiyanto, and Rini Indrayani. A review of missing values handling methods on time-series data. In 2016 International Conference on Information Technology Systems and Innovation (ICITSI), pages 1{6. IEEE, 2016.
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[26] Burim Ramosaj and Markus Pauly. Predicting missing values: a comparative study on non-parametric approaches for imputation. Computational Statistics, 34(4):1741{1764, 2019.
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[27] Peter J Rousseeuw and Mia Hubert. Robust statistics for outlier detection. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 1(1):73{79, 2011.
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[29] Donald B Rubin. Multiple imputation for nonresponse in surveys, volume 81. John Wiley & Sons, 2004.
29
[30] Akiyo Sasaki-Otomaru, Kotaro Yamasue, Osamu Tochikubo, Kyoko Saito, and Masahiko Inamori. Association of home blood pressure with sleep and physical and mental activity, assessed via a wristwatch-type pulsimeter with accelerometer in adults. Clinical and Experimental Hypertension, 42(2):131{138, 2020.
30
[31] Joseph L Schafer. Analysis of incomplete multivariate data. CRC press, 1997.
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[32] Joseph L Schafer and Maren K Olsen. Multiple imputation for multivariate missing-data problems: A data analyst's perspective. Multivariate behavioral research, 33(4):545{571,1998.
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[33] Shaun Seaman, John Galati, Dan Jackson, and John Carlin. What is meant by "missing at random"? Statistical Science, 1:257{268, 2013.
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[35] K Shobha and S Nickolas. Imputation of multivariate attribute values in big data. In Smart intelligent computing and applications, pages 53{60. Springer, 2019.
35
ORIGINAL_ARTICLE
On approximate orthogonally ring homomorphisms and orthogonally ring derivations in Banach algebras with the new type fixed point
In this paper, Using fixed point methods, we prove the stability of orthogonally ring homomorphism and orthogonally ring derivation in Banach algebras.
https://jmmrc.uk.ac.ir/article_3022_174a0906fba8691414a1615db6017c70.pdf
2021-10-01
115
124
10.22103/jmmrc.2021.16277.1120
Stability
Banach algebras
fixed point approach
ring derivations
ring homomorphisms
Ali
Bahraini
a.bahraini@iauctb.ac.ir
1
Mathematics Department-College of Science, Islamic Azad University Central Tehran Branch, Tehran, Iran.
AUTHOR
Gholamreza
Askari
g.askari@semnan.ac.ir
2
Department of Mathematics, Semnan University, Semnan, Iran.
AUTHOR
Madjid
Eshaghi Gordji
meshaghi@semnan.ac.ir
3
Department of Mathematics, Semnan University, Semnan, Iran.
LEAD_AUTHOR
[1] N. Ansari, M.H. Hooshmand, M. Eshaghi Gordji, K. Jahedi, Stability of fuzzy orthogonally -n-derivation in orthogonally fuzzy C*-algebras, J. Nonlinear Anal. Appl. 12 (2021) 533{540 .
1
[2] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950) 64{66.
2
[3] R. Badora, On approximate derivations, Math. Inequal. Appl. 9 (2006) 167{173.
3
[4] A. Bahraini, G. Askari, Homogeneous Equation Between Banach -Modules, Journal of Mathematical Analysis 9 (2018) 11{18.
4
[5] A. Bahraini, G. Askari, M. Eshaghi Gordji, R. Gholami, Stability and hyperstability of orthogonally -m-homomorphisms in orthogonally Lie C-algebras: a xed point approach , J. Fixed Point Theory Appl. (2018), 1{12.
5
[6] H. Baghani, M. E. Gordji, M. Ramezani, Orthogonal sets: The axiom of choice and proof of a xed point theorem, J. Fixed Point Theory Appl., 18 (2016), 465{477.
6
[7] M. Bavand Savadkouhi, M.E. Gordji, J.M. Rassias, N. Ghobadipour, Approximate ternary Jordan derivations on Banach ternary algebras, J. Math. Phys. 50 (2009), 20{29.
7
[8] L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: A xed point approach, Grazer Math. Ber. 346 (2004).
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[9] L. Cadariu, V. Radu, Fixed points and the stability of Jensens functional equation, J. Ineq. Pure Appl. Math. 4 (2003).
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[10] L. Cadariu, V. Radu, Fixed Point Methods for the Generalized Stability of Functional Equations in a Single Variabl, Fixed Point Theory Appl. (2008) 1{15.
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[11] M. Eshaghi, H. Habibi, Existence and uniqueness of solutions to a rst-order di erential equation via xed point theorem in orthogonal metric space, FACTA UNIVERSITATIS (NIS) Ser. Math. 34 (2019) 123-135.
11
[12] M. Eshaghi Gordji, H Habibi, Fixed point theory in generalized orthogonal metric space, J. Linear Topol. Algeb., 6 (2017), 251{260.
12
[13] M. Eshaghi Gordji, H. Habibi and M.B. Sahabi, Orthogonal sets; orthogonal contractions, Asian-Eur. J. Math. 12 (2019).
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[14] M. Eshaghi Gordji, G. Askari, N. Ansari, G. A. Anastassiou and C. Park, Stability and hyperstability of generalized orthogonally quadratic ternary homomorphisms in non-Archimedean ternary Banach algebras: a xed point approach, J. Computational Analysis And Applications, 21 (2016) 1{8.
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[15] M. Eshaghi Gordji, M. Ramezani, M. De La Sen, and Y.J. Cho, On orthogonal sets and Banach xed point theorem, Fixed Point Theory, 18 (2017), 569{578.
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[16] M. Eshaghi Gordji, R. Farokhzad and S. A. R. Hosseinioun, Ternary (; ; )-derivations on Banach ternary algebras, Int. J. Nonlinear Anal. Appl., 5 (2014) 23{35.
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[22] H. Hosseini, M. Eshaghi, Fixed Point Results in Orthogonal Modular Metric Spaces, J. Nonlinear Anal. Appl. 11 (2020) 425{436.
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36
ORIGINAL_ARTICLE
Kleen’s Theorem for BL-general L-fuzzy automata
The contribution of generl fuzzy automata to neural networks has been considerable, and dynamical fuzzy systems are becoming more and more popular and useful. Basic logic, or BL for short, has been introduced by Hájek [5] in order to provide a general framework for formalizing statements of fuzzy nature. In this note, some of the closure properties of the BL-general fuzzy automaton based on lattice valued such as union, intersection, connection and a serial connection are considered, after that, the behavior of them are discussed. Moreover, for a given BL-general fuzzy automaton on the basis of lattice valued, a complete BL-general fuzzy automaton on the basis of lattice valued is presented. Afterward, we may test the Pumping Lemma for the BL-general fuzzy automaton based on lattice valued. In particular, a connection between the behavior of BL-general fuzzy automaton based on lattice valued and its language is presented. Also, it is proven that L is a recognizable set if and only if L is rational. Also, it is driven that Kleen’s Theorem is valid for the BL-general fuzzy automaton on the basis of lattice valued. Finally, we give some examples to clarify these notions.
https://jmmrc.uk.ac.ir/article_3023_5173d44412a9875cc5b347883638b803.pdf
2021-10-01
125
144
10.22103/jmmrc.2021.17171.1134
BL-general fuzzy automata
Closure properties
Behavior of fuzzy automata
Pumping Lemma
Kleen’s Theorem
Marzieh
Shamsizadeh
shamsizadeh.m@gmail.com
1
Behbahan Khatam Alanbia University of Technology, Khouzestan, Iran
LEAD_AUTHOR
Mohammad Mehdi
Zahedi
zahedi_mm@kgut.ac.ir
2
Department of Mathematics Graduate University of Advanced Technology, Kerman, Iran
AUTHOR
Khadijeh
Abolpour
abolpor_kh@yahoo.com
3
Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran
AUTHOR
[1] K. Abolpour, M.M. Zahedi, Isomorphism between two BL-general fuzzy automata, Soft Computing, 16 (2012), 729-736.
1
[2] M. Doostfatemeh, S.C. Kremer, New directions in fuzzy automata, International Journal of Approximate Reasoning, 38 (2005), 175-214.
2
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[5] P. Hajek, Metamathematics of fuzzy logic, Kluwer, Dordrecht, (1988).
5
[6] J. E. Hopcroft, R. Motwani, J. D. Ullman, Introduction to Automata Theory, Languages and Computation, seconded., Addison-Wesley, Reading, MA, 2001.
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[8] Y. M. Li, W. Pedryez, Fuzzy nite automata and fuzzy regular expressions with membership values in lattice-ordered monoid, Fuzzy Sets and Systems, 156 (2005), 68-92.
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[9] D. S. Malik, J. N. Mordeson, Fuzzy Automata and Languages: Theory and Applications, Chapman Hall, CRC Boca Raton, London, New York, Washington DC, 2002.
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35
ORIGINAL_ARTICLE
Dynamics of a harmonic oscillator perturbed by a non-smooth velocity-dependent damping force
This paper studies the dynamics of a non-smooth vibrating system of the Filippov type. The main focus is on investigating the stability and bifurcation of a simple harmonic oscillator subjected to a non-smooth velocity-dependent damping force. In this way, we can analyze the effects of damping on the system's vibrations. For this purpose, we will find a parametric region for the existence of generalized Hopf bifurcation, in order to compute a branch of periodic orbits for the system. The tool for our purpose is the theoretical results about generalized Hopf bifurcation for planar Filippov systems. Some numerical simulations as examples are given to illustrate our theoretical results. Our theoretical and numerical findings indicate that the harmonic oscillator can experience different kinds of vibrations, in the presence of a non-smooth damping.
https://jmmrc.uk.ac.ir/article_3045_5e4ff0393ffe9a91c13aa26fea3ed64b.pdf
2021-10-01
145
162
10.22103/jmmrc.2021.17474.1140
Velocity-dependent damping
Non-smooth dynamical systems
Generalized Hopf bifurcation
Vibrations
Nonlinear oscillator
Zahra
Monfared
zahra.monfared@zi-mannheim.de
1
Department of Mathematics & Informatics and Cluster of Excellence STRUCTURES, Heidelberg University, Heidelberg, Germany and Department of Applied Mathematics, Ferdowsi University of Mashhad (FUM), Mashhad, Iran
AUTHOR
Zohreh
Dadi
dadizohreh@gmail.com
2
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran
LEAD_AUTHOR
ALi
Darijani
a.darijani@bam.ac.ir
3
Department of Mathematics, Higher Education Complex of Bam, Bam, Iran
AUTHOR
Yousef
Qasemi Nezhad Raeini
yqasemi@gmail.com
4
Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
AUTHOR
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2
26] E. S. Levitan, Forced oscillation of a spring-mass system having combined Coulomb and viscous damping, The Journal of the Acoustical Society of America, vol. 32, pp. 1265-1269, 1960.[27] Z. Q. Lu, J. M. Li, H. Ding and L. Q. Chen, Analysis and suppression of a self-excitation vibration via internal stiness and damping nonlinearity, Advances in Mechanical Engineering, vol.9, no.12, DOI: 10.1177/1687814017744024,2017.[28] A. C. J. Luo and J. Z. Huang, Discontinuous dynamics of a non-linear, self-excited, friction-induced, periodically forced oscillator, Nonlinear Analysis: Real World Applications, vol.13, pp.241-257, 2012.[29] Y. L. Ma, S. D. Yu, and D. L. Wang, Vibration analysis of an oscillator with non-smooth dry friction constraint, Journal of Vibration and Control, vol.23, no.14, pp.2328-2344, 2017.[30] O. Makarenkov, A new test for stick-slip limit cycles in dry-friction oscillators with a small nonlinearity in the friction characteristic, MECCANICA, vol.52, no.11-12, pp.2631-2640, 2017.[31] Z. Monfared, Z. Dadi, Analyzing panel flutter in supersonic flow by Hopf bifurcation, Iran. J. Numer. Anal. Optim, Vol. 4(2), 114 , 2014.[32] Z. Monfared, M. Behjaty, Modeling and dynamic behavior of a discontinuous tourism-based social-ecological dynamical system, Filomat, Vol. 33, Issue 18, Pages: 5991-6004, 2019.[33] Z. Monfared, Z. Afsharnezhad, J. Abolfazli Esfahani, Flutter, limit cycle oscillation, bifurcation and stability regions of an airfoil with discontinuous freeplay nonlinearity, Nonlinear dynamics, Vol.90, No. 3, pp. 1965-1986, 2017.[34] Z. Monfared, D. Durstewitz, Existence of n-cycles and border-collision bi-furcations in piecewise-linear continuous maps with applications to recurrent neural networks, Nonlinear dynamics, Vol. 101, 1037-1052, 2020.[35] Z. Monfared, D. Durstewitz, Transformation of ReLU-based recurrent neural networks from discrete-time to continuous-time, Proceedings of Machine Learning Research (ICML), Vol. 119, 6999-7009, 2020.[36] Z. Monfared, F. Omidi and Y. Qaseminezhad Raeini, Investigating the effect of pyroptosis on the slow CD4+ T cell depletion in HIV-1 infection, by dynamical analysis of its discontinuous mathematical model, International Journal of Biomathematics, Vol. 13, No. 06, 2050041, 2020.[37] M. Oestreich, N. Hinrichs and K. Popp, Bifurcation and stability analysis for a non-smooth friction oscillator, Archive of Applied Mechanics, vol. 66, pp. 301-314, 1996.[38] M. Pascal, Sticking and nonsticking orbits for a two-degree-of-freedom oscillator excited by dry friction and harmonic loading , Nonlinear Dynamics, vol. 77, pp. 267-276, 2014.[39] A. Stefanski, J. Wojewoda and K. Furmanik, Experimental and numerical analysis of self-excited friction oscillator , Chaos Solitons and Fractals, vol. 12, no. 9, pp. 1691-1704, 2001.[40] J. J. Sun, W. Xu and Z. F. Lin, Research on the reliability of friction system under combined additive and multiplicative random excitations, Communications in nonlinear science and numerical simulation, vol.54, pp.1-12, 2018.[41] T.G. Sitharam, Advanced foundation engineering, Indian Institute of Science, Bangalore, 2013.[42] Y-R. Wang, K-E. Hung, Damping effect of pendulum Tuned mass damper on vibration of two-dimensional rigid body, International journal of structural staibility and dynamics, 15, 02, 1450041, 2015.
3
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4
ORIGINAL_ARTICLE
On extended Real Valued Quasi-Concave Functions
In this paper, we first study the non-positive decreasing and inverse co-radiantfunctions defined on a real locally convex topological vector space X. Next, we characterize non-positive increasing, co-radiant and quasi-concave functions over X. In fact, we examine abstract concavity, upper support set and superdifferential of this class of functions by applying a type of duality. Finally, we present abstract concavity of extended real valued increasing, co-radiant and quasi-concave functions.
https://jmmrc.uk.ac.ir/article_3046_cae68e7dd5f061400741f34b3984d1a5.pdf
2021-10-01
163
180
10.22103/jmmrc.2021.17976.1158
Abstract concavity
Duality
Co-radiant function
Quasi-concave function
Upper support set
Somayeh
Mirzadeh
mirzadeh@hormozgan.ac.ir
1
Department of Mathematics, Hormozgan University, Bandar Abbas, Iran
LEAD_AUTHOR
Samaneh
Bahrami
s_bahrami53@yahoo.com
2
Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
AUTHOR
[1] M.H. Daryaei and H. Mohebi, Abstract convexity of extended real valud ICR functions, Optimization, 62(6) (2013), 835-855.
1
[2] A.R. Doagooei and H. Mohebi, Monotonic Analysis over ordered topological vector spaces: IV, Journal of Global Optimization, 45(3) (2009), 355-369.
2
[3] J. Dutta, J.E. Martınez-Legaz and A.M. Rubinov, Monotonic analysis over cones: I, Optimization, 53(2) (2004), 165-177.
3
[4] J. Dutta, J.E. Martınez-Legaz and A.M. Rubinov, Monotonic analysis over cones: II, Optimization, 53(5-6) (2004), 529-547.
4
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5
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6
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7
[8] S. Mirzadeh and H. Mohebi, Abstract concavity of increasing co-radiant and quasi-concave functions with applications in mathematical economics, Journal of Optimization Theory and Applications, 169(2) (2016), 443- 472.
8
[9] H. Mohebi and H. Sadeghi, Monotonic analysis over ordered topological vector spaces: I, Optimization, 56(3) (2007), 305-321.
9
[10] H. Mohebi and H. Sadeghi, Monotonic analysis over ordered topological vector spaces II, Optimization, 58(2) (2009), 241-249.
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14