1
|
Alcantud JCR, Khameneh AZ, Kilicman A. Aggregation of infinite chains of intuitionistic fuzzy sets and their application to choices with temporal intuitionistic fuzzy information. Inf Sci (N Y) 2020. [DOI: 10.1016/j.ins.2019.12.008] [Citation(s) in RCA: 58] [Impact Index Per Article: 14.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
2
|
Abdullahi A, Shohaimi S, Kilicman A, Hafiz Ibrahim M, Salari N. Stochastic SIS Modelling: Coinfection of Two Pathogens in Two-Host Communities. Entropy (Basel) 2019; 22:e22010054. [PMID: 33285829 PMCID: PMC7516484 DOI: 10.3390/e22010054] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Revised: 11/15/2019] [Accepted: 11/21/2019] [Indexed: 01/26/2023]
Abstract
A pathogen can infect multiple hosts. For example, zoonotic diseases like rabies often colonize both humans and animals. Meanwhile, a single host can sometimes be infected with many pathogens, such as malaria and meningitis. Therefore, we studied two susceptible classes S 1 ( t ) and S 2 ( t ) , each of which can be infected when interacting with two different infectious groups I 1 ( t ) and I 2 ( t ) . The stochastic models were formulated through the continuous time Markov chain (CTMC) along with their deterministic analogues. The statistics for the developed model were studied using the multi-type branching process. Since each epidemic class was assumed to transmit only its own type of pathogen, two reproduction numbers were obtained, in addition to the probability-generating functions of offspring. Thus, these, together with the mean number of infections, were used to estimate the probability of extinction. The initial population of infectious classes can influence their probability of extinction. Understanding the disease extinctions and outbreaks could result in rapid intervention by the management for effective control measures.
Collapse
Affiliation(s)
- Auwal Abdullahi
- Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia; (A.A.); (A.K.)
- Department of Mathematics and Computer Science, Federal University Kashere, Kashere 771103, Nigeria
| | - Shamarina Shohaimi
- Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia; (A.A.); (A.K.)
- Department of Biology, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia;
- Correspondence: ; Tel.: +60-192-747-525
| | - Adem Kilicman
- Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia; (A.A.); (A.K.)
- Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
| | - Mohd Hafiz Ibrahim
- Department of Biology, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia;
| | - Nader Salari
- Department of Biostatistics, School of Public Health, Kermanshah University of Medical Sciences, 6715847141 Kermanshah, Iran;
| |
Collapse
|
3
|
Abdullahi A, Shohaimi S, Kilicman A, Ibrahim MH. Stochastic models in seed dispersals: random walks and birth-death processes. J Biol Dyn 2019; 13:345-361. [PMID: 31056007 DOI: 10.1080/17513758.2019.1605003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2018] [Accepted: 04/01/2019] [Indexed: 06/09/2023]
Abstract
Seed dispersals deal with complex systems through which the data collected using advanced seed tracking facilities pose challenges to conventional approaches, such as empirical and deterministic models. The use of stochastic models in current seed dispersal studies is encouraged. This review describes three existing stochastic models: the birth-death process (BDP), a 2 dimensional ( 2D ) symmetric random walks and a 2D intermittent walks. The three models possess Markovian property, which make them flexible for studying natural phenomena. Only a few of applications in ecology are found in seed dispersals. The review illustrates how the models are to be used in seed dispersals context. Using the nonlinear BDP, we formulate the individual-based models for two competing plant species while the cover time model is formulated by the symmetric and intermittent random walks. We also show that these three stochastic models can be formulated using the Gillespie algorithm. The full cover time obtained by the symmetric random walks can approximate the Gumbel distribution pattern as the other searching strategies do. We suggest that the applications of these models in seed dispersals may lead to understanding of many complex systems, such as the seed removal experiments and behaviour of foraging agents, among others.
Collapse
Affiliation(s)
- A Abdullahi
- a Institute for Mathematical Research , Universiti Putra Malaysia , Serdang , Selangor , Malaysia
- b Department of Mathematics and Computer Science , Federal University Kashere , Kashere , Nigeria
| | - S Shohaimi
- a Institute for Mathematical Research , Universiti Putra Malaysia , Serdang , Selangor , Malaysia
- c Department of Biology , Universiti Putra Malaysia , Serdang , Selangor , Malaysia
| | - A Kilicman
- a Institute for Mathematical Research , Universiti Putra Malaysia , Serdang , Selangor , Malaysia
- d Department of Mathematics , Universiti Putra Malaysia , Serdang , Selangor , Malaysia
| | - M H Ibrahim
- c Department of Biology , Universiti Putra Malaysia , Serdang , Selangor , Malaysia
| |
Collapse
|
4
|
Zahedi Khameneh A, Kilicman A. A fuzzy majority-based construction method for composed aggregation functions by using combination operator. Inf Sci (N Y) 2019. [DOI: 10.1016/j.ins.2019.07.090] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
5
|
Natiq H, Said MRM, Al-Saidi NMG, Kilicman A. Dynamics and Complexity of a New 4D Chaotic Laser System. Entropy (Basel) 2019; 21:e21010034. [PMID: 33266750 PMCID: PMC7514140 DOI: 10.3390/e21010034] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Revised: 12/26/2018] [Accepted: 01/02/2019] [Indexed: 11/21/2022]
Abstract
Derived from Lorenz-Haken equations, this paper presents a new 4D chaotic laser system with three equilibria and only two quadratic nonlinearities. Dynamics analysis, including stability of symmetric equilibria and the existence of coexisting multiple Hopf bifurcations on these equilibria, are investigated, and the complex coexisting behaviors of two and three attractors of stable point and chaotic are numerically revealed. Moreover, a conducted research on the complexity of the laser system reveals that the complexity of the system time series can locate and determine the parameters and initial values that show coexisting attractors. To investigate how much a chaotic system with multistability behavior is suitable for cryptographic applications, we generate a pseudo-random number generator (PRNG) based on the complexity results of the laser system. The randomness test results show that the generated PRNG from the multistability regions fail to pass most of the statistical tests.
Collapse
Affiliation(s)
- Hayder Natiq
- Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang 43000, Malaysia
- The Branch of Applied Mathematics, Applied Science Department, University of Technology, Baghdad 10075, Iraq
| | - Mohamad Rushdan Md Said
- Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang 43000, Malaysia
- Malaysia-Italy Centre of Excellence for Mathematical Science, Universiti Putra Malaysia, UPM Serdang 43000, Malaysia
- Department of Mathematics, Universiti Putra Malaysia, UPM Serdang 43000, Malaysia
- Correspondence:
| | - Nadia M. G. Al-Saidi
- The Branch of Applied Mathematics, Applied Science Department, University of Technology, Baghdad 10075, Iraq
| | - Adem Kilicman
- Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang 43000, Malaysia
- Department of Mathematics, Universiti Putra Malaysia, UPM Serdang 43000, Malaysia
| |
Collapse
|
6
|
Affiliation(s)
| | - Adem Kilicman
- Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, Malaysia
- Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, Malaysia
| | - Abdul Razak Salleh
- School of Mathematical Sciences, Universiti Kebangsaan Malaysia, Selangor, Malaysia
| |
Collapse
|
7
|
Kilicman A, Borgohain S. Some new lacunary statistical convergence with ideals. J Inequal Appl 2017; 2017:15. [PMID: 28111513 PMCID: PMC5222947 DOI: 10.1186/s13660-016-1284-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/29/2016] [Accepted: 12/23/2016] [Indexed: 06/06/2023]
Abstract
In this paper, the idea of lacunary [Formula: see text]-statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary [Formula: see text]-statistical convergence with lacunary [Formula: see text]-summable sequences. Moreover, we study the [Formula: see text]-lacunary statistical convergence in probabilistic normed space and discuss some topological properties.
Collapse
Affiliation(s)
- Adem Kilicman
- Department of Mathematics, University Putra Malaysia, Serdang, 43400 Selangor, Malaysia
| | - Stuti Borgohain
- Department of Mathematics, University Putra Malaysia, Serdang, 43400 Selangor, Malaysia
- Department of Mathematics, Indian Institute of Technology, Bombay, Powai, 400076 Mumbai, India
| |
Collapse
|
8
|
Dutta H, Kilicman A, Altun O. Topological properties of some sequences defined over 2-normed spaces. Springerplus 2016; 5:1974. [PMID: 27900239 PMCID: PMC5108750 DOI: 10.1186/s40064-016-3646-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/27/2016] [Accepted: 11/03/2016] [Indexed: 11/10/2022]
Abstract
The paper investigates some classes of real number sequences over 2-normed spaces defined by means of Orlicz functions, a bounded sequence of strictly positive real numbers, a multiplier and a normal paranormed sequence space. Relevant properties of such classes have been investigated. Moreover, relationships among different such classes of sequences have also been studied under various parameters and conditions. Finally, the spaces are investigated for some other useful properties. The conclusion section provides many interesting facts for further research.
Collapse
Affiliation(s)
- Hemen Dutta
- Department of Mathematics, Gauhati University, Guwahati, 781014 India
| | - Adem Kilicman
- Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), 43400 Serdang, Selangor Malaysia
| | - Omer Altun
- Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), 43400 Serdang, Selangor Malaysia
| |
Collapse
|
9
|
|
10
|
Ebrahimzadeh M, Ibrahim NA, Jemain AA, Kilicman A. Claim Dependence Induced by Common Effects in Hierarchical Credibility Models. COMMUN STAT-THEOR M 2013. [DOI: 10.1080/03610926.2011.625487] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
11
|
Toutounian F, Tohidi E, Kilicman A. Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications. Abstract and Applied Analysis 2013; 2013:1-11. [DOI: 10.1155/2013/198926] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
This paper introduces Fourier operational matrices of differentiation and transmission for solving high-order linear differential and difference equations with constant coefficients. Moreover, we extend our methods for generalized Pantograph equations with variable coefficients by using Legendre Gauss collocation nodes. In the case of numerical solution of Pantograph equation, an error problem is constructed by means of the residual function and this error problem is solved by using the mentioned collocation scheme. When the exact solution of the problem is not known, the absolute errors can be computed approximately by the numerical solution of the error problem. The reliability and efficiency of the presented approaches are demonstrated by several numerical examples, and also the results are compared with different methods.
Collapse
Affiliation(s)
- F. Toutounian
- Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
- Center of Excellence on Modelling and Control Systems, Ferdowsi University of Mashhad, Mashhad, Iran
| | - Emran Tohidi
- Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
| | - A. Kilicman
- Department of Mathematics, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia
| |
Collapse
|
12
|
M. Abd-Elhafiez W, S. Mohammed U, Kilicman A. On a high performance image compression technique. ScienceAsia 2013; 39:416. [DOI: 10.2306/scienceasia1513-1874.2013.39.416] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
|
13
|
Tohidi E, Pasban A, Kilicman A, Noghabi SL. An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems. Abstract and Applied Analysis 2013; 2013:1-7. [DOI: 10.1155/2013/357931] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called linear combination property of intervals. After this stage, the linearized dynamical system is transformed into a multi domain dynamical system via computational interval partitioning. Moreover, the integral form of this multidomain dynamical system is considered. Collocating these constraints at the Legendre Gauss Lobatto (LGL) points together with using the Legendre Gauss Lobatto quadrature rule for approximating the involved integrals enables us to transform the basic OCPs into the associated nonlinear programming problems (NLPs). In all parts of this procedure, the associated control and state functions are approximated by piecewise constants and piecewise polynomials, respectively. An illustrative example is provided for confirming the accuracy and applicability of the proposed idea.
Collapse
Affiliation(s)
- Emran Tohidi
- Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran
| | - Atena Pasban
- Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran
| | - A. Kilicman
- Department of Mathematics, Universiti Putra Malaysia (UPM), 43400 Serdang, Malaysia
| | - S. Lotfi Noghabi
- Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
| |
Collapse
|
14
|
Tohidi E, Soleymani F, Kilicman A. Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems. Abstract and Applied Analysis 2013; 2013:1-9. [DOI: 10.1155/2013/535979] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
The idea of approximation by monomials together with the collocation technique over a uniform mesh for solvingstate-space analysisandoptimal controlproblems (OCPs) has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions.
Collapse
Affiliation(s)
- Emran Tohidi
- Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran
| | - F. Soleymani
- Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran
| | - Adem Kilicman
- Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Malaysia
| |
Collapse
|
15
|
|