iosr-Jm   Volume-19 ~ Issue-6 ~ Nov. – Dec. 2023

Abstract :Fuzzy set 𝐴 is a subset of set 𝑆 with membership function 𝐴(𝑥) that has membership degree 𝛼∈[0,1]. Fuzzy numbers are needed to help overcome the uncertainty that occurs, so the idea of transforming ordinary differential equations into differential equations with fuzzy initial value problems to solve the problem. The transformation of ordinary differential equations into fuzzy differential equations is based on the definition of Hukuhara differential equations. The numerical solution analysis is compared with the fourth-order Runge-Kutta method. Based on the analysis, for 𝛼<1, the (2,2,2)-differentiable form is obtained which provides a solution that is in accordan......

Keywords : differential equations, eco-epidemiologi, fuzzy, fourth order Runge-Kutta, Hukuhara generalized derivativece.

[1]. Greenhalgh, D., Q. J. A Khan, And J. S Pettigrew. 2017. An Ecoepidemiological Predator–Prey Model Where Predators Distinguish Between Susceptible And Infected Prey. Mathematical Methods In The Applied Sciences, 40(1), 146–166.
[2]. Farekh, D. 2020. Modeling Of Biological Population Using Fuzzy Differential Equations: Fuzzy Predator-Prey Models And Numerical Solutions. M.Sc. Thesis In Mathematical Modelling, Faculty Of Graduate Studie, Palestine Technical University.
[3]. Zadeh, L.A. 1965. Fuzzy Set, Information And Control, 8(3), 338-353.
[4]. Mondal, P.K., S. Jana, P. Haldar, And T.K. Kar, Dynamical Behavior Of An Epidemic Model In A Fuzzy Transmission, International Journal Of Uncertainty, Fuzziness And Knowledge-Based Systems, 23(5), 2015, 651-665.
[5]. Verma, R., S. P. Tiwari And R. K. Upadhyay 2018. Fuzzy Modeling For The Spread Of Influenza Virus And Its Possible Control, Computational Ecology And Software, 8(1), Pp. 32–45

Abstract : In this paper, the paraconsistent propositional logic LG is presented, along with its semantic characterization. It is shown that LG's set of theorems corresponds to the set of valid existential graphs, GET, which turns out to be an extension of Peirce's Gamma system, without becoming Zeman's gamma-4 system. All evidence is presented in a complete, rigorous, and detailed manner. This result is generalized by constructing the paraconsistent system of existential graphs GET4, and its semantic-deductive characterization. Finally, Zeman's Gamma-4, Gamma-4.2, and Gamma-5 existential graph systems are proven to be paraconsistent.

Key Word: Existential graphics, paraconsistent logic, semantics of possible worlds, weak negation

[1]. Brady, G., & Trimble, T. (2000). A Categorical Interpretation Of C.S. Peirce's Propositional Logic Alpha. Journal Of Pure And Applied Algebra. Sec. 149, Pg 213-239.
[2]. Henkin, L. (1949), The Completeness Of The First Order Functional Calculus. The Journal Of Symbolic Logic, 14, 3, Pg 159–166.
[3]. Oostra, A. (2010), Peirce's Alpha Graphs Applied To Intuitionist Logic. Cuadernos De Sistemas Peirceana 2, Pg 25-60.
[4]. Oostra, A. (2011), Intuitionist Beta Existential Graphs. Cuadernos De Sistemaca Peirceana 3, Pg 53-78.
[5]. Oostra, A. (2012), Existential Range Graphics Applied To Some Intuitionistic Modal Logics. Notebooks Of Peircean Systematics 4, Pg 27-50.

Abstract : The boundary knot method is a simple boundary-type meshless method. Due to the use of non-singular general solutions rather than singular fundamental solutions, there is no need to consider the artificial boundary. It has the merits of purely meshless, easy to program, high solution accuracy and so on. In this paper, with some new classes of numerical experiments, we make some conclusions concerning the effectiveness of solving Helmholtztype problems with the boundary knot method.

Key Word: Boundary knot method, meshless method, non-singular general solution, Helmholtz equation

[1] FZ Wang, MN Khan, I Ahmad, H Ahmad, H Abu-Zinadah, YM Chu. Numerical Solution Of Traveling Waves In Chemical Kinetics: Time Fractional Fishers Equations. Fractals, 30(2), 2240051, 2022.
[2] J Liu, FZ Wang, S Nadeem. A New Type Of Radial Basis Functions For Problems Governed By Partial Differential Equations. Plos ONE, 18(11): E0294938, 2023.
[3] FZ Wang, MY Shao, JL Li, ZL Zhang. A Space-Time Domain RBF Method For 2D Wave Equations. Frontiers In Physics, 11:1241196, 2023.
[4] ZQ Zhang, FZ Wang, J Zhang. The Space-Time Meshless Methods For The Solution Of One-Dimensional Klein-Gordon Equations. Wuhan University Journal Of Natural Sciences, 27(4): 313-320, 2022.
[5] SW Kang, JM Lee, YJ Kang. Vibration Analysis Of Arbitrarily Shaped Membranes Using Non-Dimensional Dynamic Influence Function. Journal Of Sound And Vibration, 221(1): 117-132, 1996

Abstract : Consider a transformation T which is measurable and measure pre-serving from a measure space (X, β, ν) to itself on the circle group of one-dimensional torus, where ν is a non-negative countably set additive function and T is Ergodic. We consider the multiplication theory of uni-tary operation. Our work concerns the abelian group of the unit circle. We first prove that the set of all eigenvalues (spectrums) of T forms a subgroup of the unit circle. This result implies that the absolute value of every eigenvalue is a constant, every spectrum is simple and 1 is a simple spectrum. We next prove that T induces a linear operator on the complex measurable functions f for each measurable functionf and the transfor-mation T , defined by Tz = cz is not weak mixing when c is not a root of unity. Finally we prove that T is ergodic if and only if 1 is a simple spectrum.

[1]. Www.Math.Chalmers.Se
[2]. "Ergodic Theory", Springer Science And Business Media Llc, 2023.
[3]. Donald L. Cohn. "Measure Theory", Springer Science And Business Media Llc, 2013
[4]. Measure And Integration, 2016.
[5]. Walters Peter An Introduction To Ergodic Theory, Springer-Verley Berlin, Printed In Germany 1975.

Abstract : In this paper, the paraconsistent propositional logic LG is presented, along with its semantic characterization. It is shown that the set of theorems of LG corresponds to the set of valid existential graphs of Charles Sanders Peirce's Gamma system. All evidence is presented in a complete, rigorous, and detailed manner. This result is generalized by constructing the paraconsistent systems of existential graphs GEG[FX]I , and their semanticdeductive characterization. Finally, Zeman's Gamma-4, Gamma-4.2, and Gamma-5 existential graph systems are proven to be paraconsistent.

Keywords. Gamma existential graphs, paraconsistent logic, semantics

[1]. Batens, D, & De Clercq, K. (2004). A Rich Paraconsistent Extension Of Full Positive Logic. Logique Et Analyse, 47(185/188), 227–257.
[2]. Brady, G., And Trimble, T. (2000). To Categorical Interpretation Of CS. Peirce's Propositional Logic Alpha. Journal Of Pure And Applied Algebra. 149. 213-239.
[3]. Hughes, G And Cresswell, M (1968). An Introduction To Modal Logic. Methuen. London.
[4]. Oostra, A. (2010), Peirce's Alpha Graphs Applied To Intuitionist Logic. Cuadernos De Sistemas Peirceana 2. Pg 25-60.
[5]. Oostra, A. (2011), Intuitionist Beta Existential Graphs. Cuadernos De Sistemaca Peirceana 3. Pg 53-78..

Abstract : In this paper, examples of an operator satisfying generalized Browder’s theorem and generalized aBrowder’s theorem but not satisfy the properties (Bb), (Bab) and (Sb) are given. The necessary and sufficient condition for their equivalence with Browder’s theorem and generalized a-Browder’s theo- rem are found. The equivalence of property (Sab) with operators satisfying generalized a-Browder’s theorem is studied. And also, the equivalence rela- tion between properties (Sab) & (Bab), (Sab) & (Bb) and (Sab) & (Sb) are found

Keywords.Browder theorem, Generalized a-Browder’s theorem and properties (Sab).

[1] P. Aiena, Fredholm And Local Spectral Theory With Applications To Multipliers, Kluwer,2004.
[2] P. Aiena And L. O. Garcia, Generalized Browders Theorem And Svep, Mediterr. J. Math. 4 (2007), 215-228.
[3] P. Aiena And L. Miller, On Generalized A-Browder’s Theorem, Studia Math. 180 (2007), 285-299.
[4] P. Aiena, Variations On Weyl’s Theorems, J. Math. Anal. Appl 324 (2006), 566-579.
[5] M. Berkani, Restriction Of An Operator To The Range Of Its Powers, Studia Math.140 (2010), 163-175.

Abstract : Structures not subjected to any kind of load are rare to be seen in real life. This makes it necessary to consider the factors that can affect the stability of structures when subjected to different loadings. There are different loading histories for instance; step load, impulse load, periodic load, and moving load. This research investigated the effect of two factors; viscous damping and geometric imperfections on the dynamic buckling load of a model structure lying on a nonlinear cubic foundation trapped by a periodic load. Two-timing regular perturbation method........

Key words: Instability, Buckling load, Periodic load, Structure, Geometric imperfections, Damping

[1]. Adhikari, S. and Woodhouse, J. (2000). Identification of damping: part 1, viscous damping, Journal of Sound and Vibrations. 243(1), 43-61.
[2]. Ahmed, M. Reda and Gareth, L. Forbes (2012). Investigation into the dynamic effects of lateral buckling of high temperature/high pressure offshore pipelines. Proceedings of Acoustics.83, 21-2.
[3]. Ahmed, Naif Al-Khazraji, Samir, Ali Al-Rabii and Hameed, Shamkhi Al-Khazaali (2017). Improvement of dynamic buckling
behavior of intermediate aluminized stainless steel column. Al-Khwarizmi Engineering Journal. 13(1), 26-41.
[4]. Amazigo, J.C. and Ette, A.M. (1987). On a two-small parameter nonlinear differential equation with application to dynamic buckling. Journal of Nigerian Math-Soc. 6, 91-102.
[5]. Artem, H.S. and Aydin, L. (2010). Exact solution and dynamic buckling analysis of a beam-column system having the elliptic type
loading. Appl, Math, Mech Engl. Ed. 31(10), 1317-1324..