Well-posedness and exponential stability for a piezoelectric beams system with magnetic and thermal effects in the presence of past history

JPRM-Vol. 19 (2023), Issue 2, pp. 116 – 134 Open Access Full-Text PDF
Hassan Messaoudi, Houssem Eddine Khochemane, Abdelouaheb Ardjouni, Salah Zitouni
Abstract: In this article, we consider the one-dimensional system of piezoelectric beams with thermal and magnetic effects in the presence of an infinite memory term acting on the mechanical equation. Under appropriate assumptions on the kernel, we prove that the system is well-posed in the sense of semigroup and by constructing a suitable Lyapunov functional. We establish that the system is exponentially stable. Moreover,our result does not depend on any relationship between system parameters.
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Comparing Zagreb Indices of Rhombus Networks

JPRM-Vol. 19 (2023), Issue 2, pp. 96 – 115 Open Access Full-Text PDF
Abdul Aleem Mughal, Usman Ali, Taha Amjad
Abstract: The study of networks by using topological indices (TIs) have been significantly become a useful attention in the physicochemical properties of compounds, pharmacology and drug delivery in the field of experimental sciences. Thus, TIs help us to study the new networks and they also play an essential role in the study of the quantitative structure property and activity relationships. In this paper, we compute the connection number (CN) based Zagreb indices in the form of first general-Zagreb connection index (ZCI), generalized first, second, third and fourth ZCIs of two rhombus type networks such as rhombus oxide and rhombus silicate. In particularly, we also find the first, second, modified first, second, third and fourth ZCIs by using main results of the abovementioned general & generalized connection based Zagreb indices. In addition, a comparison between degree and CN based Zagreb indices is done with the help of their numerical values and graphical demonstration
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Characterizing Irregularity in Planar Graph Structures

JPRM-Vol. 19 (2023), Issue 2, pp. 72 – 95 Open Access Full-Text PDF
Abdul Aleem Mughal, Raja Noshad Jamil, Abaid ur Rehman Virk
Abstract: Face irregularity strength under ρ−labeling ξ with class (α1, β1, γ1) of plane graphs is a labeling from the set of graph elements into the set of integers, that is, ξ: {V ∪ E ∪ F} → {1, 2, 3, .., ρ}, such that the face weights are distinct at any stage in the graph labeling, that is, Wξ(α1,β1,γ1)(f) ̸= Wξ(α1,β1,γ1)(g), for any two faces f and g of the graph G. The face irregular strength of a plane graph G is the least possible integer ρ such that G admits face irregular ρ−labeling. In this research, authors have examined the exact tight lower bounds for the face irregular strength of generalized plane graphs under ρ−labeling of class (α1, β1, γ1) for vertex (1, 0, 0), edge (0, 1, 0), face (0, 0, 1), vertex-face (1, 0, 1), edge-face (0, 1, 1) and entire (1, 1, 1). Results are verified by examples.
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Translation Factorable (TF) Surfaces in Three-Dimensional Isotropic Space: Unveiling Future Prospects for Control Systems

JPRM-Vol. 19 (2023), Issue 2, pp. 60 – 71 Open Access Full-Text PDF
Brahim Medjahdi, Abdelakder Belhenniche, Hanifi Zoubir
Abstract: This article introduces the concept of translation-factorable surfaces in the isotropic space 𝕀3 and presents classification theorems for these surfaces based on their isotropic mean and isotropic Gaussian curvatures, considering both zero and nonzero values. Furthermore, an additional investigation is conducted to classify translation-factorable (TF) surfaces in 𝕀3 under the condition H2=K
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A solvable three dimensional system of difference equations of second order with arbitrary powers

JPRM-Vol. 19 (2023), Issue 2, pp. 37 – 59 Open Access Full-Text PDF
M. C. Benkara Mostefa, A. C¸ete, N. Touafek, Y. Yazlik
Abstract: The solvability in a closed form of the following three-dimensional system of difference equations of second order with arbitrary powers
where the initial values x_i, y_i, z_i, i=0,1 are non-zero real numbers and the parameters a,b,c,d,h, are real numbers, will be the subject of the present work. We will also provide the behavior of the solutions of some particular cases of our system.
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Open two-point Newton-Cotes integral inequalities for differentiable convex functions via Riemann-Liouville fractional integrals

JPRM-Vol. 19 (2023), Issue 2, pp. 24 – 36 Open Access Full-Text PDF
Hamida Ayed, Badreddine Meftah
Abstract: In this paper, some open two-point Newton-Cotes type integral inequalities for functions whose first derivatives are convex via Riemann-Liouville fractional integrals are established. Our finding generalize some already known results. In order to illustrate the efficiency of our main results, some applications are given.
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On f-Derivations in Residuated Lattices

JPRM-Vol. 19 (2023), Issue 2, pp. 17 – 23 Open Access Full-Text PDF
Mbarek Zaoui, Driss Gretete, Brahim Fahid
Abstract: In this paper, as a generalization of derivation in a residuated lattice, the notion of f-derivation for a residuated lattice is introduced and some related properties of isotone (resp. contractive) f-derivations and ideal f-derivations are investigated. Also, we define principal f-derivation and their properties. Finally, we define the notion of fixed point. In particular, as an application of ideal f-derivation in Heyting algebras, we obtain that the fixed point set is still a residuated lattice.
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Approximation of Fixed Point of Multivalued Mean Nonexpansive Mappings in CAT(0) spaces

JPRM-Vol. 19 (2023), Issue 2, pp. 1 – 16 Open Access Full-Text PDF
Mujahid Abbas, Khushdil Ahmad, Khurram Shabbir
Abstract: The aim of this paper is to present the convergence results to approximate the fixed points of multivalued mean nonexpansive mappings in CAT(0) spaces. Strong and ∆-convergence results are established for these mappings using F-iterative scheme. Moreover, a numerical example is given to show the convergence behavior of the iterative scheme for multivalued mean nonexpansive mappings. The results which we derived are generalization of many results existing in literature.
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