A fixed-point approach to a multi-group SEIRV epidemic model

JPRM-Vol. 18 (2022), Issue 2, pp. 144 – 151 Open Access Full-Text PDF
Amelia Bucur
Abstract: Epidemics was always great problems in the human history and mathematicians have been challenged to bring their contribution to the management of epidemics, by using their abstract concepts in studying and forecasting their evolution. Compartmental models, have been remarkable for analysis the spread of epidemics. This paper has three objectives: to purpose a multi-group SEIRV epidemic model for studying the spread of an epidemics, to present conditions of existence for a solution to the purposed generalized SEIRV model and an example of simulations. The principal conclusion is that, the theory of fixed points can be used for the analysis of epidemics. The results of this paper adapt the results obtained in (Bucur, 2022, in International Journal of Advance Study and Research Work (IJASRW) 5(11)) and in (Guran, Bota and Naseem, 2020, in Symmetry 12, 856) to a generalization of the SEIR model.
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Realizable degree sequences of inner dual graphs of benzenoid systems

JPRM-Vol. 18 (2022), Issue 2, pp. 125 – 143 Open Access Full-Text PDF
Faqir M. Bhatti, Hasan Baloch, Mehar Ali Malik, Rameez Ragheb
Abstract: An inner dual graph of a planar rigid benzenoid (hexagonal) system is a subgraph of the triangular lattice with the constraint that any two adjacent faces in the corresponding hexagonal system must be connected via an edge in the inner dual. The maximum degree of any vertex in an inner dual graph of a hexagonal system is 6. In contrast with the already existing algorithms in the literature that are used to check a given degree sequence to be graphically realizable, in this paper, we use a a simple technique to check the realizable degree sequences of inner dual graphs of benzenoid systems that form a rich class of molecular graphs in theoretical chemistry. We restrict the maximum degree to 3 and identify, by providing necessary and sufficient conditions on the values of α, β and γ, all the degree sequences of the form d = (3α, 2β, 1γ) that are graphically (inner dual of planar rigid hexagonal system) realizable. That is, we provide general constructions of the graphs (inner dual of planar rigid hexagonal system) realizing the degree sequences of the form d = (3α, 2β, 1γ).
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Algebraic integers of pure sextic extensions

JPRM-Vol. 18 (2022), Issue 2, pp. 112 – 124 Open Access Full-Text PDF
Antonio Aparecido de Andrade, Linara St´efani Facini,Livea Cichito Esteves
Abstract: Let K = Q(θ), where θ = √6 d, be a pure sextic field with d ̸= 1 a square free integer. In this paper, we characterize completely whether {1, θ, . . . , θ5} is an integral basis of K or do not. When d ̸≡ ±1, ±17, ±10, −15, −11, −7, −3, 5, 13(mod 36) we prove that K has a power integral basis. Furthermore, for the other cases we present an integral basis.
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Analysis of closed neighbourhood indices of some Networks-II

JPRM-Vol. 18 (2022), Issue 2, pp. 100 – 111 Open Access Full-Text PDF
B. Basavanagoud, Mahammad sadiq Sayyed
Abstract: Topological indices are extensively used for establishing relationship between the chemical structure and their physico-chemical properties. Motivated by chemical applications of topological indices in the QSPR/QSAR analysis, we introduce a new topological indices that we call, second BM Index and fourth BM Index, is denoted by BM2(G) and BM4(G). Also we introduce second and fourth BM polynomials and is denoted by BM2(G, x) and BM4(G, x). In this paper, BM2(G) and BM4(G) is tested with physico-chemical properties of octane isomers such as entropy, acentric factor, enthalpy of vaporization (HVAP) and standard enthalpy of vaporization (DHVAP) using the linear models. The BM2(G) and BM4(G) shows excellent correlation with these chemical properties. Specially, BM2(G) and BM4(G) highly correlates with acentric factor (coefficient of correlation 0.9906546 and 0.9783643). Furthermore, we obtain BM2(G), BM4(G) indices and BM2(G, x), BM4(G, x) polynomials of dominating oxide network, regular triangulate oxide network, H-Naphtalenic nanotubes and nanocones of molecular graphs
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New results on periodic solutions for a nonlinear fourth-order iterative differential equation

JPRM-Vol. 18 (2022), Issue 2, pp. 88 – 99 Open Access Full-Text PDF
Rabah Khemis, Ahl`eme Bouakkaz
Abstract: The key task of this paper is to investigate a nonlinear fourth-order delay differential equation. By virtue of the fixed point theory and the Green’s functions method, we establish some new results on the existence, uniqueness and continuous dependence on parameters of periodic solutions. In addition, an example is given to corroborate the validity of our main results. Up to now, no work has been carried out on this topic. So, the findings of this paper are new and complement the available works in the literature to some degree.
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Chen and Casorati curvature inequalities for the submanifolds of quaternionic Kaehler manifolds endowed with Ricci quarter-symmetric metric connection

JPRM-Vol. 18 (2022), Issue 2, pp. 72 – 87 Open Access Full-Text PDF
Mehraj Ahmad Lone, Umair Ali Wani
Abstract: In this paper, authors have established Chen’s inequalities for the submanifolds of quaternionic Kaehler manifolds characterized by Ricci quarter-symmetric metric connection. Other than these inequalities, generalized normalized Casorati curvature inequalities have been derived.
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A Novel Approach for the Visualization of Constrained Data using GC1 Bi-Cubic Functions

JPRM-Vol. 18 (2022), Issue 2, pp. 55 – 71 Open Access Full-Text PDF
Farheen Ibraheem, Ayesha Shakeel, Muhammad Bilal Riaz
Abstract: One of the fundamental issues in engineering, computer graphics, data visualization, interpolation and many more areas is to create a shape preserving surface from supplied data points. Data can be characterized as convex, monotone and positive. This research focuses on developing new smooth and efficient shape preserving schemes for convex, monotone and positive 3D data set positioned on a rectangular mesh. For this purpose, a GC1 continuous cubic function with two free parameters have been advanced to GC1 bicubic coons surface patches. There are eight free shape parameters in each rectangular patch which are constrained to ascertain these intrinsic data attributes that is convexity, positivity and monotonicity. The proposed interpolant governs the shape of data locally and data dependent constraints on shape parameters manage the shape preservation. Moreover, proposed scheme is verified and demonstrated graphically
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On the solutions of nonlinear Caputo–Fabrizio fractional partial differential equations arising in applied mathematics

JPRM-Vol. 18 (2022), Issue 2, pp. 42 – 54 Open Access Full-Text PDF
Ali Khalouta
Abstract: This paper proposes a new semi-analytical method known as the variational iteration transform method (VITM) to obtain the solutions of the nonlinear Caputo–Fabrizio fractional partial differential equations arising in applied mathematics. For nonlinear equations in general, there is no method that gives an exact solution and, therefore, only approximate analytical solutions can be derived by using procedures such as linearization or perturbation. This method is combined form of the Aboodh transform and the variational iteration method. The advantage of VITM is the simplicity of the computations and the non-requirement of linearization or smallness assumptions. Moreover, this method enables us to overcome the difficulties arising in identifying the general Lagrange multiplier. For further illustrations of the efficiency and reliability of VITM, some numerical applications are pesented. The numerical results showed that the proposed method is efficient and precise to obtain the solutions of nonlinear fractional partial differential equations.
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On Split Equilibrium and Fixed Point Problems for Finite Family of Bregman Quasi-Nonexpansive Mappings in Banach spaces

JPRM-Vol. 18 (2022), Issue 2, pp. 23 – 41 Open Access Full-Text PDF
H. A. Abass, O. K. Narain, K. O. Oyewole, U. O. Adiele
Abstract: In this paper, we introduce a trifunction split equilibrium problem using a generalized relaxed α-monotonicity in the framework of p-uniformly convex and uniformly smooth Banach spaces. We develop an iterative algorithm for approximating a common solution of split equilibrium problem and fixed point problem for finite family of Bregman quasi-nonexpansive mappings. Using our iterative algorithm, we state and prove a strong convergence theorem for approximating a common solution of the aforementioned problems. Our iterative scheme is design in such a way that it does not require any knowledge of the operator norm. We display a numerical example to show the applicability of our result. Our result extends and complements some related results in literature.
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Generalized Identities and Inequalities of Čebyšev and Ky Fan Type for ∇−convex function

JPRM-Vol. 18 (2022), Issue 2, pp. 1 – 22 Open Access Full-Text PDF
Faraz Mehmood , Asif R. Khan
Abstract: In the present article we establish three generalizations, first generalization is related to discrete Čebyšev identity for function of higher order ∇ divided difference with two independent variables and give its special case as a sequence of higher order ∇ divided difference. Moreover, we deduce results of discrete inequality of Čebyšev involving higher order ∇−convex function. The second and third generalizations are for integral Čebyšev and integral Ky Fan identities for function of higher order derivatives with two independent variables and discuss its inequalities using ∇−convex function. Generalized results give similar results of Pěcari´c’s article [23] and recapture some established results.
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