Open Journal of mathematical Sciences (OMS)

Abstract: Motivated by Euler-Goldbach and Shallit-Zikan theorems, we introduce zeta-one functions with infinite sums of $n^{s}\pm1$ as an analogy of the Riemann zeta function. Then we compute values of these functions at positive even integers by the residue theorem.

Abstract: In this article, we focus on developing new results regarding normed quasilinear spaces. We provide a definition for soft homogenized quasilinear spaces and obtain some related results. Furthermore, we explore the floor of soft normed quasilinear spaces. Using some soft linearity and soft quasilinearity methods, we derive new results and examples. Finally, we also obtain some new consequences that we believe will facilitate the development of quasilinear functional analysis in a soft inner product quasilinear space.

Abstract: The aim of this paper is to introduce and study BiHom-associative dialgebras. We give various constructions and study their connections with BiHom-Leibniz algebras and BiHom-Poisson dialgebras. Next, we discuss the central extensions of BiHom-associative dialgebras and we describe the classification of \(n\)-dimensional BiHom-associative dialgebras for \(n\leq 4\).

Abstract: We construct the concrete categories \(\mathbf{I\text{-}Loc}\) and \(\mathbf{\mathfrak h\text{-}Loc}\) over the category \(\mathbf{Loc}\) of locales and we deduce that they are topological categories, where \(\mathbf I\) and \(\mathfrak h\) denote respectively the classes of interior and \(h\) operators of the category \(\mathbf{Loc}\) of locales.

Abstract: We consider Gibbs’ definition of chemical equilibrium and connect it with dynamic equilibrium, in terms of no substance formed. We determine the activity coefficient as a function of temperature and pressure, in reactions with or without interaction of a solvent, incorporating the error terms from Raoult’s Law and Henry’s Law, if necessary. We compute the maximal reaction paths and apply the results to electrochemistry, using the Nernst equation.

Abstract: In this paper, we interested in Wilker inequalities. We provide finer bounds than known previous. Moreover, bounds are obtained for the following trigonometric function
\[g_n(x) = \left(\frac{\sin(x)}{x}\right)^2 \left( 1 – \frac{2\left(\frac{2 x}{\pi}\right)^{2n+2}}{1-(\frac{2x}{\pi})^2}\right) +\frac{\tan(x)}{x}, \ n\geq 0.\]

Abstract: In this investigation, we aim to investigate the novel exact solutions of nonlinear partial differential equations (NLPDEs) arising in electrical engineering via the -expansion method. New acquired solutions are kink, particular kink, bright, dark, periodic combined-dark bright and combined-dark singular solitons, and hyperbolic functions solutions. The achieved distinct types of solitons solutions contain critical applications in engineering and physics. Numerous novel structures (3D, contour, and density plots) are also designed by taking the appropriate values of involved parameters. These solutions express the wave show of the governing models, actually.

Abstract:In this work, generalized Euler’s \(\Phi_w\)-function of edge weighted graphs is defined which consists of the sum of the Euler’s \(\varphi\)-function of the weight of edges of a graph and we denote it by \(\Phi_w(G)\) and the general form of Euler’s \(\Phi_w\)-function of some standard edge weighted graphs is determined. Also, we define the divisor sum \(T_{k_w}\)-function \(T_{k_w}(G)\) of the graph \(G\), which is counting the sum of the sum of the positive divisor \(\sigma_k\)-function for the weighted of edges of a graph \(G\). It is determined a relation between generalized Euler’s \(\Phi_w\)-function and generalized divisor sum \(T_{k_w}\)-function of edge weighted graphs.

Abstract: A continuous two-step block method with two hybrid points for the numerical solution of first order ordinary differential equations is proposed. The approximate solution in form of power series and its first ordered derivative are respectively interpolated at the point \(x=0\) and collocated at equally spaced points in the interval of consideration. The application of the method involves using the main scheme derived together with the additional schemes simultaneously to obtain the solution to the problem at the grid points. The analysis of the method and the results obtained from the examples considered show that the method is consistent, zero-stable, convergent and of high accuracy.

Abstract: In this paper, we use the \(\varphi ^{6}\)-model expansion method to construct the traveling wave solutions for the reaction-diffusion equation. The method of \(\varphi ^{6}\)-model expansion enables the explicit retrieval of a wide variety of solution types, such as bright, singular, periodic, and combined singular soliton solutions. Kink-type solitons, also known as topological solitons in the context of water waves, are another type of solution that can be explicitly retrieved. This study’s results might enhance the equation’s nonlinear dynamical properties. The method proposes a practical and efficient method for solving a sizable class of nonlinear partial differential equations. The dynamical features of the data are explained and highlighted using exciting graphs.

Abstract: In this paper, we introduce the notion of interval neutrosophic ideals in subtraction algebras. Also, introduce the intersection and union of interval neutrosophic sets in subtraction algebras. We prove intersection of two-interval neutrosophic ideals is also an interval neutrosophic ideal. Some exciting properties and results based on such an ideal are discussed. Moreover, we define the homomorphism and homomorphism of interval neutrosophic sets. We prove the image of an interval neutrosophic subalgebra is also an interval neutrosophic sub-algebra.

Abstract: We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one extra free parameter to them. In particular, we generalize generating functions for the continuous \(q\)-ultraspherical/Rogers, little \(q\)-Laguerre/Wall, and \(q\)-Laguerre polynomials. Depending on what type of orthogonality these polynomials satisfy, we derive corresponding definite integrals, infinite series, bilateral infinite series, and \(q\)-integrals.

Abstract: We prove that if the frame \(S\) is decaying surface non-radiating, in the sense of Definition 1, then if \(\left(\rho,\overline{J}\right)\) is analytic, either \(\rho=0\) and \(\overline{J}=\overline{0}\), or \(S\) is non-radiating, in the sense of [1]. In particularly, by the result there, the charge and current satisfy certain wave equations in all the frames \(S_{\overline{v}}\) connected to \(S\) by a real velocity vector \(\overline{v}\), with \(|\overline{v}|

Abstract:Closed-form expressions are established for dimensionless long-tome solutions of some mixed initial-boundary value problems. They correspond to three isothermal unsteady motions of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure. The fluid motion, between infinite horizontal parallel flat plates, is induced by the lower plate that applies time-dependent shear stresses to the fluid. As a check of the obtained results, the similar solutions corresponding to the classical incompressible Maxwell fluids performing same motions are recovered as limiting cases of present solutions. Finally, some characteristics of fluid motion as well as the influence of pressure-viscosity coefficient on the fluid motion are graphically presented and discussed.

Abstract:Let \(S\) be a dominating set of a graph \(G\). The set \(S\) is called a pendant dominating set of \(G\) if the induced subgraph of \(S\) contains a minimum of one node of degree one. The minimum cardinality of the pendant dominating set in \(G\) is referred to as the pendant domination number of \(G\), indicated by \(\gamma_{pe}(G)\). This article analyzes the effect of \(\gamma_{pe}(G)\) when an arbitrary node or edge is removed.

Abstract:In this paper, we have proposed new windmill graph, that is Basava wheel windmill graph. The Basava wheel windmill graph \(W^{(m)}_{n+1}\) is the graph obtained by taking \(m\geq 2\) copies of the graph \(K_1+W_{n}\) for \(n\geq 4\) with a vertex \(K_1\) in common. Inspired by recent work on topological indices, proposed new degree-based topological indices namely, general \(SK_{\alpha}\) and \(SK^{\alpha}_1\) indices of a graph \(G\). We have obtained first and second Zagreb index, F-index, first and second hyper-Zagreb index, harmonic index, Randi\(\acute{c}\) index, general Randi\(\acute{c}\) index, sum connectivity index, general sum connectivity index, atom-bond connectivity index, geometric-arithmetic index, Symmetric division deg index, Sombor index, SK indices, general \(SK_{\alpha}\) and \(SK^{\alpha}_1\) indices of Basava wheel windmill graph. Further, we have computed exact values of these topological indices of chloroquine, hydroxychloroquine and remdesiver.

Abstract:Our primary purpose is to compute explicitly traces of the Dirichlet forms related to Feller’s one-dimensional diffusions on countable sets via Fukushima’s method. For discrete measures, the obtained trace form can be described as a Dirichlet form on the graph.

Abstract:In this paper, closed forms of the sum formulas \(\sum\limits_{k=0}^{n}x^{k}W_{mk+j}^{3}\) for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.

Abstract:We construct a class of quadratic irrationals having continued fractions of period \(n\geq2\) with `small’ partial quotients for which specific integer multiples have periodic continued fractions with the length of the period being \(1\), \(2\) or \(4\), and with ‘large’ partial quotients. We then show that numbers in the period of the new continued fraction are functions of the numbers in the periods of the original continued fraction. We also show how polynomials arising from generalizations of these continued fractions are related to Chebyshev and Fibonacci polynomials and, in some cases, have hyperbolic root distribution.

Abstract:In this study, we focus on the slip effects on the peristaltic unsteady flow of magnatohydromagnetic Jeffrey fluid in a flow passage with non-conducting and flexible boundary walls. The effect of the magnetic field with varying thermal conductivity is taken under the influence of heat transfer analysis. The dimensionless system of PDEs is solved analytically, and the obtained results are computed for the temperature, pressure drop, the axial pressure gradient, axial velocity, and then these results are discussed for different values of the physical parameters of our interest. For the stream functions, the contour plots are also obtained which indicates the exact flow behavior within the flow channel, and the effects of the physical parameters on Jeffery fluid within the flow channel are discussed briefly. Our results indicate that the heat transfer coefficient decreases with an increase in thermal slip and velocity slip parameters. Furthermore, it shows that the size of the trapped bolus is greater for the inclined magnetic field as compared to the transverse magnetic field.

Abstract:This paper solves implicit differential equations involving Hilfer-Katugampola fractional derivatives with nonlocal, boundary, and impulsive conditions. In addition, some sufficient conditions are formulated for the existence and uniqueness of solutions to the given problem, and Hyers-Ulam stability results are also presented.

Abstract:In this research paper, the authors studied some problems related to harmonic summability of double Fourier series on Nörlund summability method. These results constitute substantial extension and generalization of related work of Moricz [1] and Rhodes et al., [2]. We also constructed a new result on \((N,p^{(1)}_b,p^{(2)}_a)\) by regular N\”orlund method of summability.

Abstract:The aim of this paper is to present an optimal control problem to reduce the MDR-TB (multidrug-resistant tuberculosis) and XDR-TB (extensively drug-resistant TB) cases, using controls in these compartments and controlling reinfection/reactivation of the bacteria. The model used studies the efficacy of the tuberculosis treatment taking into account the influence of HIV/AIDS and diabetes, and we prove the global stability of the disease-free equilibrium point based on the behavior of the basic reproduction number. Various control strategies are proposed with the combinations of controls. We show the existence of optimal control using Pontryagin’s maximum principle. We solve the optimality system numerically with an algorithm based on forward/backward Runge-Kutta method of the fourth-order. The numerical results indicate that the implementation of the strategy that activates all controls and of type I (starting with the highest controls) is the most cost-effective of the strategies studied. This strategy reduces significantly the number of MDR-TB and XDR-TB cases in all sub-populations, which is an important factor in combating tuberculosis and its resistant strains.

Abstract:In particular, we study repeated integrals and recurrent integrals. For each of these integrals, we develop reduction formulae for both the definite as well as indefinite form. These reduction formulae express these repetitive integrals in terms of single integrals. We also derive a generalization of the fundamental theorem of calculus that expresses a definite integral in terms of an indefinite integral for repeated and recurrent integrals. From the recurrent integral formulae, we derive some partition identities. Then we provide an explicit formula for the \(n\)-th integral of \(x^m(\ln x)^{m’}\) in terms of a shifted multiple harmonic star sum. Additionally, we use this integral to derive new expressions for the harmonic sum and repeated harmonic sum.

Abstract:In this paper, we analyze a new continuous-time epidemic model including nonlinear delay differential equations by using parameters and functions selected from a class of intervals whose algebraic basis is based on quasilinear spaces. The main idea in the model’s generic structure is based on uncertainties in the values of parameters and functions forming the model. Therefore, using an interval coefficient approach rather than the exact value of parameters and functions that define transmissions between the compartments in the population dynamics will better represent the reality. Furthermore, preferring such an approach provides more realistic scenarios for temporal and stability dynamics of a population exposed to a disease. In this study, the quasilinear space is defined to explain the mathematical background of the interval approach in the fictional chain of the model. Next, descriptions belonging to the introduced model are included. After this compartmental system is presented as two systems formed by the lower and upper endpoints of the intervals determining parameters and functions, local and global dynamics related to stabilities of the models are analyzed separately for each. Then, using some interval analysis and functional analysis methods, these results are combined, and a conclusion about the stability of the proposed epidemic model has been reached. Alongside, the performance of the proposed approach is demonstrated by a visual simulation.

Abstract:The inverse sum indeg index \(ISI(G)\) of a graph is equal to the sum over all edges \(uv\in E(G)\) of weights \(\frac{d_{u}d_{v}}{d_{u}+d_{v}}\). This paper presents the relation between the inverse sum indeg index and the chromatic number. The bounds for the spectral radius of the inverse sum indeg matrix and the inverse sum indeg energy are obtained. Additionally, the Nordhaus-Gaddum-type results for the inverse sum indeg index, the inverse sum indeg energy and the spectral radius of the inverse sum index matrix are given.

Abstract:Analytical expressions for the steady-state solutions of modified Stokes’ second problem of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are determined when the gravity effects are considered. Fluid motion is generated by a flat plate that oscillates in its plane. We discuss similar solutions for the simple Couette flow of the same fluids. Obtained results can be used by the experimentalists who want to know the required time to reach the steady or permanent state. Furthermore, we discuss the accuracy of results by graphical comparisons between the solutions corresponding to the motion due to cosine oscillations of the plate and simple Couette flow. Similar solutions for incompressible Newtonian fluids with power-law dependence of viscosity on the pressure performing the same motions and some known solutions from the literature are obtained as limiting cases of the present results. The influence of pertinent parameters on fluid motion is graphically underlined and discussed.

Abstract: In analogy with the classical theory of filters, for finitely complete or small categories, we provide the concepts of filter, \(\mathfrak{G}\)-neighborhood (short for “Grothendieck-neighborhood”) and cover-neighborhood of points of such categories, to study convergence, cluster point, closure of sieves and compactness on objects of that kind of categories. Finally, we study all these concepts in the category \(\mathbf{Loc}\) of locales.