Journal of Mathematics

The damped parametric driven nonlinear pendulum equation/oscillator (NPE), also known as the damped disturbed NPE, is examined, along with some associated oscillators for arbitrary angles with the vertical pivot. For analyzing and solving the current pendulum equation, we reduce this equation to the damped Duffing equation (DDE) with variable coefficients. After that, the DDE with variable coefficients is divided into two cases. In the first case, two analytical approximations to the damped undisturbed NPE are obtained. The first approximation is determined using the ansatz method while the second one is derived using He’s frequency formulation. In the second case, i.e., the damped disturbed NPE, three analytical approximations in terms of the trigonometric and Jacobi elliptic functions are derived and discussed using the ansatz method. The semianalytical solutions of the two mentioned cases are graphically compared with the 4^th-order Runge–Kutta (RK4) approximations. In addition, the maximum error for all the derived approximations is estimated as compared with the RK4 approximation. The proposed approaches as well as the obtained solutions may greatly help in understanding the mysteries of various nonlinear phenomena that arise in different scientific fields such as fluid mechanics, plasma physics, engineering, and electronic chips.

The effects of reduced gravity on the periodic behavior of convective heat transfer characteristics of fluid flow along the magnetized heated cone embedded in porous medium is studied in the current contribution. The mathematical form of the nonlinear partial differential equations subject to the boundary conditions for the proposed unsteady model is presented. By employing appropriate dimensionless quantities, the mathematical equations are transformed into dimensionless form to get the numerical solutions of the proposed model. The dimensionless form is further condensed to a form that is more straightforward for smooth numerical computations. Later, large simulations are run using the implicit finite difference method for appropriate range of parameters values included in the flow model. The effect of reduced gravity parameter , the Richardson parameter or mixed convection parameter , the Prandtl number Pr, and the porosity parameter , on chief physical quantities, that is, velocity profile, temperature distribution, magnetic intensity, transient skin friction, transient rate of heat transfer, and transient current density are simulated and highlighted graphically. Additionally, via careful examination and intentional discussion of physical reasoning, the physical impacts of various factors on the material qualities are examined. Applications that motivate the present work is the reduced gravity effects due to which the other nongravity forces such as thermal volume expansion, density difference, and magnetic field can induce the fluid motion.

Let and be a Banach space and its dual, respectively. In this paper, we study the relations between modulus of and modulus in and normal structure in , respectively. Among other results, we proved either , for any , or , for any , implies both and its dual have uniform normal structure.

In this paper, we propose a high-precision discrete scheme for the time-fractional diffusion equation (TFDE) with Caputo-Fabrizio type. First, a special discrete scheme of C-F derivative is used in time direction and a compact difference operator is used in space direction. Second, we discuss the convergence of the proposed method in discrete -norm and -norm. The convergence order of our discrete scheme is , where and are the temporal and spatial step sizes, respectively. The aim of this paper is to show that fractional operator without singular term is very useful for improving the accuracy of discrete scheme.

In this article, we adapt the edge-graceful graph labeling definition into block designs and define a block design with and as block-graceful if there exists a bijection such that the induced mapping given by is a bijection. A quick observation shows that every BIBD that is generated from a cyclic difference family is block-graceful when . As immediate consequences of this observation, we can obtain block-graceful Steiner triple system of order for all and block-graceful projective geometries, i.e., BIBDs. In the article, we give a necessary condition and prove some basic results on the existence of block-graceful BIBDs. We consider the case for Steiner triple systems and give a recursive construction for obtaining block-graceful triple systems from those of smaller order which allows us to get infinite families of block-graceful Steiner triple systems of order for . We also consider affine geometries and prove that for every integer and , where is an odd prime power or , there exists a block-graceful BIBD. We make a list of small parameters such that the existence problem of block-graceful labelings is completely solved for all pairwise nonisomorphic BIBDs with these parameters. We complete the article with some open problems and conjectures.

A novel method is presented for solving MADM under a sine trigonometric Pythagorean neutrosophic normal interval-valued set (ST-PyNSNIVS). An identifying feature of ST-PyNSNIVS is that it is a combination of PyNSIVS, PyNSS, and IVNSS. This article proposes a novel concept of ST-PyNSNIVWA, ST-PyNSNIVWG, ST-GPyNSNIVWA, and ST-GPyNSNIVWG. In addition, we acquired a flowchart and an algorithm that interact with MADM and are called ST-PyNSNIVWA, ST-PyNSNIVWG, ST-GPyNSNIVWA, and ST-GPyNSNIVWG, respectively. In addition to Euclidean and Hamming distances, we addressed new types of two distances in the suggested models, which are future expansions of real-life instances. The sine trigonometric aggregation operations were examined using the PyNSNIV set technique. They are more straightforward and practical, and you can arrive at the best option quickly. Consequently, the conclusions of the defined models are more accurate and closely correlated with . Our analysis shows that the investigated models are valid and useful by comparing them to some of the current models. As a final result of the study, some intriguing and enthralling findings are presented.