AppliedMath, Volume 4, Issue 2

This paper reviews some recent contributions by the authors and their associates and highlights a few innovative ideas, which led them to address some hard combinatorial network routing and ordered optimisation problems. The travelling salesman, whic...

At every point $p$ on a smooth $n$-manifold M there exist $\left(n+1\right)$ skew-symmetric tensor spaces spanning differential $r$-forms $\omega$ with $r=0,1,\cdots ,n$. Because $d\circ d$ is always zero where $d$ is the exterior differential, it follows that every exact $r$-fo...

The relationship between the inverse Langevin function and the proposed r₀-r₁-Lambert W function is defined. The derived relationship leads to new approximations for the inverse Langevin function with lower relative error bounds than comparable publi...

This paper describes various selected properties and features of negative binomial (NB) random variables, with special reference to NB2 (i.e., p = 2), and some generalizations to NBp (i.e., p ≥ 2), specifications. It presents new results (e.g., th...

The topic of efficiently finding the global minimum of multidimensional functions is widely applicable to numerous problems in the modern world. Many algorithms have been proposed to address these problems, among which genetic algorithms and their va...

If the matrix function $f\left(At\right)$ posses the properties of $f\left(At\right)=g\left(f(\left(\frac{t}{k}A\right)\right)$, then the recurrence formula $f_{i-1}=g\left(f_i\right),i=N,N-1,\cdots ,1,f\left(tA\right)=f_0$, can be established. Here, $f_N=f\left(A_N\right)={\displaystyle \sum _{j=0}^m}{a}_j{A}_N^j,A_N=\frac{t}{k^N}A$. This provides an algorithm for computing the m...

The basic reproduction, or reproductive number, is a useful index that indicates whether or not there will be an epidemic. However, it is also very important to determine whether an epidemic will eventually decrease and disappear or persist as an end...

We develop a framework for creating distortion functions that are used to construct new bivariate copulas. It is achieved by transforming non-negative random variables with Lomax-related distributions. In this paper, we apply the distortions to the b...

The main purpose of the present paper is to prove the existence of periodic solutions of the three-body problem in the 3D Kepler formulation. We have solved the same problem in the case when the three particles are considered in an external inertial...

The infinite series solution to the boundary-value problems of Laplace’s equation with discontinuous Dirichlet boundary conditions was found by using the basic method of separation of variables. The merit of this paper is that the closed-form s...

The G-modified Helmholtz equation is a partial differential equation that enables us to express gravity intensity g as a series of spherical harmonics having radial distance r in irrational powers. The Laplace equation in three-dimensional space (in...

In our study, we investigate the phenomenon of information loss, as measured by the Kullback–Leibler divergence, in a many-fermion system, such as the Lipkin model. Information loss is introduced as the number N of particles increases, particul...

This paper presents a novel deep-learning network designed to detect intervals of jump discontinuities in single-variable piecewise smooth functions from their noisy samples. Enhancing the accuracy of jump discontinuity estimations can be used to fin...

The threat posed by the COVID-19 pandemic has been accompanied by an epidemic of misinformation, causing confusion and mistrust among the public. Misinformation about COVID-19 whether intentional or unintentional takes many forms, including conspirac...

We study properties of the minimal Terracini loci, i.e., families of certain zero-dimensional schemes, in a projective plane. Among the new results here are: a maximality theorem and the existence of arbitrarily large gaps or non-gaps for the integer...

The transition zone (TZ) of hydrocarbon reservoirs is an integral part of the hydrocarbon pool which contains a substantial fraction of the deposit, particularly in carbonate petroleum systems. Consequently, knowledge of its thickness and petrophysic...

The sum of independent circular uniformly distributed random variables is also circular uniformly distributed. In this study, it is shown that a family of circular distributions based on nonnegative trigonometric sums (NNTS) is also closed under summ...

The new approach to quantum mechanics (QM) is that the mathematics of QM is the linearization of the mathematics of partitions (or equivalence relations) on a set. This paper develops those ideas using vector spaces over the field ${\mathbb{Z}}_2=\left\{0.1\right\}$ as a pedag...

The frequency deviation from the nominal working frequency in power systems is a consequence of the imbalance between total electrical loads and the aggregate power supplied by production units. The sensitivity of energy system frequency to both mino...

In this paper, an analytical exact form of the ramp function is presented. This seminal function constitutes a fundamental concept of the digital signal processing theory and is also involved in many other areas of applied sciences and engineering. I...

Accurate forecasting of the coronavirus disease 2019 (COVID-19) spread is indispensable for effective public health planning and the allocation of healthcare resources at all levels of governance, both nationally and globally. Conventional prediction...