AppliedMath, Volume 5, Issue 1

Two classes of series involving differences of harmonic numbers and the binomial coefficients $C(3n,n)$ are evaluated in closed form. The classes under consideration are ${\sum }_{k=0}^{\infty }{\displaystyle \frac{H_{3k+1}-H_k}{(3k+1)\left(\genfrac{}{}{0pt}{}{3k}{k}\right)}}\left({\displaystyle \genfrac{}{}{0pt}{}{k}{m}}\right)z^k\mathrm{and}{\sum }_{k=0}^{\infty }{\displaystyle \frac{H_{2k}-H_k}{(3k+1)\left(\genfrac{}{}{0pt}{}{3k}{k}\right)}}\left({\displaystyle \genfrac{}{}{0pt}{}{k}{}}\right)$...

We examine the modified Hill three-body problem by incorporating the oblateness of the primary body and focus on its asymptotic orbits. Specifically, we analyze and characterize homoclinic and heteroclinic connections associated with the collinear eq...

In the context of holonomic systems, the identification of virtual displacements is clear and consolidated. This provides the possibility, once the class of displacements have been coupled with Newton’s equations, for us to write the correct eq...

This work presents the Leal method for the approximation of integrals without known exact solutions, capable of multi-expanding simultaneously at different points. This method can be coupled with asymptotic approximations and the least squares method...

Artificial neural networks have proven to be an important machine learning model that has been widely used in recent decades to tackle a number of difficult classification or data fitting problems within real-world areas. Due to their significance, s...

Technical systems, which form the basis of modern technology, are structures designed to achieve a specific purpose by bringing together different components. In this respect, they have a wide field of study. Our study is aimed at the general evaluat...

This paper presents a method for hedging in markets of two-factor diffusion and jump diffusion models under the restriction of a specified probability of success. In addition, a method for hedging with a given shortfall amount is developed. A maximal...

We compare, mathematically, the text of a famous Italian novel, I promessi sposi, written by Alessandro Manzoni (source text), to its most recent English translation, The Betrothed by Michael F. Moore (target text). The mathematical theory applied do...

There has been considerable debate about whether contemporary Western societies are experiencing an increase in narcissistic tendencies, often referred to as a “narcissism epidemic”. This rise highlights the importance of understanding th...

In this article, we analyze some curvature restrictions satisfying by the concircular curvature tensor in $(2n+1)$-dimensional Sasakian manifolds with the generalized Tanaka–Webster connection $\overline{\nabla }$ admitting Ricci–Yamabe solitons....

Based on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inverse factorials are derived. A high point of the presentation is the r...

The study of contagion dynamics is a well-established domain within epidemiology, where the spread of infectious diseases is modeled and analyzed. In recent years, similar methodologies have been applied to the financial sector to understand and pred...

This article focuses on both classical and Bayesian inference of traffic intensity in a single-server Markovian queueing model considering balking. To reflect real-world situations, the article introduces the concept of balking, where customers opt n...

The modeling of the one-dimensional wave equation is the fundamental model for characterizing the behavior of vibrating strings in different physical systems. In this work, we investigate numerical solutions for the one-dimensional wave equation empl...

This study investigates M/M/n:(m/FIFO) systems with a limited queue capacity (incorporating both “waiting and rejection”). This category of systems can be considered to be mixed-service systems. They operate as queuing systems for custome...

Among the many (mostly randomized) models proposed in the last decades to study how opinions of a set of individuals interconnected by pairwise relations evolve, a novel deterministic model is introduced in this paper that is able to encompass indivi...

An efficient linearization method for solving a system of nonlinear equations was developed, showing good stability and convergence properties. It uses an unconventional and simple strategy to improve the performance of classic methods by a full-rank...

In this paper, we generalize previous results on the generalized stability of the general septic functional equation ${\Delta }_y^{8}f\left(x\right)=0$ for all $x,y\in V$.

The final goal of this paper is to organize the tools needed to study digital Quantum Communications, where classical information is entrusted to quantum states represented by density operators. A density operator is usually defined starting from a s...

Imaginary coquaternions cℍ can be represented by matrices of negative feedback $N^{-}$, positive feedback $P^{+}$, and reciprocal links $R^{\pm }$. An added environmental element $E^{\pm }$ endows biologic systems with the structure of cℍ modul...

Diabetic retinopathy (DR) is a severe microvascular complication of diabetes that affects the eyes, leading to progressive damage to the retina and potential vision loss. Timely intervention and detection are crucial for preventing irreversible damag...

This article is dedicated to the construction of neural networks for the prediction of the current–voltage characteristic (CVC). CVC is the most important characteristic of the mass transfer process in electro-membrane systems (EMS). CVC is use...

The intersection of fractals, non-Euclidean geometry, spatial autocorrelation, and urban structure offers valuable theoretical and practical application insights, which echoes the overarching goal of this paper. Its research question asks about conne...

Optimizing learning rates (LRs) in deep learning (DL) has long been challenging. Previous solutions, such as learning rate scheduling (LRS) and adaptive learning rate (ALR) algorithms like RMSProp and Adam, added complexity by introducing new hyperpa...

Haberman linking is a widely used method for comparing groups using the two-parameter logistic item response model. However, the traditional Haberman linking approach relies on joint item parameter estimation, which prevents the application of standa...

The stock market index future price forecasting is one of the imperative financial time series problems. Accurately estimated future closing prices can play important role in making trading decisions and investment plannings. This work proposes a new...

We present the derivation of generic equations describing the long gravity waves in incompressible fluid with a decaying effect. We show that in this theory, the only restriction to the surface deviation is connected to the stability condition for th...

The information paradox suggests that the black hole loses information when it emits radiation. In this way, the spectrum of radiation corresponds to a mixed (non-pure) quantum state even if the internal state generating the black hole is expected to...

According to the latest data from CryptoSlam, as of November 2024, NFT sales have approached USD 7.43 billion, with trading profits exceeding USD 33.303 million. In the buyer–seller market, the potential demand for NFT transactions continues to...

In the original publication [...]

Given the fundamental importance of the power grid in both supply and demand, frequency stability is critical to the reliable and stable function of energy systems. When energy is stored in the system, it mitigates problems caused by various disturba...