Mathematics, Volume 12, Issue 6

Prompt optimization is a crucial task for improving the performance of large language models for downstream tasks. In this paper, a prompt is a sequence of n-grams selected from a vocabulary. Consequently, the aim is to select the optimal prompt conc...

In this paper, the singularly perturbed modified Gardner equation is considered. Firstly, for the unperturbed equation, under certain parameter conditions, we obtain the exact expressions of kink wave solution and antikink wave solution by using the...

This study introduces a novel particle model for biomass fast pyrolysis, incorporating an anisotropic cylindrical particle to address mass and energy transport coupled with aerosol ejection, which previous models have overlooked. The main contributio...

The aim of this paper is to analyze a specific fourth-order matrix spectral problem involving four potentials and two free nonzero parameters and construct an associated integrable hierarchy of bi-Hamiltonian equations within the zero curvature formu...

Mega sports events generate significant media coverage and have a considerable economic impact on the host cities. Organizing such events is a complex task that requires extensive planning. The success of these events hinges on the attendees’ s...

In this paper, we present a novel family of soft sets named “soft ${\omega }_{\delta }$-open sets”. We find that this class constitutes a soft topology that lies strictly between the soft topologies of soft $\delta$-open sets and soft ${\omega }^0$-op...

This article shows a method for the statistical analysis of signals. Firstly, this method was applied to analyze the processing of signs generated by an acquisition card for pulse measurement using the synchronous demodulation method. The application...

The issue of counting independent sets of a graph, G, represented as $i\left(G\right)$, is a significant challenge within combinatorial mathematics. This problem finds practical applications across various fields, including mathematics, computer science, physics,...

This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hypergeometric functions of matrix arguments. Furthermore, we show t...

Federated Learning (FL), as an emerging paradigm in distributed machine learning, has received extensive research attention. However, few works consider the impact of device mobility on the learning efficiency of FL. In fact, it is detrimental to the...

The rational field $\mathbb{Q}$ is highly desired in many applications. Algorithms using the rational number field $\mathbb{Q}$ algebraic number fields use only integer arithmetics and are easy to implement. Therefore, studying and designing systems and expansions with co...

To describe stationary physical systems, well-known boundary problems for shielded Poisson and Sophie Germain equations are used. The obtained shielded harmonic and biharmonic systems are approximated using the finite element method and fictitiously...

This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valu...

Inductive Logic Programming (ILP) is a research field at the intersection between machine learning and logic programming, focusing on developing a formal framework for inductively learning relational descriptions in the form of logic programs from ex...

Significant public opinion events often trigger pronounced fluctuations in online discourse. While existing models have been extensively employed to analyze the propagation of public opinion, they frequently overlook the intricacies of information di...

In a targeted terminal wealth generated by bond and risky assets, where the proportion of a risky asset is gradually being phased down, we propose a divestment model in a risky asset compensated by growth in a bond (insurance). The model includes the...

Many practical problems can be classified as constrained multi-objective optimization problems. Although various methods have been proposed for solving constrained multi-objective optimization problems, there is still a lack of research considering t...

In this paper, we give a new criterion for the Cohen–Macaulayness of vertex splittable ideals, a family of monomial ideals recently introduced by Moradi and Khosh-Ahang. Our result relies on a Betti splitting of the ideal and provides an induct...

Social networks and official statistics have become vital sources of information in times of health emergencies. The ability to monitor and profile social sentiment is essential for understanding public perception and response in the context of publi...

In this paper, a new effective technique for the investigation of the higher-order trinomial differential equations $y^{\left(n\right)}\left(t\right)+p\left(t\right)y\left(\tau \left(t\right)\right)+q\left(t\right)y\left(\sigma \left(t\right)\right)=0$ is established. We offer new criteria for so-called property (A) and oscillation of the co...

In an effort to balance the distribution of services across a given territory, dispersion and diversity models typically aim to maximize the minimum distance between any pair of facilities. Specifically, in the capacitated dispersion problem (CDP), e...

The negative–positive transformation (NPT) is a widely employed technique for encrypting images on pixel blocks, commonly integrated into cryptosystems compatible with compression algorithms. The existing literature on NPT analysis can be categ...

Uniaxial compressive strength is a variable necessary for adequately characterizing a material’s mechanical properties. However, a specimen’s geometric deviations and elastic properties may lead to undesirable stress states, which cause s...

A model of a single-server queuing-inventory system (QIS) with a limited waiting buffer for consumer customers (c-customers) and catastrophes has been developed. When a catastrophe occurs, all items in the system’s warehouse are destroyed, but...

The only cases where exact distributions of estimates are known is for samples from exponential families, and then only for special functions of the parameters. So statistical inference was traditionally based on the asymptotic normality of estimates...

We apply known special functions from the literature (and these include the Fox $\mathbb{H}–$function, the exponential function, the Mittag-Leffler function, the Gauss Hypergeometric function, the Wright function, the $\mathbb{G}–$function, the Fox–Wrigh...

Digital radio frequency memory (DRFM) has emerged as an advanced technique to achieve a range of jamming signals, due to its capability to intercept waveforms within a short time. multiple-input multiple-output (MIMO) radars can transmit agile orthog...

Recent advancements in autonomous mobile robots have led to significant progress in area coverage tasks. However, challenges persist in optimizing the efficiency and computational complexity of complete coverage path planner (CCPP) algorithms for mul...

Federated learning is a distributed learning method used to solve data silos and privacy protection in machine learning, aiming to train global models together via multiple clients without sharing data. However, federated learning itself introduces c...

The advent of space exploration missions, especially those aimed at establishing a sustainable presence on the Moon and beyond, necessitates the development of efficient propulsion and mission planning techniques. This study presents a comprehensive...

The advent of deep learning has provided solutions to many challenges posed by the Internet. However, efficient localization and recognition of vulgar segments within videos remain formidable tasks. This difficulty arises from the blurring of spatial...

Laser deposition manufacturing (LDM) has drawn unprecedented attention for its advantages in manufacturing large-scale and complex metal components. During the process of LDM, a large thermal gradient is generated due to thermal cycling and heat accu...

The aim of this study is to analyze which factors affect the profitability of banks in the eurozone and to make recommendations for supporting them to achieve higher levels of profitability in particular eurozone countries. The banks operating in the...

This paper deals with the research of solutions of bounded variation (BV) to evolution inclusion coupled with a time and state dependent maximal monotone operator. Different problems are studied: existence of solutions, unicity of the solution, exist...

We study the Cauchy problem for differential–difference parabolic equations with potentials undergoing translations with respect to the spatial-independent variable. Such equations are used for the modeling of various phenomena not covered by t...

This study provides an efficient linearized difference algorithm for a diffusive Sel^′kov–Schnakenberg system. The algorithm is developed by using a finite difference method that relies on a three-level linearization approach. The boundedn...

The existence of chaos is particularly relevant, as the identification of a chaotic behavior in a time series could lead to reliable short-term forecasting. This paper evaluates the existence of nonlinearity and chaos in the underlying process of the...

Developing efficient path-planning algorithms is an essential topic in modern robotics and control theory. Autonomous rovers and wheeled and tracked robots require path generators that can efficiently cover the explorable space with minimal redundanc...

An n-person cooperative oligopoly is considered without product differentiation. It is assumed that the firms know the unit price function but have no access to the cost functions of the competitors. From market data, they have information about the...

We perform a Hamiltonian analysis of unimodular gravity in its first-order formulation, specifically a modification of the Holst action. In order to simplify the analysis, prior studies on this theory have introduced (for several reasons) additional...

We study the square root computation by Leonardo Fibonacci (or Leonardo of Pisa) in his MSS Liber Abaci from c1202 and c1228 and De Practica Geometrie from c1220. In this MSS, Fibonacci systematically describes finding the integer part of the square...

This paper investigates a two-machine group scheduling problem with sequence-independent setup times and round-trip transportation times, which is derived from the production management requirements of modern steel manufacturing enterprises. The obje...

Distributed renewable sources are one of the most promising contributors for DC microgrids to reduce carbon emission and fuel consumption. Although the battery energy storage system (BESS) is widely applied to compensate the power imbalance between d...

Spatial registration is a prerequisite for data fusion. Existing methods primarily focus on similar sensor scenarios and rely on accurate data association assumptions. To address the heterogeneous sensor registration in complex data association scena...

For regional or even global geophysical problems, the curvature of the geophysical model cannot be approximated as a plane, and its curvature must be considered. Tesseroids can fit the curvature, but their shapes vary from almost rectangular at the e...

A novel cure rate model is introduced by considering, for the number of concurrent causes, the modified power series distribution and, for the time to event, the recently proposed power piecewise exponential distribution. This model includes a wide v...

Cubic Bézier curves are widely used in computer graphics and geometric modeling, favored for their intuitive design and ease of implementation. However, self-intersections within these curves can pose significant challenges in both geometric m...

Higher education evaluation presents itself as a worldwide trend. It aims to improve performance due to its importance for economic and personal growth. Graduate activities are essential for Brazilian research and innovation systems. However, previou...

Elliptic curve cryptography (ECC) is widely acknowledged as a method for implementing public key cryptography on devices with limited resources thanks to its use of small keys. A crucial and complex operation in ECC calculations is scalar point multi...

Causal structure learning is one of the major fields in causal inference. Only the Markov equivalence class (MEC) can be learned from observational data; to fully orient unoriented edges, experimental data need to be introduced from external interven...