Mathematics

19 pages, 1414 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Wavelet and Deep Learning Framework for Predicting Commodity Prices Under Economic and Financial Uncertainty

by Lyubov Doroshenko, Loretta Mastroeni and Alessandro Mazzoccoli

Mathematics 2025, 13(8), 1346; https://doi.org/10.3390/math13081346 - 20 Apr 2025

Cited by 15 | Viewed by 3309

The analysis of commodity markets—particularly in the energy and metals sectors—is essential for understanding economic dynamics and guiding decision-making. Financial and economic uncertainty indices provide valuable insights that help reduce price uncertainty. This study employs wavelet analyses and wavelet energy-based measures to investigate [...] Read more.

The analysis of commodity markets—particularly in the energy and metals sectors—is essential for understanding economic dynamics and guiding decision-making. Financial and economic uncertainty indices provide valuable insights that help reduce price uncertainty. This study employs wavelet analyses and wavelet energy-based measures to investigate the relationship between these indices and commodity prices across multiple time scales. The wavelet approach captures complex, time-varying dependencies, offering a more nuanced understanding of how uncertainty indices influence commodity price fluctuations. By integrating this analysis with predictability measures, we assess how uncertainty indices enhance forecasting accuracy. We further incorporate deep learning models capable of capturing sequential patterns in financial time series into our analysis to better evaluate their predictive potential. Our findings highlight the varying impact of financial and economic uncertainty on the predictability of commodity prices, showing that while some indices offer valuable forecasting information, others display strong correlations without significant predictive power. These results underscore the need for tailored predictive models, as different commodities react differently to the same financial conditions. By combining wavelet-based measures with machine learning techniques, this study presents a comprehensive framework for evaluating the role of uncertainty in commodity markets. The insights gained can support investors, policymakers, and market analysts in making more informed decisions. Full article

(This article belongs to the Special Issue Advancements in Applied Mathematics for Economic Data Analytics: Models, Methods, and Applications)

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17 pages, 457 KB

Open AccessEditor’s ChoiceArticle

Hyperbolic Representation of the Richards Growth Model

by Marcin Molski

Mathematics 2025, 13(8), 1316; https://doi.org/10.3390/math13081316 - 17 Apr 2025

Cited by 1 | Viewed by 1465

Abstract

The phenomenological universalities (PU) approach is employed to derive the Richards growth function in the unknown hyperbolic representation. The formula derived can be applied in theoretical modeling of sigmoid and involuted growth of biological systems. In the model proposed, the exponent in the [...] Read more.

The phenomenological universalities (PU) approach is employed to derive the Richards growth function in the unknown hyperbolic representation. The formula derived can be applied in theoretical modeling of sigmoid and involuted growth of biological systems. In the model proposed, the exponent in the Richards function has the following clear biological meaning: it describes the number of cells doubling, leading to an increase in a biomass of the system from

m_{0}

(birth or hatching mass) to the limiting value

m_{\infty}

(mass at maturity). The generalized form of the universal growth function is derived. It can be employed in fitting the weight–age data for a variety of biological systems, including copepods, tumors, fish, birds, mammals and dinosaurs. Both the PU methodology and the Richards model can be effectively applied in the theoretical modeling of infectious disease outbreaks. To substantiate this assertion, the simplest PU-SIR (Susceptible–Infective–Removed) epidemiological model is considered. In this approach, it is assumed that the number of births is approximately equal to the number of deaths, while the impact of recovered (quarantined) individuals on the dynamics of the infection is negligible. Full article

(This article belongs to the Section E3: Mathematical Biology)

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14 pages, 360 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Prime Strictly Concentric Magic Squares of Odd Order

by Anna Louise Skelt, Stephanie Perkins and Paul Alun Roach

Mathematics 2025, 13(8), 1261; https://doi.org/10.3390/math13081261 - 11 Apr 2025

Cited by 1 | Viewed by 1577

Abstract

Magic squares have been widely studied, with publications of mathematical interest dating back over 100 years. Most studies construct and analyse specific subsets of magic squares, with some exploring links to puzzles, number theory, and graph theory. The subset of magic squares this [...] Read more.

Magic squares have been widely studied, with publications of mathematical interest dating back over 100 years. Most studies construct and analyse specific subsets of magic squares, with some exploring links to puzzles, number theory, and graph theory. The subset of magic squares this paper focuses on are those termed prime strictly concentric magic squares (PSCMS), and their general definitions, examples, and important properties are also presented. Previously, only the minimum centre cell values of PSCMS of odd order 5 to 19 were presented, by Makarova in 2015. In this paper, the corresponding list of primes for all minimum PSCMS of order 5 is given, and the number of minimum PSCMS of order 5 is enumerated. Full article

(This article belongs to the Section A: Algebra and Logic)

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14 pages, 515 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Set-Valued Approximation—Revisited and Improved

by David Levin

Mathematics 2025, 13(7), 1194; https://doi.org/10.3390/math13071194 - 4 Apr 2025

Viewed by 1138

Abstract

We address the problem of approximating a set-valued function F, where

F : [a, b] \to K (R^{d})

given its samples

{F (a + i h)}_{i = 0}^{N}

, with [...] Read more.

We address the problem of approximating a set-valued function F, where

F : [a, b] \to K (R^{d})

given its samples

{F (a + i h)}_{i = 0}^{N}

, with

h = (b - a) / N

. We revisit an existing method that approximates set-valued functions by interpolating signed-distance functions. This method provides a high-order approximation for general topologies but loses accuracy near points where F undergoes topological changes. To address this, we introduce new techniques that enhance efficiency and maintain high-order accuracy across

[a, b]

. Building on the foundation of previous publication, we introduce new techniques to improve the method’s efficiency and extend its high-order approximation accuracy throughout the entire interval

[a, b]

. Particular focus is placed on identifying and analyzing the behavior of F near topological transition points. To address this, two algorithms are introduced. The first algorithm employs signed-distance quasi-interpolation, incorporating specialized adjustments to effectively handle singularities at points of topological change. The second algorithm leverages an implicit function representation of

G r a p h (F)

, offering an alternative and robust approach to its approximation. These enhancements improve accuracy and stability in handling set-valued functions with changing topologies. Full article

(This article belongs to the Special Issue Advances in Approximation Theory and Numerical Functional Analysis)

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25 pages, 2066 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Is π a Chaos Generator?

by Natalia Petrovskaya

Mathematics 2025, 13(7), 1126; https://doi.org/10.3390/math13071126 - 29 Mar 2025

Viewed by 1381

Abstract

We consider a circular motion problem related to blind search in confined space. A particle moves in a unit circle in discrete time to find the escape channel and leave the circle through it. We first explain how the exit time depends on [...] Read more.

We consider a circular motion problem related to blind search in confined space. A particle moves in a unit circle in discrete time to find the escape channel and leave the circle through it. We first explain how the exit time depends on the initial position of the particle when the channel width is fixed. We then investigate how narrowing the channel moves the system from discrete changes in the exit time to the ultimate ‘countable chaos’ state that arises in the problem when the channel width becomes infinitely small. It will be shown in the paper that inherent randomness exists in the problem due to the nature of circular motion as the number

π

acts as a random number generator in the system. Randomness of the decimal digits of

π

results in sensitive dependence on initial conditions in the system with an infinitely narrow channel, and we argue that even a simple linear dynamical system can exhibit features of chaotic behaviour, provided that the system has inherent noise. Full article

(This article belongs to the Special Issue Applied Mathematics in Nonlinear Dynamics and Chaos)

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24 pages, 2090 KB

Open AccessFeature PaperEditor’s ChoiceReview

On Regime Switching Models

by Zhenni Tan and Yuehua Wu

Mathematics 2025, 13(7), 1128; https://doi.org/10.3390/math13071128 - 29 Mar 2025

Cited by 12 | Viewed by 16252

Abstract

Regime switching models have been widely studied for their ability to capture the dynamic behavior of time series data and are widely used in economic and financial data analysis. This paper reviews various regime switching models with various regime switching mechanisms, including threshold [...] Read more.

Regime switching models have been widely studied for their ability to capture the dynamic behavior of time series data and are widely used in economic and financial data analysis. This paper reviews various regime switching models with various regime switching mechanisms, including threshold models, hidden Markov regime switching models, hidden semi-Markov regime switching models, and smooth transition models. The focus is on regime switching models for time series, studying their underlying frameworks, popular variants, and commonly used estimation methods. In addition, six different regime switching models are compared using two real-world datasets. Full article

(This article belongs to the Special Issue Advanced Statistical Applications in Financial Econometrics)

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17 pages, 310 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Conditional Quantization for Uniform Distributions on Line Segments and Regular Polygons

by Pigar Biteng, Mathieu Caguiat, Tsianna Dominguez and Mrinal Kanti Roychowdhury

Mathematics 2025, 13(7), 1024; https://doi.org/10.3390/math13071024 - 21 Mar 2025

Cited by 3 | Viewed by 939

Abstract

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If, in the quantization some of the elements in the support are preselected, then the quantization [...] Read more.

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If, in the quantization some of the elements in the support are preselected, then the quantization is called a conditional quantization. In this paper, we investigate the conditional quantization for the uniform distributions defined on the unit line segments and m-sided regular polygons, where

m \geq 3

, inscribed in a unit circle. Full article

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14 pages, 495 KB

Open AccessEditor’s ChoiceArticle

A Fast Projected Gradient Algorithm for Quaternion Hermitian Eigenvalue Problems

by Shan-Qi Duan and Qing-Wen Wang

Mathematics 2025, 13(6), 994; https://doi.org/10.3390/math13060994 - 18 Mar 2025

Cited by 3 | Viewed by 1561

Abstract

In this paper, based on the novel generalized Hamilton-real (GHR) calculus, we propose for the first time a quaternion Nesterov accelerated projected gradient algorithm for computing the dominant eigenvalue and eigenvector of quaternion Hermitian matrices. By introducing momentum terms and look-ahead updates, the [...] Read more.

In this paper, based on the novel generalized Hamilton-real (GHR) calculus, we propose for the first time a quaternion Nesterov accelerated projected gradient algorithm for computing the dominant eigenvalue and eigenvector of quaternion Hermitian matrices. By introducing momentum terms and look-ahead updates, the algorithm achieves a faster convergence rate. We theoretically prove the convergence of the quaternion Nesterov accelerated projected gradient algorithm. Numerical experiments show that the proposed method outperforms the quaternion projected gradient ascent method and the traditional algebraic methods in terms of computational accuracy and runtime efficiency. Full article

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21 pages, 1033 KB

Open AccessFeature PaperEditor’s ChoiceArticle

On Strongly Regular Graphs and the Friendship Theorem

by Igal Sason

Mathematics 2025, 13(6), 970; https://doi.org/10.3390/math13060970 - 14 Mar 2025

Cited by 1 | Viewed by 4964

Abstract

This paper presents an alternative proof of the celebrated friendship theorem, originally established by Erdős, Rényi, and Sós in 1966. The proof relies on a closed-form expression for the Lovász

ϑ

-function of strongly regular graphs, recently derived by the author. Additionally, this [...] Read more.

This paper presents an alternative proof of the celebrated friendship theorem, originally established by Erdős, Rényi, and Sós in 1966. The proof relies on a closed-form expression for the Lovász

ϑ

-function of strongly regular graphs, recently derived by the author. Additionally, this paper considers some known extensions of the theorem, offering discussions that provide insights into the friendship theorem, one of its extensions, and the proposed proof. Leveraging the closed-form expression for the Lovász

ϑ

-function of strongly regular graphs, this paper further establishes new necessary conditions for a strongly regular graph to be a spanning or induced subgraph of another strongly regular graph. In the case of induced subgraphs, the analysis also incorporates a property of graph energies. Some of these results are extended to regular graphs and their subgraphs. Full article

(This article belongs to the Special Issue Advances in Combinatorics, Discrete Mathematics and Graph Theory)

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16 pages, 248 KB

Open AccessEditor’s ChoiceArticle

Conformal Interactions of Osculating Curves on Regular Surfaces in Euclidean 3-Space

by Yingxin Cheng, Yanlin Li, Pushpinder Badyal, Kuljeet Singh and Sandeep Sharma

Mathematics 2025, 13(5), 881; https://doi.org/10.3390/math13050881 - 6 Mar 2025

Cited by 9 | Viewed by 1499

Abstract

Conformal maps preserve angles and maintain the local shape of geometric structures. The osculating curve plays an important role in analyzing the variations in curvature, providing a detailed understanding of the local geometric properties and the impact of conformal transformations on curves and [...] Read more.

Conformal maps preserve angles and maintain the local shape of geometric structures. The osculating curve plays an important role in analyzing the variations in curvature, providing a detailed understanding of the local geometric properties and the impact of conformal transformations on curves and surfaces. In this paper, we study osculating curves on regular surfaces under conformal transformations. We obtained the conditions required for osculating curves on regular surfaces R and

\tilde{R}

to remain invariant when subjected to a conformal transformation

ψ : R \to \tilde{R}

. The results presented in this paper reveal the specific conditions under which the transformed curve

\tilde{σ} = ψ \circ σ

preserves its osculating properties, depending on whether

\tilde{σ}

is a geodesic, asymptotic, or neither. Furthermore, we analyze these conditions separately for cases with zero and non-zero normal curvatures. We also explore the behavior of these curves along the tangent vector

T_{σ}

and the unit normal vector

P_{σ}

. Full article

(This article belongs to the Special Issue Geometric Topology and Differential Geometry with Applications)

20 pages, 375 KB

Open AccessFeature PaperEditor’s ChoiceArticle

On Error Estimation and Convergence of the Difference Scheme for a Nonlinear Elliptic Equation with an Integral Boundary Condition

by Regimantas Čiupaila, Mifodijus Sapagovas, Kristina Pupalaigė and Gailė Kamilė Šaltenienė

Mathematics 2025, 13(5), 873; https://doi.org/10.3390/math13050873 - 5 Mar 2025

Cited by 2 | Viewed by 1573

Abstract

In this paper, a two-dimensional nonlinear elliptic equation with an integral boundary condition depending on two parameters is investigated. The problem is solved using the finite difference method. The error in the solution is evaluated based on the properties of M-matrices, and herewith [...] Read more.

In this paper, a two-dimensional nonlinear elliptic equation with an integral boundary condition depending on two parameters is investigated. The problem is solved using the finite difference method. The error in the solution is evaluated based on the properties of M-matrices, and herewith the convergence of the difference scheme is proved. The majorant is constructed to estimate the error of the solution of the system of difference equations. Full article

(This article belongs to the Special Issue New Trends in Nonlinear Analysis)

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27 pages, 3808 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Dynamic Modeling of Limit Order Book and Market Maker Strategy Optimization Based on Markov Queue Theory

by Fei Xie, Yang Liu, Changlong Hu and Shenbao Liang

Mathematics 2025, 13(5), 778; https://doi.org/10.3390/math13050778 - 26 Feb 2025

Viewed by 13742

Abstract

In recent years, high-frequency trading has become increasingly popular in financial markets, making the dynamic modeling of the limit book and the optimization of market maker strategies become key topics. However, existing studies often lacked detailed descriptions of order books and failed to [...] Read more.

In recent years, high-frequency trading has become increasingly popular in financial markets, making the dynamic modeling of the limit book and the optimization of market maker strategies become key topics. However, existing studies often lacked detailed descriptions of order books and failed to fully characterize the optimal decisions of market makers in complex market environments, especially in China’s A-share market. Based on Markov queue theory, this paper proposes the dynamic model of the limit order and the optimal strategy of the market maker. The model uses a state transition probability matrix to refine the market diffusion state, order generation, and trading process and incorporates indicators such as optimal quote deviation and restricted order trading probability. Then, the optimal control model is constructed and the reference strategy is derived using the Hamilton–Jacobi–Bellman (HJB) equation. Then, the key parameters are estimated using the high-frequency data of Ping An Bank for a single trading day. In the empirical aspect, the six-month high-frequency trading data of 114 representative stocks in different market states such as the bull market and bear market in China’s A-share market were selected for strategy verification. The results showed that the proposed strategy had robust returns and stable profits in the bull market and that frequent capture of market fluctuations in the bear market can earn relatively high returns while maintaining 50% of the order coverage rate and 66% of the stable order winning rate. Our study used Markov queuing theory to describe the state and price dynamics of the limit order book in detail and used optimization methods to construct and solve the optimal market maker strategy. The empirical aspect broadens the empirical scope of market maker strategies in the Chinese market and studies the stability and effectiveness of market makers in different market states. Full article

(This article belongs to the Section E: Applied Mathematics)

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23 pages, 3224 KB

Open AccessEditor’s ChoiceArticle

AMC: Adaptive Learning Rate Adjustment Based on Model Complexity

by Weiwei Cheng, Rong Pu and Bin Wang

Mathematics 2025, 13(4), 650; https://doi.org/10.3390/math13040650 - 16 Feb 2025

Cited by 13 | Viewed by 4862

Abstract

An optimizer plays a decisive role in the efficiency and effectiveness of model training in deep learning. Although Adam and its variants are widely used, the impact of model complexity on training is not considered, which leads to instability or slow convergence when [...] Read more.

An optimizer plays a decisive role in the efficiency and effectiveness of model training in deep learning. Although Adam and its variants are widely used, the impact of model complexity on training is not considered, which leads to instability or slow convergence when a complex model is trained. To address this issue, we propose an AMC (Adam with Model Complexity) optimizer, which dynamically adjusts the learning rate by incorporating model complexity, thereby improving training stability and convergence speed. AMC uses the Frobenius norm of the model to measure its complexity, automatically decreasing the learning rate of complex models and increasing the learning rate of simple models, thus optimizing the training process. We provide a theoretical analysis to demonstrate the relationship between model complexity and learning rate, as well as the convergence and convergence bounds of AMC. Experiments on multiple benchmark datasets show that, compared to several widely used optimizers, AMC exhibits better stability and faster convergence, especially in the training of complex models. Full article

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17 pages, 337 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Support Vector Machines and Model Selection for Control Chart Pattern Recognition

by Chih-Jen Su, I-Fei Chen, Tzong-Ru Tsai, Tzu-Hsuan Wang and Yuhlong Lio

Mathematics 2025, 13(4), 592; https://doi.org/10.3390/math13040592 - 11 Feb 2025

Cited by 6 | Viewed by 3070

Abstract

Resource-intensiveness often occurs in modern industrial settings; meanwhile, common issues and irregular patterns in production can lead to defects and variations in work-piece dimensions, negatively impacting products and increasing costs. Utilizing traditional process control charts to monitor the process and identify potential anomalies [...] Read more.

Resource-intensiveness often occurs in modern industrial settings; meanwhile, common issues and irregular patterns in production can lead to defects and variations in work-piece dimensions, negatively impacting products and increasing costs. Utilizing traditional process control charts to monitor the process and identify potential anomalies is expensive when intensive resources are needed. To conquer these downsides, algorithms for control chart pattern recognition (CCPR) leverage machine learning models to detect non-normality or normality and ensure product quality is established, and novel approaches that integrate the support vector machine (SVM), random forest (RF), and K-nearest neighbors (KNN) methods with the model selection criterion, named SVM-, RF-, and KNN-CCPR, respectively, are proposed. The three CCPR approaches can save sample resources in the initial process monitoring, improve the weak learner’s ability to recognize non-normal data, and include normality as a special case. Simulation results and case studies show that the proposed SVM-CCPR method outperforms the other two competitors with the highest recognition rate and yields favorable performance for quality control. Full article

(This article belongs to the Special Issue Mathematical Applications in Industrial Engineering)

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44 pages, 1327 KB

Open AccessFeature PaperEditor’s ChoiceArticle

On Spectral Graph Determination

by Igal Sason, Noam Krupnik, Suleiman Hamud and Abraham Berman

Mathematics 2025, 13(4), 549; https://doi.org/10.3390/math13040549 - 7 Feb 2025

Cited by 3 | Viewed by 6571

Abstract

The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods to construct or distinguish cospectral nonisomorphic graphs, and analyzing [...] Read more.

The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods to construct or distinguish cospectral nonisomorphic graphs, and analyzing the conditions under which a graph’s spectrum uniquely determines its structure. This paper presents an overview of both classical and recent advancements in these topics, along with newly obtained proofs of some existing results, which offer additional insights. Full article

(This article belongs to the Special Issue Graph Theory and Applications, 2nd Edition)

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24 pages, 420 KB

Open AccessEditor’s ChoiceArticle

A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers

by József Dombi, Jenő Fáró and Tamás Jónás

Mathematics 2025, 13(3), 526; https://doi.org/10.3390/math13030526 - 5 Feb 2025

Cited by 1 | Viewed by 2846

Abstract

In group decision making, the knowledge, skills, and experience of the decision-makers may not be at the same level. Hence, the need arises to take into account not only the opinion, but also the relative importance of the opinion of each decision-maker. These [...] Read more.

In group decision making, the knowledge, skills, and experience of the decision-makers may not be at the same level. Hence, the need arises to take into account not only the opinion, but also the relative importance of the opinion of each decision-maker. These relative importance values can be treated as weights. In a group decision making situation, it is not only the weighted aggregate output that matters, but also the weighted measure of the group consensus. Noting that weighted group consensus measures have not yet been intensely studied, in this study, based on well-known requirements for non-weighted consensus measures, we define six reasonable requirements for the weighted case. Then, we propose a function family and prove that it satisfies the above requirements for a weighted consensus measure. Hence, the proposed measure can be used in group decision making situations where the decision-makers have various weight values that reflect the relative importance of their opinions. The proposed weighted consensus measure is based on the fuzziness degree of the decumulative distribution function of the input scores, taking into account the weights. Hence, it may be viewed as a weighted adaptation of the so-called fuzziness measure-based consensus measure. The novel weighted consensus measure is determined by a fuzzy entropy function; i.e., this function may be regarded as a generator of the consensus measure. This property of the proposed weighted consensus measure family makes it very versatile and flexible. The nice properties of the proposed weighted consensus measure family are demonstrated by means of concrete numerical examples. Full article

(This article belongs to the Special Issue Advanced Intelligent Algorithms for Decision Making Under Uncertainty)

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50 pages, 9587 KB

Open AccessEditor’s ChoiceArticle

Uncertain Numbers

by Peng Yue

Mathematics 2025, 13(3), 496; https://doi.org/10.3390/math13030496 - 2 Feb 2025

Cited by 9 | Viewed by 5260

Abstract

This work presents a mathematical framework based on uncertain numbers to address the inherent uncertainty in nonlinear systems, a challenge that traditional mathematical frameworks often struggle to fully capture. By establishing five axioms, a formal system of uncertain numbers is developed and embedded [...] Read more.

This work presents a mathematical framework based on uncertain numbers to address the inherent uncertainty in nonlinear systems, a challenge that traditional mathematical frameworks often struggle to fully capture. By establishing five axioms, a formal system of uncertain numbers is developed and embedded within set theory, providing a comprehensive characterization of uncertainty. This framework allows phenomena such as infinity and singularities to be treated as uncertain numbers, offering a mathematically rigorous analytical approach. Subsequently, an algebraic structure for uncertain numbers is constructed, defining fundamental operations such as addition, subtraction, multiplication, and division. The framework is compatible with existing mathematical paradigms, including complex numbers, fuzzy numbers, and probability theory, thereby forming a unified theoretical structure for quantifying and analyzing uncertainty. This advancement not only provides new avenues for research in mathematics and physics but also holds significant practical value, particularly in improving numerical methods to address singularity problems and optimizing nonconvex optimization algorithms. Additionally, the anti-integral-saturation technique, widely applied in control science, is rigorously derived within this framework. These applications highlight the utility and reliability of the uncertain number framework in both theoretical and practical domains. Full article

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19 pages, 389 KB

Open AccessFeature PaperEditor’s ChoiceArticle

On the Existence and Uniqueness of Solutions for Neutral-Type Caputo Fractional Differential Equations with Iterated Delays: Hyers–Ulam–Mittag–Leffler Stability

by Ekaterina Madamlieva and Mihail Konstantinov

Mathematics 2025, 13(3), 484; https://doi.org/10.3390/math13030484 - 31 Jan 2025

Cited by 4 | Viewed by 1603

Abstract

This study investigates nonlinear Caputo-type fractional differential equations with iterated delays, focusing on the neutral type. Initially formulated by D. Bainov and the second author of the current paper between 1972 and 1978, these superneutral equations have been extensively studied in scholarly inquiry. [...] Read more.

This study investigates nonlinear Caputo-type fractional differential equations with iterated delays, focusing on the neutral type. Initially formulated by D. Bainov and the second author of the current paper between 1972 and 1978, these superneutral equations have been extensively studied in scholarly inquiry. The present research seeks to reinvigorate interest in such delays within sophisticated frameworks of differential equations, particularly those involving fractional calculus. The primary objectives are to thoroughly examine neutral-type fractional differential equations with iterated delays and provide novel insights into their existence and uniqueness by applying Bielecki’s and Chebyshev’s norms for solution constraints analysis. Additionally, this work establishes Hyers–Ulam–Mittag–Leffler stability for these equations. Full article

(This article belongs to the Special Issue Advances in Differential Dynamical Systems with Applications to Economics and Biology, 3rd Edition)

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29 pages, 8288 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Partial Least Squares Regression for Binary Data

by Laura Vicente-Gonzalez, Elisa Frutos-Bernal and Jose Luis Vicente-Villardon

Mathematics 2025, 13(3), 458; https://doi.org/10.3390/math13030458 - 30 Jan 2025

Cited by 8 | Viewed by 3572

Abstract

Classical Partial Least Squares Regression (PLSR) models were developed primarily for continuous data, allowing dimensionality reduction while preserving relationships between predictors and responses. However, their application to binary data is limited. This study introduces Binary Partial Least Squares Regression (BPLSR), a novel extension [...] Read more.

Classical Partial Least Squares Regression (PLSR) models were developed primarily for continuous data, allowing dimensionality reduction while preserving relationships between predictors and responses. However, their application to binary data is limited. This study introduces Binary Partial Least Squares Regression (BPLSR), a novel extension of the PLSR methodology designed specifically for scenarios involving binary predictors and responses. BPLSR adapts the classical PLSR framework to handle the unique properties of binary datasets. A key feature of this approach is the introduction of a triplot representation that integrates logistic biplots. This visualization tool provides an intuitive interpretation of relationships between individuals and variables from both predictor and response matrices, enhancing the interpretability of binary data analysis. To illustrate the applicability and effectiveness of BPLSR, the method was applied to a real-world dataset of strains of Colletotrichum graminicola, a pathogenic fungus. The results demonstrated the ability of the method to represent binary relationships between predictors and responses, underscoring its potential as a robust analytical tool. This work extends the capabilities of traditional PLSR methods and provides a practical and versatile solution for binary data analysis with broad applications in diverse research areas. Full article

(This article belongs to the Section D1: Probability and Statistics)

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26 pages, 3650 KB

Open AccessEditor’s ChoiceArticle

Geometrical Optics Stability Analysis of Rotating Visco-Diffusive Flows

by Oleg Kirillov

Mathematics 2025, 13(3), 382; https://doi.org/10.3390/math13030382 - 24 Jan 2025

Cited by 1 | Viewed by 1990

Abstract

Geometrical optics stability analysis has proven effective in deriving analytical instability criteria for 3D flows in ideal hydrodynamics and magnetohydrodynamics, encompassing both compressible and incompressible fluids. The method models perturbations as high-frequency wavelets, evolving along fluid trajectories. Detecting local instabilities reduces to solving [...] Read more.

Geometrical optics stability analysis has proven effective in deriving analytical instability criteria for 3D flows in ideal hydrodynamics and magnetohydrodynamics, encompassing both compressible and incompressible fluids. The method models perturbations as high-frequency wavelets, evolving along fluid trajectories. Detecting local instabilities reduces to solving ODEs for the wave vector and amplitude of the wavelet envelope along streamlines, with coefficients derived from the background flow. While viscosity and diffusivity were traditionally regarded as stabilizing factors, recent extensions of the geometrical optics framework have revealed their destabilizing potential in visco-diffusive and multi-diffusive flows. This review highlights these advancements, with a focus on their application to the azimuthal magnetorotational instability in magnetohydrodynamics and the McIntyre instability in lenticular vortices and swirling differentially heated flows. It introduces new analytical instability criteria, applicable across a wide range of Prandtl, Schmidt, and magnetic Prandtl numbers, which still remains beyond the reach of numerical methods in many important physical and industrial applications. Full article

(This article belongs to the Special Issue Numerical Simulation and Methods in Computational Fluid Dynamics)

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17 pages, 343 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Gaussian Process Regression with Soft Equality Constraints

by Didem Kochan and Xiu Yang

Mathematics 2025, 13(3), 353; https://doi.org/10.3390/math13030353 - 22 Jan 2025

Cited by 4 | Viewed by 4268

Abstract

This study introduces a novel Gaussian process (GP) regression framework that probabilistically enforces physical constraints, with a particular focus on equality conditions. The GP model is trained using the quantum-inspired Hamiltonian Monte Carlo (QHMC) algorithm, which efficiently samples from a wide range of [...] Read more.

This study introduces a novel Gaussian process (GP) regression framework that probabilistically enforces physical constraints, with a particular focus on equality conditions. The GP model is trained using the quantum-inspired Hamiltonian Monte Carlo (QHMC) algorithm, which efficiently samples from a wide range of distributions by allowing a particle’s mass matrix to vary according to a probability distribution. By integrating QHMC into the GP regression with probabilistic handling of the constraints, this approach balances the computational cost and accuracy in the resulting GP model, as the probabilistic nature of the method contributes to shorter execution times compared with existing GP-based approaches. Additionally, we introduce an adaptive learning algorithm to optimize the selection of constraint locations to further enhance the flexibility of the method. We demonstrate the effectiveness and robustness of our algorithm on synthetic examples, including 2-dimensional and 10-dimensional GP models under noisy conditions, as well as a practical application involving the reconstruction of a sparsely observed steady-state heat transport problem. The proposed approach reduces the posterior variance in the resulting model, achieving stable and accurate sampling results across all test cases while maintaining computational efficiency. Full article

(This article belongs to the Special Issue Machine Learning and Statistical Learning with Applications)

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38 pages, 9211 KB

Open AccessEditor’s ChoiceArticle

Transfinite Patches for Isogeometric Analysis

by Christopher Provatidis

Mathematics 2025, 13(3), 335; https://doi.org/10.3390/math13030335 - 21 Jan 2025

Cited by 8 | Viewed by 2357

Abstract

This paper extends the well-known transfinite interpolation formula, which was developed in the late 1960s by the applied mathematician William Gordon at the premises of General Motors as an extension of the pre-existing Coons interpolation formula. Here, a conjecture is formulated, which claims [...] Read more.

This paper extends the well-known transfinite interpolation formula, which was developed in the late 1960s by the applied mathematician William Gordon at the premises of General Motors as an extension of the pre-existing Coons interpolation formula. Here, a conjecture is formulated, which claims that the meaning of the involved blending functions can be enhanced, such that it includes any linear independent and complete set of functions, including piecewise-linear, trigonometric functions, Bernstein polynomials, B-splines, and NURBS, among others. In this sense, NURBS-based isogeometric analysis and aspects of T-splines may be considered as special cases. Applications are provided to illustrate the accuracy in the interpolation through the L₂ error norm of closed-formed functions prescribed at the nodal points of the transfinite patch, which represent the solution of partial differential equations under boundary conditions of the Dirichlet type. Full article

(This article belongs to the Special Issue Advanced Numerical and Computational Methods for Engineering and Applied Mathematical Problems, 2nd Edition)

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22 pages, 3406 KB

Open AccessEditor’s ChoiceArticle

Design of a Multi-Layer Symmetric Encryption System Using Reversible Cellular Automata

by George Cosmin Stănică and Petre Anghelescu

Mathematics 2025, 13(2), 304; https://doi.org/10.3390/math13020304 - 18 Jan 2025

Cited by 5 | Viewed by 2630

Abstract

The increasing demand for secure and efficient encryption algorithms has intensified the exploration of alternative cryptographic solutions, including biologically inspired systems like cellular automata. This study presents a symmetric block encryption design based on multiple reversible cellular automata (RCAs) that can assure both [...] Read more.

The increasing demand for secure and efficient encryption algorithms has intensified the exploration of alternative cryptographic solutions, including biologically inspired systems like cellular automata. This study presents a symmetric block encryption design based on multiple reversible cellular automata (RCAs) that can assure both computational efficiency and reliable restoration of original data. The encryption key, with a length of 224 bits, is composed of specific rules used by the four distinct RCAs: three with radius-2 neighborhoods and one with a radius-3 neighborhood. By dividing plaintext into 128-bit blocks, the algorithm performs iterative transformations over multiple rounds. Each round includes forward or backward evolution steps, along with dynamically computed shift values and reversible transformations to securely encrypt or decrypt data. The encryption process concludes with an additional layer of security by encrypting the final RCA configurations, further protecting against potential attacks on the encrypted data. Additionally, the 224-bit key length provides robust resistance against brute force attacks. Testing and analysis were performed using a custom-developed software (version 1.0) application, which helped demonstrate the algorithm’s robustness, encryption accuracy, and ability to maintain data integrity. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

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13 pages, 2779 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity

by Plamena I. Marcheva and Stoil I. Ivanov

Mathematics 2025, 13(2), 275; https://doi.org/10.3390/math13020275 - 16 Jan 2025

Cited by 3 | Viewed by 2571

Abstract

In this paper, we investigate the local convergence of Schröder’s method for finding zeros of analytic functions with unknown multiplicity. Thus, we obtain a convergence theorem that provides exact domains of initial points together with error estimates to ensure the Q-quadratic convergence [...] Read more.

In this paper, we investigate the local convergence of Schröder’s method for finding zeros of analytic functions with unknown multiplicity. Thus, we obtain a convergence theorem that provides exact domains of initial points together with error estimates to ensure the Q-quadratic convergence of Schröder’s method right from the first step. A comparison with the famous Newton’s method, based on the convergence and dynamics when it is applied to some polynomial and non-polynomial equations, is also provided. Full article

(This article belongs to the Special Issue New Trends and Developments in Numerical Analysis: 2nd Edition)

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19 pages, 308 KB

Open AccessFeature PaperEditor’s ChoiceArticle

On the Exponential Atom-Bond Connectivity Index of Graphs

by Kinkar Chandra Das

Mathematics 2025, 13(2), 269; https://doi.org/10.3390/math13020269 - 15 Jan 2025

Cited by 7 | Viewed by 3581

Abstract

Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, the literature has introduced the exponential vertex-degree-based topological [...] Read more.

Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, the literature has introduced the exponential vertex-degree-based topological index. The exponential atom-bond connectivity index is defined as follows:

e^{ABC} = e^{ABC} (Υ) = \sum_{v_{i} v_{j} \in E (Υ)} e^{\sqrt{\frac{d_{i} + d_{j} - 2}{d_{i} d_{j}}}},

where

d_{i}

is the degree of the vertex

v_{i}

in

Υ

. In this paper, we prove that the double star

D S_{n - 3, 1}

is the second maximal graph with respect to the

e^{ABC}

index of trees of order n. We give an upper bound on

e^{ABC}

of unicyclic graphs of order n and characterize the maximal graphs. The graph

K_{1} \lor (P_{3} \cup (n - 4) K_{1})

gives the maximal graph with respect to the

e^{ABC}

index of bicyclic graphs of order n. We present several relations between

e^{ABC} (Υ)

and

A B C (Υ)

of graph

Υ

. Finally, we provide a conclusion summarizing our findings and discuss potential directions for future research. Full article

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24 pages, 344 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Localization and Flatness in Quantale Theory

by George Georgescu

Mathematics 2025, 13(2), 227; https://doi.org/10.3390/math13020227 - 11 Jan 2025

Viewed by 1576

Abstract

The study of flat ring morphisms is an important theme in commutative algebra. The purpose of this article is to develop an abstract theory of flatness in the framework of coherent quantales. The first question we must address is the definition of a [...] Read more.

The study of flat ring morphisms is an important theme in commutative algebra. The purpose of this article is to develop an abstract theory of flatness in the framework of coherent quantales. The first question we must address is the definition of a notion of “flat quantale morphism” as an abstraction of flat ring morphisms. For this, we start from a characterization of the flat ring morphism in terms of the ideal residuation theory. The flat coherent quantale morphism is studied in relation to the localization of coherent quantales. The quantale generalizations of some classical theorems from the flat ring morphisms theory are proved. The Going-down and Going-up properties are then studied in connection with localization theory and flat quantale morphisms. As an application, characterizations of zero-dimensional coherent quantales are obtained, formulated in terms of Going-down, Going-up, and localization. We also prove two characterization theorems for the coherent quantales of dimension at most one. The results of the paper can be applied both in the theory of commutative rings and to other algebraic structures: F-rings, semirings, bounded distributive lattices, commutative monoids, etc. Full article

(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics, 3rd Edition)

32 pages, 2819 KB

Open AccessEditor’s ChoiceArticle

Disentangling Sources of Multifractality in Time Series

by Robert Kluszczyński, Stanisław Drożdż, Jarosław Kwapień, Tomasz Stanisz and Marcin Wątorek

Mathematics 2025, 13(2), 205; https://doi.org/10.3390/math13020205 - 9 Jan 2025

Cited by 23 | Viewed by 3302

Abstract

This contribution addresses the question commonly asked in the scientific literature about the sources of multifractality in time series. Two primary sources are typically considered. These are temporal correlations and heavy tails in the distribution of fluctuations. Most often, they are treated as [...] Read more.

This contribution addresses the question commonly asked in the scientific literature about the sources of multifractality in time series. Two primary sources are typically considered. These are temporal correlations and heavy tails in the distribution of fluctuations. Most often, they are treated as two independent components, while true multifractality cannot occur without temporal correlations. The distributions of fluctuations affect the span of the multifractal spectrum only when correlations are present. These issues are illustrated here using series generated by several model mathematical cascades, which by design build correlations into these series. The thickness of the tails of fluctuations in such series is then governed by an appropriate procedure of adjusting them to q-Gaussian distributions, and q is treated as a variable parameter that, while preserving correlations, allows for tuning these distributions to the desired functional form. Multifractal detrended fluctuation analysis (MFDFA), as the most commonly used practical method for quantifying multifractality, is then used to identify the influence of the thickness of the fluctuation tails in the presence of temporal correlations on the width of multifractal spectra. The obtained results point to the Gaussian distribution, so

q = 1

, as the appropriate reference distribution to evaluate the contribution of fatter tails to the width of multifractal spectra. An appropriate procedure is presented to make such estimates. Full article

(This article belongs to the Special Issue Recent Advances in Time Series Analysis)

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15 pages, 885 KB

Open AccessEditor’s ChoiceArticle

Estimating the Relative Risks of Spatial Clusters Using a Predictor–Corrector Method

by Majid Bani-Yaghoub, Kamel Rekab, Julia Pluta and Said Tabharit

Mathematics 2025, 13(2), 180; https://doi.org/10.3390/math13020180 - 7 Jan 2025

Cited by 4 | Viewed by 2224

Abstract

Spatial, temporal, and space–time scan statistics can be used for geographical surveillance, identifying temporal and spatial patterns, and detecting outliers. While statistical cluster analysis is a valuable tool for identifying patterns, optimizing resource allocation, and supporting decision-making, accurately predicting future spatial clusters remains [...] Read more.

Spatial, temporal, and space–time scan statistics can be used for geographical surveillance, identifying temporal and spatial patterns, and detecting outliers. While statistical cluster analysis is a valuable tool for identifying patterns, optimizing resource allocation, and supporting decision-making, accurately predicting future spatial clusters remains a significant challenge. Given the known relative risks of spatial clusters over the past k time intervals, the main objective of the present study is to predict the relative risks for the subsequent interval,

k + 1

. Building on our prior research, we propose a predictive Markov chain model with an embedded corrector component. This corrector utilizes either multiple linear regression or an exponential smoothing method, selecting the one that minimizes the relative distance between the observed and predicted values in the k-th interval. To test the proposed method, we first calculated the relative risks of statistically significant spatial clusters of COVID-19 mortality in the U.S. over seven time intervals from May 2020 to March 2023. Then, for each time interval, we selected the top 25 clusters with the highest relative risks and iteratively predicted the relative risks of clusters from intervals three to seven. The predictive accuracies ranged from moderate to high, indicating the potential applicability of this method for predictive disease analytic and future pandemic preparedness. Full article

(This article belongs to the Section E: Applied Mathematics)

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13 pages, 1675 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Genotype-Structured Modeling of Variant Emergence and Its Impact on Virus Infection

by Anass Bouchnita

Mathematics 2025, 13(1), 167; https://doi.org/10.3390/math13010167 - 6 Jan 2025

Cited by 3 | Viewed by 2611

Abstract

Variant emergence continues to pose a threat to global public health, despite the large-scale campaigns of immunization worldwide. In this paper, we present a genotype-structured model of viral infectious and evolutionary dynamics. We calibrate the model using the available estimates for SARS-CoV-2 infection [...] Read more.

Variant emergence continues to pose a threat to global public health, despite the large-scale campaigns of immunization worldwide. In this paper, we present a genotype-structured model of viral infectious and evolutionary dynamics. We calibrate the model using the available estimates for SARS-CoV-2 infection parameters and use it to study the conditions leading to the emergence of immune escaping variants. In particular, we show that the emergence of highly replicating or immune escaping variants could extend the duration of the infection, while the emergence of variants that are both highly replicating and immune escaping could provoke a rebound of the infection. Then, we show that the high frequency of mutation increases the chances of variant emergence, which promotes virus persistence. Further, simulations suggest that weak neutralization by antibodies could exert a selective pressure that favors the development of aggressive variants. These results can help public health officials identify and isolate the patients from where new variants emerge, which would make genomic surveillance efforts more efficient. Full article

(This article belongs to the Section E3: Mathematical Biology)

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20 pages, 351 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Multilevel Constrained Bandits: A Hierarchical Upper Confidence Bound Approach with Safety Guarantees

by Ali Baheri

Mathematics 2025, 13(1), 149; https://doi.org/10.3390/math13010149 - 3 Jan 2025

Cited by 8 | Viewed by 7130

Abstract

The multi-armed bandit (MAB) problem is a foundational model for sequential decision-making under uncertainty. While MAB has proven valuable in applications such as clinical trials and online advertising, traditional formulations have limitations; specifically, they struggle to handle three key real-world scenarios: (1) when [...] Read more.

The multi-armed bandit (MAB) problem is a foundational model for sequential decision-making under uncertainty. While MAB has proven valuable in applications such as clinical trials and online advertising, traditional formulations have limitations; specifically, they struggle to handle three key real-world scenarios: (1) when decisions must follow a hierarchical structure (as in autonomous systems where high-level strategy guides low-level actions); (2) when there are constraints at multiple levels of decision-making (such as both system-wide and component-level resource limits); and (3) when available actions depend on previous choices or context. To address these challenges, we introduce the hierarchical constrained bandits (HCB) framework, which extends contextual bandits to incorporate both hierarchical decisions and multilevel constraints. We propose the HC-UCB (hierarchical constrained upper confidence bound) algorithm to solve the HCB problem. The algorithm uses confidence bounds within a hierarchical setting to balance exploration and exploitation while respecting constraints at all levels. Our theoretical analysis establishes that HC-UCB achieves sublinear regret, guarantees constraint satisfaction at all hierarchical levels, and is near-optimal in terms of achievable performance. Simple experimental results demonstrate the algorithm’s effectiveness in balancing reward maximization with constraint satisfaction. Full article

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23 pages, 442 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Estimation and Model Misspecification for Recurrent Event Data with Covariates Under Measurement Errors

by Ravinath Alahakoon, Gideon K. D. Zamba, Xuerong Meggie Wen and Akim Adekpedjou

Mathematics 2025, 13(1), 113; https://doi.org/10.3390/math13010113 - 30 Dec 2024

Cited by 1 | Viewed by 1568

Abstract

For subject i, we monitor an event that can occur multiple times over a random observation window [0,

τ_{i}

). At each recurrence, p concomitant variables,

x_{i}

, associated to the event recurrence are recorded—a subset (

q \leq p

[...] Read more.

For subject i, we monitor an event that can occur multiple times over a random observation window [0,

τ_{i}

). At each recurrence, p concomitant variables,

x_{i}

, associated to the event recurrence are recorded—a subset (

q \leq p

) of which is measured with errors. To circumvent the problem of bias and consistency associated with parameter estimation in the presence of measurement errors, we propose inference for corrected estimating equations with well-behaved roots under an additive measurement errors model. We show that estimation is essentially unbiased under the corrected profile likelihood for recurrent events, in comparison to biased estimations under a likelihood function that ignores correction. We propose methods for obtaining estimators of error variance and discuss the properties of the estimators. We further investigate the case of misspecified error models and show that the resulting estimators under misspecification converge to a value different from that of the true parameter—thereby providing a basis for bias assessment. We demonstrate the foregoing correction methods on an open-source rhDNase dataset gathered in a clinical setting. Full article

(This article belongs to the Section D1: Probability and Statistics)

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19 pages, 307 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Existence of Bounded Solutions for a Class of Degenerate Fourth-Order Elliptic Equations with Convection Terms

by Salvatore D’Asero

Mathematics 2025, 13(1), 3; https://doi.org/10.3390/math13010003 - 24 Dec 2024

Viewed by 1279

Abstract

This paper deals with the existence of bounded and locally Hölder continuous weak solutions of the following nonlinear fourth-order Dirichlet problem: [...] Read more.

This paper deals with the existence of bounded and locally Hölder continuous weak solutions of the following nonlinear fourth-order Dirichlet problem:

\sum_{| α | = 1, 2} {(- 1)}^{| α |} D^{α} [A_{α} (x, u, D^{1} u, D^{2} u) - E_{α} (x) {| u |}^{λ (p_{α} - 1)} sign u] = f

in

Ω

, where the coefficients

A_{α}

satisfy a strengthened degenerate coercivity condition. Full article

(This article belongs to the Special Issue Problems and Methods in Nonlinear Analysis)

33 pages, 522 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Monochromatic Graph Decompositions Inspired by Anti-Ramsey Theory and Parity Constraints

by Yair Caro and Zsolt Tuza

Mathematics 2024, 12(23), 3665; https://doi.org/10.3390/math12233665 - 22 Nov 2024

Cited by 1 | Viewed by 4047

Abstract

We open here many new tracks of research in anti-Ramsey Theory, considering edge-coloring problems inspired by rainbow coloring and further by odd colorings and conflict-free colorings. Let G be a graph and

F

any given family of graphs. For every integer [...] Read more.

We open here many new tracks of research in anti-Ramsey Theory, considering edge-coloring problems inspired by rainbow coloring and further by odd colorings and conflict-free colorings. Let G be a graph and

F

any given family of graphs. For every integer

n \geq | G |

, let

f (n, G | F)

denote the smallest integer k such that any edge coloring of

K_{n}

with at least k colors forces a copy of G in which each color class induces a member of

F

. Observe that in anti-Ramsey problems, each color class is a single edge, i.e.,

F = {K_{2}}

. Among the many results introduced in this paper, we mention the following. (1) For every graph G, there exists a constant

c = c (G)

such that in any edge coloring of

K_{n}

with at least

c n

colors there is a copy of G in which every vertex v is incident with an edge whose color appears only once among all edges incident with v. (2) In sharp contrast to the above result we prove that if

F

is the class of all odd graphs (having vertices with odd degrees only) then

f (n, K_{k} | F) = (1 + o (1)) ex (n, K_{⌈ k / 2 ⌉})

, which is quadratic for

k \geq 5

. (3) We exactly determine

f (n, G | F)

for small graphs when

F

belongs to several families representing various odd/even coloring constraints. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

21 pages, 543 KB

Open AccessEditor’s ChoiceArticle

Brauer Configuration Algebras Induced by Integer Partitions and Their Applications in the Theory of Branched Coverings

by Agustín Moreno Cañadas, José Gregorio Rodríguez-Nieto and Olga Patricia Salazar Díaz

Mathematics 2024, 12(22), 3626; https://doi.org/10.3390/math12223626 - 20 Nov 2024

Cited by 3 | Viewed by 2325

Abstract

Brauer configuration algebras are path algebras induced by appropriated multiset systems. Since their structures underlie combinatorial data, the general description of some of their algebraic invariants (e.g., their dimensions or the dimensions of their centers) is a hard problem. Integer partitions and compositions [...] Read more.

Brauer configuration algebras are path algebras induced by appropriated multiset systems. Since their structures underlie combinatorial data, the general description of some of their algebraic invariants (e.g., their dimensions or the dimensions of their centers) is a hard problem. Integer partitions and compositions of a given integer number are examples of multiset systems which can be used to define Brauer configuration algebras. This paper gives formulas for the dimensions of Brauer configuration algebras (and their centers) induced by some integer partitions. As an application of these results, we give examples of Brauer configurations, which can be realized as branch data of suitable branched coverings over different surfaces. Full article

(This article belongs to the Special Issue Algebra and Discrete Mathematics, 4th Edition)

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19 pages, 1058 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Large Sample Behavior of the Least Trimmed Squares Estimator

by Yijun Zuo

Mathematics 2024, 12(22), 3586; https://doi.org/10.3390/math12223586 - 15 Nov 2024

Cited by 2 | Viewed by 2702

Abstract

The least trimmed squares (LTS) estimator is popular in location, regression, machine learning, and AI literature. Despite the empirical version of least trimmed squares (LTS) being repeatedly studied in the literature, the population version of the LTS has never been introduced and studied. [...] Read more.

The least trimmed squares (LTS) estimator is popular in location, regression, machine learning, and AI literature. Despite the empirical version of least trimmed squares (LTS) being repeatedly studied in the literature, the population version of the LTS has never been introduced and studied. The lack of the population version hinders the study of the large sample properties of the LTS utilizing the empirical process theory. Novel properties of the objective function in both empirical and population settings of the LTS and other properties, are established for the first time in this article. The primary properties of the objective function facilitate the establishment of other original results, including the influence function and Fisher consistency. The strong consistency is established with the help of a generalized Glivenko–Cantelli Theorem over a class of functions for the first time. Differentiability and stochastic equicontinuity promote the establishment of asymptotic normality with a concise and novel approach. Full article

(This article belongs to the Special Issue Advances in High-Dimensional Data Analysis)

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14 pages, 292 KB

Open AccessFeature PaperEditor’s ChoiceArticle

New Results on Graph Matching from Degree-Preserving Growth

by Péter L. Erdős, Shubha R. Kharel, Tamás Róbert Mezei and Zoltán Toroczkai

Mathematics 2024, 12(22), 3518; https://doi.org/10.3390/math12223518 - 11 Nov 2024

Cited by 3 | Viewed by 3664

Abstract

The recently introduced model in S. R. Kharel et al.’s study [Degree-preserving network growth. Nature Physics 2022, 18, 100–106] uses matchings to insert new vertices of prescribed degrees into the current graph of an ever-growing graph sequence. The process depends [...] Read more.

The recently introduced model in S. R. Kharel et al.’s study [Degree-preserving network growth. Nature Physics 2022, 18, 100–106] uses matchings to insert new vertices of prescribed degrees into the current graph of an ever-growing graph sequence. The process depends both on the size of the largest available matching, which is the focus of this paper, as well as on the actual choice of the matching. Here, we first show that the question of whether a graphic degree sequence, extended with a new degree

2 δ

, remains graphic is equivalent to the existence of a realization of the original degree sequence with a matching of size

δ

. Secondly, we present lower bounds for the size of the maximum matchings in any realization of the degree sequence. We then study the bounds on the size of maximal matchings in some realizations of the sequence, known as the potential matching number. We also estimate the minimum size of both maximal and maximum matchings, as determined by the degree sequence, independently of graphical realizations. Along this line we answer a question raised by T. Biedl et al.: Tight bounds on maximal and maximum matchings. Discrete Mathematics 2004, 285, 7–15. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

16 pages, 8983 KB

Open AccessEditor’s ChoiceArticle

A Finite-Time Disturbance Observer for Tracking Control of Nonlinear Systems Subject to Model Uncertainties and Disturbances

by Manh Hung Nguyen and Kyoung Kwan Ahn

Mathematics 2024, 12(22), 3512; https://doi.org/10.3390/math12223512 - 10 Nov 2024

Cited by 5 | Viewed by 3162

Abstract

In this study, a finite-time disturbance observer (FTDOB) with a new structure is originally put forward for the motion tracking problem of a class of nonlinear systems subject to model uncertainties and exogenous disturbances. Compared to existing disturbance estimator designs in the literature, [...] Read more.

In this study, a finite-time disturbance observer (FTDOB) with a new structure is originally put forward for the motion tracking problem of a class of nonlinear systems subject to model uncertainties and exogenous disturbances. Compared to existing disturbance estimator designs in the literature, in which the estimation error only converges to the origin asymptotically under assumptions that the first and/or second derivatives are vanishing, the suggested DOB is able to estimate the disturbance exactly in finite time. Firstly, uncertainties (parametric and unstructured uncertainties), unknown dynamics, and external disturbances in system dynamics are lumped into a generalized disturbance term that is subsequently estimated by the proposed DOB. Based on this, a DOB-based backstepping controller is synthesized to ensure high-accuracy tracking performance under various working conditions. The stability analysis of not only the DOB but also the overall closed-loop system is theoretically confirmed by the Lyapunov stability theory. Finally, the advantages of the proposed FTDOB and the FTDOB-based controller over other DOBs and existing DOB-based controllers are explicitly simultaneously demonstrated by a series of numerical simulations on a second-order mechanical system and comparative experiments on an actual DC motor system. Full article

(This article belongs to the Special Issue Advances in Control Systems and Automatic Control)

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12 pages, 1496 KB

Open AccessEditor’s ChoiceArticle

A Long-Memory Model for Multiple Cycles with an Application to the US Stock Market

by Guglielmo Maria Caporale and Luis Alberiko Gil-Alana

Mathematics 2024, 12(22), 3487; https://doi.org/10.3390/math12223487 - 7 Nov 2024

Cited by 2 | Viewed by 7093

Abstract

This paper proposes a long-memory model that includes multiple cycles in addition to the long-run component. Specifically, instead of a single pole or singularity in the spectrum, it allows for multiple poles and, thus, different cycles with different degrees of persistence. It also [...] Read more.

This paper proposes a long-memory model that includes multiple cycles in addition to the long-run component. Specifically, instead of a single pole or singularity in the spectrum, it allows for multiple poles and, thus, different cycles with different degrees of persistence. It also incorporates non-linear deterministic structures in the form of Chebyshev polynomials in time. Simulations are carried out to analyze the finite sample properties of the proposed test, which is shown to perform well in the case of a relatively large sample with at least 1000 observations. The model is then applied to weekly data on the S&P 500 from 1 January 1970 to 26 October 2023 as an illustration. The estimation results based on the first differenced logged values (i.e., the returns) point to the existence of three cyclical structures in the series, with lengths of approximately one month, one year, and four years, respectively, and to orders of integration in the range (0, 0.20), which implies stationary long memory in all cases. Full article

(This article belongs to the Special Issue Applied Time Series and Artificial Intelligence in Economics and Finance)

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22 pages, 780 KB

Open AccessEditor’s ChoiceArticle

Adaptive Production Rescheduling System for Managing Unforeseen Disruptions

by Andy J. Figueroa, Raul Poler and Beatriz Andres

Mathematics 2024, 12(22), 3478; https://doi.org/10.3390/math12223478 - 7 Nov 2024

Cited by 12 | Viewed by 5550

Abstract

This work presents a mixed-integer linear programming (MILP) model to solve the production rescheduling problem in a job shop manufacturing system impacted by unexpected events, aiming to minimize production costs and disruptions to the initial schedule. The approach begins by generating an optimal [...] Read more.

This work presents a mixed-integer linear programming (MILP) model to solve the production rescheduling problem in a job shop manufacturing system impacted by unexpected events, aiming to minimize production costs and disruptions to the initial schedule. The approach begins by generating an optimal production plan through batch assignments to machines. When unforeseen events, such as machine breakdowns or raw material shortages, occur, a dynamic rescheduling process is triggered, employing an iterative and reactive algorithm to adapt the plan to the real-time conditions on the shop floor. The results demonstrate that this rescheduling method efficiently adjusts to the new conditions while minimizing deviations from the original schedule, achieving solutions within acceptable computational times. Full article

(This article belongs to the Section E: Applied Mathematics)

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21 pages, 1179 KB

Open AccessEditor’s ChoiceArticle

The High-Order ADI Difference Method and Extrapolation Method for Solving the Two-Dimensional Nonlinear Parabolic Evolution Equations

by Xin Shen, Xuehua Yang and Haixiang Zhang

Mathematics 2024, 12(22), 3469; https://doi.org/10.3390/math12223469 - 6 Nov 2024

Cited by 11 | Viewed by 2029

Abstract

In this paper, the numerical solution for two-dimensional nonlinear parabolic equations is studied using an alternating-direction implicit (ADI) Crank–Nicolson (CN) difference scheme. Firstly, we use the CN format in the time direction, and then use the CN format in the space direction before [...] Read more.

In this paper, the numerical solution for two-dimensional nonlinear parabolic equations is studied using an alternating-direction implicit (ADI) Crank–Nicolson (CN) difference scheme. Firstly, we use the CN format in the time direction, and then use the CN format in the space direction before discretizing the second-order center difference quotient. In addition, we strictly prove that the proposed ADI difference scheme has unique solvability and is unconditionally stable and convergent. The extrapolation method is further applied to improve the numerical solution accuracy. Finally, two numerical examples are given to verify our theoretical results. Full article

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13 pages, 433 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Families of Planar Orbits in Polar Coordinates Compatible with Potentials

by Thomas Kotoulas

Mathematics 2024, 12(21), 3435; https://doi.org/10.3390/math12213435 - 2 Nov 2024

Viewed by 1156

Abstract

In light of the planar inverse problem of Newtonian Dynamics, we study the monoparametric family of regular orbits

f (r, θ) = c

in polar coordinates (where c is the parameter varying along the family of orbits), which are generated [...] Read more.

In light of the planar inverse problem of Newtonian Dynamics, we study the monoparametric family of regular orbits

f (r, θ) = c

in polar coordinates (where c is the parameter varying along the family of orbits), which are generated by planar potentials

V = V (r, θ)

. The corresponding family of orbits can be uniquely represented by the “slope function”

γ = \frac{f_{θ}}{f_{r}}

. By using the basic partial differential equation of the planar inverse problem, which combines families of orbits and potentials, we apply a new methodology in order to find specific potentials, e.g.,

V = A (r) + B (θ)

or

V = H (γ)

and one-dimensional potentials, e.g.,

V = A (r)

or

V = G (θ)

. In order to determine such potentials, differential conditions on the family of orbits

f (r, θ)

= c are imposed. If these conditions are fulfilled, then we can find a potential of the above form analytically. For the given families of curves, such as ellipses, parabolas, Bernoulli’s lemniscates, etc., we find potentials that produce them. We present suitable examples for all cases and refer to the case of straight lines. Full article

(This article belongs to the Section E4: Mathematical Physics)

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31 pages, 1871 KB

Open AccessEditor’s ChoiceArticle

3D Reconstruction of Geometries for Urban Areas Supported by Computer Vision or Procedural Generations

by Hanli Liu, Carlos J. Hellín, Abdelhamid Tayebi, Carlos Delgado and Josefa Gómez

Mathematics 2024, 12(21), 3331; https://doi.org/10.3390/math12213331 - 23 Oct 2024

Cited by 5 | Viewed by 3032

Abstract

This work presents a numerical mesh generation method for 3D urban scenes that could be easily converted into any 3D format, different from most implementations which are limited to specific environments in their applicability. The building models have shaped roofs and faces with [...] Read more.

This work presents a numerical mesh generation method for 3D urban scenes that could be easily converted into any 3D format, different from most implementations which are limited to specific environments in their applicability. The building models have shaped roofs and faces with static colors, combining the buildings with a ground grid. The building generation uses geographic positions and shape names, which can be extracted from OpenStreetMap. Additional steps, like a computer vision method, can be integrated into the generation optionally to improve the quality of the model, although this is highly time-consuming. Its function is to classify unknown roof shapes from satellite images with adequate resolution. The generation can also use custom geographic information. This aspect was tested using information created by procedural processes. The method was validated by results generated for many realistic scenarios with multiple building entities, comparing the results between using computer vision and not. The generated models were attempted to be rendered under Graphics Library Transmission Format and Unity Engine. In future work, a polygon-covering algorithm needs to be completed to process the building footprints more effectively, and a solution is required for the missing height values in OpenStreetMap. Full article

(This article belongs to the Special Issue Object Detection: Algorithms, Computations and Practices)

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30 pages, 10941 KB

Open AccessEditor’s ChoiceArticle

Closed-Boundary Reflections of Shallow Water Waves as an Open Challenge for Physics-Informed Neural Networks

by Kubilay Timur Demir, Kai Logemann and David S. Greenberg

Mathematics 2024, 12(21), 3315; https://doi.org/10.3390/math12213315 - 22 Oct 2024

Cited by 6 | Viewed by 4084

Abstract

Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to traditional numerical methods for solving partial differential equations (PDEs) in fluid dynamics. By using PDE-derived loss functions and auto-differentiation, PINNs can recover solutions without requiring costly simulation data, spatial gridding, or [...] Read more.

Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to traditional numerical methods for solving partial differential equations (PDEs) in fluid dynamics. By using PDE-derived loss functions and auto-differentiation, PINNs can recover solutions without requiring costly simulation data, spatial gridding, or time discretization. However, PINNs often exhibit slow or incomplete convergence, depending on the architecture, optimization algorithms, and complexity of the PDEs. To address these difficulties, a variety of novel and repurposed techniques have been introduced to improve convergence. Despite these efforts, their effectiveness is difficult to assess due to the wide range of problems and network architectures. As a novel test case for PINNs, we propose one-dimensional shallow water equations with closed boundaries, where the solutions exhibit repeated boundary wave reflections. After carefully constructing a reference solution, we evaluate the performance of PINNs across different architectures, optimizers, and special training techniques. Despite the simplicity of the problem for classical methods, PINNs only achieve accurate results after prohibitively long training times. While some techniques provide modest improvements in stability and accuracy, this problem remains an open challenge for PINNs, suggesting that it could serve as a valuable testbed for future research on PINN training techniques and optimization strategies. Full article

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30 pages, 10109 KB

Open AccessEditor’s ChoiceArticle

AI-Powered Approaches for Hypersurface Reconstruction in Multidimensional Spaces

by Kostadin Yotov, Emil Hadzhikolev, Stanka Hadzhikoleva and Mariyan Milev

Mathematics 2024, 12(20), 3285; https://doi.org/10.3390/math12203285 - 19 Oct 2024

Cited by 1 | Viewed by 2168

Abstract

The present article explores the possibilities of using artificial neural networks to solve problems related to reconstructing complex geometric surfaces in Euclidean and pseudo-Euclidean spaces, examining various approaches and techniques for training the networks. The main focus is on the possibility of training [...] Read more.

The present article explores the possibilities of using artificial neural networks to solve problems related to reconstructing complex geometric surfaces in Euclidean and pseudo-Euclidean spaces, examining various approaches and techniques for training the networks. The main focus is on the possibility of training a set of neural networks with information about the available surface points, which can then be used to predict and complete missing parts. A method is proposed for using separate neural networks that reconstruct surfaces in different spatial directions, employing various types of architectures, such as multilayer perceptrons, recursive networks, and feedforward networks. Experimental results show that artificial neural networks can successfully approximate both smooth surfaces and those containing singular points. The article presents the results with the smallest error, showcasing networks of different types, along with a technique for reconstructing geographic relief. A comparison is made between the results achieved by neural networks and those obtained using traditional surface approximation methods such as Bézier curves, k-nearest neighbors, principal component analysis, Markov random fields, conditional random fields, and convolutional neural networks. Full article

(This article belongs to the Special Issue Machine Learning and Evolutionary Algorithms: Theory and Applications)

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29 pages, 466 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Elimination Algorithms for Skew Polynomials with Applications in Cybersecurity

by Raqeeb Rasheed, Ali Safaa Sadiq and Omprakash Kaiwartya

Mathematics 2024, 12(20), 3258; https://doi.org/10.3390/math12203258 - 17 Oct 2024

Viewed by 2758

Abstract

It is evident that skew polynomials offer promising directions for developing cryptographic schemes. This paper focuses on exploring skew polynomials and studying their properties with the aim of exploring their potential applications in fields such as cryptography and combinatorics. We begin by deriving [...] Read more.

It is evident that skew polynomials offer promising directions for developing cryptographic schemes. This paper focuses on exploring skew polynomials and studying their properties with the aim of exploring their potential applications in fields such as cryptography and combinatorics. We begin by deriving the concept of resultants for bivariate skew polynomials. Then, we employ the derived resultant to incrementally eliminate indeterminates in skew polynomial systems, utilising both direct and modular approaches. Finally, we discuss some applications of the derived resultant, including cryptographic schemes (such as Diffie–Hellman) and combinatorial identities (such as Pascal’s identity). We start by considering a bivariate skew polynomial system with two indeterminates; our intention is to isolate and eliminate one of the indeterminates to reduce the system to a simpler form (that is, relying only on one indeterminate in this case). The methodology is composed of two main techniques; in the first technique, we apply our definition of a (bivariate) resultant via a Sylvester-style matrix directly from the polynomials’ coefficients, while the second is based on modular methods where we compute the resultant by using evaluation and interpolation approaches. The idea of this second technique is that instead of computing the resultant directly from the coefficients, we propose to evaluate the polynomials at a set of valid points to compute its corresponding set of partial resultants first; then, we can deduce the original resultant by combining all these partial resultants using an interpolation technique by utilising a theorem we have established. Full article

(This article belongs to the Topic Modeling and Practice for Trustworthy and Secure Systems)

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25 pages, 575 KB

Open AccessEditor’s ChoiceArticle

Mathematical Analysis of Four Fundamental Epidemiological Models for Monkeypox Disease Outbreaks: On the Pivotal Role of Human–Animal Order Parameters—In Memory of Hermann Haken

by Till D. Frank

Mathematics 2024, 12(20), 3215; https://doi.org/10.3390/math12203215 - 14 Oct 2024

Cited by 6 | Viewed by 2573

Abstract

Four fundamental models that describe the spread of Monkeypox disease are analyzed: the SIR-SIR, SEIR-SIR, SIR-SEIR, and SEIR-SEIR models. They form the basis of most Monkeypox diseases models that are currently discussed in the literature. It is shown that the way the model [...] Read more.

Four fundamental models that describe the spread of Monkeypox disease are analyzed: the SIR-SIR, SEIR-SIR, SIR-SEIR, and SEIR-SEIR models. They form the basis of most Monkeypox diseases models that are currently discussed in the literature. It is shown that the way the model subpopulations are organized in disease outbreaks and evolve relative to each other is determined by the relevant unstable system eigenvectors, also called order parameters. For all models, analytical expressions of the order parameters are derived. Under appropriate conditions these order parameters describe the initial outbreak phases of exponential increase in good approximation. It is shown that all four models exhibit maximally two order parameters and maximally one human–animal order parameter. The human–animal order parameter firmly connects the outbreak dynamics in the animal system with the dynamics in the human system. For the special case of the SIR-SIR model, it is found that the two possible order parameters completely describe the dynamics of infected humans and animals during entire infection waves. Finally, a simulation of a Monkeypox infection wave illustrates that in line with the aforementioned analytical results the leading order parameter explains most of the variance in the infection dynamics. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis of Problems in Ecology, Epidemiology and Oncology)

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8 pages, 1079 KB

Open AccessEditor’s ChoiceArticle

Riemannian Manifolds, Closed Geodesic Lines, Topology and Ramsey Theory

by Edward Bormashenko

Mathematics 2024, 12(20), 3206; https://doi.org/10.3390/math12203206 - 13 Oct 2024

Viewed by 3169

Abstract

We applied the Ramsey analysis to the sets of points belonging to Riemannian manifolds. The points are connected with two kinds of lines: geodesic and non-geodesic. This interconnection between the points is mapped into the bi-colored, complete Ramsey graph. The selected points correspond [...] Read more.

We applied the Ramsey analysis to the sets of points belonging to Riemannian manifolds. The points are connected with two kinds of lines: geodesic and non-geodesic. This interconnection between the points is mapped into the bi-colored, complete Ramsey graph. The selected points correspond to the vertices of the graph, which are connected with the bi-colored links. The complete bi-colored graph containing six vertices inevitably contains at least one mono-colored triangle; hence, a mono-colored triangle, built of the green or red links, i.e., non-geodesic or geodesic lines, consequently appears in the graph. We also considered the bi-colored, complete Ramsey graphs emerging from the intersection of two Riemannian manifolds. Two Riemannian manifolds, namely

(M_{1}, g_{1})

and

(M_{2}, g_{2})

, represented by the Riemann surfaces which intersect along the curve

(M_{1}, g_{1}) \cap (M_{2}, g_{2}) = ℒ

were addressed. Curve

ℒ

does not contain geodesic lines in either of the manifolds

(M_{1}, g_{1})

and

(M_{2}, g_{2})

. Consider six points located on the

ℒ :

{1, \dots 6} \subset ℒ

. The points

{1, \dots 6} \subset ℒ

are connected with two distinguishable kinds of the geodesic lines, namely with the geodesic lines belonging to the Riemannian manifold

(M_{1}, g_{1})

/red links, and, alternatively, with the geodesic lines belonging to the manifold

(M_{2}, g_{2})

/green links. Points

{1, \dots 6} \subset ℒ

form the vertices of the complete graph, connected with two kinds of links. The emerging graph contains at least one closed geodesic line. The extension of the theorem to the Riemann surfaces of various Euler characteristics is presented. Full article

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13 pages, 283 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Dini’s Theorem for Fuzzy Number-Valued Continuous Functions

by Juan José Font, Sergio Macario and Manuel Sanchis

Mathematics 2024, 12(20), 3209; https://doi.org/10.3390/math12203209 - 13 Oct 2024

Viewed by 1989

Abstract

This work aims to provide several versions of Dini’s theorem for fuzzy number-valued continuous functions defined on a compact set K. In this context, there is a wide variety of possibilities since, unlike the real line, we can consider different topologies and [...] Read more.

This work aims to provide several versions of Dini’s theorem for fuzzy number-valued continuous functions defined on a compact set K. In this context, there is a wide variety of possibilities since, unlike the real line, we can consider different topologies and orders on the set of fuzzy numbers. For example, we will show that the fuzzy Dini’s theorem holds for the usual partial orders and the most commonly used topologies but does not hold for all orders in general. Full article

(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)

21 pages, 389 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Constraint Qualifications and Optimality Conditions for Nonsmooth Semidefinite Multiobjective Programming Problems with Mixed Constraints Using Convexificators

by Balendu Bhooshan Upadhyay, Shubham Kumar Singh and Ioan Stancu-Minasian

Mathematics 2024, 12(20), 3202; https://doi.org/10.3390/math12203202 - 12 Oct 2024

Cited by 2 | Viewed by 2007

Abstract

In this article, we investigate a class of non-smooth semidefinite multiobjective programming problems with inequality and equality constraints (in short, NSMPP). We establish the convex separation theorem for the space of symmetric matrices. Employing the properties of the convexificators, we establish Fritz John [...] Read more.

In this article, we investigate a class of non-smooth semidefinite multiobjective programming problems with inequality and equality constraints (in short, NSMPP). We establish the convex separation theorem for the space of symmetric matrices. Employing the properties of the convexificators, we establish Fritz John (in short, FJ)-type necessary optimality conditions for NSMPP. Subsequently, we introduce a generalized version of Abadie constraint qualification (in short, NSMPP-ACQ) for the considered problem, NSMPP. Employing NSMPP-ACQ, we establish strong Karush-Kuhn-Tucker (in short, KKT)-type necessary optimality conditions for NSMPP. Moreover, we establish sufficient optimality conditions for NSMPP under generalized convexity assumptions. In addition to this, we introduce the generalized versions of various other constraint qualifications, namely Kuhn-Tucker constraint qualification (in short, NSMPP-KTCQ), Zangwill constraint qualification (in short, NSMPP-ZCQ), basic constraint qualification (in short, NSMPP-BCQ), and Mangasarian-Fromovitz constraint qualification (in short, NSMPP-MFCQ), for the considered problem NSMPP and derive the interrelationships among them. Several illustrative examples are furnished to demonstrate the significance of the established results. Full article

(This article belongs to the Special Issue Mathematical Optimization and Control: Methods and Applications)

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18 pages, 361 KB

Open AccessEditor’s ChoiceArticle

A New Class of Braided Block Codes Constructed by Convolutional Interleavers

by Sina Vafi

Mathematics 2024, 12(19), 3127; https://doi.org/10.3390/math12193127 - 6 Oct 2024

Cited by 2 | Viewed by 1930

Abstract

Parallel Concatenated Block (PCB) codes are conventionally represented as high-rate codes with low error correcting capability. To form a reliable and outstanding code, this paper presents a modification on the structure of PCB codes, which is accomplished by encoding some parity bits of [...] Read more.

Parallel Concatenated Block (PCB) codes are conventionally represented as high-rate codes with low error correcting capability. To form a reliable and outstanding code, this paper presents a modification on the structure of PCB codes, which is accomplished by encoding some parity bits of one of their component codes. For the newly proposed code, named as the braided code, non-stuff bit-based convolutional interleavers are applied, aiming to minimize the design complexity while ensuring the proper permutations of the original message and selected parity bits. To precisely determine the error correcting capability, a tight bound for the minimum weight of braided code is presented. Additionally, further analyses are provided, which verify iterative decoding performance and the complexity of the constructed code. It is concluded that an outstanding braided code is formed by utilizing a reasonable number of iterations applied at its decoding processes, while maintaining its design complexity at a level similar to other well-known codes. The significant performance of short and long-length-based braided codes is evident in both waterfall and error floor regions. Full article

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