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679,567 Results Found

  • Feature Paper
  • Article
  • Open Access
11 Citations
8,200 Views
36 Pages

24 September 2022

Empirical studies on formal methods and tools are rare. In this paper, we provide guidelines for such studies. We mention their main ingredients and then define nine different study strategies (usability testing, laboratory experiments with software...

  • Expression of Concern
  • Open Access
2 Citations
2,793 Views
1 Page
  • Article
  • Open Access
9 Citations
5,349 Views
9 Pages

Umbral Methods and Harmonic Numbers

  • Giuseppe Dattoli,
  • Bruna Germano,
  • Silvia Licciardi and
  • Maria Renata Martinelli

1 September 2018

The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.

(This article belongs to the Special Issue Mathematical Analysis and Applications)
  • Article
  • Open Access
3 Citations
3,424 Views
12 Pages

Attitudes towards Research Methods in Education: Development of the ATRMQ Scale

  • Antonio Matas-Terrón,
  • Lourdes Aranda,
  • Pablo Daniel Franco-Caballero and
  • Esther Mena-Rodríguez

The noticeable lack of knowledge among Spanish university students regarding the disciplinary content of research methodology is notable, despite the considerable potential benefits for curriculum design. This study represents the initial phase of a...

(This article belongs to the Section Higher Education)
  • Article
  • Open Access
  • Best Paper Award
466 Citations
19,138 Views
56 Pages

20 September 2020

Multi-Criteria Decision-Analysis (MCDA) methods are successfully applied in different fields and disciplines. However, in many studies, the problem of selecting the proper methods and parameters for the decision problems is raised. The paper undertak...

(This article belongs to the Special Issue Uncertain Multi-Criteria Optimization Problems)
  • Feature Paper
  • Article
  • Open Access
1 Citations
3,633 Views
30 Pages

Geometric Numerical Methods for Lie Systems and Their Application in Optimal Control

  • Luis Blanco Díaz,
  • Cristina Sardón,
  • Fernando Jiménez Alburquerque and
  • Javier de Lucas

19 June 2023

A Lie system is a nonautonomous system of first-order ordinary differential equations whose general solution can be written via an autonomous function, the so-called (nonlinear) superposition rule of a finite number of particular solutions and some p...

(This article belongs to the Special Issue Symmetry and Applications of Differential Geometry to the Differential Equations of Mathematical Physics)
  • Article
  • Open Access
3 Citations
2,903 Views
24 Pages

A Family of Multi-Step Subgradient Minimization Methods

  • Elena Tovbis,
  • Vladimir Krutikov,
  • Predrag Stanimirović,
  • Vladimir Meshechkin and ,
  • Aleksey Popov and
  • Lev Kazakovtsev
  • + 1 author+ 0 author

11 May 2023

For solving non-smooth multidimensional optimization problems, we present a family of relaxation subgradient methods (RSMs) with a built-in algorithm for finding the descent direction that forms an acute angle with all subgradients in the neighborhoo...

(This article belongs to the Section E1: Mathematics and Computer Science)
  • Systematic Review
  • Open Access
302 Views
27 Pages

AI-Based Educational Interventions for Students with Down Syndrome: A Mixed-Methods Systematic Review

  • Antonia Cascales-Martínez,
  • José David Cuesta Sáez de Tejada and
  • Carmen Sánchez-Seller

21 October 2026

Artificial intelligence (AI) is assumed to individualise learning, yet no quantitative synthesis has examined what happens when the intervention targets students with Down syndrome (DS). The review presented here analyses this effect and the extent t...

(This article belongs to the Special Issue Supporting Students with Learning Difficulties: Evidence-Based Assessment, Intervention, and Classroom Strategies)
  • Article
  • Open Access
8 Citations
2,884 Views
18 Pages

14 February 2024

The integro-differential equation with the Cauchy kernel is used in many different technical problems, such as in circuit analysis or gas infrared radiation studies. Therefore, it is important to be able to solve this type of equation, even in an app...

(This article belongs to the Special Issue Symmetric and Asymmetric Data in Solution Models, Part II)
  • Article
  • Open Access
1 Citations
2,642 Views
7 Pages

q-Functions and Distributions, Operational and Umbral Methods

  • Giuseppe Dattoli,
  • Silvia Licciardi,
  • Bruna Germano and
  • Maria Renata Martinelli

21 October 2021

The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials. These methods have helped to frame either elementary and special functions within the same logi...

(This article belongs to the Special Issue Advances in Functional Equations and Convex Analysis)
  • Article
  • Open Access
1 Citations
1,561 Views
21 Pages

7 April 2025

Factorial invariance is critical for ensuring consistent relationships between measured variables and latent constructs across groups or time, enabling valid comparisons in social science research. Detecting factorial invariance becomes challenging w...

(This article belongs to the Special Issue Exploring New Frontiers in Psychometrics: Advancing Measurement of Skills and Behaviors)
  • Article
  • Open Access
1 Citations
629 Views
22 Pages

Properties and Application of Incomplete Orthogonalization in the Directions of Gradient Difference in Optimization Methods

  • Vladimir Krutikov,
  • Elena Tovbis,
  • Svetlana Gutova,
  • Ivan Rozhnov and
  • Lev Kazakovtsev

18 December 2025

This paper considers the problem of unconstrained minimization of smooth functions. Despite the high efficiency of quasi-Newton methods such as BFGS, their performance degrades in ill-conditioned problems with unstable or rapidly varying Hessians&mda...

  • Review
  • Open Access
22 Citations
9,109 Views
38 Pages

Pyrrolizidine Alkaloids as Hazardous Toxins in Natural Products: Current Analytical Methods and Latest Legal Regulations

  • Agnieszka Lis-Cieplak,
  • Katarzyna Trześniowska,
  • Krzysztof Stolarczyk and
  • Elżbieta U. Stolarczyk

10 July 2024

Pyrrolizidine alkaloids (PAs) are toxic compounds that occur naturally in certain plants, however, there are many secondary pathways causing PA contamination of other plants, including medicinal herbs and plant-based food products, which pose a risk...

(This article belongs to the Special Issue Advanced Pharmaceutical Analytical Technology)
  • Review
  • Open Access
1 Citations
1,518 Views
26 Pages

One-Rank Linear Transformations and Fejer-Type Methods: An Overview

  • Volodymyr Semenov,
  • Petro Stetsyuk,
  • Viktor Stovba and
  • José Manuel Velarde Cantú

14 May 2024

Subgradient methods are frequently used for optimization problems. However, subgradient techniques are characterized by slow convergence for minimizing ravine convex functions. To accelerate subgradient methods, special linear non-orthogonal transfor...

(This article belongs to the Special Issue Innovations in Optimization and Operations Research)
  • Article
  • Open Access
3 Citations
3,080 Views
28 Pages

Machine Learning in Quasi-Newton Methods

  • Vladimir Krutikov,
  • Elena Tovbis,
  • Predrag Stanimirović,
  • Lev Kazakovtsev and
  • Darjan Karabašević

5 April 2024

In this article, we consider the correction of metric matrices in quasi-Newton methods (QNM) from the perspective of machine learning theory. Based on training information for estimating the matrix of the second derivatives of a function, we formulat...

(This article belongs to the Special Issue Multiple-Criteria Decision-Making and Computational Intelligence: Recent Applications II)
  • Article
  • Open Access
5 Citations
3,104 Views
26 Pages

Recurrent Neural Network Models Based on Optimization Methods

  • Predrag S. Stanimirović,
  • Spyridon D. Mourtas,
  • Vasilios N. Katsikis,
  • Lev A. Kazakovtsev and
  • Vladimir N. Krutikov

16 November 2022

Many researchers have addressed problems involving time-varying (TV) general linear matrix equations (GLMEs) because of their importance in science and engineering. This research discusses and solves the topic of solving TV GLME using the zeroing neu...

(This article belongs to the Special Issue Advances in Analysis and Application of Mathematical Optimization Algorithms)
  • Article
  • Open Access
1 Citations
1,618 Views
14 Pages

Influence of Preparation Methods on the Physicochemical and Functional Properties of NiO-CeO2/Al2O3 Catalysts

  • Laura Myltykbayeva,
  • Manshuk Mambetova,
  • Moldir Anissova,
  • Nursaya Makayeva and ,
  • Kusman Dossumov and
  • Gaukhar Yergaziyeva
  • + 1 author+ 0 author

18 August 2025

This study presents a comparative investigation of 3Ni2Ce/Al catalysts synthesized via different methods dry impregnation (DI), capillary impregnation (CI), and solution combustion synthesis (SC) for the complete oxidation of methane. The aim was to...

(This article belongs to the Section Composites Manufacturing and Processing)
  • Article
  • Open Access
16 Citations
9,279 Views
19 Pages

COVID-19 Spread Forecasting, Mathematical Methods vs. Machine Learning, Moscow Case

  • Matvey Pavlyutin,
  • Marina Samoyavcheva,
  • Rasul Kochkarov,
  • Ekaterina Pleshakova and ,
  • Sergey Korchagin,
  • Timur Gataullin,
  • Petr Nikitin and
  • Mohiniso Hidirova
  • + 3 authors+ 0 author

9 January 2022

To predict the spread of the new coronavirus infection COVID-19, the critical values of spread indicators have been determined for deciding on the introduction of restrictive measures using the city of Moscow as an example. A model was developed usin...

  • Article
  • Open Access
8 Citations
3,721 Views
15 Pages

On the Convergence Rate of Quasi-Newton Methods on Strongly Convex Functions with Lipschitz Gradient

  • Vladimir Krutikov,
  • Elena Tovbis,
  • Predrag Stanimirović and
  • Lev Kazakovtsev

21 November 2023

The main results of the study of the convergence rate of quasi-Newton minimization methods were obtained under the assumption that the method operates in the region of the extremum of the function, where there is a stable quadratic representation of...

(This article belongs to the Section E1: Mathematics and Computer Science)
  • Article
  • Open Access
8 Citations
2,943 Views
19 Pages

Computational Methods for Parameter Identification in 2D Fractional System with Riemann–Liouville Derivative

  • Rafał Brociek,
  • Agata Wajda,
  • Grazia Lo Sciuto,
  • Damian Słota and
  • Giacomo Capizzi

20 April 2022

In recent times, many different types of systems have been based on fractional derivatives. Thanks to this type of derivatives, it is possible to model certain phenomena in a more precise and desirable way. This article presents a system consisting o...

(This article belongs to the Special Issue Digital Signal Processing, Computational Methods and Sensor Networks for Engineering Application)
  • Article
  • Open Access
22 Citations
1,010 Views
48 Pages

Comparative Assessment of the Reliability of Non-Recoverable Subsystems of Mining Electronic Equipment Using Various Computational Methods

  • Nikita V. Martyushev,
  • Boris V. Malozyomov,
  • Anton Y. Demin,
  • Alexander V. Pogrebnoy and ,
  • Georgy E. Kurdyumov,
  • Viktor V. Kondratiev and
  • Antonina I. Karlina
  • + 2 authors+ 0 author

19 February 2026

The assessment of reliability in non-repairable subsystems of mining electronic equipment represents a computationally challenging problem, particularly for complex and highly connected structures. This study presents a systematic comparative analysi...

(This article belongs to the Special Issue Mathematical Foundations of Reliability Theory with Applications in Engineering and Applied Statistics)
  • Article
  • Open Access
6 Citations
5,345 Views
14 Pages

25 July 2020

The redefinition of the objectives of the European Higher Education Area (EHEA) generates novelty in the teaching design developed by universities. The constructivist perspective encourages the use of methods that promote teamwork, an interest for in...

(This article belongs to the Section Sustainable Education and Approaches)
  • Article
  • Open Access
4,239 Views
21 Pages

An effective method is a computational method that might, in principle, be executed by a human. In this paper, I argue that there are methods for computing that are not effective methods. The examples I consider are taken primarily from quantum compu...

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)
  • Article
  • Open Access
13 Citations
3,080 Views
26 Pages

Improvement of Unconstrained Optimization Methods Based on Symmetry Involved in Neutrosophy

  • Predrag S. Stanimirović,
  • Branislav Ivanov,
  • Dragiša Stanujkić,
  • Vasilios N. Katsikis and ,
  • Spyridon D. Mourtas,
  • Lev A. Kazakovtsev and
  • Seyyed Ahmad Edalatpanah
  • + 2 authors+ 0 author

16 January 2023

The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Pa...

(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry II)
  • Abstract
  • Open Access

Body composition changes in resistance-trained adults Following 8-Weeks of supplementation with a combination of plant protein and creatine monohydrate

  • Joesi M. Methods,
  • Kevin F. Holley,
  • Alex C. Schrautemeier,
  • James L. Tice and ,
  • Joshua Iannotti,
  • Anthony M. Hagele,
  • Connor J. Gaige,
  • Wyatt B. McLaughlin,
  • Ralf Jäger and
  • Chad M. Kerksick
  • + 5 authors+ 0 author

Introduction: Adequate dietary protein supports body composition changes while resistance training. Due to its complete amino acid profile, whey protein has routinely outperformed plant-based options. However, when dosed effectively, plant-based prot...

  • Article
  • Open Access
2 Citations
1,504 Views
16 Pages

N-Methods

  • Ahu Açikgöz and
  • Ferhat Esenbel

28 May 2025

In this paper, we present the concept of GN-topological space by introducing a topology defined on a subfamily of the family consisting of all convergent nets in any general topological space. Inspired by the method concept, which is a type of functi...

(This article belongs to the Section Geometry and Topology)
  • Article
  • Open Access
36 Citations
3,540 Views
40 Pages

Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws

  • Irene Gómez-Bueno,
  • Manuel Jesús Castro Díaz,
  • Carlos Parés and
  • Giovanni Russo

29 July 2021

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction opera...

(This article belongs to the Special Issue Numerical Methods for Evolutionary Problems)
  • Article
  • Open Access
4 Citations
3,796 Views
13 Pages

Statistical Multivariate Methods for the Selection of High-Yielding Rapeseed Lines with Varied Seed Coat Color

  • Agnieszka Łopatyńska,
  • Joanna Wolko,
  • Jan Bocianowski,
  • Adrian Cyplik and
  • Katarzyna Gacek

A crucial aim for rapeseed breeders is increasing the seed yield through improving yield- and silique-related traits. In this research, traits including the number of seeds per silique, silique length, silique width, and thousand-seed weight combined...

(This article belongs to the Special Issue Germplasm Resources Exploration and Genetic Breeding of Crops)
  • Article
  • Open Access
4 Citations
1,612 Views
9 Pages

7 December 2024

The Troesch problem is a well-known and important problem; the ability to solve it is important due to the practical applications of this problem. In this paper, we propose a method to solve this problem using a combination of two useful algorithms:...

(This article belongs to the Section E: Applied Mathematics)
  • Article
  • Open Access
2 Citations
1,775 Views
19 Pages

1 October 2024

In recent years, the need for high-performance computing solutions has increased due to the growing complexity of computational tasks. The use of parallel processing techniques has become essential to address this demand. In this study, an Open Compu...

(This article belongs to the Special Issue Best Practices, Challenges and Opportunities in Software Engineering)
  • Article
  • Open Access
2,627 Views
24 Pages

14 October 2022

Some matrix-splitting iterative methods for solving systems of linear equations contain parameters that need to be specified in advance, and the choice of these parameters directly affects the efficiency of the corresponding iterative methods. This p...

(This article belongs to the Special Issue Matrix Equations and Their Algorithms Analysis)
  • Feature Paper
  • Article
  • Open Access
26 Citations
10,101 Views
27 Pages

30 September 2017

The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention has to be paid to the choice of a suitable numerical technique such th...

(This article belongs to the Special Issue Computational Mechanics of Cohesive-Frictional Materials)
  • Review
  • Open Access
64 Citations
19,721 Views
16 Pages

Review of Rotor Balancing Methods

  • Liqing Li,
  • Shuqian Cao,
  • Jing Li,
  • Rimin Nie and
  • Lanlan Hou

This review is dedicated to balancing methods that are used to solve the rotor-balancing problem. To ensure a stable operation over an operating speed range, it is necessary to balance a rotor. The traditional methods, including the influence coeffic...

(This article belongs to the Section Turbomachinery)
  • Entry
  • Open Access
2 Citations
42,041 Views
10 Pages

Humans have always wanted to know what the future holds in store for them. In earlier centuries, people often sought clues to the future from sacred texts. Today, more secular approaches are increasingly used, although the older approaches to the fut...

(This article belongs to the Section Social Sciences)
  • Article
  • Open Access
5 Citations
1,858 Views
15 Pages

25 August 2023

This paper presents a numerical method for solving a two-dimensional subdiffusion equation with a Caputo fractional derivative. The problem considered assumes symmetry in both the equation’s solution domain and the boundary conditions, allowing...

(This article belongs to the Special Issue Symmetry in Computational and Mathematical Methods of Fractional Calculus)
  • Article
  • Open Access
8 Citations
2,776 Views
21 Pages

1 November 2022

The aim of this paper is the adaptation of the alternating phase truncation (APT) method for solving the two-phase time-fractional Stefan problem. The aim was to determine the approximate temperature distribution in the domain with the moving boundar...

(This article belongs to the Special Issue Trends in Fractional Modelling in Science and Innovative Technologies)
  • Article
  • Open Access
9 Citations
3,785 Views
16 Pages

A Bounded Scheduling Method for Adaptive Gradient Methods

  • Mingxing Tang,
  • Zhen Huang,
  • Yuan Yuan,
  • Changjian Wang and
  • Yuxing Peng

1 September 2019

Many adaptive gradient methods have been successfully applied to train deep neural networks, such as Adagrad, Adadelta, RMSprop and Adam. These methods perform local optimization with an element-wise scaling learning rate based on past gradients. Alt...

(This article belongs to the Special Issue Texture and Colour in Image Analysis)
  • Article
  • Open Access
5 Citations
4,377 Views
20 Pages

Single Imputation Methods and Confidence Intervals for the Gini Index

  • Encarnación Álvarez-Verdejo,
  • Pablo J. Moya-Fernández and
  • Juan F. Muñoz-Rosas

15 December 2021

The problem of missing data is a common feature in any study, and a single imputation method is often applied to deal with this problem. The first contribution of this paper is to analyse the empirical performance of some traditional single imputatio...

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)
  • Article
  • Open Access
4 Citations
3,474 Views
14 Pages

5 April 2024

The paper presents the application of MTM, RAV and ZAK methods in the determination of working methods and time norms for the technological process of sewing. The technological operation of sewing the back sleeve seam on a men’s jacket is used...

(This article belongs to the Section Manufacturing Processes and Systems)
  • Review
  • Open Access
16 Citations
4,093 Views
22 Pages

25 November 2024

Feasible and reliable predictions of separated turbulent flows are a requirement to successfully address the majority of aerospace and wind energy problems. Existing computational approaches such as large eddy simulation (LES) or Reynolds-averaged Na...

(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
  • Article
  • Open Access
28 Citations
6,732 Views
15 Pages

Quality of Life and Social Support of People on Peritoneal Dialysis: Mixed Methods Research

  • Miquel Sitjar-Suñer,
  • Rosa Suñer-Soler,
  • Afra Masià-Plana,
  • Emilia Chirveches-Pérez and ,
  • Carme Bertran-Noguer and
  • Concepció Fuentes-Pumarola
  • + 1 author+ 0 author

Although some study has been made into quality of life in patients with peritoneal dialysis, little is known about how this relates to social support. The aim of this paper was to study health-related quality of life, perceived social support and the...

(This article belongs to the Section Health Care Sciences & Services)
  • Article
  • Open Access
68 Citations
4,996 Views
36 Pages

23 December 2020

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connec...

(This article belongs to the Special Issue Dynamical Systems, Differential Equations and Applications)
  • Feature Paper
  • Review
  • Open Access
10 Citations
4,754 Views
19 Pages

24 April 2019

Physicochemical properties of chemicals as referred to in this review include, for example, thermodynamic properties such as heat of formation, boiling point, toxicity of molecules and the fate of molecules whenever undergoing or accelerating (cataly...

(This article belongs to the Section Chemical and Molecular Sciences)
  • Article
  • Open Access
1,252 Views
29 Pages

Feature selection plays a crucial role in the effectiveness of distributed denial of service (DDoS) attack detection methods, particularly as network traffic data becomes increasingly complex. This study conducts a categorical investigation of featur...

  • Article
  • Open Access
25 Citations
4,294 Views
17 Pages

23 February 2023

This study aims to develop combined methods with dual and triple use of different non-destructive test (NDT) methods and to examine the effectiveness of these methods. For this purpose, nine different high-strength concrete series were produced, and...

(This article belongs to the Topic Processing, Analysis, Modelling and Mechanics of Materials and Structures)
  • Article
  • Open Access
1 Citations
1,987 Views
16 Pages

Multigrid Methods for Computed Tomography

  • Alessandro Buccini,
  • Marco Donatelli and
  • Marco Ratto

20 March 2025

We consider the problem of computed tomography (CT). This ill-posed inverse problem arises when one wishes to investigate the internal structure of an object with a non-invasive and non-destructive technique. This problem is severely ill-conditioned,...

(This article belongs to the Section B: Mathematics)
  • Editorial
  • Open Access
3,738 Views
3 Pages

An area of very active research in econometrics over the last 30 years has been that of non- and semi-parametric methods. These methods have provided ways to complement more-traditional parametric approaches in terms of robust alternatives, as well a...

(This article belongs to the Special Issue Nonparametric Econometric Methods and Application)
  • Article
  • Open Access
4 Citations
3,725 Views
11 Pages

A Fast and Simple Solid Phase Extraction-Based Method for Glucosinolate Determination: An Alternative to the ISO-9167 Method

  • Yanfang Li,
  • Mengliang Zhang,
  • Pamela Pehrsson,
  • James M. Harnly and ,
  • Pei Chen and
  • Jianghao Sun
  • + 1 author+ 0 author

21 February 2024

Glucosinolates (GLSs) are a well-studied sulfur-containing compound found in Brassicaceae plants that play critical roles in plant resistance and human health. Correctly identifying and reliably quantifying the total and individual GLS content is of...

(This article belongs to the Section Nutraceuticals, Functional Foods, and Novel Foods)

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