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Mathematics: 10th Anniversary
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Mathematics: 10th Anniversary

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 41078

Special Issue Editors

Prof. Dr. Francisco Chiclana

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Guest Editor
School of Computer Science and Informatics, De Montfort University, The Gateway, Leicester LE1 9BH, UK
Interests: fuzzy decision making; fuzzy preference modeling; decision support systems; consensus; recommender systems; social networks; rationality/consistency; aggregation; type-2 fuzzy logic; opinion dynamics; trust propagation
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Sergei Petrovskii

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Co-Guest Editor
School of Mathematics and Actuarial Science, University of Leicester, Leicester, UK
Interests: mathematical ecology; climate change; mass extinctions; nonlinear dynamics
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Prof. Dr. Matjaz Perc

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Co-Guest Editor
Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, 2000 Maribor, Slovenia
Interests: statistical physics; cooperation; complex systems; evolutionary game theory; network science
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Prof. Dr. Antonio Di Crescenzo

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Co-Guest Editor
Department of Mathematics, University of Salerno, I-84100 Salerno, Italy
Interests: stochastic processes; applied probability; probability theory; stochastic models
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Prof. Dr. Marjan Mernik

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Co-Guest Editor
Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška cesta 46, 2000 Maribor, Slovenia
Interests: concepts and implementation of programming languages; formal language definition, attribute grammars; compiler generators; domain specific languages; grammar-based systems; grammatical inference; meta-heuristics, single and multi-objective optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The inaugural issue of Mathematics was released in March 2013, with the first publication presenting the Open Access Mathematics journal by the founding Editor-in-Chief Dr. Sergei K. Suslov, from Arizona State University (USA). Since then, many milestones have been achieved. The most significant is the indexing of Mathematics in the Emerging Sources Citation Index—Web of Science (Clarivate Analytics) (ESCI) in 2015, followed by its indexing in the Science Citation Index Expanded (SCIE) in 2018 and the obtainment of its first Journal Impact Factor (JIF) for 2018 in year 2019. Mathematics has been growing since the above-mentioned milestones, and it was decided to structure the journal into sections that cover both the research theory and practice of Mathematics: the first four sections were established in 2018 (Engineering Mathematics, Theoretical and Mathematical Ecology, Mathematics and Computer Science, and Network Science), which was followed by eight new sections in 2019 (Dynamical Systems, Computational Mathematics, Fuzzy Set Theory, Difference and Differential Equations, Financial Mathematics, Mathematical Physics, Algebra and Geometry, and Probability and Statistics) and the most recent one in 2021 (Functional Interpolation).

In the first nine years of existence of the journal Mathematics, the yearly number of publications has not stopped increasing: from 10 in its first year to 335 in 2018; and 1246 in 2019, when the journal received its first JIF (JIF2018= 1.105). Since then, the number of publications in Mathematics has not stopped increasing: 2258 in 2020 (JIF2019= 1.747) and 3293 in 2021 (JIF2021= 2.258). A preliminary analysis indicates that the next JIF2021 for Mathematics will increase to a value close to 2.468. Mathematics is a journal of high quality that receives and publishes research from all over the world. In the period 2013–2021, researchers from 132 countries have published their original research in our journal. The top-five countries in terms of research publication in Mathematics are the Peoples Republic of China, Spain, Saudi Arabia, the USA, and Russia.

The Editorial Board of Mathematics is large and consists of a great mix of highly accomplished and well-established academics and practitioners, representing many countries. Since Mathematics is celebrating its 10th anniversary by the end of 2022, we are organizing the “10th Anniversary” Special Issue (SI), and I hope that that members of the Editorial Board of each of the sections of Mathematics will consider contributing articles to celebrate their research and provide our journal readership a variety of interesting articles on historical research trends, state-of-the-art systematic reviews, current and future research challenges/applications, and creative and innovative research avenues to tackle them. This invitation is extended to all active researchers/practitioners with an interest in research on the field of mathematics towards the development of new products and services that ultimately enhance society, environment, and quality of life.

Articles submitted to this SI must fit the aims and scope of the journal Mathematics (https://www.mdpi.com/journal/mathematics/about) and the journal’s sections (https://www.mdpi.com/journal/mathematics/sections).

Prof. Dr. Francisco Chiclana
Prof. Dr. Sergei Petrovskii
Prof. Dr. Matjaž Perc
Prof. Dr. Antonio Di Crescenzo
Prof. Dr. Marjan Mernik
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical analysis
  • mathematical modeling
  • engineering mathematics
  • mathematical biology
  • mathematics and computer science
  • network science
  • dynamical systems
  • computational and applied mathematics
  • fuzzy set theory
  • difference and differential equations
  • financial mathematics
  • mathematical physics
  • algebra and geometry
  • probability and statistics
  • functional interpolation

 

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Published Papers (17 papers)

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13 pages, 413 KiB  
Article
Fractional-Modified Bessel Function of the First Kind of Integer Order
by Andrés Martín and Ernesto Estrada
Mathematics 2023, 11(7), 1630; https://doi.org/10.3390/math11071630 - 28 Mar 2023
Cited by 1 | Viewed by 2678
Abstract
The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the [...] Read more.
The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here, we generalize this MBF to include a fractional parameter, such that the exponential in the previously mentioned integral is replaced by a Mittag–Leffler function. The necessity for this generalization arises from a problem of communication in networks. We find the power series representation of the fractional MBF of the first kind as well as some differential properties. We give some examples of its utility in graph/networks analysis and mention some fundamental open problems for further investigation. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
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27 pages, 525 KiB  
Article
On Parsing Programming Languages with Turing-Complete Parser
by Boštjan Slivnik and Marjan Mernik
Mathematics 2023, 11(7), 1594; https://doi.org/10.3390/math11071594 - 25 Mar 2023
Cited by 2 | Viewed by 2694
Abstract
A new parsing method based on the semi-Thue system is described. Similar to, but with more efficient implementation than Markov normal algorithms, it can be used for parsing any recursively enumerable language. Despite its computational power, it is meant to be used primarily [...] Read more.
A new parsing method based on the semi-Thue system is described. Similar to, but with more efficient implementation than Markov normal algorithms, it can be used for parsing any recursively enumerable language. Despite its computational power, it is meant to be used primarily for parsing programming and domain-specific languages. It enables a straightforward simulation of a number of existing parsing algorithms based on context-free grammars. The list includes both top-down shift-produce methods (such as SLL and LL) and bottom-up shift-reduce methods (such as LALR and LR), as well as mixed top-down-and-bottom-up methods such as LLLR. To justify the use of the new parsing method, the paper provides numerous examples of how a parser can actually be made in practice. It is advised that the main part of the parser is based on some simple well-established approach, e.g., SLL(1), while syntactically more complicated phrases can be parsed by exploiting the full power of the new parser. These phrases may either be extensions to the original language or some embedded domain-specific language. In all such and similar cases, no part of the language is restricted to be context-free. In fact, context-sensitive languages can be handled quite efficiently. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
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10 pages, 253 KiB  
Article
On the Devylder–Goovaerts Conjecture in Ruin Theory
by Stéphane Loisel and Charles Minier
Mathematics 2023, 11(6), 1501; https://doi.org/10.3390/math11061501 - 20 Mar 2023
Viewed by 1294
Abstract
The Devylder–Goovaerts conjecture is probably the oldest conjecture in actuarial mathematics and has received a lot of attention in recent years. It claims that ruin with equalized claim amounts is always less likely than in the classical model. Investigating the validity of this [...] Read more.
The Devylder–Goovaerts conjecture is probably the oldest conjecture in actuarial mathematics and has received a lot of attention in recent years. It claims that ruin with equalized claim amounts is always less likely than in the classical model. Investigating the validity of this conjecture is important both from a theoretical aspect and a practical point of view, as it suggests that one always underestimates the risk of insolvency by replacing claim amounts with the average claim amount a posteriori. We first state a simplified version of the conjecture in the discrete-time risk model when one equalizes aggregate claim amounts and prove that it holds. We then use properties of the Pareto distribution in risk theory and other ideas to target candidate counterexamples and provide several counterexamples to the original Devylder–Goovaerts conjecture. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
12 pages, 294 KiB  
Article
On Local Time for Telegraph Processes
by Nikita Ratanov and Mikhail Turov
Mathematics 2023, 11(4), 934; https://doi.org/10.3390/math11040934 - 12 Feb 2023
Viewed by 1114
Abstract
The article consists of an introduction into the theory of passage times associated with telegraph processes. Local time for the telegraph process is defined and analysed. We provide some limited results for telegraphic local times. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
6 pages, 234 KiB  
Article
Trans-Planckian Censorship and Spacetime Singularities
by Spiros Cotsakis and John Miritzis
Mathematics 2023, 11(3), 633; https://doi.org/10.3390/math11030633 - 26 Jan 2023
Viewed by 3387
Abstract
We study the effects of trans-Planckian censorship conjecture (TCC) bounds on geodesic completeness of spacetime and the associated existence for an infinite proper time. Using Gronwall’s lemma, TCC bounds can be derived directly, leading to a result about the absence of blowup solutions. [...] Read more.
We study the effects of trans-Planckian censorship conjecture (TCC) bounds on geodesic completeness of spacetime and the associated existence for an infinite proper time. Using Gronwall’s lemma, TCC bounds can be derived directly, leading to a result about the absence of blowup solutions. We show that the TCC provides part of the required criteria for geodesic completeness, and we then provide the remaining ones, the norm of the extrinsic curvature being bounded away from zero. We also discuss the importance of these results for the classical evolution of Friedmann universes under the assumptions of global and regular hyperbolicity. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
14 pages, 1229 KiB  
Article
Solitary Wave Solutions of the Fractional-Stochastic Quantum Zakharov–Kuznetsov Equation Arises in Quantum Magneto Plasma
by Wael W. Mohammed, Farah M. Al-Askar, Clemente Cesarano and M. El-Morshedy
Mathematics 2023, 11(2), 488; https://doi.org/10.3390/math11020488 - 16 Jan 2023
Cited by 9 | Viewed by 1671
Abstract
In this paper, we consider the (3 + 1)-dimensional fractional-stochastic quantum Zakharov–Kuznetsov equation (FSQZKE) with M-truncated derivative. To find novel trigonometric, hyperbolic, elliptic, and rational fractional solutions, two techniques are used: the Jacobi elliptic function approach and the modified F-expansion method. We also [...] Read more.
In this paper, we consider the (3 + 1)-dimensional fractional-stochastic quantum Zakharov–Kuznetsov equation (FSQZKE) with M-truncated derivative. To find novel trigonometric, hyperbolic, elliptic, and rational fractional solutions, two techniques are used: the Jacobi elliptic function approach and the modified F-expansion method. We also expand on a few earlier findings. The extended quantum Zakharov–Kuznetsov has practical applications in dealing with quantum electronpositron–ion magnetoplasmas, warm ions, and hot isothermal electrons in the presence of uniform magnetic fields, which makes the solutions obtained useful in analyzing a number of intriguing physical phenomena. We plot our data in MATLAB and display various 3D and 2D graphical representations to explain how the stochastic term and fractional derivative influence the exact solutions of the FSEQZKE. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
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21 pages, 8073 KiB  
Article
A Graph Pointer Network-Based Multi-Objective Deep Reinforcement Learning Algorithm for Solving the Traveling Salesman Problem
by Jeewaka Perera, Shih-Hsi Liu, Marjan Mernik, Matej Črepinšek and Miha Ravber
Mathematics 2023, 11(2), 437; https://doi.org/10.3390/math11020437 - 13 Jan 2023
Cited by 13 | Viewed by 3812
Abstract
Traveling Salesman Problems (TSPs) have been a long-lasting interesting challenge to researchers in different areas. The difficulty of such problems scales up further when multiple objectives are considered concurrently. Plenty of work in evolutionary algorithms has been introduced to solve multi-objective TSPs with [...] Read more.
Traveling Salesman Problems (TSPs) have been a long-lasting interesting challenge to researchers in different areas. The difficulty of such problems scales up further when multiple objectives are considered concurrently. Plenty of work in evolutionary algorithms has been introduced to solve multi-objective TSPs with promising results, and the work in deep learning and reinforcement learning has been surging. This paper introduces a multi-objective deep graph pointer network-based reinforcement learning (MODGRL) algorithm for multi-objective TSPs. The MODGRL improves an earlier multi-objective deep reinforcement learning algorithm, called DRL-MOA, by utilizing a graph pointer network to learn the graphical structures of TSPs. Such improvements allow MODGRL to be trained on a small-scale TSP, but can find optimal solutions for large scale TSPs. NSGA-II, MOEA/D and SPEA2 are selected to compare with MODGRL and DRL-MOA. Hypervolume, spread and coverage over Pareto front (CPF) quality indicators were selected to assess the algorithms’ performance. In terms of the hypervolume indicator that represents the convergence and diversity of Pareto-frontiers, MODGRL outperformed all the competitors on the three well-known benchmark problems. Such findings proved that MODGRL, with the improved graph pointer network, indeed performed better, measured by the hypervolume indicator, than DRL-MOA and the three other evolutionary algorithms. MODGRL and DRL-MOA were comparable in the leading group, measured by the spread indicator. Although MODGRL performed better than DRL-MOA, both of them were just average regarding the evenness and diversity measured by the CPF indicator. Such findings remind that different performance indicators measure Pareto-frontiers from different perspectives. Choosing a well-accepted and suitable performance indicator to one’s experimental design is very critical, and may affect the conclusions. Three evolutionary algorithms were also experimented on with extra iterations, to validate whether extra iterations affected the performance. The results show that NSGA-II and SPEA2 were greatly improved measured by the Spread and CPF indicators. Such findings raise fairness concerns on algorithm comparisons using different fixed stopping criteria for different algorithms, which appeared in the DRL-MOA work and many others. Through these lessons, we concluded that MODGRL indeed performed better than DRL-MOA in terms of hypervolumne, and we also urge researchers on fair experimental designs and comparisons, in order to derive scientifically sound conclusions. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
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9 pages, 545 KiB  
Article
The Point of No Return: Evolution of Excess Mutation Rate Is Possible Even for Simple Mutation Models
by Brian Mintz and Feng Fu
Mathematics 2022, 10(24), 4818; https://doi.org/10.3390/math10244818 - 19 Dec 2022
Cited by 1 | Viewed by 1612
Abstract
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore, it is reasonable to expect that mutation rates will evolve downwards. However, we find that this need not be the case, [...] Read more.
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore, it is reasonable to expect that mutation rates will evolve downwards. However, we find that this need not be the case, examining several models of mutation. While upwards evolution of the mutation rate has been found with frequency- or time-dependent fitness, we demonstrate its possibility in a much simpler context. This work uses adaptive dynamics to study the evolution of the mutation rate, and the replicator–mutator equation to model trait evolution. Our approach differs from previous studies by considering a wide variety of methods to represent mutation. We use a finite string approach inspired by genetics as well as a model of local mutation on a discretization of the unit intervals, handling mutation beyond the endpoints in three ways. The main contribution of this work is a demonstration that the evolution of the mutation rate can be significantly more complicated than what is usually expected in relatively simple models. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
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20 pages, 4721 KiB  
Article
Detection of River Floating Garbage Based on Improved YOLOv5
by Xingshuai Yang, Jingyi Zhao, Li Zhao, Haiyang Zhang, Li Li, Zhanlin Ji and Ivan Ganchev
Mathematics 2022, 10(22), 4366; https://doi.org/10.3390/math10224366 - 20 Nov 2022
Cited by 16 | Viewed by 3934
Abstract
The random dumping of garbage in rivers has led to the continuous deterioration of water quality and affected people’s living environment. The accuracy of detection of garbage floating in rivers is greatly affected by factors such as floating speed, night/daytime natural light, viewing [...] Read more.
The random dumping of garbage in rivers has led to the continuous deterioration of water quality and affected people’s living environment. The accuracy of detection of garbage floating in rivers is greatly affected by factors such as floating speed, night/daytime natural light, viewing angle and position, etc. This paper proposes a novel detection model, called YOLOv5_CBS, for the detection of garbage objects floating in rivers, based on improvements of the YOLOv5 model. Firstly, a coordinate attention (CA) mechanism is added to the original C3 module (without compressing the number of channels in the bottleneck), forming a new C3-CA-Uncompress Bottleneck (CCUB) module for improving the size of the receptive field and allowing the model to pay more attention to important parts of the processed images. Then, the Path Aggregation Network (PAN) in YOLOv5 is replaced with a Bidirectional Feature Pyramid Network (BiFPN), as proposed by other researchers, to enhance the depth of information mining and improve the feature extraction capability and detection performance of the model. In addition, the Complete Intersection over Union (CIoU) loss function, which was originally used in YOLOv5 for the calculation of location score of the compound loss, is replaced with the SCYLLA-IoU (SIoU) loss function, so as to speed up the model convergence and improve its regression precision. The results, obtained through experiments conducted on two datasets, demonstrate that the proposed YOLOv5_CBS model outperforms the original YOLOv5 model, along with three other state-of-the-art models (Faster R-CNN, YOLOv3, and YOLOv4), when used for river floating garbage objects detection, in terms of the recall, average precision, and F1 score achieved by reaching respective values of 0.885, 90.85%, and 0.8669 on the private dataset, and 0.865, 92.18%, and 0.9006 on the Flow-Img public dataset. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
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30 pages, 7042 KiB  
Article
Analysis of a Queueing Model with MAP Arrivals and Heterogeneous Phase-Type Group Services
by Srinivas R. Chakravarthy
Mathematics 2022, 10(19), 3575; https://doi.org/10.3390/math10193575 - 30 Sep 2022
Cited by 7 | Viewed by 1949
Abstract
Queueing models have proven to be very useful in real-life applications to enable the practitioners to optimize the limited resources to conduct their businesses as well as offer services efficiently. In general, we can group such applications into two sectors: manufacturing and service. [...] Read more.
Queueing models have proven to be very useful in real-life applications to enable the practitioners to optimize the limited resources to conduct their businesses as well as offer services efficiently. In general, we can group such applications into two sectors: manufacturing and service. These two sectors cover everything we deal with on a day-to-day basis. Queues in which the services are offered in blocks (or groups or batches) are well established in the literature and have a wide variety of applications in practice. In this paper, we look at one such queueing model in which the arrivals occur according to a Markovian arrival process and the services are offered in batches of varying sizes from 1 to a finite pre-determined constant, say, b. The service times are assumed to be of phase type with representation depending on the size of the group. Thus, the distributions considered are heterogeneous from both the representation and rate points of view. The model can be studied as a GI/M/1-type queue or as a QBD-model. The model is analyzed in steady state by establishing results including on the rate matrix and the waiting time distribution and providing a number of illustrative examples. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
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12 pages, 266 KiB  
Article
An Empirical Investigation of Multinationality and Stock Price Crash Risk for MNCs in China
by Larry Su, Elmina Homapour, Fabio Caraffini and Francisco Chiclana
Mathematics 2022, 10(19), 3464; https://doi.org/10.3390/math10193464 - 23 Sep 2022
Cited by 1 | Viewed by 2179
Abstract
There is a large volume of literature in international business on multinationality. There is an equally large volume of literature in finance on stock price crash risk. However, very few studies have attempted to provide a link between these two research areas. Using [...] Read more.
There is a large volume of literature in international business on multinationality. There is an equally large volume of literature in finance on stock price crash risk. However, very few studies have attempted to provide a link between these two research areas. Using an unbalanced panel data consisting of 473 multinational corporations (MNCs) publicly listed in the Chinese stock markets during 2004 to 2020, this paper is one of the first to empirically investigate whether and to what extent multinationality affects stock price crash risk. The paper finds strong evidence that multinational operation is negatively related to stock price crash risk. In addition, MNCs with better corporate governance quality experience larger decline in stock price crash risk when the degree of multinationality increases. Furthermore, MNCs with higher stock market liquidity experience lower crash risk. An important implication is that companies should strengthen their corporate governance and market liquidity while “going global”. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
30 pages, 444 KiB  
Article
Weighted Mean Inactivity Time Function with Applications
by Antonio Di Crescenzo and Abdolsaeed Toomaj
Mathematics 2022, 10(16), 2828; https://doi.org/10.3390/math10162828 - 9 Aug 2022
Viewed by 1439
Abstract
We consider an extension of the mean inactivity time based on a non-negative weight function. We show various properties of the new notion, and relate it to various functions of interest in reliability theory and information measures, such as the dynamic cumulative entropy, [...] Read more.
We consider an extension of the mean inactivity time based on a non-negative weight function. We show various properties of the new notion, and relate it to various functions of interest in reliability theory and information measures, such as the dynamic cumulative entropy, the past entropy, the varentropy, and the weighted cumulative entropy. Moreover, based on the comparison of weighted mean inactivity times, we introduce and study a new stochastic order and compare it with other suitable orders. We also discuss some results about the variance of transformed random variables and the weighted generalized cumulative entropy. Then, we investigate certain connections with the location-independent riskier order. Finally, we pinpoint several characterizations and preservation properties of the new stochastic order under shock models, random maxima, and notions of renewal theory. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
48 pages, 1094 KiB  
Article
RNGSGLR: Generalization of the Context-Aware Scanning Architecture for All Character-Level Context-Free Languages
by Žiga Leber, Matej Črepinšek, Marjan Mernik and Tomaž Kosar
Mathematics 2022, 10(14), 2436; https://doi.org/10.3390/math10142436 - 13 Jul 2022
Cited by 3 | Viewed by 1608
Abstract
The limitations of traditional parsing architecture are well known. Even when paired with parsing methods that accept all context-free grammars (CFGs), the resulting combination for any given CFG accepts only a limited subset of corresponding character-level context-free languages (CFL). We present a novel [...] Read more.
The limitations of traditional parsing architecture are well known. Even when paired with parsing methods that accept all context-free grammars (CFGs), the resulting combination for any given CFG accepts only a limited subset of corresponding character-level context-free languages (CFL). We present a novel scanner-based architecture that for any given CFG accepts all corresponding character-level CFLs. It can directly parse all possible specifications consisting of a grammar and regular definitions. The architecture is based on right-nulled generalized LR (RNGLR) parsing and is a generalization of the context-aware scanning architecture. Our architecture does not require any disambiguation rules to resolve lexical conflicts, it conceptually has an unbounded parser and scanner lookahead and it is streaming. The added robustness and flexibility allow for easier grammar development and modification. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
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17 pages, 1028 KiB  
Article
Collaboration Effect by Co-Authorship on Academic Citation and Social Attention of Research
by Pablo Dorta-González and María Isabel Dorta-González
Mathematics 2022, 10(12), 2082; https://doi.org/10.3390/math10122082 - 15 Jun 2022
Cited by 6 | Viewed by 2279
Abstract
Academic citation and social attention measure different dimensions of the impact of research results. Both measures do not correlate with each other, and they are influenced by many factors. Among these factors are the field of research, the type of access, and co-authorship. [...] Read more.
Academic citation and social attention measure different dimensions of the impact of research results. Both measures do not correlate with each other, and they are influenced by many factors. Among these factors are the field of research, the type of access, and co-authorship. In this study, the increase in the impact due to co-authorship in scientific articles disaggregated by field of research and access type, was quantified. For this, the citations and social attention accumulated until the year 2021 by a total of 244,880 research articles published in the year 2018, were analyzed. The data source was Dimensions.ai, and the units of study were research articles in Economics, History and Archaeology, and Mathematics. As the main results, a small proportion of the articles received a large part of the citations and most of the social attention. Both citations and social attention increased, in general, with the number of co-authors. Thus, the greater the number of co-authors, the greater the probability of being cited in academic articles and mentioned on social media. The advantage in citation and social attention due to collaboration is independent of the access type for the publication. Furthermore, although collaboration with an additional co-author is in general positive in terms of citation and social attention, these positive effects reduce as the number of co-authors increases. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
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12 pages, 282 KiB  
Article
A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton–Kantorovich Iterations-II
by Samundra Regmi, Ioannis K. Argyros, Santhosh George and Michael I. Argyros
Mathematics 2022, 10(11), 1839; https://doi.org/10.3390/math10111839 - 27 May 2022
Cited by 1 | Viewed by 1188
Abstract
This article is an independently written continuation of an earlier study with the same title [Mathematics, 2022, 10, 1225] on the Newton Process (NP). This process is applied to solve nonlinear equations. The complementing features are: the smallness of the initial approximation is [...] Read more.
This article is an independently written continuation of an earlier study with the same title [Mathematics, 2022, 10, 1225] on the Newton Process (NP). This process is applied to solve nonlinear equations. The complementing features are: the smallness of the initial approximation is expressed explicitly in turns of the Lipschitz or Hölder constants and the convergence order 1+p is shown for p∈(0,1]. The first feature becomes attainable by further simplifying proofs of convergence criteria. The second feature is possible by choosing a bit larger upper bound on the smallness of the initial approximation. This way, the completed convergence analysis is finer and can replace the classical one by Kantorovich and others. A two-point boundary value problem (TPBVP) is solved to complement this article. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
14 pages, 285 KiB  
Article
On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain
by Carlo Bianca and Marco Menale
Mathematics 2022, 10(9), 1407; https://doi.org/10.3390/math10091407 - 22 Apr 2022
Cited by 1 | Viewed by 1316
Abstract
This paper is devoted to the mathematical analysis of a spatially homogeneous thermostatted kinetic theory framework with an unbounded activity domain. The framework consists of a partial integro-differential equation with quadratic nonlinearity where the domain of the activity variable is the whole real [...] Read more.
This paper is devoted to the mathematical analysis of a spatially homogeneous thermostatted kinetic theory framework with an unbounded activity domain. The framework consists of a partial integro-differential equation with quadratic nonlinearity where the domain of the activity variable is the whole real line. Specifically the mathematical analysis refers firstly to the existence and uniqueness of the solution for the related initial boundary value problem; Secondly the investigations are addressed to the existence of a class of self-similar solutions by employing the Fourier transform method. In particular the main result is obtained for a nonconstant interaction rate and a nonconstant force field. Conclusions and perspectives are discussed in the last section of the paper. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)

Review

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35 pages, 2336 KiB  
Review
Modeling Languages for Internet of Things (IoT) Applications: A Comparative Analysis Study
by Sadik Arslan, Mert Ozkaya and Geylani Kardas
Mathematics 2023, 11(5), 1263; https://doi.org/10.3390/math11051263 - 6 Mar 2023
Cited by 11 | Viewed by 4166
Abstract
Modeling languages have gained ever-increasing importance for the Internet of Things (IoT) domain for improving the productivity and quality of IoT developments. In this study, we analyzed 32 different modeling languages that have been designed for IoT software development in terms of a [...] Read more.
Modeling languages have gained ever-increasing importance for the Internet of Things (IoT) domain for improving the productivity and quality of IoT developments. In this study, we analyzed 32 different modeling languages that have been designed for IoT software development in terms of a set of requirements that were categorized into three groups: language definition, language features, and tool support. Some key findings are as follows: (1) performance is the most supported quality property (28%); (2) most languages offer a visual notation set only, while 6% provide both textual and visual notation sets; (3) most languages (88%) lack formally precise semantic definitions; (4) most languages (94%) support the physical, deployment, and logical modeling viewpoints, while the behavior, logical, and information viewpoints are rarely supported; (5) almost none of the languages enable extensibility; (6) Java (34%) and C (21%) are the most preferred programming languages for model transformation; (7) consistency (77%) and completeness (64%) are the most supported properties for the automated checking of models; and (8) most languages (81%) are not supported with any websites for sharing case studies, source code, tools, tutorials, etc. The analysis results can be useful for language engineers, practitioners, and tool vendors for better understanding the existing languages for IoT, their weak and strong points, and IoT industries’ needs in future language and modeling toolset developments. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
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