Order dimension theory measures the complexity of partially ordered sets by quantifying how far they are from being linearly ordered. In this paper we study classical bounding results for order dimension within the framework of reverse mathematics. We focus on principles asserting that the dimension of a poset can be bounded in terms of the dimension of subposets obtained by removing chains or points, denoted by $\mathsf{DBi_n}$, $\mathsf{DBc_n}$, and $\mathsf{DB_p}$. We prove that, over $\mathsf{RCA}_0$, both $\mathsf{DBi_n}$ and $\mathsf{DBc_n}$ are equivalent to $\mathsf{WKL}_0$. To analyze $\mathsf{DB_p}$, we introduce a natural strengthening $\mathsf{DB^+_p}$ and show that both $\mathsf{DB_p}$ and $\mathsf{DB^+_p}$ are provable from $\mathsf{WKL}_0$ and from $\mathsf{I}Σ^0_2$, while $\mathsf{B}Σ^0_2$ does not suffice to prove $\mathsf{DB^+_p}$. The latter result is obtained by showing that the statement \lq\lq $\mathsf{DB^+_p}$ is computably true\rq\rq\ is equivalent to $\mathsf{I}Σ^0_2$.
Formal mathematics is mathematics done within the framework of a formal logic. It offers major benefits to mathematicians as well as to computing professionals, engineers, and scientists who use mathematics in their work. The standard approach to formal mathematics, in which mathematics is done with the help of a proof assistant and all details are formally proved and mechanically checked, achieves these benefits and offers a very high level of assurance that the results produced are correct. However, since the main goal of the standard approach is certification, the proof assistants supporting the standard approach are generally complex, based on unfamiliar logics, difficult to learn how to use, and far removed from mathematical practice. Thus the standard approach does not adequately serve mathematics practitioners who are more interested in communicating mathematical ideas than in formally certifying their correctness or who prefer not to make the investment needed to gain proficiency in the use of proof assistants. This paper presents an alternative to the standard approach that focuses on communication and accessibility, the two weaknesses of the standard approach. It is called the free approach to formal mathematics since it is free of the obligation to formally prove and mechanically check all details of a mathematical development. The paper argues that the free approach would serve the needs of the average mathematics practitioner much better than the standard approach. It describes an implementation of the free approach based on a logic named Alonzo, a practice-oriented version of Alonzo Church's formulation of simple type theory. And it calls for the mathematics community to develop logics, software, and libraries of formal mathematical knowledge to support the free approach and to train mathematics practitioners to use them.
Leonhard Ziegler, Michael Grabatin, Daniela Pöhn
et al.
Abstract While self-sovereign identities (SSI) have been gaining more traction, the topic of SSI security has yet to be addressed. Especially regarding response procedures to security incidents, no prior work is available. However, incident response processes are essential to systematically respond to a security incident in a timely manner. We first evaluate the current state-of-the-art by conducting a literature survey and contacting organizations that offer SSI. The insights underpin the subject’s relevance, highlighting that incident response capabilities are just starting to be developed. Contributing to this development, we identify the challenges of building a security incident response process for SSI. Mainly, the decentralized nature inhibits the utilization of known best practices, which all focus on building a centralized incident response capability. However, even in the case of SSI, some centralized entities may exist. Therefore, we design two variants of SIR processes: one more centralized and one more decentralized. For the latter, the problem size is reduced in the first step by identifying all the stakeholders within an SSI ecosystem and then analyzing possible proactive and reactive measures each participant can access. This procedure leads to the grouping of SSI system participants into three distinct domains of incident response. For each domain, different capabilities for handling incidents are introduced depending on the involved stakeholders, their infrastructure, and their goals. To demonstrate the procedures, incident scenarios for each domain highlight the workflows during incident handling.
This study presents a facial emotion recognition network based on UniRepLKNet to address the difficulty in effectively capturing feature information and preventing key facial information from occupying a more prominent position in the facial emotion recognition process. Moreover, to extract facial emotional features more accurately, the study designs a masked polarized self-attention module that combines U-Net and a polarized self-attention mechanism. This module can deeply mine the dependency between channels and spaces. It can also strengthen the influence of local key information of the face on emotion recognition through a multi-scale feature fusion strategy. The study optimizes UniRepLKNet, a universal large kernel Convolutional Neural Network (CNN), and proposes the EmoRepLKNet neural network structure. In EmoRepLKNet, the mask-polarized self-attention module enables the network to extract key information for facial emotion recognition. Combined with the wide receptive field of large kernel CNN, facial emotions can be recognized effectively. Experimental results show that on the facial emotion recognition dataset FER2013, EmoRepLKNet achieves an accuracy of 76.20%, outperforming existing comparison models and significantly improving facial emotion recognition accuracy compared to that of UniRepLKNet. Additionally, on the single-label portion of the RAF-DB dataset, the proposed method achieves an accuracy of 89.67%.
Abstract With the advent of 5G/6G technologies and the continued advancement of communication systems, the shift toward low-loss microwave dielectrics has become essential. In this context, inorganic complex microwave dielectric materials offer the potential for various combinations and partial or complete substitutions, resulting in a wide range of new compounds. The fabrication method, dopant concentration, and crystal structure significantly influence the electronic properties of these materials. Importantly, this work focuses on several recently reported titanium-, silicon-, and zirconium-based materials, such as CaTiO₃, MgTiO₃, MgSiO₃, and CaZrO₃. However, comprehensive review studies on microwave dielectric materials remain limited, and the fundamental relationship between their crystal structures and dielectric properties is still not fully understood. This review highlights microstructural characteristics-particularly grain size and density-in complex hybrid metal oxides. Additionally, it provides a comprehensive analysis of microwave dielectric properties, with a focus on ABX3 perovskites for electronic applications such as 5G/6G communication systems. To the best of our knowledge, there is no extensive reviews connecting the crystal structures of diverse hybrid complex metal oxides with their corresponding microwave dielectric properties.
Yulia M. T. A. Putri, Muhammad I. Syauqi, Isnaini Rahmawati
et al.
Abstract The growing demand for sustainable energy sources has spurred significant studies to optimize the potency of fuel cell technology. Direct urea fuel cell (DUFC) has gained attention due to their energy density, eco‐friendliness, and potential applications in power generation using urea from various sources, including wastewater and urine. Efficient electrocatalysts are pivotal in DUFCs, and nickel‐based catalysts, particularly in the form of NiOOH, have demonstrated cost effectiveness, excellent stability in alkaline media, and good activity for urea oxidation reaction. However, low‐density and durability are still the major limitation in the overall DUFC performance. This review provides a comprehensive analysis of the latest development in Ni‐based catalysts, covering synthesis methods, factors influencing the catalytic activity as well as their implications for DUFC performance durability and commercial viability. In addition, another important factor including the use of different oxidant and electrolyte medium is also elaborated. Based on this review, 2D‐3D Ni‐based materials with the addition of other metals and the use of non‐oxide nickel binary compound are predicted to be the future evolution of the effective nickel‐based catalysts.
Research data infrastructures form the cornerstone in both cyber and physical spaces, driving the progression of the data-intensive scientific research paradigm. This opinion paper presents an overview of global research data infrastructure, drawing insights from national roadmaps and strategic documents related to research data infrastructure. It emphasizes the pivotal role of research data infrastructures by delineating four new missions aimed at positioning them at the core of the current scientific research and communication ecosystem. The four new missions of research data infrastructures are: (1) as a pioneer, to transcend the disciplinary border and address complex, cutting-edge scientific and social challenges with problem- and data-oriented insights; (2) as an architect, to establish a digital, intelligent, flexible research and knowledge services environment; (3) as a platform, to foster the high-end academic communication; (4) as a coordinator, to balance scientific openness with ethics needs.
Information technology, Electronic computers. Computer science
Wireless monitoring systems for the marine environment are important for rapidly growing subsea developments. The power supply of wireless sensor nodes within the monitoring systems, however, is a major challenge. This study proposes a novel piezoelectric wave energy converter (pWEC) device to power the wireless sensing nodes. Unlike previous studies, the proposed device utilizes contactless pWEC technology in which a spring pendulum provides a two-stage frequency amplification of 3.8 times for low-frequency wave environments. The pWEC device consists of a floating body, inner pendulum, spring pendulum, magnets and piezoelectric sheets. In order to harvest the energy from relatively low frequency ocean waves, the pWEC device is designed to have an enhanced energy-capturing frequency. The effects of internal pendulum mass, spring pendulum weight, pendulum length and spring stiffness on wave energy absorption are investigated using theoretical and numerical analysis combined with laboratory experiments. The slider that drives the motion of the piezoelectric sheet vibrates at up to 3.8 times the wave frequency. To test the piezoelectric generators in the laboratory environment, a mechanical structure is set up to simulate the motion of the external floating body and the internal wave energy converter under the action of waves. When the four piezoelectric plates are arranged horizontally, the average output power per plate is increased by 2.4 times, and a single piezoelectric plate can generate an average of 10 mW of power. The proposed piezoelectric wave energy converter device has the potential to provide long-term energy supply for small ocean monitoring platforms at remote locations with reasonable wave energy resources.
\emph{TxGraffiti} is a data-driven, heuristic-based computer program developed to automate the process of generating conjectures across various mathematical domains. Since its creation in 2017, \emph{TxGraffiti} has contributed to numerous mathematical publications, particularly in graph theory. In this paper, we present the design and core principles of \emph{TxGraffiti}, including its roots in the original \emph{Graffiti} program, which pioneered the automation of mathematical conjecturing. We describe the data collection process, the generation of plausible conjectures, and methods such as the \emph{Dalmatian} heuristic for filtering out redundant or transitive conjectures. Additionally, we highlight its contributions to the mathematical literature and introduce a new web-based interface that allows users to explore conjectures interactively. While we focus on graph theory, the techniques demonstrated extend to other areas of mathematics.
The second world war saw a major influx of mathematical talent into the areas of cryptanalysis and cryptography. This was particularly true at the UK's Government Codes and Cypher School (GCCS) at Bletchley Park. The success of introducing mathematical thinking into activities previously dominated by linguists is well-studied, but the reciprocal question of how the cryptologic effort affected the field of mathematics has been less investigated. Although their cryptologic achievements are not as celebrated as those of Turing, Tutte and Welchman, Bletchley Park's effort was supplemented by more eminent mathematicians, and those who would achieve eminence and provide leadership and direction for mathematical research in the United Kingdom. Amongst their number were Ian Cassels, Sandy Green, Philip Hall, Max Newman and Henry Whitehead. This paper considers how the experience of these and other mathematicians at Bletchley Park may have informed and influenced the mathematics that was produced in their post-war careers.
This is the second volume of a textbook for a two-semester course in mathematical analysis. This second volume is about analysis of multi-variable functions. The topics covered include Euclidean spaces, convergence of sequences, open sets and closed sets, limits and continuity, uniform continuity, connectedness, compactness, intermediate value theorem, extreme value theorem, partial derivatives, differentiability, chain rule, mean value theorem, first and second order approximations, local extrema, inverse function theorem, implicit function theorem, constrained extrema problems and Lagrange multipliers, Riemann integrals of functions of several variables, Jordan measurable sets, iterated integrals, Fubini's theorem, change of variables theorem, Fourier series and its convergence, Fourier transforms.
In this short review, I will summarize my research experience in three fields in applied mathematics: mathematical biology, applied probability, and applied discrete mathematics. Specifically, I will show how each project was initiated, and what wrong approaches were applied. Such details are important in learning how to do research, but they cannot be read out from research papers. I wish that students and junior researchers in applied mathematics could learn a lesson from this summary.
The paper is concerned with the mathematical theory and numerical approximation of systems of partial differential equations (pde) of hyperbolic, pseudo-parabolic type. Some mathematical properties of the initial-boundary-value problem (ibvp) with Dirichlet boundary conditions are first studied. They include the weak formulation, well-posedness and existence of traveling wave solutions connecting two states, when the equations are considered as a variant of a conservation law. Then, the numerical approximation consists of a spectral approximation in space based on Legendre polynomials along with a temporal discretization with strong stability preserving (SSP) property. The convergence of the semidiscrete approximation is proved under suitable regularity conditions on the data. The choice of the temporal discretization is justified in order to guarantee the stability of the full discretization when dealing with nonsmooth initial conditions. A computational study explores the performance of the fully discrete scheme with regular and nonregular data.
In this article we discuss how abstraction boundaries can help tame complexity in mathematical research, with the help of an interactive theorem prover. While many of the ideas we present here have been used implicitly by mathematicians for some time, we argue that the use of an interactive theorem prover introduces additional qualitative benefits in the implementation of these ideas.
A Vehicular Ad-Hoc Network(VANET) is a Mobile Ad-Hoc Network(MANET) composed of mobile vehicular nodes.It does not rely on infrastructure to either establish a communication link orrealize communication. Owingto the high mobility of vehicles and limited wireless-communication resources, it is difficult for VANETs to guarantee Quality of Service(QoS).To solve this problem, this paper introduces a Software-Defined Network(SDN).In particular, amulti-constrained QoS routing algorithm suitable for Doftware-Defined Vehicular Ad-Hoc Network(SDN-VANET) is proposedthatharnessesthe advantages of SDN control and forwarding separation to ensurevehicle QoS.First, the SDN controller schedules a vehicle's service based on deadline constraints.Second, this paper proposesan Adaptive Hybrid Shuffled Frog-Leaping Algorithm(AH-SFLA).The SDN controller calculates the appropriate value of the data on the transmission link according to the QoS index and the global topology information and uses this as a benchmark to search for an optimized path.At the same time, alternative link mechanisms and QoS resource consumption thresholds are set to implement routing maintenance in order toreduce the probability of network failures.Finally, mininet-wifi and SUMO are combined to build an SDN-VANET environment, and the AH-SFLA routing algorithm is compared with the performances ofIGA and IICSFLA.The experimental results show that compared with IGA and IICSFL, AH-SFLA can improve the average end-to-end delay index by 57.74% and 46.6%, reduce the packet-loss rate by 29.9% and 18.6%, and increase the cost of standardized routing by 36.93% and 27.2%, respectively, effectively guaranteeingQoS in VANET.
The multidimensional integral equation of second kind with a homogeneous of degree (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mi>n</mi></mrow></semantics></math></inline-formula>) kernel is considered. The special class of continuous functions with a given asymptotic behavior in the neighborhood of zero is defined. It is proved that, if the free term of the integral equation belongs to this class and the equation itself is solvable, then its solution also belongs to this class. To solve this problem, a special research technique is used. The above-mentioned technique is based on the decomposition of both the solution and the free term in spherical harmonics.