Congruence Research Articles

Using Theory and Practice to Develop Lottery Ticket Warning Messages as a Means of Promoting More Responsible Gambling

Background Playing the lottery is considered a public health concern in many countries due to financial losses associated with it, but also due to other harmful health and social problems. Focus of the article Informed by both theory and practice, this article focuses on developing lottery ticket warning messages targeting players harmed by excessive spending to promote sustainable behavior change. Research Question What should be communicated in lottery ticket warning messages targeting people at risk to facilitate behavior change and maintain it? Approach We bridge the gap between theory and practice and illustrate how theoretical models and current communications can shape messages. Specifically, we identify and examine lottery ticket warning messages and analyze their relative congruence to prevailing theories to assess the potential effectiveness of the messages and to recommend warning labels for lottery tickets. In addition, we incorporate knowledge used by cognitive psychologists in counselling to create warnings more likely to motivate and sustain behavior change. Importance to the Social Marketing Field Merging academic theory with existent communications ensures better knowledge translation and potentially better outcomes. Introducing verified techniques from Cognitive Behavior Therapy into social marketing initiatives could be a step forward into triggering behavior change. Methods A literature review was conducted to identify and select theoretical models appropriate to guide communications for lottery tickets harmful consumption. Searches were conducted to identify initiatives aiming at persuading and helping at-risk individuals to change their behavior in a healthy manner. Social marketing campaign messages were then compared with theoretical paradigms to identify ways in which campaign messages could be improved. Results Results show campaign messages were relatively consistent with some aspects of the theoretical models. Warning messages provide information that is relevant to the target audience and describe the severity and vulnerability of irresponsible consumption. They also attempt to decrease perceived costs and increase perceived self-efficacy in a variety of ways. Some also attempt to modify cognitive distortions the audience has in respect to chances of winning. However, initiatives should also increase consumers’ perceptions of the response-efficacy by emphasizing their agency, and further enhance individuals’ perception of self-efficacy by incorporating strategies from the Cognitive Model. Recommendations for Research and Practice Academics and practitioners can build on each other’s knowledge on an ongoing basis. By making it default to always consider both theory and practice, initiatives are likely to become more effective. Managers responsible for developing warning messages and implementing social marketing campaigns can experiment with the various theoretical approaches to determine which are comparatively more effective for their situations. Limitations Future research is needed to test the comparative effectiveness of these theories as a basis of creating persuasive warning messages.

From roadmap to regulation: will there be a transatlantic approach to governing artificial intelligence?

ABSTRACT The transformative nature and accelerating pace of development of Artificial Intelligence (AI) technologies have generated frenzied political debate and urgent calls for regulation. The European Union’s (EU) AI Act is one of the earliest, most ambitious, legally binding efforts to regulate high-risk AI systems. This article argues that the thrust of the EU’s focus on ‘ethical and secure’ AI and its first-mover regulatory status have helped to foster transatlantic cooperation on AI governance. To probe this assertion, the article analyzes the ethical underpinnings and key provisions of the AI Act and compares them to policy developments in the United States. The analysis provides preliminary evidence of policy similarities across the Atlantic from an alignment of ethical concerns to a shared understanding of the risks and associated need for common guidelines and standards in the AI sector. Tracing agreements within the EU-US Trade and Technology Council (TTC) suggests further cooperation and relative congruence in the EU and US approaches to AI.

Non-fragile output-feedback control for delayed memristive bidirectional associative memory neural networks against actuator failure

This article investigates the stabilization property for the modeled memristive bidirectional associative memory neural networks with time-varying delay when the faulty signals received from the fluctuated controller. The non-fragile output-feedback controller is taken into account to counteract the impact of gain perturbations to end up with robust fault-tolerant setup. To tackle the weak signals in the actuator received from the fluctuated controller, control gain matrices encompass situations intended to memory non-fragile output-feedback controller. Based on the Lyapunov stability theory, differential inclusion theory, and congruence transformation, the sufficient condition for the global asymptotic stabilization property for the designed fault-tolerant memristive bidirectional associative memory neural network model is obtained in terms of linear matrix inequality by utilizing Wirtinger's inequality. Finally, numerical examples are approached with the state performance plots of the proposed memristive bidirectional associative memory neural network model with respect to the time-domain plane, to confirm the stabilization results and it illustrates the working mechanism of the designed controller.

Quasivarieties of algebras whose compact relative congruences are principal

Quasivarieties of algebras whose compact relative congruences are principal

Quotient Permutation BF-Algebras and Quotient Maps

The permutation BF-algebras was given as a new class of BF-algebras and their basic features in this work were studied. We considered and discussed some new notions in permutation BF-algebras, like permutation BF1/BF2-algebras, permutation BF-ideals, permutation BF-subalgebras, normal permutation BF-subalgebras. We further looked at the homomorphism of BF-algebras, congruence relation, quotient permutation BF-algebras, and Quotient map.

Grey relations

PurposeThe goal of this article is to introduce the notion of a grey relation between grey sets using grey numbers.Design/methodology/approachThis study uses the grey number to create novel ideas of grey sets. We suggest several operations that can be performed on it, including the union, intersection, join, merge, and composition of grey relations. In addition, we present the definitions of reflexive, symmetric, and transitive grey relations and analyze certain characteristics associated with them. Furthermore, we formulate the concept of the grey equivalence relation, apply it to the study of the grey equivalence class over the grey relation, and go over some of its features.FindingsWe present new algebraic aspects of grey system theory by defining grey relations and then analyzing their characteristic features.Practical implicationsThis paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. This paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. As such, it can be applied to create rough approximations as well as congruences in algebras, topologies, and semigroups.Originality/valueThe presented notions are regarded as new algebraic approaches in grey system theory for the first time. Additionally, some fundamental operations on grey relations are also investigated. Consequently, different types of grey relations, such as reflexive, symmetric, and transitive relations, are discussed. Then, the grey equivalence class derived from the grey equivalence relation is demonstrated, and its properties are examined.

Numerical Evidence for a Refinement of Deligne’s Period Conjecture for Jacobians of Curves

Let A / Q be a Jacobian variety and let F be a totally real, tamely ramified, abelian number field. Given a character ψ of F / Q , Deligne’s Period Conjecture asserts the algebraicity of the suitably normalized value L ( A , ψ , 1 ) at s = 1 of the Hasse-Weil-Artin L-function of the ψ -twist of A. We formulate a conjecture regarding the integrality properties of the family of normalized L-values ( L ( A , ψ , 1 ) ) ψ , and its relation to the Tate-Shafarevich group of A over F. We numerically investigate our conjecture through p-adic congruence relations between these values.

Some Results on Filters and Congruence Relations of Hoops

Some Results on Filters and Congruence Relations of Hoops

Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras

Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras

TESTING THE ELONGATION OF 3-TUPLES RELATING TO POLYNOMIALS AND POLYGONAL NUMBERS WITH PECULIAR PROCLAMATION

In this paper, special 2-tuples with elements stand well-known polynomials and polygonal numbers with different sides that exclusively meet the property that the summation or difference of two elements provides a square can be stretched to 3-tuples but not 4-tuples with the same characteristics are displayed. Also, the similar characteristics of all such 3-tuples are checked with numerical values by Python programs. KEYWORDS: Diophantine m-tuples, Congruence relations, polygonal numbers, polynomials

High order congruences for M-ary partitions

For a sequence M=(mi)i=0∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M=(m_{i})_{i=0}^{\\infty }$$\\end{document} of integers such that m0=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_{0}=1$$\\end{document}, mi≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_{i}\\ge 2$$\\end{document} for i≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$i\\ge 1$$\\end{document}, let pM(n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_{M}(n)$$\\end{document} denote the number of partitions of n into parts of the form m0m1⋯mr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_{0}m_{1}\\cdots m_{r}$$\\end{document}. In this paper we show that for every positive integer n the following congruence is true: pM(m1m2⋯mrn-1)≡0mod∏t=2rM(mt,t-1),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} p_{M}(m_{1}m_{2}\\cdots m_{r}n-1)\\equiv 0\\ \\ \\left( \ extrm{mod}\\ \\prod _{t=2}^{r}\\mathcal {M}(m_{t},t-1)\\right) , \\end{aligned}$$\\end{document}where M(m,r):=mgcd(m,lcm(1,…,r))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {M}(m,r):=\\frac{m}{\ extrm{gcd}\\big (m,\ extrm{lcm}(1,\\ldots ,r)\\big )}$$\\end{document}. Our result answers a conjecture posed by Folsom, Homma, Ryu and Tong, and is a generalisation of the congruence relations for m-ary partitions found by Andrews, Gupta, and Rødseth and Sellers.

A system-level interface sampling and reduction method for component mode synthesis with varying parameters

This paper presents a new interface sampling and reduction method for varying parameters within the framework of the component mode synthesis (CMS) method. In the conventional interpolation-based parametric reduced-order model (IB-PROM) based on CMS, reduced subsystems are synthesized, and interface degrees-of-freedom are reduced via the secondary eigenvalue analysis in the online stage, which is essential to obtain highly reduced system matrices. However, it inhibits rapid parameter updating and requires extra computational resources in the online stage. In the present study, the pre-reduced interface sampling method is proposed by synthesizing substructures and reducing the interface before beginning the online stage. The interface solution is obtained through offline and online adaptation, likewise the procedure of computing the interior solution of previous studies. Additionally, congruence transformations are applied to each reduced interface, which is mandatory for interpolating symmetric positive definite matrices with respect to a new input parameter. As a result, the online performance of IB-PROM is greatly enhanced, showing rapid and near real-time adaptations to the variations in system parameters.

A Study on Rough Fuzzy Bipolar Soft Ideals in Semigroups

The theories of rough sets (RSs) and soft sets (SSs) are practical mathematical techniques to accommodate data uncertainty. On the other hand, fuzzy bipolar soft sets (FBSSs) can address uncertainty and bipolarity in various situations. The key objective of this study is to establish the notions of rough fuzzy bipolar soft ideals in semigroup (SG), which is an extension of the idea of rough fuzzy bipolar soft sets in a SG. Also, we have analyzed the roughness in the bipolar fuzzy subsemigroup (BF-SSG) by employing a congruence relation (CR) defined on the SG and investigating several related characteristics. Further, the idea is expanded to the rough fuzzy bipolar soft ideal, rough fuzzy bipolar soft interior ideal, and rough fuzzy bipolar soft bi-ideal in SGs. Moreover, it is observed that CR and complete CR (CCR) are critical in developing rough approximations of fuzzy bipolar soft ideals. Therefore, their related characteristics are studied via CRs and CCRs.

Congruence relation between Stirling numbers of the first and second kinds

Congruence relation between Stirling numbers of the first and second kinds

An Improved Sorting Algorithm for Periodic PRI Signals Based on Congruence Transform

Recently, a signal sorting algorithm based on the congruence transform has been proposed, which is effective in dealing with the staggered Pulse Repetition Interval (PRI) signals. It can effectively sort the staggered PRI signals and obtain the sub-PRI sequence directly without sub-PRI ranking, and it is less affected by interfered pulses and pulse loss. Nevertheless, we find that the algorithm causes pseudo-peaks in the remainder histogram when sorting signals such as sliding PRI, sinusoidal PRI, etc. (collectively referred to as periodic PRI signal in this paper) and pseudo-peaks will cause errors in signal sorting. To solve the issue of pseudo-peaks when sorting periodic PRI signals, an improved sorting algorithm based on congruence transform is proposed. According to the analysis of the congruence characteristics of the periodic PRI signal, a novel method is proposed to identify pseudo-peaks based on the histogram peak amplitude and symmetric difference set. The signal sorting algorithm based on congruence transform is improved to achieve a good sorting effect on periodic PRI signals. Simulation experiments demonstrate that the novel algorithm can effectively sort periodic PRI signals and improve Precall, Pd, and Pf by 6.9%, 5.1%, and 3.2%, respectively, compared to the typical similar algorithms.

H∞ observer-based controller synthesis for fractional order systems over finite frequency range

This paper focuses on the H∞ observer-based control problem for fractional order systems (FOSs) over finite frequency range. Firstly, as an extension to the KYP lemma, the structure singular value–μ and its upper bound are analyzed and determined. The necessary and sufficient conditions of the H∞ performance for FOSs over finite frequency range are given through the generalized μ analysis method. This method is different from the traditional μ-analysis method, which is only suitable for integer order systems. Secondly, according to these obtained LMI-based criteria for H∞ performance index and a key projection lemma, we design an H∞ observer-based controller to stabilize the estimation error and decrease the H∞ norm for the FOS simultaneously. With the help of the matrix congruence transformation, the feedback gain matrix is parameterized by a scalar matrix. Thirdly, to deal with the nonlinear terms in matrix inequalities, an iterative linear matrix inequality (ILMI) algorithm is developed. Finally, two numerical examples are provided to explain the correctness of the established results.

A Study on Quotient Structures of Bipolar Fuzzy Finite State Machines

This article introduces different congruence relations on the bipolar fuzzy set associated with the bipolar fuzzy finite state machine. Each congruence relation associates a semigroup with the bipolar fuzzy finite automata. We also discuss characterizing a bipolar fuzzy finite state machine by defining an admissible relation.

Parabolic Tamari Lattices in Linear Type B

We study parabolic aligned elements associated with the type-$B$ Coxeter group and the so-called linear Coxeter element. These elements were introduced algebraically in (Mühle and Williams, 2019) for parabolic quotients of finite Coxeter groups and were characterized by a certain forcing condition on inversions. We focus on the type-$B$ case and give a combinatorial model for these elements in terms of pattern avoidance. Moreover, we describe an equivalence relation on parabolic quotients of the type-$B$ Coxeter group whose equivalence classes are indexed by the aligned elements. We prove that this equivalence relation extends to a congruence relation for the weak order. The resulting quotient lattice is the type-$B$ analogue of the parabolic Tamari lattice introduced for type $A$ in (Mühle and Williams, 2019).

[formula omitted] gain-scheduled dynamic output feedback control with transient performance applied to electrical microgrid

This paper introduces an approach for designing gain-scheduled dynamic output feedback controllers for continuous-time Linear Parameter-Varying (LPV) systems. The aim is to improve transient response by incorporating both D-stability and H∞ criteria into the synthesis conditions. We achieve this by employing changes of variables and congruence transformations, which lead to new synthesis conditions expressed as linear matrix inequalities. Additional fine-tuned scalar parameters can be used to enhance further the controller performance in terms of less conservative H∞ guaranteed costs. To assess the effectiveness of our proposed synthesis procedure, we conduct computational experiments in the context of a microinverter-based distributed power generation system. These experiments take into account real-world operational characteristics, providing a comprehensive evaluation of our approach. The results demonstrate that the designed controller effectively ensures the desired closed-loop system behavior, even when dealing with state noise and discretization errors originating from digital implementation.

Hyper L-algebras

In this paper, we introduced the notion of hyper [Formula: see text]-algebras as a generalization of [Formula: see text]-algebras. We studied basic properties of them and investigated the relationship among hyper [Formula: see text]-algebras and some other hyper logical algebras such as hyper ([Formula: see text],BCI) BCK-algebras and hyper hoops. In the following, we defined the notions of (weak) hyper ideals in hyper [Formula: see text]-algebras and then by considering the congruence relation (relative to a hyper ideal) on the hyper [Formula: see text]-algebra, we constructed the quotient hyper [Formula: see text]-algebras and investigated some properties of them.