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We consider codimension 2 sphere congruences in pseudo-conformal geometry that are harmonic with respect to the conformal structure of an orthogonal surface. We characterise the orthogonal surfaces of such congruences as either $S$-Willmore surfaces, quasi-umbilical surfaces, constant mean curvature surfaces in 3-dimensional space forms or surfaces of constant lightlike mean curvature in 3-dimensional lightcones. We then investigate Bryant's quartic differential in this context and show that generically this is divergence free if and only if the surface under consideration is either superconformal or orthogonal to a harmonic congruence of codimension 2 spheres. We may then apply the previous result to characterise surfaces with such a property., 15 pages

Let G be a finite group. For a positive integer d, let s d N ( G ) denote the smallest integer l such that every sequence S over G of length | S | ≥ l has a nonempty product-one subsequence T with | T | ≡ 0 (mod d). In this paper, we mainly study this invariant for dihedral groups D 2 n and metacyclic groups C p ⋉ s C q .

Solving quadratic congruence equations is an expensive operation widely employed in cryptographic constructions for secure IoT applications. Recently, two outsourcing algorithms were proposed by Zhang et al. to solve quadratic congruence equations by employing Cippolla’s algorithm. It was claimed that all the inputs and outputs can be obscured in these two algorithms. However, we present two passive attacks in this paper to show that all the inputs and outputs can be recovered efficiently by just a curious server, which implies the two outsourcing algorithms are insecure. To fix them, we further propose an improved outsourcing algorithm to solve quadratic congruence equations, which is more efficient and the privacy of actual inputs and outputs can be protected very well.

We construct a canonical basis for the space of weakly holomorphic Drinfeld modular forms. And we find that the basis elements satisfy a generating function and the duality among coefficients of the basis elements. Moreover we obtain the congruence properties of t-expansion coefficients of these functions under some conditions.

We present a result that the modular equation of a Hauptmodul for a certain congruence subgroup Γ H ( N , t ) of genus zero satisfies Kronecker's congruence relation. This generalizes the author's previous result about Γ 1 ( m ) ⋂ Γ 0 ( m N ) . Furthermore we show that the similar result holds for a certain congruence subgroup Γ of genus zero with [ Γ : Γ H ( N , t ) ] = 2 . Finally we prove a conjecture of Lee and Park, asserting that the modular equation of the continued fraction of order six satisfies a certain form of Kronecker's congruence relation.

The extent to which men and women sort into different jobs and organizations—namely, gender differences in supply-side labor market processes—is a key determinant of workplace gender composition. This study draws on theories of congruence to uncover a unique organization-level driver of gender differences in job seekers’ behavior. We first argue and show that congruence between leadership gender and organizational claims is a key mechanism that drives job seekers’ interest. Specifically, many organizational claims are gender-typed, such that social claims activate the female stereotype, whereas business claims activate the male stereotype. Thus, whereas female-led organizations making social claims are gender-congruent, male-led firms making the same claims are gender-incongruent. Beyond demonstrating a general preference among job seekers for congruence, we also find that female job seekers are most interested in working for organizations that are simultaneously congruent and provide credible signals that they are fair and equitable employers. The congruence of leadership gender and organizational claims thus affects the gender composition of applicant pools for otherwise identical jobs.

In this paper, we introduce the concept of $ j $-hyperfilters, for all positive integers $ 1\leq j \leq n $ and $ n \geq 2 $, on (ordered) $ n $-ary semihypergroups and establish the relationships between $ j $-hyperfilters and completely prime $ j $-hyperideals of (ordered) $ n $-ary semihypergroups. Moreover, we investigate the properties of the relation $ \mathcal{N} $, which is generated by the same principal hyperfilters, on (ordered) $ n $-ary semihypergroups. As we have known from [21] that the relation $ \mathcal{N} $ is the least semilattice congruence on semihypergroups, we illustrate by counterexample that the similar result is not necessarily true on $ n $-ary semihypergroups where $ n\geq 3 $. However, we provide a sufficient condition that makes the previous conclusion true on $ n $-ary semihypergroups and ordered $ n $-ary semihypergroups where $ n\geq 3 $. Finally, we study the decomposition of prime hyperideals and completely prime hyperideals by means of their $ \mathcal{N} $-classes. As an application of the results, a related problem posed by Tang and Davvaz in [31] is solved.

Molecular methods have revolutionised virtually every area of biology, and metazoan phylogenetics is no exception: molecular phylogenies, molecular clocks, comparative phylogenomics, and developmental genetics have generated a plethora of molecular data spanning numerous taxa and collectively transformed our understanding of the evolutionary history of animals, often corroborating but at times opposing results of more traditional approaches. Moreover, the diversity of methods and models within molecular phylogenetics has resulted in significant disagreement among molecular phylogenies as well as between these and earlier phylogenies. How should this broad and multifaceted problem be tackled? I argue that the answer lies in integrating evidence to infer the best evolutionary scenario. I begin with an overview of recent development in early metazoan phylogenetics, followed by a discussion of key conceptual issues in phylogenetics revolving around phylogenetic evidence, theory, methodology, and interrelations thereof. I then argue that the integration of different kinds of evidence (e.g. molecular, morphological, ecological) is necessary for arriving at the best evolutionary scenario (causal explanation) rather than merely the best-fitting cladogram (statistical explanation). Finally, I discuss the prospects of this view in stimulating interdisciplinary cross-talk in early metazoan research and beyond, and challenges that need to be overcome.

This study explores how the college-going culture at a no-excuses charter school with high college enrollment rates shaped students’ worldviews and trajectories. Drawing on 7 months of ethnographic fieldwork, I found that the school boosted college enrollment through student compliance to the college accountability policies rather than through the transmission of dominant cultural resources. Alignment between a student’s worldview and the school’s approach mediated their ability to draw on their full range of resources to participate in the college choice process and forge postsecondary trajectories they believed in. These findings foreshadow the potential impacts of “College for All” accountability structures and underscore the importance of cultural congruence in college-going cultures.

The extent to which voters and parties agree on policies is an important way through which political scientists have empirically studied political representation. This opinion congruence is most often measured by comparing preferences on a number of policy statements. While the selection of policy statements has not escaped scholarly attention, its impact on the reliability of congruence scores, i.e. the degree to which similar levels of opinion congruence are found when different samples of policy statements are used, has been less investigated. This article looks at which factors of statements samples and voters affect the reliability of congruence measures. It does so by simulating over 5 million opinion congruence scores on the basis of a dataset containing 134 voter and party policy preferences. It finds that both the number of statements and their topic diversity positively affect the reliability of congruence estimates. In addition, the congruence estimates of politically less sophisticated voters are more reliable but only when many left-right policy statements are included in the statement selection. Finally, explorative analyses suggest that increasing topic diversity also increases the validity of congruence measures.

In 2010, Sun and Tauraso proved the combinatorial congruence $$\begin{aligned} \sum _{k=0}^{p^r-1}\frac{1}{2^k}{2k\atopwithdelims ()k} \equiv (-1)^{\frac{p^r-1}{2}} \pmod {p}. \end{aligned}$$ Later, Guo and Zeng gave a q-analogue of this congruence: for any positive odd integer n, $$\begin{aligned} \sum _{k=0}^{n-1}\frac{(q;q^2)_k}{(q;q)_k}q^{k} \equiv (-1)^{\frac{(n-1)}{2}}q^{\frac{n^2-1}{4}} \pmod {\Phi _n(q)}, \end{aligned}$$ where $$\Phi _n(q)$$ represents the n-th cyclotomic polynomial in q and $$(a,q)_n$$ is the q-shifted factorial. In this paper, we shall provide some generalizations of Guo and Zeng’s q-congruences.

PurposeThis study provides a systematic review of the literature within the manufacturing strategy (MS) domain focusing on the congruence aspect of different strategic functions to determine the state-of-the-art research progression and the trend of publications.Design/methodology/approachWe have adopted a five-stage review methodology consisting - 1) Article Identification; 2) Inclusion/Exclusion; 3) Review of the Articles; 4) Literature Analysis; 5) Future research directions. 121 articles focusing on congruence aspects and specific to the MS domain are identified and reviewed. Bibliometric analysis comprising keyword co-occurrence using a VOSviewer© software, and citation analysis is performed. Further, content analysis is carried out to categorize articles based on the type of research methodology, type of tool/method used, and aspects considered for congruence study.FindingsBased on the research gaps identified in the existing literature on the congruence aspect within the MS domain, this study offers future research directions. Majorly, the work found is an empirical survey. Literature scants to develop a framework that helps to quantify the congruence between two strategic functions.Research limitations/implicationsThis study facilitates researchers and practitioners to understand the congruence between different strategic aspects studied in the literature and the level of fit between them. Further, the identified research directions can encourage researchers and practitioners to conceive novel approaches to conduct future works on congruence theme.Originality/valueThe unicity of the current review lies in its theme, i.e. congruence aspect within MS. To the best of author's knowledge, no comparable study is observed to review the congruence aspect in any other domain.

The aim of this paper is to introduce fuzzy ideals and fuzzy (weak) congruence relations of L-algebras. We give a sufficient and necessary condition for a fuzzy set to be a fuzzy ideal of an L-algebra. After obtaining a necessary condition for a fuzzy set to be a fuzzy ideal of L-algebras, we construct an example to show that the condition is not sufficient. For CKL-algebras, however, we prove that it is both necessary and sufficient. Then we give a process to generate a fuzzy ideal by a fuzzy set of CKL-algebras. Finally, we establish a correspondence between fuzzy ideals and fuzzy weak congruence relations of L-algebras, and get homomorphism theorems induced by fuzzy congruence relations.

The relevance of the macro-context for understanding political trust has been widely studied in recent decades, with increasing attention paid to micro–macro level interactive relationships. Most of these studies rely on theorising about evaluation based on the quality of representation, stressing that more-educated citizens are most trusting of politics in countries with the least corrupt public domains. In our internationally comparative study, we add to the micro–macro interactive approach by theorising and testing an additional way in which the national context is associated with individual-level political trust, namely evaluation based on substantive representation. The relevance of both types of evaluation is tested by modelling not only macro-level corruption but also context indicators of the ideological stances of the governing cabinet (i.e., the level of its economic egalitarianism and cultural liberalism), and interacting these with individual-level education, economic egalitarianism and cultural liberalism, respectively. As we measure context characteristics separately from people's ideological preferences, we are able to dissect how the macro-context relates to the levels of political trust of different subgroups differently. Data from three waves (2006, 2010, 2014) of the European Social Survey (68,294 respondents in 24 European countries and 62 country-year combinations), enriched with country-level data derived from various sources, including the Chapel Hill Expert Survey, are used in the multi-level regression analyses employed to test our hypotheses. We found support for the micro–macro level interactions theorised by the evaluation based on the quality of representation approach (with higher levels of trust among more-educated citizens in less corrupt countries), as well as for evaluation based on substantive representation in relation to cultural issues (with higher levels of trust among more culturally liberal citizens in countries with more culturally liberal governing cabinets). Our findings indicate that the latter approach is at least equally relevant as the approach conventionally used to explain context differences in political trust. Finally, we conclude our study with a discussion of our findings and avenues for future research.

Destination image has become a crucial topic in tourism studies. However, research has scarcely considered multiple online content sources when studying the image of destinations. This paper examines different types of user-generated content in order to evaluate whether and how this content reflects the evolution of a destination’s image, and its congruence therein. The research focuses on a multi-asset tourist destination, i.e., one which draws different market segments. The results show a relatively high degree in congruence and evolution of the destination’s attractions, but also questions bits of theories on communication congruence as well as attractions’ evolution theories.

A number of frameworks have been developed examining destination competitiveness. While most recognise the roles crises can play, specific issues related to crisis and crisis management have not be...

Consider the algebraic function $\Phi_{g,n}$ that assigns to a general $g$-dimensional abelian variety an $n$-torsion point. A question first posed by Kronecker and Klein asks: What is the minimal $d$ such that, after a rational change of variables, the function $\Phi_{g,n}$ can be written as an algebraic function of $d$ variables? Using techniques from the deformation theory of $p$-divisible groups and finite flat group schemes, we answer this question by computing the essential dimension and $p$-dimension of congruence covers of the moduli space of principally polarized abelian varieties. We apply this result to compute the essential $p$-dimension of congruence covers of the moduli space of genus $g$ curves, as well as its hyperelliptic locus, and of certain locally symmetric varieties., Comment: 26 pages. Minor revisions. Comments welcome!

In this paper we study solvability and nilpotency of an expanded group relative to the nearring of zero and congruence preserving functions of the expanded group. A particular case of interest is when the expanded group is a nearring module. This leads to consequences when an expanded group is viewed as a nearring module over its nearring of zero preserving polynomial functions.

Civil society organizations (CSOs) can facilitate collective action. This makes understanding what shapes whether people are likely to engage with CSOs critically important. This paper argues that whether an organization is perceived as congruent – similar to an individual in values – is a key determinant of whether individuals will engage with it. I use a conjoint survey experiment to test how organizational attributes signaling congruence influence respondents’ willingness to attend a hypothetical organization’s meetings. I find that individuals are more likely to choose organizations that are more likely to be congruent with them, except when it comes to funding. These findings imply that an individual’s level of comfort with a CSO matters for engagement; thus, CSOs need to consider how they match to their publics when reaching out to potential joiners. Furthermore, donors seeking to support CSOs need to pay attention to their impact on perceptions of congruence.

The instructional congruence framework has been used to enhance congruence between students’ non-dominant backgrounds and science instruction in upper grades. The purpose of this paper is to propos...

Consider an oriented curve $\Gamma$ in a domain $D$ in the plane $\boldsymbol R^2$. Thinking of $D$ as a piece of paper, one can make a curved folding in the Euclidean space $\boldsymbol R^3$. This can be expressed as the image of an "origami map" $\Phi:D\to \boldsymbol R^3$ such that $\Gamma$ is the singular set of $\Phi$, the word "origami" coming from the Japanese term for paper folding. We call the singular set image $C:=\Phi(\Gamma)$ the crease of $\Phi$ and the singular set $\Gamma$ the crease pattern of $\Phi$. We are interested in the number of origami maps whose creases and crease patterns are $C$ and $\Gamma$, respectively. Two such possibilities have been known. In the authors' previous work, two other new possibilities and an explicit example with four such non-congruent distinct curved foldings were established. In this paper, we determine the possibility of the number $N$ of congruence classes of curved foldings with the same crease and crease pattern. As a consequence, if $C$ is a non-closed simple arc, then $N=4$ if and only if both $\Gamma$ and $C$ do not admit any symmetries. On the other hand, when $C$ is a closed curve, there are infinitely many distinct possibilities for curved foldings with the same crease and crease pattern, in general., Comment: 29 pages, 7 figures

PurposeThis study examines the prominence and congruence or “fit” between corporate social responsibility (CSR) activities and medical tourism providers (MTPs). In doing so, this study seeks to understand the forms of CSR commonly used in the marketing of health-care services by international MTPs.Design/methodology/approachExploratory quantitative content analysis methods are used to examine CSR communication provided by MTPs. Descriptive statistics and analyses of variance are used to analyze the data.FindingsResults show that 22% of MTP websites provided CSR information. There was a high degree of congruence or “fit” between the MTPs and the CSR. Furthermore, each MTP averaged between three and six CSR engagements demonstrating a commitment to not only the practice of CSR but also the stakeholders and communities who benefit.Research limitations/implicationsThis analysis focused on organizational websites and did not examine CSR communications delivered through alternative media channels (e.g. digital platforms, promotional brochures, print advertising, etc.).Practical implicationsThis study adds to the CSR framework in the medical tourism context by discovering what forms of CSR are commonly used in the marketing and promotion of international health services and further analyzes the strategic communication techniques used to deliver these messages.Social implicationsCSR is argued to have direct impacts on employee satisfaction, investor relations and consumer behavior; therefore, current findings may contribute to the development of measurement tools for empirical studies that test relationships between the persuasiveness of CSR messages on the attitudes of medical tourists.Originality/valueResearch inquiries into the CSR strategic communication practices help to identify strengths and opportunities, while informing reputation management and relationship-building practices.

Abstract. Drawing on the person–organization fit theory, we investigate how the value congruence between employees’ collectivist values and their perception of organizational collectivism influences organizational embeddedness. Based on a survey of 515 working adults, the polynomial regression and response surface analysis results support that embeddedness is highest in the presence of both high individual and organizational collectivism. Additionally, the smaller the discrepancy between the two perceptions, the more embedded the employees. Our study contributes to the cultural perspectives in the organizational embeddedness research by theorizing and measuring the impact of collectivism at the individual level. The findings also contribute to the person–organization fit theory by identifying a value congruence approach to organizational embeddedness.

In this paper, by using norms, we define the concept of intuitionistic fuzzy equivalence relations and intuitionistic fuzzy congruence relations on ring R and we investigate some assertions. Also we define intuitionistic fuzzy ideals of ring R under norms and compare this with fuzzy equivalence relation and fuzzy congruence relation on ring R such that we define new introduced ring.

In this paper, we investigate the joint functional distribution of Selberg zeta functions for principal congruence subgroups. We prove that the joint universality theorem for these zeta functions holds in the strip 0.85 σ 1 . As a corollary, we obtain the functional independence for the zeta functions.

We prove a congruence modulo 16 relating the class numbers h ( − 4 p ) , h ( 16 p ) of quadratic orders and Zagier's sum m ( 4 p ) associated to 4 p , when p ≡ 1 (mod 4) is a prime. This gives an analogy to Chua-Gunby-Park-Yuan's congruence established when p ≡ 3 (mod 4), and generalizes a recent work by Cheng and Guo. In particular, when p ≡ 1 (mod 4) is a prime, it is shown that the class number h ( − 4 p ) is divisible by 16 if and only if the Zagier sum m ( 4 p ) is divisible by 16.

In 2012, Chan proved a number of congruences for the coefficients of Ramanujan’s ϕ \phi function. In this paper, we prove some new congruences modulo powers of 2 and 3 for Ramanujan’s ϕ \phi function by employing Newman’s identities and theta function identities.

In 19th century, Fermat's little theorem ``$a^p\equiv a({\rm mod}\;p)$ for $a\in\mathbb Z$, $p$ prime'' was generalized in two directions: Schonemann proved a corresponding congruence for the coefficients of monic polynomials, whereas Gauss found a congruence result with $p$ replaced by any $n\in\mathbb N$. Here, we shall give an elementary proof of the common generalization of these two results.

Public opinion about climate change is well documented, but policymaker attitudes are less known. To examine the foundations for policymaking, we analyze congruence in policymaker-citizen attitudes concerning climate change. We use surveys conducted among the Finnish policymaking elite (n = 675) and a representative sample of the Finnish voting-age population (n = 1,701) in 2018–19, which included identical items of climate change concern and willingness to reduce personal living standards to curb climate change. Policymakers demonstrate much more concern for climate change and willingness to pay, suggesting a significant attitudinal disconnect between policymakers and citizens. The incongruence remains when taking personal income into account. In terms of party support, policymaker opinion aligns with opinions of voters of the green party in Finland. We speculate as to whether the observed opinion incongruence could restrict policymakers’ possibilities to make climate-friendly policies and whether climate-skeptic populist parties could use it for political gain. acceptedVersion

Fix distinct primes $\ell$ and $f$, a finite field $\mathbf{F}_{q}$ such that $q \equiv 1 \pmod{\ell f}$, and a character $\chi : \mathbf{F}_{q}^{\times} \to \mathbf{C}^{\times}$ of exact order $\ell f$. We present a new $\ell$-adic congruence for the Jacobi sum $J(\chi^{\ell}, \chi^{f})$. These Jacobi sums are Frobenius eigenvalues of the curve $y^{\ell} = x^{f} + 1$.

Taking residual finiteness as a starting point, we consider three related finiteness properties: weak subsemigroup separability, strong subsemigroup separability and complete separability. We investigate whether each of these properties is inherited by Sch\"utzenberger groups. The main result of this paper states that for a finitely generated commutative semigroup $S$, these three separability conditions coincide and are equivalent to every $\mathcal{H}$-class of $S$ being finite. We also provide examples to show that these properties in general differ for commutative semigroups and finitely generated semigroups. For a semigroup with finitely many $\mathcal{H}$-classes, we investigate whether it has one of these properties if and only if all its Sch\"utzenberger groups have the property., Comment: 27 pages

The purpose of the present article is to prove that the Diophantine equation n^x + 13^y = z^2 has exactly one solution (n, x, y, z) = (2, 3, 0, 3) where x, y and z are non-negative integers and n is a positive integer with n ≡ 2 (mod 39) and n + 1 is not a square number. In particular, (3, 0, 3) is a unique solution (x, y, z) in non-negative integers of the Diophantine equation 2^x + 13^y = z^2

This paper concerns the congruence frame in the setting of partial frames, which, in contrast to full frames, do not necessarily have all joins. Examples of these include bounded distributive lattices, o and k frames. A new class of congruences, called Heyting congruences, helps to illuminate the structure of these congruence frames. Defining these involves the very useful free frame over a partial frame. We investigate the relationship between Heyting congruences and co-atoms of the congruence frame, showing how different the cases of full and partial frames can be. The Madden congruence, which yields the least dense quotient, is recognized as a particular Heyting congruence. While the collection of all Heyting congruences on a partial frame is in general not even a meet-semilattice, joining each of them with the Madden congruence results in a collection with considerably more interesting structure.

The problem of the solvability of the congruence $$g(p_1)+\dots+g(p_k)\equiv m\pmod{q}$$ in primes $$p_1,\ldots,p_k\leq N$$ , $$N\leq q^{1-\gamma}$$ , $$\gamma>0$$ , is addressed. Here $$g(x)\equiv a\overline{x}+bx\pmod{q}$$ , $$\overline{x}$$ is the inverse of the residue $$x$$ , i.e., $$\overline{x}x\equiv 1\pmod{q}$$ , $$q\geq 3$$ , and $$a$$ , $$b$$ , $$m$$ , and $$k\geq 3$$ are arbitrary integers with $$(ab,q)=1$$ . The analysis of this congruence is based on new estimates of the Kloosterman sums with primes. The main result of the study is an asymptotic formula for the number of solutions in the case when the modulus $$q$$ is divisible by neither $$2$$ nor $$3$$ .

The Swing Lemma, proved by G. Gratzer in 2015, describes how a congruence spreads from a prime interval to another in a slim (having no $$\mathsf {M}_{3}$$ sublattice), planar, semimodular lattice. We generalize the Swing Lemma to planar semimodular lattices.