Hasil untuk "Religions. Mythology. Rationalism"

Jusheng Zhang, Ningyuan Liu, Qinhan Lyu et al.

Deep neural networks typically treat nonlinearities as fixed primitives (e.g., ReLU), limiting both interpretability and the granularity of control over the induced function class. While recent additive models (like KANs) attempt to address this using splines, they often suffer from computational inefficiency and boundary instability. We propose the Rational-ANOVA Network (RAN), a foundational architecture grounded in functional ANOVA decomposition and Padé-style rational approximation. RAN models f(x) as a composition of main effects and sparse pairwise interactions, where each component is parameterized by a stable, learnable rational unit. Crucially, we enforce a strictly positive denominator, which avoids poles and numerical instability while capturing sharp transitions and near-singular behaviors more efficiently than polynomial bases. This ANOVA structure provides an explicit low-order interaction bias for data efficiency and interpretability, while the rational parameterization significantly improves extrapolation. Across controlled function benchmarks and vision classification tasks (e.g., CIFAR-10) under matched parameter and compute budgets, RAN matches or surpasses parameter-matched MLPs and learnable-activation baselines, with better stability and throughput. Code is available at https://github.com/jushengzhang/Rational-ANOVA-Networks.git.

Vefa Goksel, Rafe Jones

Bicritical rational functions -- those with precisely two critical points -- include the well-studied families of unicritical polynomials and quadratic rational functions. In this article we lay out general foundations for studying arithmetic dynamical properties of bicritical rational functions, and prove new Galois-theoretic results for a family with special properties. We study the field of definition of the critical points, and give a normal form up to Möbius conjugacy over this field. As a corollary, we show that after a finite extension of the ground field, the arboreal Galois representation attached to a bicritical rational function injects into an iterated wreath product of cyclic groups. We then examine the family of quadratic $φ\in \mathbb{Q}(x)$ with critical points $γ_1$ and $γ_2$ such that $φ(γ_1) = γ_2$. Adapting methods of Odoni-Stoll in the polynomial case to rational functions, we show that the arboreal representation is surjective for an infinite subfamily.

Sumito Hasegawa, Kazuki Kanai, Yasuhiro Oki

In this paper, we study the rationality problem for multinorm one tori, a natural generalization of norm one tori. For multinorm one tori that split over finite Galois extensions with nilpotent Galois group, we prove that stable rationality and retract rationality are equivalent, and give a criterion for the validity of the above two conditions. This generalizes the result of Endo (2011) on the rationality problem for norm one tori. To accomplish it, we introduce a generalization of character groups of multinorm one tori. Moreover, we establish systematic reduction methods originating in work of Endo (2001) for an investigation of the rationality problem for arbitrary multinorm one tori. In addition, we provide a new example for which the multinorm principle holds.

Оксана Василівна Горкуша

У статті, присвяченій базовим світоглядним настановам фундатора українського академічного релігієзнавства професора Анатолія Колодного, у її другій частині, висвітлюється творчість релігієзнавця в період незалежної України. Саме в ці роки видатний український мислитель доклав титанічних інтелектуальних і дієвих зусиль для формування українського академічного релігієзнавства як самостійної, предметно, об’єктно та методологічно окресленої галузі гуманітарних наук. Його численними науковими ініціативами вибудувано історіографічний дискурс української духовно-культурної спадщини та викладено послідовну історію релігійних і релігієзнавчих здобутків українців.

Josephine Ngozi Akah, Anthony Chinaemerem Ajah

This study examined how cross-cultural methodological approach can improve research on environmental sustainability in Africa. What is considered as the traditional methodological approaches to environmental sustainability in the continent are based on siloed traditions and revelation/intuition, and therefore low in creativity. Worse still, whereas ideas from other cultures could infuse new perspectives, creativity, and innovation, many scholars in areas studies insist on methodological monism because of a deeper interest in preserving cultural identity of the regions they study. This approach negatively affects area studies in general and African studies in particular. Thus, two questions guided this study: (i) how can cross-cultural approach to the study of the environment improve its sustainability in Africa; and (ii) to what degree do traditional approaches to knowledge enhance creativity and innovation to environmental sustainability in Africa? To answer these questions, this study adopted, qualitative research methods. Data for the study were generated from secondary sources and analysed using phenomenological, hermeneutic, and critical philosophical approaches. This study argues that insistence on methodological monism is a disservice to environmental sustainability around the world. The study also demonstrates that exploring and incorporating ideas from non-African – particularly modern scientific frameworks – will be beneficial to the continent.

Gabriele Di Antonio, Gianni Valerio Vinci, Luciano Pietronero et al.

Taking informed decisions, namely acting rationally, is an individual attitude of paramount relevance in nature and human societies. In this work, we study how rationality spreads in a community. To this end, through an agent-based model, we analyse the dynamics of a population whose individuals, endowed with a rational attitude controlled by a numerical parameter, play a simple game. The latter consists of multiple strategies, each associated with a given reward. The proposed model is then used as a benchmark for studying the behaviour of Bitcoin users, inferred by analysing transactions recorded in the Blockchain. Remarkably, a population undergoing a sharp transition from irrational to rational attitudes shows a behavioural pattern similar to that of Bitcoin users, whose rationality showed up as soon as their cryptocurrency became worth just a few cents (USD). To conclude, a behavioural analysis that relies on an entropy measure combined with a simple agent-based model allows us to detect the rise of rationality across a community. Although further investigations are essential to corroborate our results, we deem the proposed approach could also get used for studying other social phenomena and behaviours.

Nathan Bowler, Florian Gut

We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after countably many turns a complete infinite graph contained in her coloured edges where the vertex set of the subgraph is order-isomorphic to the rationals. It is Breaker's goal to prevent Maker from achieving this. We prove that there is a winning strategy for Maker in this game. We also prove that there is a winning strategy for Breaker in the game where Maker must additionally make the vertex set of her complete graph dense in the rational numbers.

Hans-Peter Schröcker, Zbyněk Šìr

We solve the so far open problem of constructing all spatial rational curves with rational arc length functions. More precisely, we present three different methods for this construction. The first method adapts a recent approach of (Kalkan et al. 2022) to rational PH curves and requires solving a modestly sized system of linear equations. The second constructs the curve by imposing zero-residue conditions, thus extending ideas of previous papers by (Farouki and Sakkalis 2019) and the authors themselves (Schröcker and Šír 2023). The third method generalizes the dual approach of (Pottmann 1995) from planar to spatial curves. The three methods share the same quaternion based representation in which not only the PH curve but also its arc length function are compactly expressed. We also present a new proof based on the quaternion polynomial factorization theory of the well known characterization of the Pythagorean quadruples.

Carlos Ribeiro Caldas Filho, Jacqueline Ziroldo Dolghie

O presente artigo pretende aplicar para a interpretação do filme Os Irmãos Cara de Pau (The Blues Brothers, 1980), de John Landis, o que o crítico literário canadense Northrop Frye afirmou em relação à Bíblia como sendo o “grande código” da arte.  A premissa básica do artigo é que o filme de Landis segue a estrutura básica de três narrativas bíblicas (Êxodo 3.1-10, Isaías 6.1-8 e Atos dos Apóstolos 9.1-15) nas quais há uma manifestação do sagrado, seguida de um comissionamento para uma missão. O artigo apresenta algumas considerações sobre a relação entre cinema e Bíblia, seguidas de uma apresentação do filme propriamente. Depois disso, comenta-se sobre três narrativas bíblicas de chamado e comissionamento, que entendemos fornecem a linha narrativa seguida pelo filme. Como base teórica, o artigo trabalhou principalmente com a ideia de sagrado selvagem, de Roger Bastide, e do elemento indizível do sagrado, a partir de Rudolf Otto.

Stella Avanesova

Martin Jakobsen

This paper presents a theological critique of divine command theory, a metaethical theory stating that moral wrongness is constituted by God’s command. First, I argue that this theory does not qualify as a Christian moral theory because it lacks connections to central parts of Christian theology, such as Christology. This argument does not imply that the theory is wrong nor that it is inconsistent with Christianity—only that it is not Christian as such. Second, I argue that divine command theory does not fit well with the New Testament’s vision of the moral life, in which being conformed to the image of Christ has primacy over adherence to law. This argument implies that the Christian ethicist should look elsewhere for a metaethical theory. I next argue in favour of a moral theory of imitation, in which the moral life consists of imitating God, the prime exemplar of goodness, which is made possible through an imitation of Christ.

M. Naufal Firosa Ahda, Yusuf Ratu Agung

Penelitian ini bertujuan untuk mengetahui konsep sujud (meditasi) pada ajaran Sapta Darma, serta memahami bagaimana efek dan prosesnya ketika mencapai kesadaran penuh (“satrio utomo”). Metode yang digunakan adalah metode kualitatif dengan pendekatan fenomenologi. Teknik pengumpulan data ditempuh melalui wawancara mendalam, observasi, dan dokumentasi terhadap penghayat kepercayaan Sapta Darma yang sedang­ mendalami sujud. Hasil penelitian menunjukkan bahwa sujud dalam Sapta Darma memiliki beberapa konsep yang mengandung unsur filosofis serta memberikan efek psikologis kepada subjek. Efek psikologis, yang dirasakan pada umumnya setelah mendalami sujud, menunjukkan bahwa mereka memiliki kesadaran penuh yang dapat dicapai melalui beberapa tahapan, antara lain mampu mengendalikan “sebelas saudara” (nafsu); mampu memahami diri sendiri; berdarma (berperilaku baik); welas asih; memiliki kewaskitaan (kepekaan), bijaksana; racut; dan dikehendaki oleh Tuhan Yang Mahakuasa.

Ionuț Mihai POPESCU

At the beginning of the twentieth century, nationality was the most important element of collective identity, but it already heralded an era of decline of this collective identity. The assertion of the individual and of their rights as well as the disappearance of the seduction exercised by the great ideals brought two great challenges: What is the principle of solidarity (collective identity) according to which a community is organized? How can societies with a diluted collective identity meet non-conflictingly with those with a strong collective identity? The answers are still to be discovered; we only have reference points. What we can say for sure is that it is very tempting to revert to the former strong collective identity, but it only generates bigger issues than the ones it seems to solve. We consider that the care for the only available world, the reflective assumption of options of collective identity that were previously self-evident, the cultivation of “capillary” ties between individuals with different collective identities and defining a public space meant to develop the specificity of the individual, without breaking the solidarity of the community, are among the landmarks that indicate the direction of the answers to the challenges mentioned above.

Stavros Konstantinidis, Mitja Mastnak, Juraj Sebej

We consider the problem of partitioning effectively a given symmetric (and irreflexive) rational relation R into two asymmetric rational relations. This problem is motivated by a recent method of embedding an R-independent language into one that is maximal R-independent, where the method requires to use an asymmetric partition of R. We solve the problem when R is realized by a zero-avoiding transducer (with some bound k): if the absolute value of the input-output length discrepancy of a computation exceeds k then the length discrepancy of the computation cannot become zero. This class of relations properly contains all recognizable, all left synchronous, and all right synchronous relations. We leave the asymmetric partition problem open when R is not realized by a zero-avoiding transducer. We also show examples of total wordorderings for which there is a relation R that cannot be partitioned into two asymmetric rational relations such that one of them is decreasing with respect to the given word-ordering.

Jeffrey M. Hokanson, Caleb C. Magruder

Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational approximation problem, from fixed point methods like the Sanathanan-Koerner iteration and Vector Fitting, to partial interpolation methods like Adaptive Anderson Antoulas (AAA). While these methods can often find rational approximations with a small residual norm, they are unable to find optimizers with respect to a weighted l2 norm with a square dense weighting matrix. Here we develop a nonlinear least squares approach constructing rational approximations with respect to this norm. We explore this approach using two parameterizations of rational functions: a ratio of two polynomials and a partial fraction expansion. In both cases, we show how we can use Variable Projection (VARPRO) to reduce the dimension of the optimization problem. As many applications seek a real rational approximation that can be described as a ratio of two real polynomials, we show how this constraint can be enforced in both parameterizations. Although this nonlinear least squares approach often converge to suboptimal local minimizers, we find this can be largely mitigated by initializing the algorithm using the poles of the AAA algorithm applied to the same data. This combination of initialization and nonlinear least squares enables us to construct rational approximants using dense and potentially ill-conditioned weight matrices such as those that appear as a step in new H2 model reduction algorithm recently developed by the authors.

Keith Ball

This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that are on the face of it very simple. As a consequence, the Riemann hypothesis can be restated as what looks like a rather conventional spectral problem but which is related to the one found by Connes in his analysis of the zeta function. However the point here is that the rational approximations look to be susceptible of quantitative estimation.

Hildegunn Valen Kleive

This article focuses on understandings of the divine and how everyday life experiences motivate for religious practices among young Tamil Hindus in North Western Norway. Their religiosity is discussed in relation to Hindu traditions as well as to contemporary religion. The findings suggest that coping and balancing strategies generate a young Tamil Hindu religiosity with features resembling several traditions. The analysis is based on field notes from observations, questionnaire responses and interviews. The participants are between 16 and 25 years of age. Keywords: Hinduism, Tamil, youth, rural Norway, concept of God, everyday religion   Denne artikkelen handler om hvordan unge tamilhinduer på Nordvestlandet i Norge oppfatter det guddommelige og hvordan hverdagslige erfaringer motiverer for religiøs praksis. Deres religiøsitet blir drøftet i lys av hindutradisjoner samt vestlig samtidsreligiøsitet. Mestring og balanse synes å være viktige anliggender for ungdommene, og det genererer en religiøsitet som gjenspeiler trekk fra flere tradisjoner. Analysen er basert på feltnotater fra observasjoner, spørreskjemaresponser og intervjuer. Deltakerne i undersøkelsen er mellom 16 og 25 år. Nøkkelord: Hinduisme, tamil, ungdom, distrikts-Norge, gudsoppfatning, hverdagsreligion

Hustwit J. R.

The reaction to multiple religious belonging has been fraught with anxiety in the monotheistic traditions. Nevertheless, increasing numbers of people report belonging to multiple religions. I propose that it is most useful to think of multiple religious belonging not so much as an expression of choice, but just the opposite. Multiple religious belonging is best explained as the ontological condition of two or more religious traditions constituting the self, so that the self’s possibilities are constrained by those religions. Furthermore, I argue that multiple religious belonging per se does not threaten traditional religious communities. Threats are by definition future possibilities, and ontologically speaking, we always already belong to multiple religions. We belong to multiple religions because every religious tradition is an amalgam of earlier distinct traditions. There is nothing new about multiple religious belonging. It is nearly unremarkable. Two philosophers in particular-one a twentieth-century German phenomenologist, the other a second-century Indian Buddhist-have given particularly careful examination of the phenomenon of belonging. Hans-Georg Gadamer’s concept of Wirkungsgeschichte [history of effects] and Nāgārjuna’s teaching of śūnyatā [emptiness] both imply that multiple religious belonging is the ontological condition of all human beings, and that producing any monolithic religious identity requires significant mental gymnastics.

Georgy Belousov

Let $\varphi$ be a rational map $\mathbb{P}^2 \dashrightarrow\mathbb{P}^2$ that preserves the rational volume form $\frac{\mathrm{d}x}{x}\wedge\frac{\mathrm{d}y}{y}$. Sergey Galkin conjectured that in this case $\varphi$ is necessarily birational. We show that such a map preserves the element $\{x,y\}$ of the second K-group $K_2(\mathbf{k}(x,y))$ up to multiplication by a constant, and restate this condition explicitly in terms of mutual intersections of the divisors of coordinates of $\varphi$ in a way suitable for computations.

C. P. Anil Kumar

Many questions about triangles and quadrilaterals with rational sides, diagonals and areas can be reduced to solving certain Diophantine equations. We look at a number of such questions including the question of approximating arbitrary triangles and quadrilaterals by those with rational sides,diagonals and areas. We transform these problems into questions on the existence of infinitely many rational solutions on a two parameter family of quartic curves. This is further transformed to a two parameter family of elliptic curves to deduce our main result concerning density of points on a line which are at a rational distance from three collinear points (Theorem 4). We deduce from this a new proof of density of rational quadrilaterals in the space of all quadrilaterals (Theorem 39). The other main result (Theorem 3) of this article is on the density of rational triangles which is related to analyzing rational points on the unit circle. Interestingly, this enables us to deduce that parallelograms with rational sides and area are dense in the class of all parallelograms. We also give a criterion for density of certain sets in topological spaces using local product structure and prove the density Theorem 6 in the appendix section. An application of this proves the density of rational points as stated in Theorem 31.