Hasil untuk "Religions. Mythology. Rationalism"

Avisek Bist, Namita Behera

Numerical computations involving rational matrices often benefit from preserving underlying matrix structures such as symmetry, Hermitian properties, or sparsity that reflect physical, geometric, or algebraic characteristics of the system. Maintaining such structures enhances stability, accuracy, and efficiency. Linearization, a technique that reformulates rational matrix problems as generalized eigenvalue problems (GEPs) of larger matrices, is widely used but does not automatically retain structure. In this chapter, we focus on structured linearizations, which preserve both the spectral information of the original rational matrix and its intrinsic structural properties. To achieve this, we present the construction of a family of linearizations called generalized Fiedler pencils with repetition (GFPR), which we prove to be valid linearizations for rational matrices. Moreover, we demonstrate that the GFPR family serves as a versatile framework for generating structured linearizations, specifically symmetric, skew-symmetric, T-even, and T-odd linearizations, provided the original rational matrix exhibits the corresponding structure. These structured linearizations facilitate the use of specialized, structure-preserving algorithms, reduce numerical errors, and yield physically meaningful solutions in application

Osamu Fujino

We extend Hacon--M\textsuperscript{c}Kernan's rational chain connectedness theorem to the complex analytic setting. As a consequence, we prove that the fibers of any resolution of singularities of complex analytic kawamata log terminal singularities are rationally chain connected. In contrast to the original approach, we avoid the use of extension theorems and instead rely on the minimal model program.

Francesco Veneziano, Solomon Vishkautsan

We study how the field of definition of a rational function changes under iteration. We provide a complete classification of polynomials with the property that the field of definition of one of their iterates drops in degree (over a given base field). We show with families of examples that this characterization does not hold for rational functions. Finally, we also classify fractional linear transformations with this property.

Andrey Sudakov

Kant’s doctrine of religion has been repeatedly accused from different perspectives of having committed a rationalistic reduction of religious faith to a «faith of reason», or of claims to reinterpret by means of reason the body of beliefs of a revealed religion. The article investigates the Königsberg philosopher’s ideas concerning the boundary strip between philosophical and biblical theology as well as the criterion of an illegal trespass of this borderline. Only the philosopher’s claim to complement, modify or reinterpret of the dogmatic tenets of a historical religion, by means of reason alone, or to review the practical targeting of the dogmatic doctrines of a church, i.e. an «engagement in theology», proves to be, according to Kant, such a criterion; by contrast, an interpretation of church dogmatics which is devoid of any creedal claims does not imply an illegitimate reinterpretation of dogmatics. Contrarily, a criticism of Kant for such a reinterpretation, or even a mere presumption of its possibility in principle, does itself imply, as a matter of fact, a trespass of borderlines as determinated by Kant, a kind of hermeneutical dumbness of such criticism, its incapacity to accept its opponent in its specific intellectual quality. Such a dumbness may be caused by the difference in conceptions about the possibility and the essence of rational philosophical theology in doctrines of religion developed from an irrationalist, a speculative metaphysical and a moral-practical perspective, the first of which was intrinsically foreign to Kant’s mind, the second had been overcome by him in the result of the Copernican turn, and only the third made up the core of his own critical philosophy of religion. On this third position of philosophical theology comprehensive cognition of «God’s own properties» is held to be unattainable for human beings, and yet is everything knowable in the field of faith and theology acknowledged to be a product of practical reason. The limitation upon the claims of «theory» provides such a philosophical theology with genuine philosophical modesty, while its affirmation of ethico-theology as the only possible basis of rational doctrine of religion allows it to display a genuine awareness of the philosophy’s dignity as a science of reason. F.K.Forberg’s and Leo Tolstoy’s philosophies of religion, in spite of their superficial resemblance with the ethico-theological project, do not distinguish themselves at the least with that kind of philosophical modesty, digressing in two different ways from the science of reason towards a tcommon sense theory and providing an opportunity for critique of established religion from the perspective of the latter.

Hong Zhang, Cheryl Zhenyu Qian

Since the emergence of digital media in the 1990s, a new realm of interaction between the visual arts and religion has been forged and evolved. The spread of visual media technologies has significantly influenced the study of religious visual art worldwide after the 1990s. Despite this, the field of religious visual art during the digital era is still relatively uncharted, with a notable absence of comprehensive theoretical frameworks. To address this gap, the present paper employs bibliometric methods, conducting a thorough review and analysis of 2544 pieces of international academic literature in the domain of religion and visual arts post-1990s. The analytical framework is structured into three primary sections, each dedicated to answering key questions: (1) what constitutes the inherent relationship in the study of religion and visual art?, (2) what disciplinary context do these interplays occur within?, and (3) in which domains and regions does this interplay predominantly unfold? The outcomes of this rigorous analysis offer valuable insights into interdisciplinary influences and evolving research trends within the realm of religious visual art. These findings stand to benefit art researchers and practitioners, providing a comprehensive overview of potential avenues for the exploration of visual arts with religious themes. Through a systematic investigation, this research endeavors to heighten scholars’ awareness of the significance of visual arts in the field of religion and illuminate the interdisciplinary trends at the intersection of religion and visual arts.

Hendri Mulyana Sendjaja

Artem Malyshev

The article is devoted to the discussion of the late 19th century between the priest Ioann Petropavlovsky and the famous archbishop Savva (Tikhomirov) on the problem of the moral perfections of Christ according to His human nature. The published academic lecture by Petropavlovsky "Jesus Christ is the God-Man", its criticism in the "Diary" of Savva (Tikhomirov), Petropavlovsky's response to criticism and response to the discussion by protopresbyter Ioann Yanyshev are analyzed. According to Petropavlovsky, who acted for reasons of proving the divinity of Christ, the Savior, during His earthly life, struggled with the instincts of His humanity, what was an important moment on the path of His free acquisition of His moral perfections. Thus, Christ can be an effective example for us to follow. Savva (Tikhomirov) considered this position to be contrary to the teaching of the Church, while Yanyshev supported ideas of Petropavlovsky. I examine the genesis of this problem about the nature of the moral perfections of Christ in Russian theology, which is rooted in the theology of st. Innokenty of Kherson. The latter, accepting the Kantian setting of practical philosophy – freedom of choice between good and evil is the possibility of moral development – was the first in the history of Russian theological thought to put forward the hypothesis that Christ could have sinned during His earthly life, but did not sin. The hypothesis made sense as a response to Kant's subtle criticism of traditional Christology, put forward by him in his work "Religion within the Limits of Reason Alone". Along with the consideration of these problems, the article attempts to clarify the genesis of the moral-apologetic logic used by Petropavlovsky to prove the divinity of Christ. At the end of the article, Petropavlovsky's theses are considered on the subject of their self-contradictions and examined in the context of patristic theology.

Yuhao Yang, Chao Huang, Lianghao Xia et al.

In this paper, we introduce a new self-supervised rationalization method, called KGRec, for knowledge-aware recommender systems. To effectively identify informative knowledge connections, we propose an attentive knowledge rationalization mechanism that generates rational scores for knowledge triplets. With these scores, KGRec integrates generative and contrastive self-supervised tasks for recommendation through rational masking. To highlight rationales in the knowledge graph, we design a novel generative task in the form of masking-reconstructing. By masking important knowledge with high rational scores, KGRec is trained to rebuild and highlight useful knowledge connections that serve as rationales. To further rationalize the effect of collaborative interactions on knowledge graph learning, we introduce a contrastive learning task that aligns signals from knowledge and user-item interaction views. To ensure noise-resistant contrasting, potential noisy edges in both graphs judged by the rational scores are masked. Extensive experiments on three real-world datasets demonstrate that KGRec outperforms state-of-the-art methods. We also provide the implementation codes for our approach at https://github.com/HKUDS/KGRec.

Haoqian Zhang, Mahsa Bastankhah, Louis-Henri Merino et al.

Blockchain systems often rely on rationality assumptions for their security, expecting that nodes are motivated to maximize their profits. These systems thus design their protocols to incentivize nodes to execute the honest protocol but fail to consider out-of-band collusion. Existing works analyzing rationality assumptions are limited in their scope, either by focusing on a specific protocol or relying on non-existing financial instruments. We propose a general rational attack on rationality by leveraging an external channel that incentivizes nodes to collude against the honest protocol. Our approach involves an attacker creating an out-of-band bribery smart contract to motivate nodes to double-spend their transactions in exchange for shares in the attacker's profits. We provide a game theory model to prove that any rational node is incentivized to follow the malicious protocol. We discuss our approach to attacking the Bitcoin and Ethereum blockchains, demonstrating that irrational behavior can be rational in real-world blockchain systems when analyzing rationality in a larger ecosystem. We conclude that rational assumptions only appear to make the system more secure and offer a false sense of security under the flawed analysis.

Katsuhiko Kuribayashi

The Félix-Tanré rational model for the polyhedral product of a fibre inclusion is considered. In particular, we investigate the rational model for the polyhedral product of a pair of Lie groups corresponding to arbitrary simplicial complex and the rational homotopy group of the polyhedral product. Furthermore, it is proved that for a partial quotient $N$ associated with a toric manifold $M$, the following conditions are equivalent: (i) $N=M$. (ii) The odd-degree rational cohomology of $N$ is trivial. (iii) The torus bundle map from $N$ to the Davis-Januszkiewicz space is formalizable.

Taylor Brysiewicz, Fulvio Gesmundo, Avi Steiner

It is a classical result that there are $12$ (irreducible) rational cubic curves through $8$ generic points in $\mathbb{P}_{\mathbb{C}}^2$, but little is known about the non-generic cases. The space of $8$-point configurations is partitioned into strata depending on combinatorial objects we call quatroids, a higher-order version of representable matroids. We compute all $779777$ quatroids on eight distinct points in the plane, which produces a full description of the stratification. For each stratum, we generate several invariants, including the number of rational cubics through a generic configuration. As a byproduct of our investigation, we obtain a collection of results regarding the base loci of pencils of cubics and positive certificates for non-rationality.

Alex Cowan, Kimball Martin

We investigate the distribution of degrees and rationality fields of weight 2 newforms. In particular, we give heuristic upper bounds on how often degree $d$ rationality fields occur for squarefree levels, and predict finiteness if $d \ge 7$. When $d=2$, we make predictions about how frequently specific quadratic fields occur, prove lower bounds, and conjecture that $\mathbb{Q}(\sqrt 5)$ is the most common quadratic rationality field.

Nesya Rubinstein-Shemer

This article deals with the rulings of Sheikh Rāʾid Badīr, who served as a mediator between the Israeli government and the Muslim community over the course of the pandemic. As a senior leader and scholar of the southern branch of the Islamic Movement in Israel, Sheikh Rāʾid Badīr’s <i>fatwās</i> have historically addressed the unique circumstances and situational difficulties faced by Muslims living in Israel.

Marjan Turnšek

This paper presents Blessed Anthony Martin Slomšek as a man who led an above-average virtuous life. The author presents Slomšek concretely in the exercise of the main or cardinal virtues of prudence (wisdom), justice, cordiality and temperance throughout his life. He also shows their gradual growth. In the process of Slomšek's beatification, the extraordinary influence of Slomšek's personality became clear, as other people were drawn to him as a kind of ≫incandescence≪ for these virtues. Slomšek's extraordinary pastoral zeal was not only based on theoretical teaching but also rooted in a personally lived life of the cardinal virtues, which shaped him into an extremely harmonious and positive personality. Given the gradual resurgence of interest in the virtues in both ethics and morality, it is very appropriate to present and examine Slomšek's virtuous life.

Salahuddin Akbar Agus Panuntun Hsm, Mohammad Asikin, Budi Waluya et al.

The ability to think creatively is very important to be developed in students, especially when learning is starting to shift to blended learning where students are required to be able to organize portions and also how to learn independently, for this reason, students in this era need to grow their creative abilities to be able to keep up with educational developments. This study aims to conduct studies related to factors that can foster creative thinking skills. The research method used in this study is the SLR (Systematic Literture Review) method. Data collection is done by collecting similar research articles and limiting it to the topic of mathematical creative thinking skills. The articles used in this study were 20 articles with the topic of creative thinking skills. Based on the literature review, the most influencing factors in creative thinking skills are problem-based models and open-ended approaches. For this reason, using the CPS model with an open-ended approach will provide a model with a new alternative approach that can be tried to improve creative thinking skills.

Dr. J.T. Igba

This paper interrogates the portrait of YHWH that emerges in the face of the pain and suffering of Jeremiah and the covenant people of YHWH. The paper attends to the question through a combination of synchronic and canonical methods in reading the book of Jeremiah. Through a theological analysis and exposition of some key texts, which includes Jeremiah 8:18-9:3 11:18- 12:13; and 32:1-15, this paper demonstrates that the portrait of YHWH that emerges is not a God who watches the suffering of his covenant people helplessly, hardheartedly or dispassionately from without, but is himself grief-stricken in the suffering of his people, so that he might eventually bring suffering to an end and hold all that are complicit accountable. The paper discusses the call of Jeremiah in the light of its connotation of forthcoming suffering and pain and the non-insulation of the prophet and YHWH’s covenant people from the coming suffering. This is followed by an expose on the nature of the suffering of YHWH as portrayed by Jeremiah in his poetry of lament in 8:18-9:3 as well as the vital function of Jeremiah 32 in the suffering of YHWH’s people.

Tom-Eric Krijger

Em 1933, um ano após a sua tomada de posse como Presidente do Conselho de Portugal, António de Oliveira Salazar conseguiu ver aprovada uma nova Constituição, reorganizando a política, a sociedade civil e a economia portuguesas numa base corporativista. Este artigo aborda o interesse notável que o Estado Novo salazarista despertou nos círculos dos partidos políticos cristãos nos Países Baixos (Holanda) por volta de 1940. Procura-se argumentar que tal interesse teve a ver com a então segmentação institucional da sociedade holandesa, na base de diferenças políticas e religiosas, conhecida na historiografia como ‘verzuiling’ ou ‘pilarização’. Alguns intelectuais católicos defendiam que a comunidade católica holandesa não devia contentar-se com o seu próprio ‘zuil’ ou ‘pilar’, mas, pelo contrário, devia aspirar a uma reconfiguração da sociedade em conformidade com a Doutrina Social da Igreja Católica, a exemplo do Estado Novo português. Por outro lado, alguns ‘fazedores de opinião’ protestantes holandeses consideravam o Estado Novo como paradigma de um estado estruturado ‘organicamente’, exibindo uma alternativa para a segregação ‘pilarizada’ na nação holandesa, algo que eles contestavam profundamente. Além disso, os admiradores holandeses de Salazar, tanto católicos como protestantes, acreditavam que o Estado Novo se baseava em princípios que ofereciam tanto uma solução para a crise política e económica que afetava a Holanda na década de 1930, como um fundamento para a reconstrução do seu país depois da invasão alemã-nazi em 1940.

António Montes Moreira

Froilán M. Dopico, Silvia Marcaida, María C. Quintana et al.

Block full rank pencils introduced in [Dopico et al., Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems, Linear Algebra Appl., 2020] allow us to obtain local information about zeros that are not poles of rational matrices. In this paper we extend the structure of those block full rank pencils to construct linearizations of rational matrices that allow us to recover locally not only information about zeros but also about poles, whenever certain minimality conditions are satisfied. In addition, the notion of degree of a rational matrix will be used to determine the grade of the new block full rank linearizations as linearizations at infinity. This new family of linearizations is important as it generalizes and includes the structures appearing in most of the linearizations for rational matrices constructed in the literature. In particular, this theory will be applied to study the structure and the properties of the linearizations in [P. Lietaert et al., Automatic rational approximation and linearization of nonlinear eigenvalue problems, submitted].

Ranjan Kumar Das, Rafikul Alam

Structured rational matrices such as symmetric, skew-symmetric, Hamiltonian, skew-Hamiltonian, Hermitian, and para-Hermitian rational matrices arise in many applications. Linearizations of rational matrices have been introduced recently for computing poles, eigenvalues, eigenvectors, minimal bases and minimal indices of rational matrices. For structured rational matrices, it is desirable to construct structure-preserving linearizations so as to preserve the symmetry in the eigenvalues and poles of the rational matrices. With a view to constructing structure-preserving linearizations of structured rational matrices, we propose a family of Fiedler-like pencils and show that the family of Fiedler-like pencils is a rich source of structure-preserving strong linearizations of structured rational matrices. We construct symmetric, skew-symmetric, Hamiltonian, skew-Hamiltonian, Hermitian, skew-Hermitian, para-Hermitian and para-skew-Hermitian strong linearizations of a rational matrix $G(λ)$ when $G(λ)$ has the same structure. Further, when $G(λ)$ is real and symmetric, we show that the transfer functions of real symmetric linearizations of $G(λ)$ preserve the Cauchy-Maslov index of $G(λ).$ We describe the recovery of eigenvectors, minimal bases and minimal indices of $G(λ)$ from those of the linearizations of $G(λ)$ and show that the recovery is operation-free.