In light of Kim's conjecture on regular polytopes of dimension four, which is a generalization of Waring's problem, we establish asymptotic formulas for representing any sufficiently large integer as a sum of numbers in the form of those regular 4-polytopes. Moreover, we are able to obtain a more general result of the asymptotics for any degree-four polynomial $f$ satisfying $f(0)=0$ and $f(1)=1$.
The Bible translated into South Africa’s indigenous languages has a colonial history. For the Vhavenḓa people, the 1936 and 1998 Bible translations are revered as icons that hold a privileged position. However, this paper argues that these two translations should be seen as colonial language tools that do not serve the culture of the Vhavenḓa people. Instead, they can be viewed as weapons against them. These translations distorted the Tshivenḓa language by imposing distorted and foreign concepts of God, thereby rendering the Vhavenḓa people to have been without knowledge of God.
This article is a research report on the international colloquium entitled ‘Re-Imagining Curricula for a Just University in a Vibrant Democracy’, hosted by the University of Pretoria in 2017 to address a series of prospective changes in religious studies curricula in African and non-African universities. Anchored in the principles of the Draft Framework Document, a South African manifesto authored by a team of specialists from the University of Pretoria advocating educational reform in the field of religion, the colloquium debated the necessity of curricular change from the perspective of ecodomy, seen as a constructive attempt to modify university curricula to include relevant approaches to religion. Consequently, the discussions revolved around the idea of ‘ecodomical change’ as a socially transformative step towards achieving community development in tertiary education religious institutions.
Contribution: This article, however, focused on the Draft Framework Document and its distinctive contribution to the pedagogy of theology and religious studies within the University of Pretoria.
Nigeria is a multi-ethnic and multicultural society, and therefore, Nigeria’s religious inclinations differ broadly. There are currently three religions dominant in Nigeria, namely Christianity, Islam and African Traditional Religion (ATR). These three religions, especially the first two, have demonstrated varying levels of fanaticism in the past leading to many recounted crises and jungle justice incidents in Nigeria. Because of Nigerian politics, we have witnessed the use of armed thugs by politicians to harass and even kill party opponents and displace their families. These two factors have caused many young, highly skilled persons to flee Nigeria for a safer haven. This study therefore tries to review current religious fanaticism and electioneering thuggery leading to loss of lives and property, which consequently sees to the fall of the Nigerian economy and the subsequent enthronement of insecurity in the country. It suggests that these factors are foundational problems consequent to the amalgamation of 1914 and are leading causes for the rapid rate of migration of Nigerian experts out of the country.
Contribution: At a time when Nigeria is in dire need of great brains to help in its developmental struggle, politicians and religious bigots have constituted a serious blockade to this ambition. This article is a review of recent political and religious turmoil in Nigeria with a view to call the attention of all warring religious and political stakeholders to the damage their extremism has already caused and to also bring the attention of Nigerians to the foundation of these problems, namely the amalgamation and the need to address it.
In this article, we construct a class of explicit, smooth and spherically symmetric solutions to the asymptotically flat vacuum constraint equations which have ADM mass of arbitrary sign ($- \infty$, negative, zero, positive). As a direct consequence, there exist asymptotically flat vacuum initial data sets whose metrics are exactly negative mass Schwarzschild outside a given ball. We emphasize that our result does not contradict the spacetime positive energy theorem proven by Eichmair, instead it shows that the decay rate at infinity of the symmetric $(0,2)$-tensor $k$ stated in the theorem is sharp. The key argument we use in the article is classical, based on the conformal method, in which the conformal equations are equivalently transformed into a single nonlinear equation of functions of one variable.
Pensar sobre a relação entre religião, sociedade e democracia
geralmente significa pensar sobre religião em termos de comunidades
religiosas constituídas e analisar e criticar sua ideologia e prática
simbólica e social. Entretanto, isto sempre pressupõe uma certa
interpretação do que é religião e de quem é o portador de crenças
religiosas. Foi o filósofo judeu Walter Benjamin que, há 100 anos,
chamou a atenção para o fato de que, na sociedade moderna, não só as
igrejas e comunidades religiosas são portadoras de convicções
religiosas, mas também o moderno Estado-nação, que se autodenomina
secular. Sua tese é que o capitalismo assume as funções e tarefas das
comunidades religiosas tradicionais, especialmente as das igrejas
católica e protestante. Contudo, isto acontece não para trazer liberdade, mas para subjugar e reprimir as pessoas.
Scholars have divided opinions concerning the role of women in the covenant community of Israel. While some argue that women are placed in a secondary position, others looked at the covenant directives as ambiguous with regard to women. However, covenant renewal creates the opportunity to modify and innovate existing covenants to respond to the new needs of covenant receivers. Using the discourse theory of Paul Ricoeur, the author argues that Luke 10:38-42 is a covenant renewal discourse. The discourse aims at redefining women’s roles in the covenant community. The study concludes that women have new roles that empower them to make meaningful contributions to society.
Developing Bogoliubov theory of weakly interacting Bose gas in uncompacted three-dimension space, quantum fluctuation energy of one component dilute gas of Bose-Einstein condensate (BEC) confined to two parallel plates investigated at zero-temperature in grand canonical ensemble (GCE) with Neumann boundary condition (BC). The Casimir force considered in comparison to the one with Robin BC, Dirichlet BC and periodic BC.
In this paper, we prove convergence of the high codimension mean curvature flow in the sphere to either a round point or a totally geodesic sphere assuming a pinching condition between the norm squared of the second fundamental form and the norm squared of the mean curvature and the background curvature of the sphere. We show that this pinching is sharp for dimension $n\geq 4$ but is not sharp for dimension $n=2,3$. For dimension $n=2$ and codimension $2$, we consider an alternative pinching condition which includes the normal curvature of the normal bundle. Finally, we sharpen the Chern-do Carmo-Kobayashi curvature condition for surfaces in the four sphere - this curvature condition is sharp for minimal surfaces and we conjecture it to be sharp for curvature flows in the sphere.
The debatable church orderly relevance between 1618, 1816 and 1951 in relation to the church order of the Netherdutch Reformed Church of Africa: The above-mentioned dates from the past, although distant from each other, are linked to each other and influential in the church law debate, even in recent times. The intention of this paper is to link the dates as well as the events associated with the mentioned dates from the past with the church order of the Netherdutch Reformed Church of Africa which was determined during the church’s 71st synod meeting during 2016. Churches in South Africa originated from the 16th century Reformation should accommodate each other even with some different viewpoints especially in connection with church law as formulated and practised in different churches.
Contribution: The contribution of this paper is to point out that the relation between the mentioned dates indicate important milestones in the church orderly past, in the Netherlands and in South Africa and should be treated with caution, especially in reference to the church order of the Netherdutch Reformed Church of Africa.
We do not need ‘the earth’ as the space for encounter and cooperation between world religions in the way Moltmann suggests. Firstly, this fails to do justice to the contemporary situation concerning religious diversity: people from different religions have no problem in working together either for promoting ecological goals or for fighting them together. Within religions, there are often greater divergences between eco-friendly and anti-ecological adherents of that same religion. Secondly, Moltmann’s proposal misguidedly confuses boundaries of beliefs and boundaries of grammar concerning religious diversity. Paying attention to religions as grammar provides a more accurate picture of the reality concerning world religions from an ecological perspective. In the final section of this article, I present some suggestions on moving forward in the debate about ecology from within this new perspective. We need to keep in mind that it is not religions but people who have opinions about ecology. The dialogue that needs to take place is not a high-level bureaucratic one between officials of different religions but one between people. In this grassroots-level discussion, it is important to listen to the other person rather than to consider him or her as a representative of his or her religion. We should not allow people to claim an entire religion for their position, dismissing others as revisionists. Religions are grammars that can express both eco-friendly and anti-ecological messages.
Contribution: This article contributes to an in-depth understanding of religious diversity; it proves the usefulness of the distinction between grammar and beliefs in the study of religion and demonstrates this using the case of ecotheology as an example.
El hombre moderno y contemporáneo anhela la verdad, es decir, la búsqueda de servicio de sentido a su existencia, pero en su interior experimenta una distancia, una incoherencia, una inadecuación entre lo que es y lo que quiere ser, entre lo que piensa y lo que vive. A partir del planteamiento tanto de una nueva concepción de verdad, esta vez ya no según la definición clásica, que se da solo desde el pensamiento sino, de un modo más totalizante desde la voluntad, que implica las decisiones y las acciones, como de la asunción del método ascético que, según Blondel, consiste en la negación voluntaria, en una privación positiva, en despojarse de sí mismo, la tesis central de este artículo es que el hombre pueda ponerse en camino para responder a esa anhelada adecuación interior, a esa pregunta por la búsqueda y sentido de plenitud en su existencia, del mismo modo como lo hizo Jesucristo, al decidir y actuar despojándose de sí mismo.
We realize the simple Lie superalgebra G(3) as supersymmetry of various geometric structures, most importantly super-versions of the Hilbert-Cartan equation (SHC) and Cartan's involutive PDE system that exhibit G(2) symmetry. We provide the symmetries explicitly and compute, via the first Spencer cohomology groups, the Tanaka-Weisfeiler prolongation of the negatively graded Lie superalgebras associated with two particular choices of parabolics. We discuss non-holonomic superdistributions with growth vector (2|4,1|2,2|0) deforming the flat model SHC, and prove that the second Spencer cohomology group gives a binary quadratic form, thereby providing a "square-root" of Cartan's classical binary quartic invariant for generic rank 2 distributions in a 5-dimensional space. Finally, we obtain super-extensions of Cartan's classical submaximally symmetric models, compute their symmetries and observe a supersymmetry dimension gap phenomenon.
Resumen
En este trabajo se sintetiza y comenta la sexta edición del libro de título como indica el encabezamiento del presente artículo. El libro es de indudable calidad sobre el tema antropológico para un público creyente e iniciado en teología porque da un enfoque cristiano y católico en contraste con otras percepciones de la cuestión a lo largo de la historia hasta la fecha de publicación. En concreto, presentamos un resumen de la revelación bíblica sobre la antropología tanto del Antiguo (teocéntrica) como del Nuevo Testamento (cristocéntrica) siguiendo al autor del libro. El resto de su contenido es comentado de acuerdo al estudio sistemático que realiza el autor sobre el hombre como ser unitario (alma-cuerpo), como ser personal (y su dignidad), como ser creativo (y su actividad en el mundo), y como ser creado (y su origen). Tras una revisión de su contenido, hemos comentado algunos aspectos de interés personal como son el objetivo del autor del libro, lo que aporta sobre la fe, su originalidad en el contexto bíblico y eclesial además de otras perspectivas relacionadas, posiciones difíciles de entender, su interés pastoral y pedagógico, y finalmente planteamos alguna cuestión que surge leyendo el texto.
Palabras clave: antropología; Biblia; hombre; teología.
Abstract
In this work we sinthetize and comment the sixth edition of the book of title as it is indicated in heading of this article. The book has an undoubtable quality about the anthropologic theme for a believer public and initiated in theology because it gives a Christian and Catholic focus in contrasting with other perceptions of the question along the history until the date of publication. Concretely, we present a summary of biblical revelation on anthropology from both Ancient (theocentric) and New Testament (Christcentric) following the author of the book. Rest of its content is commented according to systematic study realized by author about the man as unitary being (soul-body), as personal being (and his dignity), as creative being (and his activity in the world), and as created being (and his origin). After a revision of its content, we have commented some aspects of personal interest as they are the objective of author of book, what it apports over the faith, its originality in the biblical and ecclesial context moreover of other related perspectives, difficult positions of understanding, its pastoral and pedagogic interest, and finally we raise some question which arises reading the text..
Keywords: anthropology; Bible; man; theology.
Orcid: https://orcid.org/0000-0001-6648-4472
In this article, we make a generalization of classical fixed point theorems by using the concept of half-continuity and then apply it to improve the nonuniqueness result for solutions to the vacuum Einstein conformal equations shown by the author in arxiv.org/abs/1507.01081
We study high codimension mean curvature flow of a submanifold $\mathcal{M}^n$ of dimension $n$ in Euclidean space $\mathbb{R}^{n+k}$ subject to the quadratic curvature condition $ |A|^{2}\leq c_n |H|^{2}, c _n = \min\{ \frac{4}{3n} , \frac{1}{n-2}\}$. This condition extends the notion of two-convexity for hypersurfaces to high codimension submanifolds. We analyse singularity formation in the mean curvature flow of high codimension by directly proving a pointwise gradient estimate. We then show that near a singularity the surface is quantitatively cylindrical.
We prove that codimension two surfaces satisfying a nonlinear curvature condition depending on normal curvature are smoothly deformed by mean curvature flow to round points.
This article investigates attitudes to Bible translation as mirrored in the Letter of Aristeas, Philo’s treatise On the Life of Moses, and the prologue to the book of Ben Sira. In each of these documents, its respective author reflects on the translation of the Hebrew Scriptures into Greek. The author of the Letter of Aristeas was concerned about a possible revision of a translation that was highly esteemed and tried to preserve it by alluding to the “canon formula” (Deut 4.2). Philo considered the Greek Torah as divinely inspired, presuming a strictly literal translation which was the perfect image of its source text. The article mentions today’s followers of these two writers whose views can be criticized from the point of view of modern translation theory. The translator of the book of Ben Sira, on the other hand, showed a balanced opinion which can serve as a model for today’s Bible translators.
C-projective structures are analogues of projective structures in the complex setting. The maximal dimension of the Lie algebra of c-projective symmetries of a complex connection on an almost complex manifold of C-dimension $n>1$ is classically known to be $2n^2+4n$. We prove that the submaximal dimension is equal to $2n^2-2n+4+2δ_{3,n}$. If the complex connection is minimal (encoded as a normal parabolic geometry), the harmonic curvature of the c-projective structure has three components and we specify the submaximal symmetry dimensions and the corresponding geometric models for each of these three pure curvature types. If the connection is non-minimal, we introduce a modified normalization condition on the parabolic geometry and use this to resolve the symmetry gap problem. We prove that the submaximal symmetry dimension in the class of Levi-Civita connections for pseudo-Kähler metrics is $2n^2-2n+4$, and specializing to the Kähler case, we obtain $2n^2-2n+3$. This resolves the symmetry gap problem for metrizable c-projective structures.
We report the detection of a Cold Neptune m_planet=21+/-2MEarth orbiting a 0.38MSol M dwarf lying 2.5-3.3 kpc toward the Galactic center as part of a campaign combining ground-based and Spitzer observations to measure the Galactic distribution of planets. This is the first time that the complex real-time protocols described by Yee et al. (2015), which aim to maximize planet sensitivity while maintaining sample integrity, have been carried out in practice. Multiple survey and follow-up teams successfully combined their efforts within the framework of these protocols to detect this planet. This is the second planet in the Spitzer Galactic distribution sample. Both are in the near-to-mid disk and clearly not in the Galactic bulge.