Quantum fluctuations of the metric, three-geometries and conformal embeddings in four-manifolds

In this paper, connections between the path integrals for four-dimensional quantum gravity and string theory are emphasized. It is shown that there is a natural relation between these two path integrals based on the theorems on embeddings of two-dimensional surfaces in four dimensions and four-dimensional manifolds in ten dimensions. The isometry groups of the three-geometries that are spatial hypersurfaces confomally embedded in the four-manifolds are required to be subgroups of [Formula: see text], which is the invariance group of the Pfaffian differential system satisfied by one form in the cotangent bundles on the four-manifolds. Based on this and other physical conditions, the three-geometries are restricted to be [Formula: see text], [Formula: see text] and [Formula: see text] with a boundary, which may be included in the quantum gravitational path integral over four-manifolds which are closed at initial times followed by an exponential expansion compatible with supersymmetry.

Re-discovering Evolution: A National Literature between Tautology and Renewal

This article attempts to analyze the evolution of literary thinking as a key concept in the systematic study of a national literature. Methodological requirements to describe literary dynamics as completely as possible prompt a rediscovery of the evolutionary principle, which can be characterized both as an open system of meaning-making and a dialectic of the constant and the changeable contingent on the temporal factor. The focus of this paper is on transitional states, borderline phenomena, semantic recoding, the release of new possibilities of a national literature, and explosive points of literary development when artistic discovery is perceived as a breakthrough challenging inertial normativity. The article reconstructs concepts of A. Bergson, G. Gukovsky, and especially Yu. Tynyanov who developed the notion of “literature as a system” in its natural relation to literary evolution.

The periodic law of the chemical elements: ‘ The new system of atomic weights which renders evident the analogies which exist between bodies ' []

The historical roots, the discovery and the modern relevance of Dmitri Mendeleev's remarkable advance have been the subject of numerous scholarly works. Here, with a brief overview, we hope to provide a link into the contents of this special issue honouring the great scientist. Mendeleev's advance, announced in March 1869, as he put it in 1889, to the ‘… then youthful Russian Chemical Society… ’, first set out the very basis of the periodic law of the chemical elements, the natural relation between the properties of the elements and their atomic weights. This was, and still is, the centrepiece of a historical journey for chemistry to today's position as a pre-eminent science. This article is part of the theme issue ‘Mendeleev and the periodic table'.

Spatial orientations

Whereas the dative and ablative case markers are primarily used in combination with verbs denoting movement to and from some object, the locative signifies that all movement is absent. This natural relation justifies a simultaneous discussion of these case forms in deictic pronouns. These markers play a crucial role in expressions based on the genitive-possessive construction applied to nouns denoting a space. Such constructions fulfil the same job as prepositional phrases in other languages. Interestingly, these space nouns are used as pure adjectives as well, and in the final sections two other peculiarities are illustrated. Besides a fully fledged genitive-possessive construction, for metaphorical usage there is a construct without the genitive, the possessive part of which has much in common with a postposition. Secondly, adverbial phrases based on nouns denoting some location have come into existence in a similar way.

Keutuhan Nada dan Makna dalam Susunan Bahasa Al-quran

This article aimed to describe three focuses: first, how sounds oflanguage signify its meaning; second, how composition of sounds correspondsto the composition of meaning; and third, what are the proofs that the soundsof al-Qur’an verses compose its meanings. Research approach of this articleis qualitative approach using library research. Based on phonological andsemantic studies, this research concludes that the relation between wordsand its meaning in Arabic is natural relation; sounds of al-Qur’an thereforeindicates its meaning; and it can be proofed by analysing al-Qur’an fromphonological and semantic perspective

Dueños y poseedores de la naturaleza: la relación artificial-natural en la Dióptrica de Descartes

RESUMENLa interpretación actual de la ciencia cartesiana ya no concibe ésta como una mera deducción desde los principios metafísicos, sino que reivindica el papel de la experiencia en ella. El presente artículo tratará de dar un paso más, defendiendo que existe una dimensión instrumental en la ciencia cartesiana. Para ello, se analizará la modificación que Descartes realiza en la Dióptrica de la relación artificial-natural y que posibilita una lectura instrumentalista.PALABRAS CLAVEDESCARTES, ARTIFICIAL, NATURAL, INSTRUMENTALISMO, CIENCIAABSTRACTThe current interpretation of the Cartesian science no longer sees it as a mere deduction from the metaphysical principles, but claims the role of experience in it. This paper will try to go one step further, arguing that there is an instrumental dimension in the Cartesian science. With this purpose in mind, we will analyze the modification performed by Descartes in the Dioptrics regarding the artifitial-natural relation, which enables this instrumentalist reading.KEYWORDS DESCARTES, ARTIFICIAL, NATURAL, INSTRUMENTALISM, SCIENCE

Toeplitz operators with distributional symbols on Bergman spaces

We study the boundedness and compactness of Toeplitz operators Ta on Bergman spaces $A^p(\mathbb{D})$, 1 < p < ∞. The novelty is that we allow distributional symbols. It turns out that the belonging of the symbol to a weighted Sobolev space $\smash{W_\nu^{-m,\infty}(\mathbb{D})}$ of negative order is sufficient for the boundedness of Ta. We show the natural relation of the hyperbolic geometry of the disc and the order of the distribution. A corresponding sufficient condition for the compactness is also derived.

SUPERCONFORMAL QUANTUM MECHANICS VIA WIGNER–HEISENBERG ALGEBRA

We show the natural relation between the Wigner Hamiltonian and the conformal Hamiltonian. A model in (super)conformal quantum mechanics with (super)conformal symmetry in the Wigner–Heisenberg algebra picture [x, px] = i(1+cP) (P being the parity operator) is presented. In this context, the energy spectrum, the Casimir operator, raising and lowering operators are defined.