Transcendence and interiority in architecture : a study of Hagia Sofia, 532-537

The late historian Robin Evans, takes up the debate symbolised between Wblfflin, proposing that meaning is directly accessible through the form of a building, and Wittkower, arguing that meaning lies behind the form of architecture, in other texts and ideas. The focus of their argument is the centralised church of the Renaissance, which holds a special place in the history of architecture for all three historians. Evans\u27 argument makes detours into the histories of theology, geometry and mathematics attempting to find how architecture participates with these fields. He concludes that architecture, in its singular artistic physicality &quot;suspends our disbelief in the ideal&quot;, offering a world that does not reflect culture, in all its fullness, but rather supplements culture\u27s incompleteness. Architecture, like art is able to resolve that which in society and in other fields remains a contradiction, giving a picture (albeit fictional) of a harmonious and unified order. Does architecture aspire towards transcendence, if so, what is transcendental value in architecture? In this essay I want to turn to Hagia Sofia (Istanbul, 532-537), a church that marks the beginning of a Christian empire relocated to the East of Rome, in Constantinople, built one thousand years before the Renaissance churches; and a building that symbolises the shift towards a domed centralised form, away from a basilica form. Hagia Sofia is an architecture, observed and described in an almost devotional manner, as though addressing the architecture of the church is equivalent to a pious person addressing the church itself, and more significantly, addressing the Divine figure of God, through the architecture of the church. What role does Hagia Sofia play in the kind of artistic mastery that Evans is proposing?<br /

An Alternative Natural Deduction for the Intuitionistic Propositional Logic

A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via translations from sequent calculus derivations to natural deduction derivations and back.This work is supported by the Ministary of Science and Technology of Serbia, grant number ON174026

A generalization of MacMahon's formula

We generalize the generating formula for plane partitions known as MacMahon's formula as well as its analog for strict plane partitions. We give a 2-parameter generalization of these formulas related to Macdonald's symmetric functions. The formula is especially simple in the Hall-Littlewood case. We also give a bijective proof of the analog of MacMahon's formula for strict plane partitions.Comment: 19 pages, 5 figure

Fast strategies in biased Maker--Breaker games

We study the biased $(1:b)$ Maker--Breaker positional games, played on the edge set of the complete graph on $n$ vertices, $K_n$. Given Breaker's bias $b$, possibly depending on $n$, we determine the bounds for the minimal number of moves, depending on $b$, in which Maker can win in each of the two standard graph games, the Perfect Matching game and the Hamilton Cycle game

What determines the distribution of shallow convective mass flux through cloud base?

The distribution of cloud-base mass flux is studied using large-eddy simulations (LES) of two reference cases, one representing conditions over the tropical ocean, and another one representing mid-latitude conditions over land. To examine what sets the difference between the two distributions, nine additional LES cases are set up as variations of the two reference cases. We find that the total surface heat flux and its changes over the diurnal cycle do not influence the distribution shape. The latter is also not determined by the level of organization in the cloud field. It is instead determined by the ratio of the surface sensible heat flux to the latent heat flux, the Bowen ratio $B$. $B$ sets the thermodynamic efficiency of the moist convective heat cycle, which determines the portion of the total surface heat flux that can be transformed into mechanical work of convection against mechanical dissipation. The thermodynamic moist heat cycle sets the average mass flux per cloud $\langle m \rangle$, and through $\langle m \rangle$ it also controls the shape of the distribution. An expression for $\langle m \rangle$ is derived based on the moist convective heat cycle and is evaluated against LES. This expression can be used in shallow cumulus parameterizations as a physical constraint on the mass flux distribution. The similarity between the mass flux and the cloud area distributions indicate that $B$ also has a role in shaping the cloud area distribution, which could explain its different shapes and slopes observed in previous studies.Comment: submitted to J. Atmos. Sci., revise

Non-classical behavior of atoms in an interferometer

We have studied the properties of the non-classical behavior of atoms in a double-slit interferometer. An indication of this behavior for metastable helium was reported by Kurtsiefer, Pfau and Mlynek [Nature 386, 150 (1997)] showing distinctive negative values of the Wigner function, which was reconstructed from the measured diffraction data. Our approach to explain this non-classical behavior is based on the de Broglie-Bohm-Vigier-Selleri understanding of the wave-particle duality and compatible statistical interpretation of the atomic wave function. It follows from the results that the atomic motion is non-classical because it does not obey the laws of classical mechanics. However, there is no evidence that this atomic behavior violates the classical probability law of the addition of probabilities.Comment: 10 pages, 9 figure