Research on Geometrical Errors of Geokhod Prototype Shell Based on Coordinate Control Data

The article contains results of a research on geometric accuracy of a geokhod prototype shell. The article outlines the general structural features of geokhod bodies, and the main principles of manufacturing in test production. An overview of approaches to modeling of shell error occurrence is given. The researches were conducted on the basis of data obtained by coordinate control over the stabilizing section shell. The data were studied by statistical methods and analyzed in terms of their compliance with previously proposed mathematical models of formation of geokhod shell inaccuracies. It is shown that available mathematical models can not completely explain the origin of all the errors. The authors attribute unexplained geokhod shell errors as deformations caused by welding

Research on Geometric Errors of Intermediate Unit Shell of a Geokhod

This article includes the research results on production errors of intermediate unit shell of a geokhod prototype model. There has been a problem stated concerning the accuracy of geokhod shells; constructive and technological particularities of a intermediate unit have been specified. A short summary has been conducted of the types of approach to the determination of shell errors of large equipment. The research was performed on the basis of data received by means of coordinate control of a gekhod prototype model in a production environment. The captured data have been researched by means of statistical methods and analyzed with the purpose of unveiling the factors affecting the errors. It was showed in the article that the errors can be partially explained by the production errors of body sectors and the errors of their relative assembling position. It was demonstrated that at least a part of errors is conditioned by reasons which are not taken into account in the process of a pure geometric description of the intermediate unit manufacturing process

Research on Geometric Errors of Intermediate Unit Shell of a Geokhod

This article includes the research results on production errors of intermediate unit shell of a geokhod prototype model. There has been a problem stated concerning the accuracy of geokhod shells; constructive and technological particularities of a intermediate unit have been specified. A short summary has been conducted of the types of approach to the determination of shell errors of large equipment. The research was performed on the basis of data received by means of coordinate control of a gekhod prototype model in a production environment. The captured data have been researched by means of statistical methods and analyzed with the purpose of unveiling the factors affecting the errors. It was showed in the article that the errors can be partially explained by the production errors of body sectors and the errors of their relative assembling position. It was demonstrated that at least a part of errors is conditioned by reasons which are not taken into account in the process of a pure geometric description of the intermediate unit manufacturing process

Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property

In a recent paper, we proved that a large class of spacetimes, not necessarily homogeneous or isotropous and relevant at a cosmological level, possesses a preferred codimension one submanifold, i.e., the past cosmological horizon, on which it is possible to encode the information of a scalar field theory living in the bulk. Such bulk-to-boundary reconstruction procedure entails the identification of a preferred quasifree algebraic state for the bulk theory, enjoying remarkable properties concerning invariance under isometries (if any) of the bulk and energy positivity, and reducing to well-known vacua in standard situations. In this paper, specialising to open FRW models, we extend previously obtained results and we prove that the preferred state is of Hadamard form, hence the backreaction on the metric is finite and the state can be used as a starting point for renormalisation procedures. That state could play a distinguished role in the discussion of the evolution of scalar fluctuations of the metric, an analysis often performed in the development of any model describing the dynamic of an early Universe which undergoes an inflationary phase of rapid expansion in the past.Comment: 41 page

Rigorous steps towards holography in asymptotically flat spacetimes

Scalar QFT on the boundary $\Im^+$ at null infinity of a general asymptotically flat 4D spacetime is constructed using the algebraic approach based on Weyl algebra associated to a BMS-invariant symplectic form. The constructed theory is invariant under a suitable unitary representation of the BMS group with manifest meaning when the fields are interpreted as suitable extensions to $\Im^+$ of massless minimally coupled fields propagating in the bulk. The analysis of the found unitary BMS representation proves that such a field on $\Im^+$ coincides with the natural wave function constructed out of the unitary BMS irreducible representation induced from the little group $\Delta$, the semidirect product between SO(2) and the two dimensional translational group. The result proposes a natural criterion to solve the long standing problem of the topology of BMS group. Indeed the found natural correspondence of quantum field theories holds only if the BMS group is equipped with the nuclear topology rejecting instead the Hilbert one. Eventually some theorems towards a holographic description on $\Im^+$ of QFT in the bulk are established at level of $C^*$ algebras of fields for strongly asymptotically predictable spacetimes. It is proved that preservation of a certain symplectic form implies the existence of an injective $*$-homomorphism from the Weyl algebra of fields of the bulk into that associated with the boundary $\Im^+$. Those results are, in particular, applied to 4D Minkowski spacetime where a nice interplay between Poincar\'e invariance in the bulk and BMS invariance on the boundary at $\Im^+$ is established at level of QFT. It arises that the $*$-homomorphism admits unitary implementation and Minkowski vacuum is mapped into the BMS invariant vacuum on $\Im^+$.Comment: 62 pages, amslatex, xy package; revised section 2 and the conclusions; corrected some typos; added some references; accepted for pubblication on Rev. Math. Phy

SNARC-like compatibility effects for physical and phenomenal magnitudes: A study on visual illusions

Both numerical and non-numerical magnitudes elicit similar Spatial-Numerical Association of Response Codes (SNARC) effects, with small magnitudes associated with left hand responses and large magnitudes associated with right hand responses (Dehaene, Bossini, Giraux, 1993). In the present study, we investigated whether the phenomenal size of visual illusions elicits the same SNARC-like effect revealed for the physical size of pictorial surfaces. Four experiments were conducted by using the Delboeuf illusion (Experiment 1) and the Kanizsa triangle illusion (Experiments 2, 3 & 4). Experiment 1 suggests the presence of a SNARC-like compatibility effect for the physical size of the inducers, while this effect was not revealed for the phenomenal size of the induced elements, possibly masked by a stronger effect of the inducers. A SNARC-like effect for the phenomenal size of the Kanizsa triangle was revealed when participants directly compared the size of the triangles (Experiment 4). Conversely, when participants performed an indirect task (orientation judgment), the SNARC-like effect was present neither for the illusory nor for the physical displays (Experiments 2 & 3). The effect revealed for the size of illusory triangles was comparable to that of real triangles with physical contours, suggesting that both phenomenal and physical magnitudes similarly elicit SNARC-like effects

Wightman Functions' Behaviour on the Event Horizon of an Extremal Reissner-Nordstr\"om Black Hole

A weaker Haag, Narnhofer and Stein prescription as well as a weaker Hessling Quantum Equivalence Principle for the behaviour of thermal Wightman functions on an event horizon are analysed in the case of an extremal Reissner-Nordstr\"{o}m black hole in the limit of a large mass. In order to avoid the degeneracy of the metric in the stationary coordinates on the horizon, a method is introduced which employs the invariant length of geodesics which pass the horizon. First the method is checked for a massless scalar field on the event horizon of the Rindler wedge, extending the original procedure of Haag, Narnhofer and Stein onto the {\em whole horizon} and recovering the same results found by Hessling. Afterwards the HNS prescription and Hessling's prescription for a massless scalar field are analysed on the whole horizon of an extremal Reissner-Nordstr\"{o}m black hole in the limit of a large mass. It is proved that the weak form of the HNS prescription is satisfyed for all the finite values of the temperature of the KMS states, i.e., this principle does not determine any Hawking temperature. It is found that the Reissner-Nordstr\"{o}m vacuum, i.e., $T=0$ does satisfy the weak HNS prescription and it is the only state which satisfies weak Hessling's prescription, too. Finally, it is suggested that all the previously obtained results should be valid dropping the requirements of a massless field and of a large mass black hole.Comment: 27 pages, standard LaTex, no figures, final version containing the results following from Hessling's principle as they appeared in the other paper gr-qc/9510016, minor changes in the text and in references, it will appear on Class. Quant. Gra