A non-singular black hole model as a possible end-product of gravitational collapse

In this paper we present a non-singular black hole model as a possible end-product of gravitational collapse. The depicted spacetime which is type [II,(II)], by Petrov classification, is an exact solution of the Einstein equations and contains two horizons. The equation of state in the radial direction, is a well-behaved function of the density and smoothly reproduces vacuum-like behavior near r=0 while tending to a polytrope at larger r, low density, values. The final equilibrium configuration comprises of a de Sitter-like inner core surrounded by a family of 2-surfaces of matter fields with variable equation of state. The fields are all concentrated in the vicinity of the radial center r=0. The solution depicts a spacetime that is asymptotically Schwarzschild at large r, while it becomes de Sitter-like for vanishing r. Possible physical interpretations of the macro-state of the black hole interior in the model are offered. We find that the possible state admits two equally viable interpretations, namely either a quintessential intermediary region or a phase transition in which a two-fluid system is in both dynamic and thermodynamic equilibrium. We estimate the ratio of pure matter present to the total energy and in both (interpretations) cases find it to be virtually the same, being 0.83. Finally, the well-behaved dependence of the density and pressure on the radial coordinate provides some insight on dealing with the information loss paradox.Comment: 12 Pages, 1 figure. Accepted for publication in Phys. Rev.

Mathematical Modelling of Dynamical Processes Under Interval Experimental Data

A brief discussion on a new methodology for solving mathematical problems involving interval input data and for scientific computing with result verification is presented. Some examples for the impact of this methodology on particular mathematical modelling situations are given. A brief report on a newly developed program system MODYNA, which is designed according to the new methodology, is presented

On the Algebraic Properties of Convex Bodies

AMS subject classification: 52A01, 13C99.The algebraic properties of the convex bodies are studied. A theorem of H. Rådström for embedding of convex bodies in a normed vector space is generalized by using a natural extension of the multiplication by scalar.This work was partially supported by the Bulgarian National Science Fund under grant No. MM-521/95

Synthesis of Quantum Logic Circuits

We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state-space of an n-qubit register is not finite and contains exponential superpositions of classical bit strings. Our proposed circuits are asymptotically optimal for respective tasks and improve published results by at least a factor of two. The circuits for generic quantum computation constructed by our algorithms are the most efficient known today in terms of the number of expensive gates (quantum controlled-NOTs). They are based on an analogue of the Shannon decomposition of Boolean functions and a new circuit block, quantum multiplexor, that generalizes several known constructions. A theoretical lower bound implies that our circuits cannot be improved by more than a factor of two. We additionally show how to accommodate the severe architectural limitation of using only nearest-neighbor gates that is representative of current implementation technologies. This increases the number of gates by almost an order of magnitude, but preserves the asymptotic optimality of gate counts.Comment: 18 pages; v5 fixes minor bugs; v4 is a complete rewrite of v3, with 6x more content, a theory of quantum multiplexors and Quantum Shannon Decomposition. A key result on generic circuit synthesis has been improved to ~23/48*4^n CNOTs for n qubit

Spectroscopic and physical parameters of Galactic O-type stars. II. Observational constraints on projected rotational and extra broadening velocities as a function of fundamental parameters and stellar evolution

Rotation is of key importance for the evolution of hot massive stars, however, the rotational velocities of these stars are difficult to determine. Based on our own data for 31 Galactic O stars and incorporating similar data for 86 OB supergiants from the literature, we aim at investigating the properties of rotational and extra line-broadening as a function of stellar parameters and at testing model predictions about the evolution of stellar rotation. Fundamental stellar parameters were determined by means of the code FASTWIND. Projected rotational and extra broadening velocities originate from a combined Ft + GOF method. Model calculations published previously were used to estimate the initial evolutionary masses. The sample O stars with Minit > 50 Msun rotate with less that 26% of their break-up velocity, and they also lack objects with v sin i 35 Msun on the hotter side of the bi-stability jump, the observed and predicted rotational rates agree quite well; for those on the cooler side of the jump, the measured velocities are systematically higher than the predicted ones. In general, the derived extra broadening velocities decrease toward cooler Teff, whilst for later evolutionary phases they appear, at the same v sin i, higher for high-mass stars than for low-mass ones. None of the sample stars shows extra broadening velocities higher than 110 km/s. For the majority of the more massive stars, extra broadening either dominates or is in strong competition with rotation. Conclusions: For OB stars of solar metallicity, extra broadening is important and has to be accounted for in the analysis. When appearing at or close to the zero-age main sequence, most of the single and more massive stars rotate slower than previously thought. Model predictions for the evolution of rotation in hot massive stars may need to be updated.Comment: 15 pages, 10 figures, accepted for publication in A &

Constant-degree graph expansions that preserve the treewidth

Many hard algorithmic problems dealing with graphs, circuits, formulas and constraints admit polynomial-time upper bounds if the underlying graph has small treewidth. The same problems often encourage reducing the maximal degree of vertices to simplify theoretical arguments or address practical concerns. Such degree reduction can be performed through a sequence of splittings of vertices, resulting in an _expansion_ of the original graph. We observe that the treewidth of a graph may increase dramatically if the splittings are not performed carefully. In this context we address the following natural question: is it possible to reduce the maximum degree to a constant without substantially increasing the treewidth? Our work answers the above question affirmatively. We prove that any simple undirected graph G=(V, E) admits an expansion G'=(V', E') with the maximum degree <= 3 and treewidth(G') <= treewidth(G)+1. Furthermore, such an expansion will have no more than 2|E|+|V| vertices and 3|E| edges; it can be computed efficiently from a tree-decomposition of G. We also construct a family of examples for which the increase by 1 in treewidth cannot be avoided.Comment: 12 pages, 6 figures, the main result used by quant-ph/051107

Adsorption Way of the Loss of Moon's Atmosphere

Theory on gas adsorption by lunar surface to explain loss of lunar atmospher

Efficient Multi-stage Inference on Tabular Data

Many ML applications and products train on medium amounts of input data but get bottlenecked in real-time inference. When implementing ML systems, conventional wisdom favors segregating ML code into services queried by product code via Remote Procedure Call (RPC) APIs. This approach clarifies the overall software architecture and simplifies product code by abstracting away ML internals. However, the separation adds network latency and entails additional CPU overhead. Hence, we simplify inference algorithms and embed them into the product code to reduce network communication. For public datasets and a high-performance real-time platform that deals with tabular data, we show that over half of the inputs are often amenable to such optimization, while the remainder can be handled by the original model. By applying our optimization with AutoML to both training and inference, we reduce inference latency by 1.3x, CPU resources by 30%, and network communication between application front-end and ML back-end by about 50% for a commercial end-to-end ML platform that serves millions of real-time decisions per second

Modeling and Simulation of Janus-like Nanoparticles Formation by Solid-Gas Exothermic Reactions

Theoretical model for the simulation of synthesis of Janus-like particles (JP) consisting two different phases using the Carbon Combustion Synthesis of Oxides (CCSO) is presented. The model includes the variation of sample initial porosity, carbon concentration and oxygen flow rate used to predict the formation of JP features. The two temperature (2T) combustion model of chemically active submicron-dispersed mixture of two phases including ferroelectric and ferromagnetic was implemented and assessed by using the experimentally estimated activation energy of 112±3.3 kJ/mol and combustion temperature. The experimental values allowed to account the thermal and concentration expansion effect along with the dispersion by the slip-jump simulation for high Knudsen numbers. The model predicted that the smaller initial porosity of the combustion media creates higher formation rate of Janus-like particles. The simulation of slippage and jumps of the gas temperature allowed the scale-bridging between macro- and micro- structures

DIAGNOSTICAL VALUE OF LIQUOR CHANGES IN BRAIN STROKE PATIENTS

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