Entanglement, EPR correlations and mesoscopic quantum superposition by the high-gain quantum injected parametric amplification

We investigate the multiparticle quantum superposition and the persistence of multipartite entanglement of the quantum superposition generated by the quantum injected high-gain optical parametric amplification of a single photon. The physical configuration based on the optimal universal quantum cloning has been adopted to investigate how the entanglement and the quantum coherence of the system persists for large values of the nonlinear parametric gain g.Comment: 9 pages, 5 figure

Skeletal Torsion Tunneling and Methyl Internal Rotation: The Coupled Large Amplitude Motions in Phenyl Acetate

The rotational spectrum of phenyl acetate, CH3 COOC6 H5, is measured using a free jet absorption millimeter-wave spectrometer in the range from 60 to 78 GHz and two pulsed jet Fourier transform microwave spectrometers covering a total frequency range from 2 to 26.5 GHz. The features of two large amplitude motions, the methyl group internal rotation and the skeletal torsion of the CH3 COO group with respect to the phenyl ring C6 H5 (tilted at about 70◦ ), characterize the spectrum. The vibrational ground state is split into four widely spaced sublevels, labeled as A0, E0, A1, and E1, each of them with its set of rotational transitions and with additional interstate transitions. A global fit of the line frequencies of the four sublevels leads to the determination of 51 spectroscopic parameters, including the ∆EA0/A1 and ∆EE0/E1 vibrational splittings of ~36.4 and ~33.5 GHz, respectively. The V3 barrier to methyl internal rotation (~136 cm−1 ) and the skeletal torsion B2 barrier to the orthogonality of the two planes (~68 cm−1 ) are deduced

Definition of First Order Language with Arbitrary Alphabet. Syntax of Terms, Atomic Formulas and their Subterms

Second of a series of articles laying down the bases for classical first order model theory. A language is defined basically as a tuple made of an integer-valued function (adicity), a symbol of equality and a symbol for the NOR logical connective. The only requests for this tuple to be a language is that the value of the adicity in = is -2 and that its preimage (i.e. the variables set) in 0 is infinite. Existential quantification will be rendered (see [11]) by mere prefixing a formula with a letter. Then the hierarchy among symbols according to their adicity is introduced, taking advantage of attributes and clusters. The strings of symbols of a language are depth-recursively classified as terms using the standard approach (see for example [16], definition 1.1.2); technically, this is done here by deploying the ‘-multiCat' functor and the ‘unambiguous’ attribute previously introduced in [10], and the set of atomic formulas is introduced. The set of all terms is shown to be unambiguous with respect to concatenation; we say that it is a prefix set. This fact is exploited to uniquely define the subterms both of a term and of an atomic formula without resorting to a parse tree.Mathematics Department "G. Castelnuovo", Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Roma, ItalyGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.Marco B. Caminati. Preliminaries to classical first order model theory. Formalized Mathematics, 19(3):155-167, 2011, doi: 10.2478/v10037-011-0025-2.Marco B. Caminati. First order languages: Further syntax and semantics. Formalized Mathematics, 19(3):179-192, 2011, doi: 10.2478/v10037-011-0027-0.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Katarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711-717, 1991.Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990.Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.W. Pohlers and T. Glaß. An introduction to mathematical logic. Vorlesungsskriptum, WS, 93, 1992.Marta Pruszyńska and Marek Dudzicz. On the isomorphism between finite chains. Formalized Mathematics, 9(2):429-430, 2001.Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990

The experimental gas-phase structures of 1,3,5-trisilylbenzene and hexasilylbenzene and the theoretical structures of all benzenes with three or more silyl substituents

The structures of 1,3,5-trisilylbenzene and hexasilylbenzene in the gas phase have been determined by electron diffraction, and that of 1,3,5-trisilylbenzene by X-ray crystallography. The structures of three trisilylbenzene isomers, three tetrasilylbenzenes, pentasilylbenzene and hexasilylbenzene have been computed, ab initio and using Density Functional Theory, at levels up to MP2/6-31G*. The primary effect of silyl substituents is to narrow the ring angle at the substituted carbon atoms. Steric interactions between silyl groups on neighbouring carbon atoms lead first to displacement of these groups away from one another, and then to displacement out of the ring plane, with alternate groups moving to opposite sides of the ring. In the extreme example, hexasilylbenzene, the SiCCSi dihedral angle is 17.8(8)°

Minimal clinically important difference for asthma endpoints: an expert consensus report

Minimal clinically important difference (MCID) can be defined as the smallest change or difference in an outcome measure that is perceived as beneficial and would lead to a change in the patient's medical management.The aim of the current expert consensus report is to provide a "state-of-the-art" review of the currently available literature evidence about MCID for end-points to monitor asthma control, in order to facilitate optimal disease management and identify unmet needs in the field to guide future research.A series of MCID cut-offs are currently available in literature and validated among populations of asthmatic patients, with most of the evidence focusing on outcomes as patient reported outcomes, lung function and exercise tolerance. On the contrary, only scant and partial data are available for inflammatory biomarkers. These clearly represent the most interesting target for future development in diagnosis and clinical management of asthma, particularly in view of the several biologic drugs in the pipeline, for which regulatory agencies will soon require personalised proof of efficacy and treatment response predictors

Minimal clinically important difference for asthma endpoints: an expert consensus report

Minimal clinically important difference (MCID) can be defined as the smallest change or difference in an outcome measure that is perceived as beneficial and would lead to a change in the patient's medical management.The aim of the current expert consensus report is to provide a "state-of-the-art" review of the currently available literature evidence about MCID for end-points to monitor asthma control, in order to facilitate optimal disease management and identify unmet needs in the field to guide future research.A series of MCID cut-offs are currently available in literature and validated among populations of asthmatic patients, with most of the evidence focusing on outcomes as patient reported outcomes, lung function and exercise tolerance. On the contrary, only scant and partial data are available for inflammatory biomarkers. These clearly represent the most interesting target for future development in diagnosis and clinical management of asthma, particularly in view of the several biologic drugs in the pipeline, for which regulatory agencies will soon require personalised proof of efficacy and treatment response predictors

About Bianchi I with VSL

In this paper we study how to attack, through different techniques, a perfect fluid Bianchi I model with variable G,c and Lambda, but taking into account the effects of a $c$-variable into the curvature tensor. We study the model under the assumption,div(T)=0. These tactics are: Lie groups method (LM), imposing a particular symmetry, self-similarity (SS), matter collineations (MC) and kinematical self-similarity (KSS). We compare both tactics since they are quite similar (symmetry principles). We arrive to the conclusion that the LM is too restrictive and brings us to get only the flat FRW solution. The SS, MC and KSS approaches bring us to obtain all the quantities depending on \int c(t)dt. Therefore, in order to study their behavior we impose some physical restrictions like for example the condition q<0 (accelerating universe). In this way we find that $c$ is a growing time function and Lambda is a decreasing time function whose sing depends on the equation of state, w, while the exponents of the scale factor must satisfy the conditions $\sum_{i=1}^{3}\alpha_{i}=1$ and $\sum_{i=1}^{3}\alpha_{i}^{2}<1,$ $\forall\omega$, i.e. for all equation of state$,$ relaxing in this way the Kasner conditions. The behavior of $G$ depends on two parameters, the equation of state $\omega$ and $\epsilon,$ a parameter that controls the behavior of $c(t),$ therefore $G$ may be growing or decreasing.We also show that through the Lie method, there is no difference between to study the field equations under the assumption of a $c-$var affecting to the curvature tensor which the other one where it is not considered such effects.Nevertheless, it is essential to consider such effects in the cases studied under the SS, MC, and KSS hypotheses.Comment: 29 pages, Revtex4, Accepted for publication in Astrophysics & Space Scienc

Electron penetration in the nucleus and its effect on the quadrupole interaction

A series expansion of the interaction between a nucleus and its surrounding electron distribution provides terms that are well-known in the study of hyperfine interactions: the familiar quadrupole interaction and the less familiar hexadecapole interaction. If the penetration of electrons into the nucleus is taken into account, various corrections to these multipole interactions appear. The best known one is a scalar correction related to the isotope shift and the isomer shift. This paper discusses a related tensor correction, which modifies the quadrupole interaction if electrons penetrate the nucleus: the quadrupole shift. We describe the mathematical formalism and provide first-principles calculations of the quadrupole shift for a large set of solids. Fully relativistic calculations that explicitly take a finite nucleus into account turn out to be mandatory. Our analysis shows that the quadrupole shift becomes appreciably large for heavy elements. Implications for experimental high-precision studies of quadrupole interactions and quadrupole moment ratios are discussed. A literature review of other small quadrupole-like effects is presented as well

The Effects of Social Ties on Coordination: Conceptual Foundations for an Empirical Analysis

International audienceThis paper investigates the influence that social ties can have on behavior. After defining the concept of social ties that we consider, we introduce an original model of social ties. The impact of such ties on social preferences is studied in a coordination game with outside option. We provide a detailed game theoretical analysis of this game while considering various types of players, i.e., self-interest maximizing, inequity averse, and fair agents. In addition to these approaches that require strategic reasoning in order to reach some equilibrium, we also present an alternative hypothesis that relies on the concept of team reasoning. After having discussed the differences between the latter and our model of social ties, we show how an experiment can be designed so as to discriminate among the models presented in the paper