The Inverse Gaussian Models: Analogues of Symmetry, Skewness and Kurtosis

The inverse Gaussian (IG) family is strikingly analogous to the Gaussian family in terms of having simple inference solutions, which use the familiar ², t and F distributions, for a variety of basic problems. Hence, the IG family, consisting of asymmetric distributions is widely used for modelling and analyzing nonnegative skew data. However, the process lacks measures of model appropriateness corresponding to and ₂, routinely employed in statistical analyses. We use known similarities between the two families to define a concept termed IG-symmetry, an analogue of the symmetry, and to develop IG-analogues ₁ and ₂ of and ₂, respectively. Interestingly, the asymptotic null distributions of the sample versions d ₁, d ₂ of ₁, ₂ are exactly the same as those of their normal counterparts and b ₂. Some applications are discussed, and the analogies between the two families, enhanced during this study are tabulated.     

Nonlinearity of strong interaction and doorway states for one-nucleon transfer reactions

The experimental data on the doorway states for one-nucleon transfer reactions permit to reveal the many-particle nucleon-nucleon forces resulting from the nonlinearity of strong interaction. The three-particle and four-particle forces are found to be of the same magnitude as the two-particle ones in contrast to the finding from the few-nucleon systems. The origin of this difference is explained. Received: 14 May 2002 / Accepted: 4 June 2002 / Published online: 19 November 2002 RID="a" ID="a"e-mail: birbrair@thd.pnpi.spb.ru Communicated by V.V. Anisovich     

EPR entangled states and complex fractional Fourier transformation

Starting from the Einstein-Podolsky-Rosen entangled state representations of continuous variables we derive a new formulation of complex fractional Fourier transformation (CFFT). We find that two-variable Hermite polynomials are just the eigenmodes of the CFFT. In this way the CFFT is linked to the appropriate operator transformation between two kinds of entangled states in the context of quantum mechanics. In so doing, the CFFT of quantum mechanical wave functions can be derived more directly and concisely. Received 21 February 2002 / Received in final form 1st June 2002 Published online 24 September 2002 RID="*" ID="*"Work supported by National Natural Science Foundation of China under grant 10175057 and the President Foundation of Chinese Academy of Science. RID="a" ID="a"e-mail: fhym@ustc.edu.cn     

Data analysis for a gravitational wave antenna with resonant capacitive transducer

Summary We present here a new approach which simplifies considerably the data analysis for gravitational-wave antennas equipped with resonant transducer, based on the representation of the antenna as two independent oscillators. In fact, we can apply to each of the two modes of these antennas the same data analysis procedures already in use for antennas with nonresonant transducer and then compute the coincidences between the outputs of the two modes. The results deduced by such a procedure are in good agreement with the experimental results from the data collected in March 1984 with our 2270 kg 5056 Al bar cooled at liquid-helium temperature (T=4.2 K). The performances of the algorithms are presented in terms of the effective noise temperatures and sensitivity to short bursts of gravitational waves. With our experimental values, obtained by using a FET amplifier, we get an instrumental sensitivityF(v) of 6 J/m² Hz. We have also evaluated the sensitivity of the detector for monochromatic gravitational waves with frequencies in bandwidths of ≏0.4 Hz around the frequenciesv ₋ andv ₊, for one month of observation:h ₀≏3·10⁻²³.

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Riassunto Si presenta un nuovo approccio che semplifica notevolmente l’analisi dei dati per antenne gravitazionali con trasduttore risonante, basato sulla rappresentazione dell’antenna come due oscillatori indipendenti. A ciascuno dei modi di tali antenne si applicano le procedure di analisi dei dati già usati per le antenne con trasduttore risonante e si calcolano quindi le coincidenze tra le uscite dei due modi. I risultati dedotti mediante tale procedura sono in buon accordo con i risultati sperimentali relativi ai dati raccolti nel marzo 1984 con la nostra sbarra di Al 5056 da 2270 kg raffreddata alla temperatura dell’elio liquido (T=4.2 K). Si presentano le prestazioni degli algoritmi in termini delle temperature efficaci di rumore e della sensibilità per brevi fiotti di onde gravitazionali. Con i nostri valori sperimentali, ottenuti usando un amplificatore a FET, si ha una sensibilità strumentaleF(v) di 6 J/m² Hz. Si è anche calcolata la sensibilità del rivelatore per onde gravitazionali monocromatiche in bande di frequenza di circa 0.4 Hz attorno alle frequenzev ₋ ev ₊, per un mese di ossevazione:h ₀≏3.·10⁻²³.

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Резюме Предлагается новый подход, котрый значительно упрощает анализ данных для антенн гравитационных волн с резонансным емкостным датчиком, основанный на представлении антенны в виде двух независимых осцилляторов. Мы можем применить к каждой из двух мод этих антенн процедуры анализа данных, которые ыже использовались для антенн с нерезонансными датчиками, а затем вычислить совпадения между результатами на выходе для двух мод. Результаты, полученные с помощью такой процедуры, хорошо согласуются с экспериментальными результатами, собранными в марте 1984 года с помощью 2270 кг 5056 Al антенны, охлажденной до температуры жидкого гелия (T=4.2 К). Описываются алгоритмы анализа, исходя из эффективных температур шума и чувствительности к коротким вспышкам гравитационных волн. Используя экспериментальные значения, полученные с помощью FET усилителя, мы определяем инструментальную чувствительностьF(v)≈6Дж/M² Гц. Мы также оцениваем чувствительность детектора для монохроматических гравитационных волн в полосе частот 0.4 Гц вблизи частот,v ₋ иv ₊ для одного месяца наблюдения:h ₀≏3·10⁻²³.

     

The gravitational wave antenna in Frascati

Summary We report on the cryogenic gravitational detector operating at 1763 Hz in Frascati. The antenna was equipped with a resonant capacitive transducer and a d.c. SQUID as an amplifier. After a test run in 1987, the detector was cooled again in the present configuration and took data for nearly two months in June and July 1988. A preliminary data analysis shows a noise temperature of 115 mK, but we expect to lower it further by applying improved filtering tecniques. During the same period two other cryogenic antennae were operating, and we plan to undertake a correlation analysis between the output of the three detectors. To speed up publication, the proofs were not sent to the authors and were supervised by the Scientific Committee.     

The Electromagnetic Sector of the Evans Field Theory

No Heading The equations of the electromagnetic sector of the Evans field theory are given in terms of differential geometry and are based on the well-known structure relations and Bianchi identities. The equations thus complete Einsteins basic axiom, that physics is derived from geometry, and extend the axiom to electrodynamics. Precise tests are suggested for the theory using the interaction of circularly polarized electromagnetic radiation with a non-relativistic electron beam. These tests include; the inverse Faraday effect (IFE), radiatively induced fermion resonance (RFR), and the electromagnetic Aharonov-Bohm (EMAB) effect.     

Asymptotics of a Boundary Crossing Probability of a Brownian Bridge with General Trend

Let us consider a signal-plus-noise model h(z)+B ₀(z), z [0,1], where > 0, h: [0,1] , and B ₀ is a Brownian bridge. We establish the asymptotics for the boundary crossing probability of the weighted signal-plus-noise model for , that is P (sup _{z [0,1]} w(z)( h(z)+B ₀(z))>c), for , (1) where w: [0,1] [0, is a weight function and c>0 is arbitrary. By the large deviation principle one gets a result with a constant which is the solution of a minimizing problem. In this paper we show an asymptotic expansion that is stronger than large deviation. As byproduct of our result we obtain the solution of the minimizing problem occurring in the large deviation expression. It is worth mentioning that the probability considered in (1) appears as power of the weighted Kolmogorov test applied to the test problem H ₀: h 0 against the alternative K: h>0 in the signal-plus-noise model.     

Comments on “determinism,realism, and Stapp's 1985 proof of nonlocality”

An earlier argument by the author, that Stapp's 1985 proof of quantum locality contains an implicit element of realism, is elaborated. Refuted thereby is Clifton's criticism that the author's argument was based on a misinterpretation of counterfactual analysis.