scholarly journals Spectral statistics of permutation matrices

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120508 ◽  
Author(s):  
Idan Oren ◽  
Uzy Smilansky
Keyword(s):  
Number Theory ◽  
Point Of View ◽  
Spectral Form ◽  
Permutation Matrices ◽  
Divisor Functions ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Subject ◽  
Spectral Statistics ◽  
The Mean

We compute the mean two-point spectral form factor and the spectral number variance for permutation matrices of large order. The two-point correlation function is expressed in terms of generalized divisor functions, which are frequently discussed in number theory. Using classical results from number theory and casting them in a convenient form, we derive expressions which include the leading and next to leading terms in the asymptotic expansion, thus providing a new point of view on the subject, and improving some known results.

The Effect of Waking Suggestion on Post-Hypnotic Amnesia

1981 ◽  
Vol 11 (1) ◽  
pp. 44-46 ◽  
Author(s):  
D.P. Fourie
Keyword(s):  
Point Of View ◽  
The Other ◽  
Hypnotic Susceptibility ◽  
The Subject ◽  
The Mean ◽  
The Difference ◽  
The One ◽  
The Relationship ◽  
Female Subjects

It is increasingly realized that hypnosis may be seen from an interpersonal point of view, meaning that it forms part of the relationship between the hypnotist and the subject. From this premise it follows that what goes on in the relationship prior to hypnosis probably has an influence on the hypnosis. Certain of these prior occurences can then be seen as waking suggestionns (however implicitly given) that the subject should behave in a certain way with regard to the subsequent hypnosis. A study was conducted to test the hypothesis that waking suggestions regarding post-hypnotic amnesia are effective. Eighteen female subjects were randomly divided into two groups. The groups listened to a tape-recorded talk on hypnosis in which for the one group amnesia for the subsequent hypnotic experience and for the other group no such amnesia was suggested. Thereafter the Stanford Hypnotic Susceptibility Scale was administered to all subjects. Only the interrogation part of the amnesia item of the scale was administered. The subjects to whom post-hypnotic amnesia was suggested tended to score lower on the amnesia item than the other subjects, as was expected, but the difference between the mean amnesia scores of the two groups was not significant.

scholarly journals Bifurcation and anomalous spectral accumulation in an oval billiard

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
Hironori Makino
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Limited Region ◽  
Classical Dynamical System ◽  
Classical Trajectories ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Spectral Statistics ◽  
Math Phys ◽  
Good Agreement

Abstract The spectral statistics of a quantum oval billiard whose classical dynamical system shows bifurcations is numerically investigated in terms of the two-point correlation function (TPCF), which is defined as the probability density of finding two levels at a specific energy interval. The eigenenergy levels at the bifurcation point are found to show anomalous accumulation, which is observed as a periodic spike oscillation of the TPCF. We analyzed the eigenfunctions localizing onto the various classical trajectories in the phase space and found that the oscillation is supplied from a limited region in the phase space that contains the bifurcating orbit. We also show that the period of the oscillation is in good agreement with the period of a contribution from the bifurcating orbit to the semiclassical TPCF obtained by Gutzwiller’s trace formula [J. Math. Phys. 12, 343 (1971)].

Spectral statistics of unitary ensembles

2018 ◽  
Author(s):  
Freeman Dyson
Keyword(s):  
Orthogonal Polynomials ◽  
Polynomial Method ◽  
Real Numbers ◽  
Fredholm Determinants ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Spectral Statistics ◽  
Matrix Ensembles ◽  
Gap Probability ◽  
Computing Correlation

This article focuses on the use of the orthogonal polynomial method for computing correlation functions, cluster functions, gap probability, Janossy density, and spacing distributions for the eigenvalues of matrix ensembles with unitary-invariant probability law. It first considers the classical families of orthogonal polynomials (Hermite, Laguerre, and Jacobi) and some corresponding unitary ensembles before discussing the statistical properties of N-tuples of real numbers. It then reviews the definitions of basic statistical quantities and demonstrates how their distributions can be made explicit in terms of orthogonal polynomials. It also describes the k-point correlation function, Fredholm determinants of finite-rank kernels, and resolvent kernels.

scholarly journals On the relation of the air and evaporation temperatures to the temperature of the dew-point, as determined by Mr. Glaisher's hygrometrical tables founded on the factors deduced from the six-hourly observations made at the Royal Observatory, Greenwich

1851 ◽  
Vol 5 ◽  
pp. 953-953
Keyword(s):  
Personal Experience ◽  
Point Of View ◽  
Dew Point ◽  
Practical Point ◽  
Advantages And Disadvantages ◽  
Royal Observatory ◽  
The Subject ◽  
The Mean ◽  
Annual Amount

After pointing out the importance of the hygrometer, both in a scientific and a practical point of view, the author goes into the question of the advantages and disadvantages attending the use of Daniell’s hygrometer, and the relative merits of this instrument and the dry and wet-bulb thermometers. Although satisfied of the accuracy of Mr. Glaisher’s Tables (founded on the Greenwich Observations), which show at once the relation of the temperature of evaporation to that of the dew-point, he was unwilling to abandon the use of Daniell’s apparatus for that of the wet and dry-bulb thermometers, slight as is the trouble of observing them, without personal experience of the correctness of the tables from which the dew-point was to be deduced. He therefore instituted a series of perfectly comparable observations by the two methods, and in this communication gives the results obtained from them during a period of twenty months. From a comparison of the dew-points determined by the two methods, he concludes that the results show in a striking manner the extreme accuracy of Mr. Glaisher’s Tables, and afford additional testimony to the value of the Greenwich Hygrometrical Observations, and the resulting formula on which those tables are founded. The author then refers to the subject of evaporation, and gives the results of his own observations at Whitehaven during six years, viz. from 1843 to 1848 inclusive. From these he states that the mean annual amount of evaporation is 30·011 inches; and the mean quantity of rain for the same period being 45·255 inches, the depth of the water precipitated exceeds that taken up by evaporation, on the coast in latitude 54½°, by 15·244 inches.

scholarly journals Scale-Invariant Correlation Functions of Cosmological Density Fluctuations in the Strong Clustering Regime and the Stability

1999 ◽  
Vol 183 ◽  
pp. 274-274
Author(s):  
Taihei Yano ◽  
Naoteru Gouda
Keyword(s):  
Correlation Function ◽  
Spatial Correlation ◽  
Correlation Functions ◽  
Power Index ◽  
Nonlinear Regime ◽  
Peculiar Velocity ◽  
Strongly Nonlinear ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Mean

We have investigated the scale-invariant solutions of the BBGKY equations for spatial correlation functions of cosmological density fluctuations and the mean relative peculiar velocity in the strongly nonlinear regime. It is found that the solutions for the mean relative physical velocity depend on the three-point spatial correlation function and the skewness of the velocity fields. We find that the stable condition in which the mean relative physical velocity vanishes on the virialized regions is satisfied only under the assumptions which Davis & Peebles took in there paper. It is found, however, that their assumptions may not be general in real. The power index of the two-point correlation function in the strongly nonlinear regime depends on the mean relative peculiar velocity, the three-point correlation function and the skewness. If self-similar solutions exist, then the power index in the strongly nonlinear regime is related to the power index of the initial power spectrum and its relation depends on the three-point correlation function and the skewness through the mean relative peculiar velocity. We also investigate stability of the solutions of the BBGKY equations for two-point spatial correlation functions. In the case that the background skewness is equal to 0, we found that there is no local instability in the strongly non-linear regime.

scholarly journals Anti-de-Sitter-Maxwell-Yang-Mills Black Holes Thermodynamics from Nonlocal Observables Point of View

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
H. El Moumni
Keyword(s):  
Black Hole ◽  
Phase Structure ◽  
Entanglement Entropy ◽  
Point Of View ◽  
De Sitter ◽  
Yang Mills ◽  
Fixed Charges ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Grand Canonical

In this paper we analyze the thermodynamic properties of the Anti-de-Sitter black hole in the Einstein-Maxwell-Yang-Mills-AdS gravity (EMYM) via many approaches and in different thermodynamical ensembles (canonical/grand canonical). First, we give a concise overview of this phase structure in the entropy-thermal diagram for fixed charges and then we investigate this thermodynamical structure in fixed potentials ensemble. The next relevant step is recalling the nonlocal observables such as holographic entanglement entropy and two-point correlation function to show that both observables exhibit a Van der Waals-like behavior in our numerical accuracy and just near the critical line as the case of the thermal entropy for fixed charges by checking Maxwell’s equal area law and the critical exponent. In the light of the grand canonical ensemble, we also find a newly phase structure for such a black hole where the critical behavior disappears in the thermal picture as well as in the holographic one.

The mean density and two-point correlation function for the CfA redshift survey slices

1988 ◽  
Vol 332 ◽  
pp. 44 ◽  
Author(s):  
Valerie de Lapparent ◽  
Margaret J. Geller ◽  
John P. Huchra
Keyword(s):  
Correlation Function ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Redshift Survey ◽  
The Mean

scholarly journals On the Rating of a Special Stop Loss Cover

1977 ◽  
Vol 9 (1-2) ◽  
pp. 33-41 ◽  
Author(s):  
Gunnar Benktander
Keyword(s):  
Mean Value ◽  
Point Of View ◽  
Approximation Formula ◽  
Present Contribution ◽  
Safe Side ◽  
The Subject ◽  
The Mean ◽  
Risk Rate ◽  
Stop Loss ◽  
Made In

Stop Loss reinsurance has attracted the interest of ASTIN members for years. May I recall the paper of Borch [1] in which he demonstrates some optimality qualities of the stop loss reinsurance from the ceding company's point of view, the contribution of Kahn [2] and the paper of Pesonen [3]. I also mention the paper of Esscher [4] and Verbeek's contribution [5]. Going back to the pre-ASTIN days we find a paper of Dubois [6].The rating problems have been dealt with by several authors. Let me recall the rating formula worked out by a group of Dutch Actuaries some 20 years ago. This was based on the assumption that the mean and the standard deviation were known. Based on Chebycheff's inequality an approximation formula was worked out which, of course, was heavily on the safe side.Even younger members of ASTIN are probably familiar with the studies made in the early sixties by a group of Swedish Actuaries, the results of which were presented by Bohman at the Actuarial Congress in London in 1964. Partly based on this, Bühlmann worked out some tables which he used for rating purposes.My present contribution to the subject may not justify the above reviews, particularly as I will deal with a very special retention situation which a practical underwriter will rightly not accept, namely a stop-loss point as low as equal to the mean value of the distribution.My excuse for this is that the formula deduced is very handy and that it is of value to the underwriter to know the stop loss risk rate also at this low level.

A Modified Chair Geometry for Whole Body Counting

1976 ◽  
Vol 15 (05) ◽  
pp. 246-247
Author(s):  
S. C. Jain ◽  
G. C. Bhola ◽  
A. Nagaratnam ◽  
M. M. Gupta
Keyword(s):  
Marked Improvement ◽  
Point Of View ◽  
Whole Body ◽  
Spatial Response ◽  
Body Counting ◽  
The Subject ◽  
Whole Body Counting ◽  
The Buddha

SummaryIn the Marinelli chair, a geometry widely used in whole body counting, the lower part of the leg is seen quite inefficiently by the detector. The present paper describes an attempt to modify the standard chair geometry to minimise this limitation. The subject sits crossed-legged in the “Buddha Posture” in the standard chair. Studies with humanoid phantoms and a volunteer sitting in the Buddha posture show that this modification brings marked improvement over the Marinelli chair both from the point of view of sensitivity and uniformity of spatial response.

Applying Circle Game to Enhance Students’ Speaking Skill

2020 ◽  
Vol 7 (2) ◽  
pp. 119
Author(s):  
Putri Denaya Side Ayu ◽  
Heri Hidayatullah ◽  
Sri Ariani
Keyword(s):  
Action Research ◽  
Learning Process ◽  
Active Involvement ◽  
Post Test ◽  
Speaking Skill ◽  
The Subject ◽  
The Mean ◽  
Classroom Action Research ◽  
Speaking Skills

This Collaborative Classroom Action Research aimed at enhancing students’ speaking skill through the application of Circle Game. It was conducted in one cycle consisting of two meetings. The subject was the seventh of C class of SMPN 2 Alas Barat consisting of 22 students. The types of data were qualitative (acquiring observation during the learning process) and quantitative (speaking tests). The results qualitatively showed that the implementation of Circle Game enhanced the students’ speaking skills. Such improvement could be seen from their enthusiasm, their interesting feeling in various materials presented by the teacher, their active involvement. In the quantitative findings, the result also showed a higher value of the mean score of the post-test (77.34) rather than the pre-test (75.75). In conclusion, the use of Circle Game can improve students’ speaking skill.

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