The Pioneer Anomaly and a Machian Universe

We discuss astronomical and astrophysical evidence, which we relate to the principle of zero-total energy of the Universe, that imply several relations among the mass M, the radius R and the angular momentum L of a "large" sphere representing a Machian Universe. By calculating the angular speed, we find a peculiar centripetal acceleration for the Universe. This is an ubiquituous property that relates one observer to any observable. It turns out that this is exactly the anomalous acceleration observed on the Pioneers spaceships. We have thus, shown that this anomaly is to be considered a property of the Machian Universe. We discuss several possible arguments against our proposal.Comment: 6 pages including front page. Publishe

General moments of the inverse real Wishart distribution and orthogonal Weingarten functions

Let $W$ be a random positive definite symmetric matrix distributed according to a real Wishart distribution and let $W^{-1}=(W^{ij})_{i,j}$ be its inverse matrix. We compute general moments $\mathbb{E} [W^{k_1 k_2} W^{k_3 k_4} ... W^{k_{2n-1}k_{2n}}]$ explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study for Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse.Comment: 29 pages. The last version differs from the published version, but it includes Appendi

Randomised clinical non-inferiority trial of breathing-based meditation and cognitive processing therapy for symptoms of post-traumatic stress disorder in military veterans

Objective Test whether Sudarshan Kriya Yoga (SKY) was non-inferior to cognitive processing therapy (CPT) for treating symptoms of post-traumatic stress disorder (PTSD) among veterans via a parallel randomised controlled non-inferiority trial. Setting Outpatient Veterans Affairs healthcare centre. Participants 85 veterans (75 men, 61% white, mean age 56.9) with symptoms of PTSD participated between October 2015 and March 2020: 59 participants completed the study. Interventions SKY emphasises breathing routines and was delivered in group format in a 15-hour workshop followed by two 1-hour sessions per week for 5 weeks. CPT is an individual psychotherapy which emphasises shifting cognitive appraisals and was delivered in two 1-hour sessions per week for 6 weeks. Measures The primary outcome measure was the PTSD Checklist-Civilian Version (PCL-C). The secondary measures were the Beck Depression Inventory-II (BDI-II) and Positive and Negative Affect Scale (PANAS). Results Mean PCL-C at baseline was 56.5 (±12.6). Intent-to-treat analyses showed that PCL-C scores were reduced at 6 weeks (end of treatment) relative to baseline (SKY, −5.6, d=0.41, n=41: CPT, −6.8, d=0.58, n=44). The between-treatment difference in change scores was within the non-inferiority margin of 10 points (−1.2, 95% CI −5.7 to 3.3), suggesting SKY was not inferior to CPT. SKY was also non-inferior at 1-month (CPT–SKY: −2.1, 95% CI −6.9 to 2.8) and 1-year (CPT–SKY: −1.8, 95% CI −6.6 to 2.9) assessments. SKY was also non-inferior to CPT on the BDI-II and PANAS at end of treatment and 1 month, but SKY was inferior to CPT on both BDI-II and PANAS at 1 year. Dropout rates were similar (SKY, 27%, CPT, 34%: OR=1.36, 95% CI 0.51 to 3.62, p=0.54). Conclusions SKY may be non-inferior to CPT for treating symptoms of PTSD and merits further consideration as a treatment for PTSD

Exact solutions of the radial Schrodinger equation for some physical potentials

By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and Kratzer potentials in two dimensions. The energy levels of all the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained.Comment: 13 page

Energy and Flux Measurements of Ultra-High Energy Cosmic Rays Observed During the First ANITA Flight

The first flight of the Antarctic Impulsive Transient Antenna (ANITA) experiment recorded 16 radio signals that were emitted by cosmic-ray induced air showers. For 14 of these events, this radiation was reflected from the ice. The dominant contribution to the radiation from the deflection of positrons and electrons in the geomagnetic field, which is beamed in the direction of motion of the air shower. This radiation is reflected from the ice and subsequently detected by the ANITA experiment at a flight altitude of 36km. In this paper, we estimate the energy of the 14 individual events and find that the mean energy of the cosmic-ray sample is 2.9 EeV. By simulating the ANITA flight, we calculate its exposure for ultra-high energy cosmic rays. We estimate for the first time the cosmic-ray flux derived only from radio observations. In addition, we find that the Monte Carlo simulation of the ANITA data set is in agreement with the total number of observed events and with the properties of those events.Comment: Added more explanation of the experimental setup and textual improvement

The Woody Guthrie Centennial Bibliography

This bibliography updates two extensive works designed to include comprehensively all significant works by and about Woody Guthrie. Richard A. Reuss published A Woody Guthrie Bibliography, 1912–1967 in 1968 and Jeffrey N. Gatten\u27s article “Woody Guthrie: A Bibliographic Update, 1968–1986” appeared in 1988. With this current article, researchers need only utilize these three bibliographies to identify all English-language items of relevance related to, or written by, Guthrie