The importance of the Selberg integral

It has been remarked that a fair measure of the impact of Atle Selberg's work is the number of mathematical terms which bear his name. One of these is the Selberg integral, an n-dimensional generalization of the Euler beta integral. We trace its sudden rise to prominence, initiated by a question to Selberg from Enrico Bombieri, more than thirty years after publication. In quick succession the Selberg integral was used to prove an outstanding conjecture in random matrix theory, and cases of the Macdonald conjectures. It further initiated the study of q-analogues, which in turn enriched the Macdonald conjectures. We review these developments and proceed to exhibit the sustained prominence of the Selberg integral, evidenced by its central role in random matrix theory, Calogero-Sutherland quantum many body systems, Knizhnik-Zamolodchikov equations, and multivariable orthogonal polynomial theory.Comment: 43 page

Chiral Random Matrix Theory: Generalizations and Applications

Kieburg M. Chiral Random Matrix Theory: Generalizations and Applications. Bielefeld: Fakultät für Physik; 2015

Physical Activity, Wellness and Health: Challenges, Benefits and Strategies

Regular physical activity (PA) is both a preventive measure and a cure for non-communicable diseases. Moreover, PA improves mental health, quality of life, and well-being. Conversely, physical inactivity and sedentary lifestyles have negative impacts on individuals, families, and society, as evidenced in particular by the spread of the obesity epidemic. PA has proven to be a low-cost alternative for the treatment and prevention of disease. Therefore, interventions to prevent avoidable diseases by increasing the proportion of physically active people are fundamental. The Special Issue “Physical Activity, Wellness and Health: Challenges, Benefits and Strategies” was collected research articles on anthropometric determinants of health and performance, PA and healthy habits, exercise and diet, exercise and body composition, interventions to promote PA for people of all ages, strategies for the implementation of an active life, and the beneficial effects of exercise on metabolic syndrome. A total of 20 articles were published, falling mainly into the following three areas: anthropometry, health, and sport; health benefits of exercise; population studies and strategies for an active life. All of the studies support strategies to promote PA and reduce sedentary behavior among adolescents, adults and the elderly. There is no doubt that regular exercise is beneficial to health, but the general population should be encouraged to engage in more of it

On the generalised Selberg integral of Richards and Zheng

In a recent paper Richards and Zheng compute the determinant of a matrix whose entries are given by beta-type integrals, thereby generalising an earlier result by Dixon and Varchenko. They then use their result to obtain a generalisation of the famous Selberg integral. In this note we point out that the Selberg-generalisation of Richards and Zheng is a special case of an integral over Jack polynomials due to Kadell. We then show how an integral formula for Jack polynomials of Okounkov and Olshanski may be applied to prove Kadell's integral along the lines of Richards and Zheng

Aeronautical engineering: A cumulative index to a continuing bibliography (supplement 274)

This publication is a cumulative index to the abstracts contained in supplements 262 through 273 of Aeronautical Engineering: A Continuing Bibliography. The bibliographic series is compiled through the cooperative efforts of the American Institute of Aeronautics and Astronautics (AIAA) and the National Aeronautics and Space Administration (NASA). Seven indexes are included: subject, personal author, corporate source, foreign technology, contract number, report number, and accession number

Aeronautical engineering: A cumulative index to a continuing bibliography

This bibliography is a cumulative index to the abstracts contained in NASA SP-7037(210) through NASA SP-7037(221) of Aeronautical Engineering: A Continuing Bibliography. NASA SP-7037 and its supplements have been compiled through the cooperative efforts of the American Institute of Aeronautics and Astronautics (AIAA) and the National Aeronautics and Space Administration (NASA). This cumulative index includes subject, personal author, corporate source, foreign technology, contract number, report number, and accession number indexes

A cumulative index to a continuing bibliography on aeronautical engineering

This bibliography is a cumulative index to the abstracts contained in NASA-SP-7037(184) through NASA-SP-7037(195) of Aeronautical Engineering: A Continuing Bibliography. NASA SP-7037 and its supplements have been compiled through the cooperative efforts of the American Institute of Aeronautics and Astronautics (AIAA) and the National Aeronautics and Space Administration (NASA). This cumulative index includes subject, personal author, corporate source, foreign technology, contract, report number, and accession number indexes