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European Mathematical Society Publishing House
2024-03-29 13:10:34
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=30&iss=1&update_since=2024-03-29
Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
30
1994
1
On Non-real Eigenvalues of Schrödinger Operators in a Weighted Hilbert Space
Masaharu
Arai
Nihon University, TOKYO, JAPAN
Osanobu
Yamada
Kyoto University, KYOTO, JAPAN
Partial differential equations
General
1
14
10.2977/prims/1195166274
http://www.ems-ph.org/doi/10.2977/prims/1195166274
Quantized Enveloping Algebras Associated with Simple Lie Superalgebras and Their Universal R-matrices
Hiroyuki
Yamane
Osaka University Graduate School of Science, OSAKA, JAPAN
Nonassociative rings and algebras
General
15
87
10.2977/prims/1195166275
http://www.ems-ph.org/doi/10.2977/prims/1195166275
Generalised Mean Averaging Interpolation by Discrete Cubic Splines
Manjulata
Shrivastava
R.D. University, JABALPUR, INDIA
The aim of this work is to introduce for a discrete function, certain discrete integrals which may reduce in particular to usual Riemann Stieltjes integrals. We name them as Discrete Stieltjes integrals. The existence and convergence of a discrete cubic interpolatory spline whose discrete Stieltjes integrals between consecutive meshpoints match with the corresponding integrals of a given periodic discrete function, are studied.
Approximations and expansions
General
89
95
10.2977/prims/1195166276
http://www.ems-ph.org/doi/10.2977/prims/1195166276
The Singularities of Type Ak of Holonomic Systems
Nguyen
Dai
Institute of Mathematics, HANOI, VIETNAM
Partial differential equations
General
97
109
10.2977/prims/1195166277
http://www.ems-ph.org/doi/10.2977/prims/1195166277
Quantized Radiation States from the Infinite Dicke Model
Reinhard
Honegger
Universität Tübingen, TÜBINGEN, GERMANY
Alfred
Rieckers
Universität Tübingen, TÜBINGEN, GERMANY
By interpreting infinitely many two-level atoms as a mean field quantum lattice system in a recent paper the time evolution of the Dicke Maser model has been elaborated in terms of operator algebraic methods. Using these results, here the emitted radiation of the infinite Dicke model is investigated. It is shown how the collective behaviour of the atoms influences the quantized radiation, which for large times becomes classically coherent (in the sense of Glauber). The field modes which are (approximately) resonant with the level-splitting energy of the atoms are found to be the essential part of the generated coherent light, and thereby determine its macroscopic nature. Furthermore, the destruction and revival of coherence, the mean number of the emitted photons during the time evolution, as well as their spatial distribution are discussed.
Functional analysis
General
111
138
10.2977/prims/1195166278
http://www.ems-ph.org/doi/10.2977/prims/1195166278
Existence of the Greek Letter Elements in the Stable Homotopy Groups of E(n)*-Localized Spheres
Katsumi
Shimomura
Kochi University, KOCHI, JAPAN
Masaaki
Yokotani
Okayama University, OKAYAMA, JAPAN
Let E2*.*(X) denote the E2-term of the Adams-Novikov spectral sequence converging to the homotopy groups of X. We can define the Greek letter elements in E2*.*(LnS0) in the same way as those in E2*.*(S0). We show that these of E2*.*(LnS0) are permanent cycles, though we know little for E2*.*(S0).
Algebraic topology
General
139
150
10.2977/prims/1195166279
http://www.ems-ph.org/doi/10.2977/prims/1195166279
The E7 Commuting Squares Produce D10 as Principal Graph
David
Evans
University of Wales Cardiff, CARDIFF, UNITED KINGDOM
Yasuyuki
Kawahigashi
University of Tokyo, TOKYO, JAPAN
We prove that the (two) connections, or commuting squares, on the Coxeter-Dynkin diagram E7 produce a subfactor with principal graph D10. This was conjectured by J.-B. Zuber in connection with modular invariants in conformal field theory, and solve the last case of computing the flat parts of the connections on Coxeter-Dynkin diagrams with index less than 4.
Functional analysis
General
151
166
10.2977/prims/1195166280
http://www.ems-ph.org/doi/10.2977/prims/1195166280