- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 01:30:21
6
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=29&iss=4&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
29
1993
4
General Integral Representation of the Holomorphic Functions on the Analytic Subvariety
Shu Jin
Chen
Xiamen University, XIAMEN, FUJIAN, CHINA
Several complex variables and analytic spaces
General
511
533
10.2977/prims/1195166741
http://www.ems-ph.org/doi/10.2977/prims/1195166741
On a Linear Structure of the Quotient Variety by a Finite Reflexion Group
Kyoji
Saito
Kyoto University, KYOTO, JAPAN
Algebraic geometry
General
535
579
10.2977/prims/1195166742
http://www.ems-ph.org/doi/10.2977/prims/1195166742
An r-Matrix Approach to Nonstandard Classes of Integrable Equations
Boris
Konopelchenko
Russian Academy of Sciences, NOVOSIBIRSK, RUSSIAN FEDERATION
Walter
Oevel
Loughborough University, LOUGHBOROUGH, UNITED KINGDOM
Three different decompositions of the algebra of pseudo-differential operators and the corresponding r-matrices are considered. Three associated classes of nonlinear integrable equations in 1 +1 and 2 + 1 dimensions are discussed within the framework of generalized Lax equations and Sato's approach. The 2 +1-dimensional hierarchies are associated with the Kadomtsev-Petviashvili (KP) equation, the modified KP equation and a Dym equation, respectively. Reductions of the general hierarchies lead to other known integrable 2 + 1-dimensional equations as well as to a variety of integrable equations in 1 +1 dimensions. It is shown, how the multi-Hamiltonian structure of the 1 + 1-dimensional equations can be obtained from the underlying r-matrices. Further, intimate relations between the equations associated with the three different r-matrices are revealed. The three classes are related by Darboux theorems originating from gauge transformations and reciprocal links of the Lax operators. These connections are discussed on a general level, leading to a unified picture on (reciprocal) Backlund and auto-Backlund transformations for large classes of integrable equations covered by the KP, the modified KP, and the Dym hierarchies.
Global analysis, analysis on manifolds
General
581
666
10.2977/prims/1195166743
http://www.ems-ph.org/doi/10.2977/prims/1195166743
Pairings in Categories
Nobuyuki
Oda
Fukuoka University, FUKUOKA, JAPAN
We study a categorical generalization of some of the basic results of the homotopy theory which have been obtained in the category of topological spaces with base point. They are some of the results of Gottlieb, Hilton, Hoo, Lim, Varadarajan, Woo and Kim and others. To carry out categorical approach, we define pseudo-product, pseudo-coproduct and homotopy relation in general categories. These concepts enable us to define pairings and copairings in categories. Some of the classical results mentioned above are generalized to the categories with product, coproduct and zero object.
Category theory; homological algebra
General
667
680
10.2977/prims/1195166744
http://www.ems-ph.org/doi/10.2977/prims/1195166744
Théorème de Division et Stabilité de Systèmes Holonomes
Nguyen
Dai
Institute of Mathematics, HANOI, VIETNAM
Partial differential equations
General
681
707
10.2977/prims/1195166745
http://www.ems-ph.org/doi/10.2977/prims/1195166745
The Strong Bernstein-Gelfand-Gelfand Resolution for Generalized Kac-Moody Algebras, I — The Existence of the Resolution
Satoshi
Naito
Shizuoka University, SHIZUOKA, JAPAN
Nonassociative rings and algebras
General
709
730
10.2977/prims/1195166746
http://www.ems-ph.org/doi/10.2977/prims/1195166746