Showing papers in "Nagoya Mathematical Journal in 1977"
TL;DR: The main purpose of as discussed by the authors is to classify all prehomogeneous vector spaces when p is irreducible, and to investigate their relative invariants and the regularity of their regularity.
Abstract: Let G be a connected linear algebraic group, and p a rational representation of G on a finite-dimensional vector space V , all defined over the complex number field C . We call such a triplet ( G, p, V ) a prehomogeneous vector space if V has a Zariski-dense G -orbit. The main purpose of this paper is to classify all prehomogeneous vector spaces when p is irreducible, and to investigate their relative invariants and the regularity.
587 citations
TL;DR: In this paper, it has been pointed out that a much more manageable structure is obtained from quantum theory if the time parameter t is chosen imaginary instead of real, and that the Schrodinger equation turns into a generalized heat equation, time ordered correlation functions transform into the moments of a probability measure.
Abstract: It has often been pointed out that a much more manageable structure is obtained from quantum theory if the time parameter t is chosen imaginary instead of real. Under a replacement of t by i·t the Schrodinger equation turns into a generalized heat equation, time ordered correlation functions transform into the moments of a probability measure, etc. More recently this observation has become extremely important for the construction of quantum dynamical models, where criteria were developed by E. Nelson, by K. Osterwalder and R. Schrader and others [8] which would permit the reverse transition to real time after one has constructed an imaginary time (“Euclidean”) model.
61 citations
TL;DR: In this article, it was shown that the Schlafli function can be expressed in terms of hyperlogarithmic functions, namely iterated integrals of forms with logarithm poles in the sense of K. T. Chen.
Abstract: In this note it is shown that Schlafli function can be simply expressed in terms of hyperlogarithmic functions, namely iterated integrals of forms with logarithmic poles in the sense of K. T. Chen (Theorem 1). It is also discussed the relation between Schlafli function and hypergeometric ones of Mellin-Sato type (Theorem 2). From a combinatorial point of view the structure of hyperlogarithmic functions seem very interesting just as the dilog log (so-called Abel-Rogers function) has played a crucial part in Gelfand-Gabriev-Losik’s formula of 1st Pontrjagin classes. See also [3].
45 citations
TL;DR: In this paper, the authors employ the following standard notations: Θs: structure sheaf of S. Ks: the canonical bundle on S. q(S) = dimc HKS, Θ8), the irregularity.
Abstract: Let S be a compact complex protective and smooth variety of dimc2, shortly a surface. We employ the following standard notations: Θs: structure sheaf of S. Ks: the canonical bundle on S. pg(S) = dimc H\S, Ks), geometric genus. q(S) = dimc HKS,Θ8), the irregularity. cl(S) and c2(S), the Chern numbers of S. £(S) = Euler class of Θs = (pg + 1 q)(S) = -^(c\ + c2)(S) For any divisor D on S we let \D\ be the linear system corresponding to it, and if p19 , pm e S we let \D — p1 — p2 — — pm\ be the subsystem of divisors through pl9 ,pm. If D1 and D2 are two divisors, (D19D2) denotes their intersection number, and D1 — D2 means that the divisors are linearly equivalent. We shall write the group action on Pic (S), additively, so, if for instance C is a divisor and F a line bundle such that [C] = F we simply write C 2F. Finally, if F e Pic (S), we put h(F) = dimc H (S, F).
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TL;DR: In this article, a condition under which a sequence of elements in a commutative noetherian local ring A form an A -sequence is given. But it is not known whether the condition holds for all elements in the local ring.
Abstract: In this note we exhibit a condition under which a sequence of elements a 1 , …, a n in a commutative noetherian local ring A form an A -sequence, and derive a number of corollaries.
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TL;DR: In this paper, a unitary representation of the multi-parameter Brownian motion in terms of the multiparameter white noise has been proposed, where the Radon transform is adapted to the group SL(n + 1,R) to observe probabilistic structures of the motion.
Abstract: The multi-parameter Brownian motion introduced by P. Levy is not only a basic random field but also gives us interesting fine probabilistic structures as well as important properties from the view point of analysis. We shall be interested in investigation of such structures and properties by expressing the Brownian motion in terms of the multiparameter white noise. The expression naturally requires basic tools from analysis, in particular the Radon transform. While there arises the special linear group SL(n + 1,R), to which the Radon transform is adapted, and the group plays an important role in observing probabilistic structures of the Brownian motion. To be more interested, we can give some deep insight to unitary representations of SL(n + 1, R) through our discussion. Before we come to our topic, we shall have a quick review of the one dimensional case, emphasizing the following three points: 1) The ordinary Brownian motion B(t), teR, has an integral representation
TL;DR: The existence and uniqueness of solutions of the Cauchy problem have been established by B. L. Rozovskii [8] as mentioned in this paper, who considered the stochastic differential equation, with initial condition, where B t, t ≧ 0, is a one-dimensional Brownian motion and L x is a second order uniformly elliptic partial differential operator satisfying some additional conditions that will be described in §2.
Abstract: Let us consider the stochastic differential equation, with initial condition, where B t , t ≧ 0, is a one-dimensional Brownian motion, and L x is a second order uniformly elliptic partial differential operator satisfying some additional conditions that will be described in §2. The existence and the uniqueness of solutions of the Cauchy problem have been established by B. L. Rozovskii [8].
TL;DR: In this paper, the suite X designera un groupe abelien localement compact et separe, and ξ designera la mesure de Haar sur X. Pour simplifier la discussion, on supposera toujours que X est a base denombrable.
Abstract: Dans toute la suite X designera un groupe abelien localement compact et separe, et ξ designera la mesure de Haar sur X. Pour simplifier la discussion, on supposera toujours que X est a base denombrable.
TL;DR: In this paper, a weaker version of the Cohen structure theorem for complete local rings holds for any (not necessarily complete) local ring, and a quasi-coefficient field is used to derive a local ring.
Abstract: In this note we will make a few observations on the structure of fields and local rings. The main point is to show that a weaker version of Cohen structure theorem for complete local rings holds for any (not necessarily complete) local ring. The consideration of non-complete case makes the meaning of Cohen’s theorem itself clearer. Moreover, quasi-coefficient fields (or rings) are handy when we consider derivations of a local ring.
TL;DR: In this article, the authors studied the topological conjugacy problem of a diίfeomorphism on a neighbourhood of a hyperbolic set, and proved that for any set there is an arbitrarily slight extension to which a subshift of finite type is semi-conjugate.
Abstract: Hartman proved that a diίfeomorphism is topologically conjugate to a linear map on a neighbourhood of a hyperbolic fixed point ([3]). In this paper we study the topological conjugacy problem of a diίfeomorphism on a neighbourhood of a hyperbolic set, and prove that for any hyperbolic set there is an arbitrarily slight extension to which a subshift of finite type is semi-conjugate. In the sequel, M denotes a compact C°° manifold with some Riemannian metric | |.
TL;DR: In this paper, the authors consider a Riemann surface with a parabolic end and show that a density P = P(z)dxdy (z = x + iy) is a 2-form on with nonnegative locally Holder continuous coefficients.
Abstract: Consider a parabolic end Ω of a Riemann surface in the sence of Heins [2] (cf. Nakai [3]). A density P = P(z)dxdy (z = x + iy) is a 2-form on with nonnegative locally Holder continuous coefficients P(z). A density P is said to be finite if the integral
TL;DR: In this article, the authors propose a method to solve the problem of "uniformity" and "uncertainty" in the context of health care, and propose a solution.
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TL;DR: In this article, the authors investigated the hypoellipticity for a class of degenerate equations of the second order with complex coefficients as a direct extension of the results obtained in [8].
Abstract: In this paper, we shall investigate the hypoellipticity for a class of degenerate equations of the second order with complex coefficients as a direct extension of the results obtained in [8]. As is well known, the satisfactory general results about hypoellipticity of real operators of the second order have been obtained in [3] and [9], where the assumption that the operators are real plays a crucial role and our aim of this paper is to study the operators with complex coefficients. Our method may be considered as a generalization of the usual variational method replacing the Garding inequality by the estimate (2.15), (cf. [3], [5]). Let R be 2V-dimensional Euclidean space regarded as a direct product of three Euclidean spaces ΛJ, Λj} and R] (m + n + 1 = N) and generic point of R will be denoted by (a?, y, t) = (xl9 , xm, ylf -, yn, t). We shall mainly consider a partial differential equation of the form