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Volume 57 (2005)
- Issue 4 Pages 935-
- Issue 3 Pages 619-
- Issue 2 Pages 309-
- Issue 1 Pages 1-
Predecessor
- Proceedings of the Physico-Mathematical Society of Japan. 3rd Series
- Proceedings of the Tokyo Mathematico-Physical Society. 2nd Series
- Tokyo Sugaku-Butsurigakukwai Kiji-Gaiyo
- Tokyo Sugaku-Butsurigakkwai Hokoku
- Tokyo Sugaku-Butsurigaku Kwai Kiji
- Tokyo Sugaku-Butsurigaku Kwai Kiji
- Tokyo Sugaku Kaisya Zasshi
Volume 57, Issue 4
Displaying 1-13 of 13 articles from this issue
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Benoît AUDOUBERT, Tu Chanh NGUYEN, Mutsuo OKA2005 Volume 57 Issue 4 Pages 935-957
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSLet p and q be integers such that p > q ≥q 2 and q divides p. Let \varphi (q) be the Euler number of q. We exhibit a Zariski \varphi(q)-ple, distinguished by the Alexander polynomial, whose curves are tame torus curves of type (p, q), with q smooth irreducible components of degree p, and one single singular point topologically equivalent to the Brieskorn-Pham singularity\ \ v^q+u^{qp^2}=0.View full abstractDownload PDF (298K) -
Toshihiko MASUDA2005 Volume 57 Issue 4 Pages 959-1001
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSPopa proved that strongly amenable subfactors of type III_1 with the same type II and type III principal graphs are completely classified by their standard invariants. In this paper, we present a different proof of this classification theorem based on Connes and Haagerup's arguments on the uniqueness of the injective factor of type III_1.View full abstractDownload PDF (427K) -
Yoshiaki FUKUMA2005 Volume 57 Issue 4 Pages 1003-1044
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSLet (X, L) be a quasi-polarized variety defined over the complex number field. Then there are several invariants of (X, L), for example, the sectional genus and the \vD-genus. In this paper we introduce the i-th \vD-genus \vDi(X, L) for every integer i with 0≤ i≤ n=\dim X. This is a generalization of the \vD-genus. Furthermore we study some properties of \vDi(X, L) and we will propose some problems.View full abstractDownload PDF (324K) -
Hidetoshi TAHARA2005 Volume 57 Issue 4 Pages 1045-1065
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSLet us consider the following nonlinear singular partial differential equation (t ∂/∂ t)^m u =F ( t, x, {(t ∂/∂ t)^j (∂/∂ x)α u }j+α ≤ m, j<m ) in the complex domain with two independent variables (t, x) ∈ \BC^2. When the equation is of totally characteristic type, this equation was solved in \cite{ct2} and \cite{resont} under certain Poincaré condition. In this paper, the author will prove the uniqueness of the solution under the assumption that u(t, x) is holomorphic in {(t, x) ∈ \BC^2 ; 0 < |t|<r, | \arg t| < θ, |x|<R} for some r>0, θ >0, R>0 and that it satisfies u(t, x) =O(|t|^a ) (as t \longrightarrow 0) uniformly in x for some a>0. The result is applied to the problem of removable singularities of the solution.View full abstractDownload PDF (249K) -
Yasunori OKABE, Masaya MATSUURA2005 Volume 57 Issue 4 Pages 1067-1076
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSIn this paper, we shall develop the linear causal analysis for the system consisting of two flows in a real inner product space and give an algorithm for calculating the non-linear filter for a discrete stochastic system which is given by two discrete time stochastic processes, to be called a signal process and an observation process, based upon the theory of KM_2O-Langevin equations.View full abstractDownload PDF (199K) -
Piotr DOWBOR2005 Volume 57 Issue 4 Pages 1077-1127
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSFor a given finite dimensional k-algebra A which admits a presentation in the form R/G, where G is an infinite group of k-linear automorphisms of a locally bounded k-category R, a class of modules lying out of the image of the“push-down”functor associated with the Galois covering R→ R/G, is studied. Namely, the problem of existence and construction of the so called non-regularly orbicular indecomposable R/G-modules is discussed. For a G-atom B (with a stabilizer G_B), whose endomorphism algebra has a suitable structure, a representation embedding \varPhiB(f, s)|:\isl(s)(kG_B)→ \mod(R/G), which yields large families of non-regularly orbicular indecomposable R/G-modules, is constructed (Theorem 2.2). An important role in consideration is played by a result interpreting some class of R/G-modules in terms of Cohen-Macaulay modules over certain skew grup algebra (Theorem 3.3). Also, Theorems 4.5 and 5.4, adapting the generalized tensor product construction and Galois covering scheme, respectively, for Cohen-Macaulay modules context, are proved and intensively used.View full abstractDownload PDF (456K) -
Xuan Thinh DUONG, Lixin YAN2005 Volume 57 Issue 4 Pages 1129-1152
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSLet {\scrX} be a space of homogeneous type. Assume that L has a bounded holomorphic functional calculus on L^2(\varOmega) and L generates a semigroup with suitable upper bounds on its heat kernels where \varOmega is a measurable subset of {\scrX}. For appropriate bounded holomorphic functions b, we can define the operators b(L) on L^p({\varOmega}), 1≤ p≤ ∞. We establish conditions on positive weight functions u, v such that for each p, 1<p<∞, there exists a constant c_p such that ∈t_{\varOmega} |b(L)f(x)|^p u(x)dμ(x) ≤ c_p //b//^p∞ ∈t_{\varOmega} |f(x)|^p v(x)dμ(x) for all f∈ L^p(vdμ). \\ ∈dent
Applications include two-weight L^p inequalities for Schrödinger operators with non-negative potentials on \bm{R}^n and divergence form operators on irregular domains of \bm{R}^n.View full abstractDownload PDF (302K) -
Shizuo KAJI2005 Volume 57 Issue 4 Pages 1153-1165
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSIn \cite{BG}, it is proved that the Whitehead length of a space Z is less than or equal to the nilpotency of \varOmega Z. As for rational spaces, those two invariants are equal. We show this for a 1-connected rational space Z by giving a way to calculate those invariants from a minimal model for Z. This also gives a way to calculate the nilpotency of an homotopy associative rational H-space.View full abstractDownload PDF (212K) -
Dedicated to Professor Isao Wakabayashi with great respectShigeru KANEMITSU, Yoshio TANIGAWA, Masami YOSHIMOTO2005 Volume 57 Issue 4 Pages 1167-1177
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSIn this note we are going to generalize Prudnikov's method of using a double integral to deduce relations between the Riemann zeta-values, so as to prove intriguing relations between double zeta-values of depth 2. Prior to this, we shall deduce the most well-known relation that expresses the sum ∑_{j=1}m-2 ξ(j+1)ξ(m-j) in terms of ξ_2(1, m).View full abstractDownload PDF (176K) -
Norio KONNO2005 Volume 57 Issue 4 Pages 1179-1195
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSIn this paper we consider the one-dimensional quantum random walk X^{\varphi} _n at time n starting from initial qubit state \varphi determined by 2 × 2 unitary matrix U. We give a combinatorial expression for the characteristic function of X^{\varphi}_n. The expression clarifies the dependence of it on components of unitary matrix U and initial qubit state \varphi. As a consequence, we present a new type of limit theorems for the quantum random walk. In contrast with the de Moivre-Laplace limit theorem, our symmetric case implies that X^{\varphi} _n/n converges weakly to a limit Z^{\varphi} as n → ∞, where Z^{\varphi} has a density 1/π (1-x^2) √{1-2x^2} for x ∈ (- 1/√{2}, 1/√{2}). Moreover we discuss some known simulation results based on our limit theorems.View full abstractDownload PDF (309K) -
Nobushige KUROKAWA, Masato WAKAYAMA2005 Volume 57 Issue 4 Pages 1197-1216
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSWe provide an extended interpretation of the zeta regularized product in \cite{D}. This allows us to get regularized product expressions of Holder's double sine function and its companion, i.e. the double and triple trigonometric functions. The expressions may reasonably explain the ladder structure among these multiple trigonometric functions. We also introduce the notion of finite ladders of functions which helps us understand the meaning behind these regularizations.View full abstractDownload PDF (250K) -
Teruyuki YORIOKA2005 Volume 57 Issue 4 Pages 1217-1228
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSWe show that (1) sstick plus \cov\cM>\aleph_1 implies the existence of a destructible gap and (2) \clubsuit plus \cof\cM=\aleph_1 implies the existence of a destructible gap.View full abstractDownload PDF (230K) -
Koichiro IKEDA2005 Volume 57 Issue 4 Pages 1229-1234
Published: 2005
Released on J-STAGE: December 25, 2008
JOURNAL FREE ACCESSWe show that any saturated generic graph satisfying some property (*) is strictly stable or ω-stable. As a corollary, we obtain that any saturated generic pseudoplane is strictly stable or ω-stable.View full abstractDownload PDF (168K)
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