bluuebunny/crossref_metadata_2025_split huggingface dataset:
A decomposition of additive functionals of finite energy
Authors: Fukushima Masatoshi 
Published: July 2016

The celebrated Ito formula for the n-dimensional Brownian motion Xt and for u ∈ C2(Rn) runs as follows:(0.1) In § 6 of this paper we extend this to the case where u is any element of the Sobolev space H1R(n) and accordingly Δu is a tempered distribution which is not even a signed measure in general. As a consequence the second term of the right hand side of (0.1) may not be of bounded variation in t.
Spectral properties of first order ordinary differential operators with short range potentials
Authors: Itatsu S. , Kaneta H. 
Published: July 2016

The purpose of the present paper is to give a complete proof of the theorem which will be used in a paper of the second author [4].We will discuss certain spectral properties of selfadjoint ordinary differential operators of the form iA(d/dx) + V acting in L2(R)n = Σ ⊕ L2(R)n, where A is a real diagonal constant matrix and V an Hermitian matrix valued function on R which satisfies some conditions to be stated in the sequel.
On a criterion for the class number of a quadratic number field to be one
Authors: Kutsuna Masakazu 
Published: July 2016

G. Rabinowitsch [3] generalized the concept of the Euclidean algorithm and proved a theorem on a criterion in order that the class number of an imaginary quadratic number field is equal to one:Theorem.It is necessary and sufficient for the class number of an imaginary quadratic number fieldD= 1 — 4m, m> 0,to be one that x2—x+m is prime for any integer x such that1 ≤x≤m— 2.
Duality between D(X) and with its application to picard sheaves
Authors: Mukai Shigeru 
Published: July 2016

As is well known, for a real vector space V, the Fourier transformation
gives an isometry between L2(V) and L2(Vv), where Vv is the dual vector space of V and < , >: V×Vv → R is the canonical pairing.
A generalization of a theorem of marotto
Authors: Shiraiwa Kenichi , Kurata Masahiro 
Published: July 2016

In 1975, Li and Yorke [3] found the following fact. Let f: I→ I be a continuous map of the compact interval I of the real line R into itself. If f has a periodic point of minimal period three, then f exhibits chaotic behavior. The above result is generalized by F.R. Marotto [4] in 1978 for the multi-dimensional case as follows. Let f: Rn → Rn be a differentiate map of the n-dimensional Euclidean space Rn (n ≧ 1) into itself. If f has a snap-back repeller, then f exhibits chaotic behavior.In this paper, we give a generalization of the above theorem of Marotto. Our theorem can also be regarded as a generalization of the Smale’s results on the transversal homoclinic point of a diffeomorphism.
Tensor products of positive definite quadratic forms, V
Authors: Kitaoka Yoshiyuki 
Published: July 2016

Our aim is to proveTHEOREM. Let L be a positive lattice of E-type such that [L: L̃] < ∞ and L̃ is indecomposable.
(i)If L ≅ L1 ⊗ L2for positive lattices L1, L2, then L1, L2 are of E-type and [L1: L̃1], [L2:L̃2] < ∞ and L̃1, L̃2 are indecomposable.(ii)If L is indecomposable with respect to tensor product, then for each indecomposable positive lattice X we have(1)L ⊗ X ≅ L ⊗ Y implies X ≅ Y for a positive lattice Y,(2)If X= ⊗t L ⊗ X′ where X′ is not divided by L, then O(L ⊗ X) is generated by O(L), O(X′) and interchanges of L’s, and(3)L ⊗ X is indecomposable.
Définition des pseudogroupes infinitésimaux de Lie intransitifs—Théorème fondamental de réalisation en dimension deux
Authors: Quê Ngô van , Tho Vo van 
Published: July 2016

Soit G un groupe de Lie opérant de manière localement effective sur une variété différentiable M. Pour tout sous-groupe à un paramètre {gt, t ∈ R} de G, on a le champ de vecteurs associé X dit de Killing sur M:Le faisceau correspondant de tous les champs de vecteurs de Killing du groupe de transformations G sera noté par θ; il est démontré [7] qu’il existe un ouvert ^ partout dense dans M, dit de régularité tel que:
Julia directions of entire functions of smooth growth
Authors: Yoshida H. 
Published: July 2016

Let f(z) be entire i.e. analytic in the finite whole plane Z. The order of f(z) is defined aswhere A ray χ(θ) = {z = r·eiθ : 0 < r < + ∞} is called a Julia direction of f(z) if, in any open sector containing the ray, f(z) takes all values of Z, with at most one finite exceptional value, infinitely often.
On the Lp bound for degenerate elliptic operators with two variables in the ill posed problem
Authors: Hasesaka Nobuo , Hayasida Kazuya 
Published: July 2016

Let Ω be an open set in the upper half plane {y > 0}, whose boundary is denoted by ∂Ω. Let ∂Ω contain an open segment Γ lying on the x-axis.We consider the following system of first order degenerating on y = 0:where kj, μj are real constants and bjk are in L∞(Ω), further kj are non-negative integers.
Topological stability of solenoidal automorphisms
Authors: Aoki Nobuo 
Published: July 2016

In [10] A. Morimoto proved that every topologically stable homeomorphism of a compact manifold M has the pseudo-orbit tracing property in the case dim (M) ≥ 2. Further, in studying relation between the topological stability and other stability of diffeomorphisms, he showed the followingTheorem A. Let Rr be the r-dimensional vector group and φ be a group automorphism of Rr.
On the Gorensteinness of Rees and form rings of almost complete intersections
Authors: Goto Shiro , Shimoda Yasuhiro 
Published: July 2016

Let A be a Noetherian local ring and p a prime ideal in A. Letand call them, respectively, the Rees ring and the form ring of p. The purpose of this paper is to clarify, provided p is an almost complete intersection in A (cf. (2.1) for definition), when the rings R(p) and G(p) are Gorenstein.
On the topological structure of affinely connected manifolds
Authors: Higa Tatsuo 
Published: July 2016

The purpose of the present paper is to investigate the relationship between the topological structure and differential geometric objects for affinely connected manifolds.Let M be a compact, connected and oriented Riemannian manifold, Pr(M) the vector space of all parallel r-forms on M and br(M) the r-th Betti number of M.
Conformal invariance of white noise
Authors: Hida Takeyuki , Lee Ke-Seung , Lee Sheu-San 
Published: July 2016

The remarkable link between the structure of the white noise and that of the infinite dimensional rotation group has been exemplified by various approaches in probability theory and harmonic analysis. Such a link naturally becomes more intricate as the dimension of the time-parameter space of the white noise increases. One of the powerful method to illustrate this situation is to observe the structure of certain subgroups of the infinite dimensional rotation group that come from the diffeomorphisms of the time-parameter space, that is the time change. Indeed, those subgroups would shed light on the probabilistic meanings hidden behind the usual formal observations. Moreover, the subgroups often describe the way of dependency for Gaussian random fields formed from the white noise as the time-parameter runs over the basic parameter space.The main purpose of this note is to introduce finite dimensional subgroups of the infinite dimensional rotation group that have important probabilistic meanings and to discuss their roles in probability theory. In particular, we shall see that the conformal invariance of white noise can be described in terms of the conformal group which is a finite dimensional Lie subgroup of the infinite dimensional rotation group.
Some examples of stochastically stable homeomorphisms
Authors: Sasaki Takeshi 
Published: July 2016

Recently A. Morimoto [1] has proved the Takens conjecture in the tolerance stability by using the notion of pseudo-orbits and the stochastic stability. He also characterized group automorphisms of a torus to be stochastically stable and clarified the relations to other stabilities.In this paper we shall give the condition for spherical or projective linear transformations to be stochastically stable.
An example on canonical isomorphism
Authors: Nakai Mitsuru 
Published: July 2016

A nonnegative locally Hölder continuous second order differential P = P(z)dxdy (z = x + iy) on a Riemann surface R is referred to as a density on R. A density P is said to be finite if P is integrable over R, i.e.(1) ∫ R P(z)dxdy < ∞.
Some properties of ordinal diagrams
Authors: Yasugi Mariko 
Published: July 2016

The theory of ordinal diagrams has been a most powerful means for consistency proofs of some systems of second order arithmetic. The last existing result in this line is the consistency proofs of the systems with the provably -comprehension axiom and the -comprehension axiom respectively (cf. [6]). In order to pursue the consistency problem further, one needs investigate the theory of ordinal diagrams in two directions—refinement and strengthening of the theory.For this purpose we have begun to search for some properties concerning ordinal diagrams and some variations of the theory of ordinal diagrams. The reader is requested to refer to §26 of [7] for the basic knowledge of ordinal diagrams.
Analytic discs in symplectic spaces
Authors: Baracco Luca , Zampieri Giuseppe 
Published: July 2016

We develop some symplectic techniques to control the behavior under symplectic transformation of analytic discs A of X = ℂn tangent to a real generic submanifold R and contained in a wedge with edge R.We show that if A* is a lift of A to T* X and if χ is a symplectic transformation between neighborhoods of po and qo, then A is orthogonal to po if and only if Ã:= πχA* is orthogonal to qo. Also we give the (real) canonical form of the couples of hypersurfaces of ℝ2n ⋍ ℂn whose conormal bundles have clean intersection. This generalizes [10] to general dimension of intersection.Combining this result with the quantized action on sheaves of the “tuboidal” symplectic transformation, we show the following: If R, S are submanifolds of X with R ⊂ S and then the conditions can be characterized as opposite inclusions for the couple of closed half-spaces with conormal bundles In §3 we give some partial applications of the above result to the analytic hypoellipticity of CR hyperfunctions on higher codimensional manifolds by the aid of discs (cf. [2], [3] as for the case of hypersurfaces).
The Calogero-Moser partition for G(m, d, n)
Authors: Bellamy Gwyn 
Published: July 2016

AbstractWe show that it is possible to deduce the Calogero-Moser partition of the irreducible representations of the complex reflection groups G(m,d, n) from the corresponding partition for G(m,1,n). This confirms, in the case W = G(m,d,n), a conjecture of Gordon and Martino relating the Calogero-Moser partition to Rouquier families for the corresponding cyclotomic Hecke algebra.
Alternative polarizations of Borel fixed ideals
Authors: Yanagawa Kohji 
Published: July 2016

AbstractFor a monomial idealIof a polynomial ringS, apolarizationofIis a square-free monomial idealJof a larger polynomial ringsuch thatS/Iis a quotient of/Jby a (linear) regular sequence. We show that a Borel fixed ideal admits a nonstandard polarization. For example, while the usual polarization sendsours sends it tox1y2y3Using this idea, we recover/refine the results onsquare-free operationin the shifting theory of simplicial complexes. The present paper generalizes a result of Nagel and Reiner, although our approach is very different.
Functions with finite Dirichlet sum of orderpand quasi-monomorphisms of infinite graphs
Authors: Hattori Tae , Kasue Atsushi 
Published: July 2016

AbstractIn this paper, we study some potential theoretic properties of connected infinite networks and then investigate the space ofp-Dirichlet finite functions on connected infinite graphs, via quasi-monomorphisms. A main result shows that if a connected infinite graph of bounded degrees possesses a quasi-monomorphism into the hyperbolic space form of dimensionnand it is notp-parabolic forp > n -1, then it admits a lot ofp-harmonic functions with finite Dirichlet sum of orderp.
Bounds of modes and unimodal processes with independent increments
Authors: Sato Ken-Iti 
Published: July 2016

A probability measure μ is called unimodal if there is a point α such that the distribution function of μ is convex on (− ∞, α) and concave on (α, ∞). The point α is called a mode of μ. When μ is unimodal, the mode of μ is not always unique; the set of modes is a one point set or a closed interval. If μ is a unimodal distribution with finite variance, Johnson and Rogers [6] give a boundwhere m and v are mean and variance of μ (see also [11]).
On Conditions of Differentiability of Locally Compact Groups
Authors: Kuranishi Masatake 
Published: July 2016

A formulation of the differentiability of the product function of a locally compact group at the identity may be given in the following way: In a sufficiently small euclidean neighborhood of the identity product satisfies the condition:
where M(λ) is a function such that M(λ) → 0 as λ → 0, From this we can deduce easily.
On the Existence of the Resolvent Kernel for Elliptic Differential Operator in a Compact Riemann Space
Authors: Yosida Kôsaku 
Published: July 2016

We consider the differential operator
in an n-dimensional (n≧2), orientiable, compact Riemann space R with the metric ds2 = gij(x)dxidxj. Here bij(x) is a contravariant tensor such that the quadratic form and ai(x) changes, by the coordininates transformation x → x̅, as follows:
.
Studies on Riemannian Homogeneous Spaces
Authors: Nomizu Katsumi 
Published: July 2016

The purpose of the present paper is to give the details of the results announced in the C. R. notes [7], [8] and [9].In I which corresponds to [7], we shall develop a method for the study of affine transformations of a Riemannian manifold and prove Lemma 5 which is fundamental for the results in I and II. This part of our work has been motivated by a result of K. Yano [12] stating that the largest connected group of affine transformations of a compact orientable Riemannian manifold consists of isometries. Our method will have further applications to some other problems concerning or involving the connected group of isometries of a Riemannian manifold (for example, [10]).
On the Dimension of Modules and Algebras (III): Global Dimension
Authors: Auslander Maurice 
Published: July 2016

Let Λ be a ring with unit. If A is a left Λ-module, the dimension of A (notation: 1.dimΛA) is defined to be the least integer n for which there exists an exact sequence0 → Xn → … → X0 → A → 0where the left Λ-modules X0, …, Xn are projective. If no such sequence exists for any n, then 1. dimAA = ∞. The left global dimension of Λ is1. gl. dim Λ = sup 1. dimAAwhere A ranges over all left Λ-modules, The condition 1. dimA A < n is equivalent with (A, C) = 0 for all left Λ-modules C. The condition 1.gl. dim Λ < n is equivalent with = 0. Similar definitions and theorems hold for right Λ-modules.
On Exceptional Values of a Meromorphic Function
Authors: Ohtsuka Makoto 
Published: July 2016

M. Brelot [1] has shown that if u(z) is subharmonic in an open set D in the z-plane with boundary C and is bounded from above in a neighborhood of a boundary point z0, which is contained in a set E ⊂ C of inner harmonic measure zero with respect to D, and such that z0 is a regular point for Dirichlet problem in D, then(1) .
Un raffinement du théorème de Golod-Safarevic
Authors: Maire Christian 
Published: July 2016

Abstract.Soientkun corps de nombres,pun nombre premier, etLlap-tour de Hilbert dek; G= Gal(L/k). Dans ce papier, on se propose de donner un raffinement du critère de Golod-Safarevic appliqué àG, construit en filtrant le groupe de nombres Λ = {x∈k×/(x) =}. Ce raffinement permettra alors de montrer qu’un corps quadratique réel dont le groupe des classes contient un sous-groupe de la forme (4, 4, 4, 4), possède une 2-tour de Hilbert infinie.
On the classification theorem for CR mappings
Authors: Hayashimoto Atsushi 
Published: July 2016

Abstract.Let f: M → M′ be a real analytic CR mapping between hyper-surfaces with f(p) = q, where p ∈ M and q ∈ M′. In this paper, the relation between the type at p and the one at q is considered. As a corollary of the type condition theorem (Theorem 1.1), a classification theorem, which states that under certain type condition, any real analytic CR mapping as above is constant, is proved.
Fano 4-Folds with scroll structure
Authors: Langer Adrian 
Published: July 2016

Abstract.We classify smooth Fano 4-folds with second betti number b2 = 2, possesing adjunction theoretic scroll structure. These manifolds occur to be projectivisations of coherent sheaves over Fano manifolds. The paper deals mainly with projectivisations of non-locally free rank 2 Fano sheaves over Fano 3-folds with b2 = 1, using Mori theory. By the way, we classify nef and big rank 2 bundles over P2 with the first Chern class (3).
On the determinism of the distributions of multiple Markov non-Gaussian symmetric stable processes
Authors: Kojo Katsuya 
Published: July 2016

Abstract.Consider a non-Gaussian SαS process X = {X(t); t ∈ T} which is expressed as a canonical representation , and is continuous in probability. If X is n-ple Markov, then X has determinism of dimension n + 1. That is, any SαS process having the same (n + l)-dimensional distributions with X is identical in law with X.
Representations and interpolations of harmonic Bergman functions on half-spaces
Authors: Choe Boo Rim , Yi Heungsu 
Published: July 2016

Abstract.On the setting of the half-space of the euclidean n-space, we prove representation theorems and interpolation theorems for harmonic Bergman functions in a constructive way. We also consider the harmonic (little) Bloch spaces as limiting spaces. Our results show that well-known phenomena for holomorphic cases continue to hold. Our proofs of representation theorems also yield a uniqueness theorem for harmonic Bergman functions. As an application of interpolation theorems, we give a distance estimate to the harmonic little Bloch space. In the course of the proofs, pseudohyperbolic balls are used as substitutes for Bergman metric balls in the holomorphic case.
On the Gauss mean-value formula for class number
Authors: Chamizo Fernando , Iwaniec Henryk 
Published: July 2016

Abstract.In his masterworkDisquisitiones Arithmeticae, Gauss stated an approximate formula for the average of the class number for negative discriminants. In this paper we improve the known estimates for the error term in Gauss approximate formula. Namely, our result can be written asfor every ∊ > 0, whereH(−n) is, in modern notation,h(−4n). We also consider the average ofh(−n) itself obtaining the same type of result.Proving this formula we transform firstly the problem in a lattice point problem (as probably Gauss did) and we use a functional equation due to Shintani and Dirichlet class number formula to express the error term as a sum of character and exponential sums that can be estimated with techniques introduced in a previous work on the sphere problem.
The blowup of solutions for 3-D axisymmetric compressible Euler equations
Authors: Yin Huicheng , Qiu Qingjiu 
Published: July 2016

AbstractIn this paper, for three dimensional compressible Euler equations with small perturbed initial data which are axisymmetric, we prove that the classical solutions have to blow up in finite time and give a complete asymptotic expansion of lifespan.
Dirichlet series and automorphic functions associated to a quadratic form
Authors: Peter Manfred 
Published: July 2016

AbstractStarting from the reciprocity law for Gaussian sums attached to an integral quadratic form we prove functional equations for a new kind of Dirichlet series in two variables. For special values of one variable they are of Hecke type with respect to the other variable. With Weil’s converse theorem we derive automorphic functions which generalize Siegel’s genus invariant and the automorphic functions of Cohen and Zagier.
Galois Sections in Absolute Anabelian Geometry
Authors: Mochizuki Shinichi 
Published: July 2016

AbstractWe show that isomorphisms between arithmetic fundamental groups of hyperbolic curves over p-adic local fields preserve the decomposition groups of all closed points (respectively, closed points arising from torsion points of the underlying elliptic curve), whenever the hyperbolic curves in question are isogenous to hyperbolic curves of genus zero defined over a number field (respectively, are once-punctured elliptic curves [which are not necessarily defined over a number field]). We also show that, under certain conditions, such isomorphisms preserve certain canonical “integral structures” at the cusps [i.e., points at infinity] of the hyperbolic curve.
Examples of Weak Hopf Algebras Arising from Vacant Double Groupoids
Authors: Andruskiewitsch Nicolás , Mombelli Juan Martín 
Published: July 2016

AbstractWe construct explicit examples of weak Hopf algebras (actually face algebras in the sense of Hayashi [H]) via vacant double groupoids as explained in [AN]. To this end, we first study the Kac exact sequence for matched pairs of groupoids and show that it can be computed via group cohomology. Then we describe explicit examples of finite vacant double groupoids.
On the Complement of Levi-Flats in Kähler Manifolds of Dimension ≥ 3
Authors: Ohsawa Takeo 
Published: July 2016

AbstractApplying the L2 method of solving the -equation, it is shown that compact Kähler manifolds of dimension ≥ 3 admit no Levi flat real analytic hypersurfaces whose complements are Stein.
Toeplitz Algebras on Strongly Pseudoconvex Domains
Authors: Cao Guangfu 
Published: July 2016

AbstractIn the present paper, it is proved that theK0-group of a Toeplitz algebra on any strongly pseudoconvex domain is always isomorphic to theK0-group of the relative continuous function algebra, and is thus isomorphic to the topologicalK0-group of the boundary of the relative domain. Further there exists a ring isomorphism between theK0-groups of Toeplitz algebras and the Chern classes of the relative boundaries of strongly pseudoconvex domains. As applications of our main result,K-groups of Toeplitz algebras on some special strongly pseudoconvex domains are computed. Our results show that the Toeplitz algebras on strongly pseudoconvex domains have rich structures, which deeply depend on the topological structures of relative domains. In addition, the first cohomology groups of Toeplitz algebras are also computed.
An Uncountably Infinite Number of Indecomposable Totally Reflexive Modules
Authors: Takahashi Ryo 
Published: July 2016

AbstractSeveral years ago, Huneke and Leuschke proved a theorem solving a conjecture of Schreyer. It asserts that an excellent Cohen-Macaulay local ring of countable Cohen-Macaulay type which is complete or has uncountable residue field has at most a one-dimensional singular locus. In this paper, it is verified that the assumption of the excellent property can be removed, and the theorem is considered over an arbitrary local ring. The main purpose of this paper is to prove that the existence of a certain prime ideal and a certain totally reflexive module implies the existence of an uncountably infinite number of isomorphism classes of indecomposable totally reflexive modules.
Limits of Characters of Wreath Products 𝔖n(T) of a Compact GroupTWith the Symmetric Groups and Characters of 𝔖∞(T), I
Authors: Hirai Takeshi , Hirai Etsuko , Hora Akihito 
Published: July 2016

AbstractIn the first half of this paper, all the limits of irreducible characters ofGn= 𝔖n(T) asn→ ∞ are calculated. The set of all continuous limit functions onG= 𝔖∞(T) is exactly equal to the set of all characters ofGdetermined in [HH6]. We give a necessary and sufficient condition for a series of irreducible characters ofGnto have a continuous limit and also such a condition to have a discontinuous limit. In the second half, we study the limits of characters of certain induced representations ofGnwhich are usually reducible. The limits turn out to be characters ofG, and we analyse which of irreducible components are responsible to these limits.