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A Set Theory Founded on Unique Generating Principle
Authors: Ono Katuzi
Published: July 2016

The most important thing for a set theory seems to be that it can generate new mathematical objects, and I think that there must be an underlying principle, simple and unique, which unifies the acts of generating. The naive set theory has a unique generating principle, which defines, by any proposition on a variablex, the set of allx’ssatisfying the proposition. Certainly, we must restrict this generating principle so as to exclude all contradictions it contains, without losing its essential rôle as logic of mathematics, and at the same time we would like to keep its uniqueness and simplicity.
On Modules of Trivial Cohomology over a Finite Group, II (Finitely Generated Modules)
Authors: Nakayama Tadasi
Published: July 2016

Let G be a finite group. A(left) G-module A of G is said to be of trivial cohomology when Hn(H, A)= 0 for all rational integers n and for all subgroups H of G. The main purpose of the present note is to determine the structure of finitely generated G-modules of trivial cohomology, which turns out to be remarkably simple (See Theorem 1 and Corollary 3 below). We prove also an (easy) localization theorem for cohomological triviality.
Generalized Jacobian Varieties and Separable Abelian Extensions of Function Fields
Authors: Morikawa Hisasi
Published: July 2016

Using Frobenius automorphisms ingeniouslly, S. Lang has established an elegant theory of unramified class fields of function fields in several variables over finite fields [2]. As an application of class field theory and theory of reduction he has proved that any separable unramified abelian extension of a function field of one variable comes from a pull back of a separable ingeny of its jacobian variety [3].
A theta relation in genus 4
Authors: Freitag Eberhard , Oura Manabu
Published: July 2016

The 2gtheta constants of second kind of genusggenerate a graded ring of dimensiong(g +1)/2. In the caseg ≥3 there must exist algebraic relations. In genusg =3 it is known that there is one defining relation. In this paper we give a relation in the caseg =4. It is of degree 24 and has the remarkable property that it is invariant under the full Siegel modular group and whose Φ-image is not zero. Our relation is obtained as a linear combination of code polynomials of the 9 self-dual doubly-even codes of length 24.
Symplectic fillings of links of quotient surface singularities
Authors: Bhupal Mohan , Ono Kaoru
Published: July 2016

We study symplectic deformation types of minimal symplectic fillings of links of quotient surface singularities. In particular, there are only finitely many symplectic deformation types for each quotient surface singularity.
Existence of regular coverings associated with leaves of codimension one foliations
Authors: Ikegami Gikō
Published: July 2016

In this paper we are concerned with transversely orientable codimension one foliations. Let be a Cr-foliation as above in a smooth manifold M, r ≧ 1, and let F0 be a closed leaf of . A neighborhood U of F0 is called a bicollar of F0 in this paper if there is a normal line bundle : U → F0 with respect to a fixed Riemannian metric on M such that each fibre of is transverse to .
Picard principle for finite densities on some end
Authors: Kawamura Michihiko
Published: July 2016

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 Hölder continuous coefficients P(z). A density P is said to be finite if the integral
On the deficiencies of meromorphic mappings of Cn into PNC
Authors: Mori Seiki
Published: July 2016

Let f(z) be a non-degenerate meromorphic mapping of the n-dimensional complex Euclidean space Cn into the N-dimensional complex projective space PNC. A generalization of results of Edrei-Fuchs [2] for meromorphic mappings of C into PNC was given by Toda [5], and an estimate of K(λ) for meromorphic mappings of Cn into PNC was done by Noguchi [4]. In this note we generalize several results of Edrei-Fuchs [2] in the case of meromorphic mappings of Cn into PNC.
On the analyticity of the locus of singularity of real analytic solutions with minimal dimension
Authors: Kaneko Akira
Published: July 2016

Let P(x, D) be a linear partial differential operator with real analytic coefficients and let C ⊂ Rn be a germ of closed subset, say at the origin. We say that C is (the locus of) an irremovable singularity of a real analytic solution u of P(x, D)u = 0 if u is defined outside C on a neighborhood Ω of 0 but cannot be extended to the whole neighborhood Ω even as a hyperfunction solution of P(x, D)u = 0. This usage of the word “singularity” is the same as the one for the analytic functions in complex analysis, and is different of the usual usage of “singularities of solutions” in the theory of partial differential equations.
Topological entropy and periodic points of a factor of a subshift of finite type
Authors: Shimomura Takashi
Published: July 2016

Let X be a compact space and f be a continuous map from X into itself. The topological entropy of f, h(f), was defined by Adler, Konheim and McAndrew [1]. After that Bowen [4] defined the topological entropy for uniformly continuous maps of metric spaces, and proved that the two entropies coincide when the spaces are compact. The definition of Bowen is useful in calculating entropy of continuous maps.
The ring of invariants of matrices
Authors: Teranishi Yasuo
Published: July 2016

We denote by M(n) the space of all n × n-matrices with their coefficients in the complex number field C and by G the group of invertible matrices GL(n, C). Let W = M(n)i be the vector space of l-tuples of n × ra-matrices. We denote by ρ: G → GL(W) a rational representation of G defined as follows:

if S ∈ G, A(i) ∈ M(n) (i = 1, 2, …, l).
Hadamard matrices of order 36 with automorphisms of order 17
Authors: Tonchev Vladimir D.
Published: July 2016

A Hadamard matrix of order n is an n by n matrix of 1’s and − 1’s such that HHt − nI. In such a matrix n is necessarily 1, 2 or a multiple of 4. Two Hadamard matrices H1 and H2 are called equivalent if there exist monomial matrices P, Q with PH1Q = H2. An automorphism of a Hadamard matrix H is an equivalence of the matrix to itself, i.e. a pair (P, Q) of monomial matrices such that PHQ = H. In other words, an automorphism of H is a permutation of its rows followed by multiplication of some rows by − 1, which leads to reordering of its columns and multiplication of some columns by − 1. The set of all automorphisms form a group under composition called the automorphism group (Aut H) of H. For a detailed study of the basic properties and applications of Hadamard matrices see, e.g. [1], [7, Chap. 14], [8].
One Parametric Motion in Klein Spaces
Authors: Kurita Minoru
Published: July 2016

On the euclidean plane one-parametric motion is in general a roulett motion, exceptions being a translation at each instant and a rotation with a fixed center; here we mean by a roulett motion a motion in which a certain curve rolls on another fixed curve without slipping. In this paper we extend this fact to the case of Klein spaces and investigate in detail especially the cases of the euclidean space and the projective space.
Unitary Representations of Some Linear Groups
Authors: Itô Seizô
Published: July 2016

Recently I. Gelfand and M. Neumark [2] have determined the types of irreducible unitary representations of the group G1 of linear transformations of the straight line. The analogous result is obtained for the group G2 of transformations z → az + b in the complex-number plane , where a and b run over all complex numbers with the exception of a = 0, which may be considered as the group of all sense-preserving similar transformations in the two-dimensional euclidean space E2.
Classification of Mappings of an (n + 2)-Complex into an (n − 1)-Connected Space with Vanishing (n + 1)-st Homotopy Group
Authors: Shimada Nobuo , Uehara Hiroshi
Published: July 2016

The present paper is concerned with the classification and corresponding extension theorem of mappings of the (n+-2)-complex Kn+2 (n>2) into the space Y whose homotopy groups πi(Y) vanish for i < n and i = n+1, and the n-th homotopy group πn(Y) of which has a finite number of generators. Our methods followed here are essentially analogous to those of Steenrod [2].
On One-parameter Subgroups in Finite Dimensional Locally Compact Group with No Small Subgroups
Authors: Kuranishi Masatake
Published: July 2016

Let G be a locally compact topological group and let U be a neighborhood of the identity in G. A curve g(λ) (|λ| ≦ 1) in G, which satisfies the conditions,

g(s)g(t) = g(s + t) (|s|, |f|, |s + t| ≦ l),

is called a one-parameter subgroup of G. If there exists a neighborhood U1 of the identity in G such that for every element x of U1 there exists a unique one-parameter subgroup g(λ) which is contained in U and g(1) =x, we shall call, for the sake of simplicity, that U has the property (S). It is well known that the neighborhoods of the identity in a Lie group have the property (S). More generally it is proved that if G is finite dimensional, locally connected, and is without small subgroups, G has the same property. In this note, these theorems will be generalized to the case when G is unite dimensional and without small subgroups.
On the Behavior of an Analytic Function about an Isolated Boundary Point
Authors: Ohtsuka Makoto
Published: July 2016

Let D be an open set in the 2-plane, C its boundary, z0 a point on C, and f(z) a one-valued meromorphic function in D.
On a Covering Surface over an Abstract Riemann Surface
Authors: Ohtsuka Makoto
Published: July 2016

1. Let be an abstract Riemann surface in the sense of Weyl-Radó, and an open covering surface over . If a curve C = {P(t);0≦t<1} on tends to the ideal boundary of but its projection terminates at an inner point of as t→1, we shall say that C determines an accessible boundary point (which will be abbreviated by A.B.P.) of relatively to . The set of all the A.B.P.S of relative to will be called accessible boundary (relative to ) and denoted by 3i() or by (, ). Throughout in this paper () will be supposed to be non-empty.
On the Dimension of Modules and Algebras, I
Authors: Eilenberg Samuel , Ikeda Masatoshi , Nakayama Tadasi
Published: July 2016

In [5], Ikeda-Nagao-Nakayama gave a characterization of algebras of cohomological dimension ≦n In a subsequent paper [4] Eilenberg gave an alternative treatment of the same question. The present paper is devoted to the discussion of a number of questions suggested by the results of [4] and [5]. Among others it is shown that the conditions employed in stating the main results in [4] and [5] are equivalent, so that the main results of these two papers are in accord. Further, the cohomological dimension of a residue-algebra is studied in terms of that of the original algebra and the (module-) dimension of the associated ideal. The terminology and notation employed here are that of [3].
On Affine Transformations of a Riemannian Manifold
Authors: Hano Jun-Ichi
Published: July 2016

In this paper we establish some theorems about the group of affine transformations on a Riemannian manifold. First we prove a decomposition theorem (Theorem 1) of the largest connected group of affine transformations on a simply connected complete Riemannian manifold, which corresponds to the decomposition theorem of de Rham [4] for the manifold. In the case of the largest group of isometries, a theorem of the same type is found in de Rham’s paper [4] in a weaker form. Using Theorem 1 we obtain a sufficient condition for an infinitesimal affine transformation to be a Killing vector field (Theorem 2). This result includes K. Yano’s theorem [13] which states that on a compact Riemannian manifold an infinitesimal affine transformation is always a Killing vector field. His proof of the theorem depends on an integral formula which is valid only for a compact manifold. Our method is quite different and is based on a result [11] of K. Nomizu.
Arithmetic of Orthogonal Groups (II)
Authors: Ono Takashi
Published: July 2016

In [0], the writer proved some theorems of Hasse type for two orthogonal groups which operate on the same vector space. In this paper, we shall further generalize those results in two directions. One is to consider the propositions of that type for two orthogonal groups which operate respectively on two vector spaces whose dimensions are different from each other, and the other is to deal with some conspicuous subgroups of an orthogonal group simultaneously which play important roles in the structure theory for orthogonal groups. For this reason, the present paper consists of three steps §1, §2 and §3 which give the generalizations in the above sense of the results in the corresponding sections of [0].
Cycles on Algebraic Varieties
Authors: Morikawa Hisasi
Published: July 2016

In the present note, applying the theory of harmonic integrals, we shall show some results on cycles on algebraic varieties and give a new birational invariant.
Über die Zwischensysteme der Aussagenlogik
Authors: Umezawa Toshio
Published: July 2016

Die klassische Aussagenlogik ist, bekanntlich, in dem Sinne vollständig, dass die Hinzufügung einer klassisch nicht beweisbaren Formel als Axiom dieses Systems stets einen Widerspruch nach sich zieht. Die Vollständigkeit (in diesem Sinne) kann für intuitionistische Aussagenlogik nicht bestehen, weil noch immer die Formel A ∨ Ā (der Satz vom ausgeschlossenen Dritten) hinzugefügt werden kann. Es steht aber die Frage, ob man aus der intuitionistischen Aussagenlogik durch Hinzufügung einer klassisch beweisbaren und intuitionistisch nicht beweisbaren Formel stets die klassischen Aussagenlogik bekommt.
Sur un Théorème Étoilé de Gross
Authors: Ohtsuka Makoto
Published: July 2016

Nous continuerons l’étude du premier théorème étoilé de Gross, faite dans le mémoire de l’auteur: Théorèmes étoilés de Gross et leurs applications, Ann. Inst. Fourier, 5 (1955), pp. 1-28; ce mémoire sera cité avec l’abréviation [A]
Corrections to My Paper “On Krull’s Conjecture Concerning Valuation Rings”
Authors: Nagata Masayoshi
Published: July 2016

The proof of Theorem 1 in the paper “On Krull’s conjecture concerning valuation rings” (vol. 4 (1952) of this journal) is not correct. We want to give here a corrected proof of the theorem: From p. 30, l. 14 to p. 31, l. 7 should be changed as follows.
Problèmes D’universalité s’Introduisant dans l’Algébrisation de la Logique Mathématique I
Authors: Ponasse Daniel
Published: July 2016

L’objet de ce mémoire est essentiellement la recherche et l’étude de structures algébriques permettant de traduire le Calcul propositionnel et le Calcul des prédicats restreint du premier ordre. Nous avons guidé et limité cette recherche en imposant aux ensembles algébriques introduits de satisfaire simultanément aux trois conditions:

—

donner une représentation du Calcul Logique sous sa forme la plus classique, c’est à dire avant l’obtention d’un anneau booléien par passage au quotient. Ce sera le rôle des structures “prébooléiennes”.

—

posséder un ensemble d’opérations traduisant un procédé de décision tel que celui des tableaux sémantiques, qui correspondent ici aux “tableaux de réduction”. —avoir un caractère universel dans leur construction à partir des atomes.
A Remark on Orthogonality Relations in Finite Groups
Authors: Iizuka Kenzo , Nakayama Tadasi
Published: July 2016

On the basis of Prof. R. Brauer’s fundamental work, certain orthogonality relations for characters of finite groups have recently been studied by Brauer himself, M. Osima, and one of the present writers; see Iizuka [7] and the references there. In the present short note some general remarks on orthogonality relations, dealing with “blocks” and “sections” of general type, are given first. They are of elementary, and often formal, nature and their proofs are merely combinations of known arguments. So, no deep significance is claimed on them, in comparison with the above alluded results based on deeper arithmetico-group-theoretical considerations. However, applied to blocks and sections of such deeper nature, our remarks give some rather useful informations on them. Thus, for instance, the “maximality” feature of 77-blocks is given a formulation (Prop. 5 below) finer than the one given in [71 Further, some new types of blocks and sections can be constructed, again in application of our remarks to such classical ones. These new blocks and sections give thus new orthogonality relations and we hope that some of them may turn to have some significance. There arize also several problems, which are stated at the end of the present note and to some of which we wish to come back elsewhere.
On Characterizations of Linear Groups III
Authors: Suzuki Michio
Published: July 2016

In his address at the International Congress of Mathematicians at Amsterdam [1] Professor R. Brauer proposed a problem of characterizing various groups of even order by the properties of the involutions contained in these groups and he gave characterizations of the general projective linear groups of low dimensions along these lines. The detail of the one-dimensional case has been published in [5], but the two-dimensional case has not appeared yet in detail. His work was followed by Suzuki [7], Feit [6] and Walter [11]. The present paper is a continuation of [73 and discusses a characterization of the two-dimensional projective unitary group over a finite field of characteristic 2. The precise conditions which characterize the group in question will be stated in the first section. The method employed here is similar to the one used in [7]. An application of group characters provides a formula for the order. However a difficulty comes in when one attempts to identify the group. In order to overcome this difficulty we will use a method primarily designed to study a class of doubly transitive permutation groups (cf. [9]). We need also a group theoretical characterization of a class of doubly transitive groups called (ZT)-groups. This is a generalization of a result in [8], and may be of in dependent interest.
Block Idempotents and Normal p-Subgroups
Authors: Reynolds W. F.
Published: July 2016

In the theory of modular representations of a finite group G in an algebraically closed field Ω of characteristic p, Brauer has proved a useful reduction theorem for blocks [2, §§11, 12], [5, (88.8)], which can be reformulated as follows:

THEOREM 1 (Brauer). Let P bean arbitraryp-subgroup of G; let N = NG(P) and W = PCG(P).
Formal System Having Just One Primitive Notion
Authors: Ono Katuzi
Published: July 2016

In this paper, I would like to point out some characteristic features of formal systems having just one primitive notion. Most remarkable systems of this kind may be Zermelo’s and Fraenkel’s set-theories, both having just one primitive notion ∈.
On Development of Formal Systems Starting from Primitive Logic
Authors: Ono Katuzi
Published: July 2016

It has beenmy programto develop fundamental theories of mathematics starting from TABOOS and standing on theprimitive logicLO at first instead of starting from AXIOMS and standing on the fairly brought up logic, thelower classical logicLK. This was proposed in my work [1].
On a Characteristic Feature of the Positive Logics
Authors: Ono Katuzi , Ito Jiro
Published: July 2016

In this short note, we would like to point out that the following property (called ASSUMPTION REMOVABILITY in the present paper) is characteristic of the positive logics, the primitive logic LO, the positive predicate logics LP (intuitionistic) and LQ (classical):

ASSUMPTION REMOVABILITY. If any propositioncan be deduced from some assumptionhaving no primitive notions in common ivith, thenis also provable without any assumption.
Some Results and Problems Concerning Chordal Principal Cluster Sets
Authors: Bagemihl F.
Published: July 2016

Let Γ be the unit circle and D be the open unit disk in the complex plane, and denote the Riemann sphere by Ω. By an arc at a point ζ∈Γ we mean a continuous curve such that |z(t)| < 1 for 0 ≦ t < 1 and . A terminal subarc of an arc Λ at ζ is a subarc of the form z = z (t) (t0 ≦ t < 1), where 0 ≦ t0<1. Suppose that f(z) is a meromorphic function in D. Then A(f) denotes the set of asymptotic values of f; and if ζ∈Γ, then C(f, ζ) means the cluster set of f at ζ and is the outer angular cluster set of f at ζ (see [13]).
Sur les Fonctions Méromorphes aux Limites Fines
Authors: Toda Nobushige
Published: July 2016

Dans ce mémoire, on continue d’étudier sur les fonctions à des limites fines que J. L. Doob a trouvées [5]. On a trouvé quelques propriétés des fonctions dans [10]. Dans le paragraphe 2 on donne une condition suffisante afin qu’une fonction admette une limite fine et on étudie sur l’indice harmonique d’un spot asymptotique d’une fonction à une limite fine. Le paragraphe 3 est consacré aux études d’autres propriétés.
PL-Submanifolds and Homology Classes of a PL-Manifold
Authors: Adachi Masahisa
Published: July 2016

This paper is devoted to the problem of the realisation of homology classes of a PL-manifold by PL-submanifolds.

The present study is founded on the consideration of Thorn complexes M(PLk), M(SPLk) for PL-microbundles which is defined by R. Williamson [5]. We shall apply Thom’s method [4] to PL-manifolds.

The author is grateful to Professors R. Shizuma and K. Shiraiwa for their kind criticisms.
Generalization of Levi-Oka’s Theorem Concerning Meromorphic Functions
Authors: Kajiwara Joji , Sakai Eiichi
Published: July 2016

As Fuks [3] stated, every domain of holomorphy or meromorphy over Cn is analytically convex in the sense of Hartogs. Oka [6] proved that every domain over Cn analytically convex in the sense of Hartogs is a domain of holomorphy. Therefore a domain of meromorphy over Cn coincides with a domain of holomorphy over Cn.
Definitions for a Class of Plane Quasiconformal Mappings
Authors: Gehring F. W.
Published: July 2016

This report is a survey of some of the many different ways of characterizing a class of plane quasiconformal mappings. This class was considered by Ahlfors [4] in his treatment of the Teichmiiller problem, and it has been studied rather extensively in the last ten years.
A Method of Two-Level Simplification of Boolean Functions
Authors: Umezawa Toshio
Published: July 2016

There are a number of methods to find minimal two-level forms for a given Boolean function, e g. Harvard’s group [1], Veitch [2], Quine [3], [4], Karnaugh [5], Nelson [6], [7] etc,. This paper presents an approach which is suitable for mechanical or automatic computation, as the Harvard method and the Quine method are so. On the other hand, it shares the same property as the Veitch method in the sense that some of essential prime implicants may be found before all prime implicants are computed. It also adopts the procedure to reduce the necessary steps for computation which is shown in Lawler [8]. The method described is applicable to the interval of Boolean functions f, g such that f implies g where for simplification of sum form the variables occurring in g also occur in f and for product form the variables in f also occur in g.
On the Balayage for Logarithmic Potentials
Authors: Ninomiya Nobuyuki
Published: July 2016

In this paper, we shall consider the logarithmic potential

where μ is a positive measure in the plane, P and Q are any points and PQ denotes the distance from P to Q. In general, consider the potential

of a positive measure μ taken with respect to a kernel K(P, Q) which is a continuous function in P and Q and may be + ∞ for P = Q. A kernel K (P, Q) is said to satisfy the balayage principle if, given any compact set F and any positive measure μ with compact support, there exists a positive measure μ′ supported by F such that K(P, μ′) = K(P, μ) on F with a possible exception of a set of k-capacity zero and K(P, μ′)≦K(P, μ) everywhere. A kernel K(P, Q) is said to satisfy the equilibrium principle if, given any compact set F there exists a positive measure λ supported by F such that K(P, λ) = V (a constant) on F with a possible exception of a set of K-capacity zero and K(p, λ)≦V everywhere.
A Note on Tangent Bundles
Authors: Shiraiwa Kenichi
Published: July 2016

The tangent bundle of a differentiable manifold is an important invariant of a differentiable structure. It is determined neither by the topological structure nor by the homotopy type of a manifold. But in some cases tangent bundles depend only on the homotopy types of manifolds.
The Genus Field and Genus Number in Algebraic Number Fields
Authors: Furuta Yoshiomi
Published: July 2016

Let k be an algebraic number field and K be its normal extension of finite degree. Then the genus field K* of K over k is defined as the maximal unramified extension of K which is obtained from K by composing an abelian extension over k2). We call the degree (K*: K) the genus number of K over k.
On the Non-Minimal Martin Boundary Points
Authors: Ikegami Teruo
Published: July 2016

In a Green space Ω we can introduce Martin’s topology and make it the Martin space Ω, Ω is a dense open subset of and the kernel

can be extended continuously to , where G(p, x) is a Green function in Ω and y0 the fixed point of Ω. is a metric space. is divided into two disjoint subsets Δ0, Δ1 and s ∊ Δ1 is characterized by the fact that K(s, x) is a minimal positive harmonic function in x∊Ω.
A Categorical setting for Determinants and Traces
Authors: Röhrl Helmut
Published: July 2016

The aim of this paper is to investigate some applications of a certain universal problem. The universal problem deals with categories C which for every object A have some ‘‘structure” on the set C(A, A) of endomorphisms of A and calls for a universal solution, relative to this structure, that is associated with C(A, A) and centralizes the set of automorphisms of A. The commutative version of this universal problem asks for a universal solution, relative to the said structure, that abelianizes the canonical monoid structure of C(A, A).
On Level Curves of Harmonic and Analytic Functions on Riemann Surfaces
Authors: Yamashitad Shinji
Published: July 2016

In this note we shall denote by R a hyperbolic Riemann surface. Let HP′(R) be the totality of harmonic functions u on R such that every subharmonic function | u | has a harmonic majorant on R. The class HP′(R) forms a vector lattice under the lattice operations:
A Note on Galois Cohomology Groups of Algebraic Tori
Authors: Amano Kazuo
Published: July 2016

Let k be a complete field of characteristic 0 whose topology is defined by a discrete valuation and let T be an algebraic torus of dimension d defined over k. As is well known, T has a splitting field K which is a finite Galois extension of k with Galois group . For a ring R, denote by TR the subgroup of R-rational points of T. Then TK and T0K, DK being a valuation ring of K, become -modules in the usual manner.
N-manifolds carrying bounded but no Dirichlet finite harmonic functions
Authors: Hada Dennis , Sario Leo , Wang Cecilia
Published: July 2016

Among the most remarkable results in the theory of harmonic functions on Riemann surfaces is the strictness of the inclusion relations OG < OHB < OHD, established by Ahlfors [1,2], Royden [2,4], and Tôki [8] two decades ago. Subsequently the strictness of the relations OG < OHP < OHB was shown and a somewhat simpler proof of OHB < OHD given by Sario [5] and Tôki [9]. Here OG is the class of parabolic surfaces, and OHP, OHB, OHD stand for the classes of surfaces which do not carry nonconstant harmonic functions which are positive, bounded, or Dirichlet finite, respectively.
Towards a problem in deformations of polarized algebraicK3 surfaces
Authors: Comenetz D.
Published: July 2016

A nonsingular algebraic surfaceVis called aK3surface if i) 1 =i.e. a canonical divisorKvonVis linearly equivalent to zero; and ii). When the characteristic is zero, condition ii) is equivalent to ii)′q= dimension of the Albanese variety ofV= 0, and always ii) implies ii)′ as in fact≥q ≥0, but in non-zero characteristic it can happen that>q([6], [15]). When ii)′ is true, the algebraic and linear equivalences of divisors coincide onV, because of the duality between Picard and Albanese varieties ofV, [8].
On the structure of splitting fields of stationary Gaussian processes with finite multiple Markovian property
Authors: Okabe Yasunori
Published: July 2016

Let X = (X(t); t ∈ R) be a real stationary mean continuous Gaussian process with expectation zero which is purely nondeterministic. In this paper we shall investigate the structure of splitting fields of X having finite multiple Markovian property using the results in [6]. We follow the notations and terminologies in [6].
On boundaries of Schottky spaces
Authors: Sato Hiroki
Published: July 2016

Let S be a compact Riemann surface and let Sn be the surface obtained from S in the course of a pinching deformation. We denote by Γn the quasi-Fuchsian group representing Sn in the Teichmüller space T(Γ), where Γ is a Fuchsian group with U/Γ = S (U: the upper half plane). Then in the previous paper [7] we showed that the limit of the sequence of Γn is a cusp on the boundary ∂T(Γ). In this paper we will consider the case of Schottky space . Let Gn be a Schottky group with Ω(Gn)/Gn = Sn. Then the purpose of this paper is to show what the limit of Gn is.
On Galois groups of class two extensions over the rational number field
Authors: Shirai Susumu
Published: July 2016

Let Q be the rational number field, K/Q be a maximal Abelian extension whose degree is some power of a prime l, and let f(K) be the conductor of K/Q; if l = 2, let K be complex, and if in addition f(K) ≡ 0 (mod 2), let f(K) ≡ 0 (mod 16). Denote by (K) the Geschlechtermodul of K over Q and by K̂ the maximal central l-extension of K/Q contained in the ray class field mod (K) of K. A. Fröhlich [1, Theorem 4] completely determined the Galois group of K̂ over Q in purely rational terms. The proof is based on [1, Theorem 3], though he did not write the proof in the case f(K) ≡ 0 (mod 16). Moreover he gave a classification theory of all class two extensions over Q whose degree is a power of l. Hence we know the set of fields of nilpotency class two over Q, because a finite nilpotent group is a direct product of all its Sylow subgroups. But the theory becomes cumbersome, and it is desirable to reconstruct a more elementary one.
A geometric characterization of Cn and open balls
Authors: Shiga Kiyoshi
Published: July 2016

The purpose of this paper is to give a result concerning the problem of geometric characterizations of the Euclidean n-space Cn and bounded domains. It is well known that a simply connected Riemann surface is biholomorphic to one of the Riemann sphere, the complex plane and the unit disc. And there are several results concerning the geometric characterization of these spaces. To show that some simply connected open Riemann surface is biholomorphic to the complex plane or the unit disc, it is sufficient to see that there exist non constant bounded sub-harmonic functions or not. But in the higher dimensional case, there is no uniformization theorem. By this reason to show that some complex manifold is biholomorphic to Cn or an open ball, we must construct a biholomorphic mapping directly.
On the vanishing and the positivity of intersection multiplicities over local rings with small non complete intersection loci
Authors: Kurano Kazuhiko
Published: July 2016

Throughout this paperAis a commutative Noetherian ring of dimensiondwith the maximal ideal m and we assume that there exists a regular local ringSsuch thatAis a homomorphic image ofS, i.e.,A=S/Ifor some idealIofS. Furthermore we assume thatAis equi-dimensional, i.e., dimA= dimA/for any minimal prime idealofA. We put

.
Characterizations of filter regular sequences and unconditioned strong d-sequences
Authors: Khashyarmanesh K. , Salarian Sh. , Zakeri H.
Published: July 2016

The first part of the paper is concerned, among other things, with a characterization of filter regular sequences in terms of modules of generalized fractions. This characterization leads to a description, in terms of generalized fractions, of the structure of an arbitrary local cohomology module of a finitely generated module over a notherian ring. In the second part of the paper, we establish homomorphisms between the homology modules of a Koszul complex and the homology modules of a certain complex of modules of generalized fractions. Using these homomorphisms, we obtain a characterization of unconditioned strong d-sequences.
Classification d’orbites pour une classe d’espaces préhomogènes
Authors: Muller Iris
Published: July 2016

Dans cet article, on donne la classification des orbites des préhomogènes de type parabolique (g0, g1) correspondants aux paraboliques maximaux, notés (Δ, λ0), suivants: (A2n-1, αn), (Bn, α1) ou (Dn, α1), (Cn, αn), (D2n, α2n) ou (D2n, α2n-1), (E7, α7), (F4, α1), (E6, α2), (E7, α1), (E8, α8) lorsque F est un corps local ou global de caractéristique zéro, à l’aide de formes quadratiques, ceci lorsque le sous-espace radiciel est de dimension un.
Pre-weighted homogeneous map germs—Finite determinacy and topological triviality
Authors: Saia Marcelo Jose
Published: July 2016

In this paper we introduce the notion of G-pre-weighted homogeneous map germ, (G is one of Mather’s groups A or K) and show that any G-pre-weight ed homogeneous map germ is G-finitely determined. We also give an explicit “order”, based on the Newton polyhedron of a pre-weighted homogeneous germ of function, such that the topological structure is preserved after perturbations by terms of higher order.
Some properties of isolating blocks for planar systems
Authors: Yu Shu-Xiang
Published: July 2016

In this paper, some qualitative properties of trajectories inside an isolating block for planar differential equations are obtained.
Some applications of Serre duality in CR manifolds
Authors: Laurent-Thiébaut Christine , Leiterer Jürgen
Published: July 2016

Applying the methods of Serre duality in the setting of CR manifolds we prove approximation theorems and we study the Hartogs-Bochner phenomenon in 1-concave CR generic manifolds.
Boundedness of homogeneous fractional integrals on Lp for N/α ≤ P ≤ ∞
Authors: Ding Yong , Lu Shanzhen
Published: July 2016

In this paper we study the map properties of the homogeneous fractional integral operator TΩ, α on Lp(ℝn) for n/α ≤ p ≤ ∞.

We prove that if Ω satisfies some smoothness conditions on Sn−1 then TΩ, α is bounded from Ln/α(ℝn) to BMO(ℝn), and from Lp(ℝn) (n/α < p ≤ ∞) to a class of the Campanato spaces l, λ (ℝn), respectively. As the corollary of the results above, we show that when Ω satisfies some smoothness conditions on Sn−1 the homogeneous fractional integral operator TΩ, α is also bounded from Hp(ℝn) (n/(n + α) ≤ p ≤ 1) to Lq(ℝn) for 1/q = 1/p-α/n. The results are the extensions of Stein-Weiss (for p = 1) and Taibleson-Weiss’s (for n/(n + α) ≤ p < 1) results on the boundedness of the Riesz potential operator Iα on the Hardy spaces Hp(ℝn).
Localization lemmas for the Bergman metric at plurisubharmonic peak points
Authors: Herbort Gregor
Published: July 2016

LetDbe a bounded pseudoconvex domain in ℂnand ζ ∈ D. ByKDandBDwe denote the Bergman kernel and metric ofD, respectively. Given a ballB=B(ζ,R), we study the behavior of the ratioKD/KD∩B(w) whenw∈D∩Btends towards ζ. It is well-known, that it remains bounded from above and below by a positive constant. We show, that the ratio tends to 1, aswtends to ζ, under an additional assumption on the pluricomplex Green functionD(·,w) ofDwith pole atw, namely that the diameter of the sublevel setsAw:={z∈D|D(z, w) < −1} tends to zero, asw→ ζ. A similar result is obtained also for the Bergman metric. In this case we also show that the extremal function associated to the Bergman kernel has the concentration of mass property introduced in [DiOh1], where the question was discussed how to recognize a weight function from the associated Bergman space. The hypothesis concerning the setAwis satisfied for example, if the domain is regular in the sense of Diederich-Fornæss, ([DiFo2]).
Isomonodromic deformation of Fuchsian projective connections on elliptic curves
Authors: Kawai Shingo
Published: July 2016

We consider isomonodromic deformations of second-order Fuchsian differential equations on elliptic curves. The isomonodromic deformations are described as a completely integrable Hamiltonian system.
Real canonical cycle and asymptotics of oscillating integrals
Authors: Barlet Daniel
Published: July 2016

Let Xℝ ⊂ ℝN a real analytic set such that its complexification Xℂ ⊂ ℂN is normal with an isolated singularity at 0. Let fℝ : Xℝ → ℝ a real analytic function such that its complexification fℂ : Xℂ → ℂ has an isolated singularity at 0 in Xℂ. Assuming an orientation given on to a connected component A of we associate a compact cycle Γ(A) in the Milnor fiber of fℂ which determines completely the poles of the meromorphic extension of or equivalently the asymptotics when T → ±∞ of the oscillating integrals . A topological construction of Γ(A) is given. This completes the results of [BM] paragraph 6.
Contact Schwarzian Derivatives
Authors: Fox Daniel J. F.
Published: July 2016

H. Sato introduced a Schwarzian derivative of a contactomorphism of ℝ3 and with T. Ozawa described its basic properties. In this note their construction is extended to all odd dimensions and to non-flat contact projective structures. The contact projective Schwarzian derivative of a contact projective structure is defined to be a cocycle of the contactomorphism group taking values in the space of sections of a certain vector bundle associated to the contact structure, and measuring the extent to which a contactomorphism fails to be an automorphism of the contact projective structure. For the flat model contact projective structure, this gives a contact Schwarzian derivative associating to a contactomorphism of ℝ2n−1 a tensor which vanishes if and only if the given contactomorphism is an element of the linear symplectic group acting by linear fractional transformation.
Lp Estimates for Multilinear Operators of Strongly Singular Integral Operators
Authors: Li Junfeng , Lu Shanzhen
Published: July 2016

In this paper, the authors get the Lp estimates for the commutators generated by strongly singular integral operators and BMO functions and the corresponding multilinear operators by the scale changing method introduced by Carleson and Sjölin.
Uniqueness Problem for Meromorphic Mappings with Truncated Multiplicities and Moving Targets
Authors: Dethloff Gerd , Tan Tran Van
Published: July 2016

In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of ℙm into ℙPn with (3n+1) moving targets and truncated multiplicities.
Unboundedness of the Ball Bilinear Multiplier Operator
Authors: Diestel Geoff , Grafakos Loukas
Published: July 2016

For all n > 1, the characteristic function of the unit ball in ℝ2n is not the symbol of a bounded bilinear multiplier operator from Lp(ℝn) × Lq(ℝn) to Lr(ℝn) when 1/p + 1/q = 1/r and exactly one of p, q, or r′ = r/(r – 1) is less than 2.
Unitarization of Loop Group Representations of Fundamental Groups
Authors: Dorfmeister Josef , Wu Hongyou
Published: July 2016

In this paper, we give a characterization of the simultaneous unitarizability of any finite set of SL(2, ℂ)-valued functions on and determine all possible ways of the unitarization. Such matrix functions can be regarded as images of the generators for the fundamental group of a surface in an -family, and the results of this paper have applications in the construction of constant mean curvature surfaces in space.
A New Version of α-Tight Closure
Authors: Vraciu Adela
Published: July 2016

Hara and Yoshida introduced a notion of α-tight closure in 2003, and they proved that the test ideals given by this operation correspond to multiplier ideals. However, their operation is not a true closure. The alternative operation introduced here is a true closure. Moreover, we define a joint Hilbert-Kunz multiplicity that can be used to test for membership in this closure. We study the connections between the Hara-Yoshida operation and the one introduced here, primarily from the point of view of test ideals. We also consider variants with positive real exponents.
Descent for l-Adic Polylogarithms
Authors: Douai Jean-Claude , Wojtkowiak Zdzisław
Published: July 2016

Let L be a finite Galois extension of a number field K. Let G:= Gal(L/K). Let z1,…, zN ∊ L* \ {1} and let m1 …, mN ∊ ℚl. Let us assume that the linear combination of l-adic polylogarithms (constructed in some given way) is a cocycle on GL and that the formal sum is G-invariant. Then we show that cn determines a unique cocycle sn on GK. We also prove a weak version of Zagier conjecture for l-adic dilogarithm. Finally we show that if c2 is “motivic” (m1,…, mN ∊ ℚ) then s2 is also “motivic”.
Equi-Distribution of Values for the Third and the Fifth Painlevé Transcendents
Authors: Shimomura Shun
Published: July 2016

We show equi-distribution properties of values for the third and the fifth Painlevé transcendents in a sectorial domain. For our purpose we define a characteristic function of sectorial domain type by employing value distribution theory in a half plane. Some special cases admit analogues of Borel exceptional values. Similar results are obtained for modified versions of these Painlevé transcendents, which are of infinite growth order.
Variétés Singulières et Extension des Fonctions Holomorphes
Authors: Duquenoy Vincent , Mazzilli Emmanuel
Published: July 2016

In this paper, we study a problem of extension of holomorphic functions given on a complex hypersurface with singularities on the boundary of a strictly pseudoconvex domain.
Hereditary Semi-Primary Rings and Tri-Angular Matrix Rings
Authors: Harada Manabu
Published: July 2016

It is well known that the semi-simple rings with minimum conditions coincide with the rings of global homological dimension zero and that the hereditary rings coincide with the rings of global dimension one. Eilenberg, Jans, Nagao and Nakayama gave some properties of hereditary rings in [4] and [11], which relate to global dimension of factor rings. As an example of non-commutative hereditary ring we know a tri-angular matrix ring over a semi-simple ring.
Character Theory of Finite Groups with Trivial Intersection Subsets
Authors: Walter John H.
Published: July 2016

This paper arose out of an effort to present a result which simplifies the application of the theory of blocks to what is often called the theory of exceptional characters. In order to obtain the most effective use of this result, it is necessary to reformulate part of this theory. Thus we present a development which explains an application of R. Brauer’s main theorem on generalized decomposition numbers. In particular, we improve a result of D. Gorenstein and the author [8; Proposition 25]. These results are needed in a forthcoming paper and will simplify somewhat the use of this theory in existing papers. We are interested principally in determining the values of certain irreducible characters on trivial intersection subsets. The organization of the theory presented here is influenced by an exposition of M. Suzuki [13] and uses concepts introduced by W. Feit and J. G. Thompson [7]. Also it is hoped that this exposition will serve as an introduction to the theory.
A Theorem of Harrison, Kummer Theory, and Galois Algebras
Authors: Chase S. U. , Rosenberg Alex
Published: July 2016

Let R be a field and S a separable algebraic closure of R with galois group R. In [8] Harrison succeeded in describing R/′R in terms of R only. More precisely, he constructed a certain complex (R, Q/Z) and proved Homc, where Homc denotes continuous homomorphisms and H2 stands for the second cohomology group of the complex . In this paper, which is mainly expository in nature, we reexamine Harrison’s proof and show how [8] connects with Kummer theory and the theory of galois algebras [16]. We emphasize that most of the ideas on which this paper is based originate in [8].
Galois Theory for Rings with Finitely Many Idempotents
Authors: Villamayor O. E. , Zelinsky D.
Published: July 2016

In [5], Chase, Harrison and Rosenberg proved the Fundamental Theorem of Galois Theory for commutative ring extensions S ⊃ R under two hypotheses: (i) 5 (and hence R) has no idempotents except 0 and l; and (ii) 5 is Galois over R with respect to a finite group G—which in the presence of (i) is equivalent to (ii′): S is separable as an R-algebra, finitely generated and projective as an R-module, and the fixed ring under the group of all R-algebra automorphisms of S is exactly R.
A Note on Triple Systems and Totally Geodesic Submanifolds in a Homogeneous Space
Authors: Sagle Arthur A.
Published: July 2016

In the study of nonassociative algebras various “triple systems” frequently arise from the associator function and other multilinear objects. In particular Lie triple systems arise in the study of Jordan algebras and a generalization of a Lie triple system arises in Malcev algebras. Lie triple systems also are used to study totally geodesic submanifolds of a Riemannian symmetric space. We shall show how a generalization of Lie triple systems also arises from the study of curvature and geodesies of a torsion free connexion on a manifold and bring out the relation of this to various nonassociative algebras.
ε-Entropy of the Brownian Motion with the Multi-Dimensional Spherical Parameter
Authors: Baba Yoshikazu
Published: July 2016

M.S. Pinsker [3] has given a general method of calculating the ε-entropy of a Gaussian process and obtained, for example, an exact proof of the estimate for the ε-entropy of the ordinary Brownian motion B(t), 0 ≦ t ≦ 1, which was presented without proof by A.N. Kolmogorov [1].
Spectral Type of One-Parameter Group of Unitary Operators with Transversal Group
Authors: Kowada Masasi
Published: July 2016

It is an important problem to determine the spectral type of automorphisms or flows on a probability measure space. We shall deal with a unitary operator U and a 1-parameter group of unitary operators {Ut} on a separable Hilbert space H, and discuss their spectral types, although U and {Ut} are not necessarily supposed to be derived from an automorphism or a flow respectively.
On the Galois Cohomology Group of the Ring of Integers in a Global Field and its Adele Ring
Authors: Furuta Yoshiomi , Sawada Yasuaki
Published: July 2016

By a global field we mean a field which is either an algebraic number field, or an algebraic function field in one variable over a finite constant field. The purpose of the present note is to show that the Galois cohomology group of the ring of integers of a global field is isomorphic to that of the ring of integers of its adele ring and is reduced to asking for that of the ring of local integers.
The Singular Measure of a Dirichlet Space
Authors: Itô Masayuki
Published: July 2016

We [4], [5] examined some properties of balayaged measures in the theory of a Dirichlet space. In those papers, we showed that the singular measure of a Dirichlet space plays some important roles. In this paper, we shall precisely examine some properties of the singular measure of a Dirichlet space. Let X be a locally compact Hausdorff space in which there exists a positive Radon measure ξ which is everywhere dense in X.
A System of Mutually Contradictory n Abstractions Whose Proper Sub-Systems Are all Mutually Consistent
Authors: Ono Katuzi , Ohta Minolu
Published: July 2016

It has been pointed out by K. ONO that there is a pair of mutually contradictory abstractions, each of which is self-consistent. Afterwards, Y. INOUE pointed out that there is a vast class of such pairs which is as vast as the class of all the Russell-type paradoxes. It must be a natural course of matter to ask the following question: For every number n, is there a system of mutually contradictory abstractions whose proper subsystems are all mutually consistent?