bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Auslander-Reiten quiver of an infinitesimal group
Authors: Farnsteiner Rolf
Published: July 2016

Letbe an infinitesimal group scheme, defined over an algebraically closed field of characteristic p. We employ rank varieties of-modules to study the stable Auslander-Reiten quiver of the distribution algebra of. As in case of finite groups, the tree classes of the AR-components are finite or infinite Dynkin diagrams, or Euclidean diagrams. We classify the components of finite and Euclidean type in caseis supersolvable or a Frobenius kernel of a smooth, reductive group.
On the unramified common divisor of discriminants of integers in a normal extension
Authors: Oka Satomi
Published: July 2016

Let F be an algebraic number field of a finite degree, and K be a normal extension over F of a finite degree n. Let be a prime ideal of F which is unramified in K/F, be a prime ideal of K dividing such that . Denote by δ(K/F) the greatest common divisor of discriminants of integers of K with respect to K/F. Then, divides δ(K/F) if and only if
Gorenstein Schemes on General Hypersurfaces of ℙr
Authors: Ragusa Alfio , Zappalà Giuseppe
Published: July 2016

It is completely known the characterization of all Hilbert functions and all graded Betti numbers for 3-codimensional arithmetically Gorenstein subschemes of ℙr (works of Stanley [St] and Diesel [Di]). In this paper we want to study how geometrical information on the hypersurfaces of minimal degree containing such schemes affect both their Hilbert functions and graded Betti numbers. We concentrate mainly on the case of general hypersurfaces and of irreducible hypersurfaces, for which we find strong restrictions for the Hilbert functions and graded Betti numbers of their subschemes.
A bound on certain local cohomology modules and application to ample divisors
Authors: Albertini Claudia , Brodmann Markus
Published: July 2016

We consider a positively graded noetherian domain R = ⊕n∈NoRn for which R0 is essentially of finite type over a perfect field K of positive characteristic and we assume that the generic fibre of the natural morphism π: Y = Proj(R) → Y0 = Spec(R0) is geometrically connected, geometrically normal and of dimension > 1. Then we give bounds on the “ranks” of the n-th homogeneous part H2(R)n of the second local cohomology module of R with respect to R+:= ⊕m>0Rm for n < 0. If Y is in addition normal, we shall see that the R0-modules H2R+ (R)n are torsion-free for all n < 0 and in this case our bounds on the ranks furnish a vanishing result. From these results we get bounds on the first cohomology of ample invertible sheaves in positive characteristic.
Morse inequalities for covering manifolds
Authors: Todor Radu , Chiose Ionuţ , Marinescu George
Published: July 2016

We study the existence of L2 holomorphic sections of invariant line bundles over Galois coverings. We show that the von Neumann dimension of the space of L2 holomorphic sections is bounded below under weak curvature conditions. We also give criteria for a compact complex space with isolated singularities and some related strongly pseudoconcave manifolds to be Moishezon. As applications we prove the stability of the previous Moishezon pseudoconcave manifolds under perturbation of complex structures as well as weak Lefschetz theorems.
Formulae for the relative class number of an imaginary abelian field in the form of a determinant
Authors: Kučera Radan
Published: July 2016

There is in the literature a lot of determinant formulae involving the relative class number of an imaginary abelian field. Usually such a formula contains a factor which is equal to zero for many fields and so it gives no information about the class number of these fields. The aim of this paper is to show a way of obtaining most of these formulae in a unique fashion, namely by means of the Stickelberger ideal. Moreover some new and non-vanishing formulae are derived by a modification of Ramachandra’s construction of independent cyclotomic units.
Existence of functions in weighted sobolev spaces
Authors: Futamura Toshihide , Mizuta Yoshihiro
Published: July 2016

The aim of this paper is to determine when there exists a quasicontinuous Sobolev function whose trace is the characteristic function of a bounded set where with

As application we discuss the existence of harmonic measures for weighted p-Laplacians in the unit ball.
On the Galois module structure of ideal class groups
Authors: Komatsu Toru , Nakano Shin
Published: July 2016

Let K/k be a Galois extension of a number field of degree n and p a prime number which does not divide n. The study of the p-rank of the ideal class group of K by using those of intermediate fields of K/k has been made by Iwasawa, Masley et al., attaining the results obtained under respective constraining assumptions. In the present paper we shall show that we can remove these assumptions, and give more general results under a unified viewpoint. Finally, we shall add a remark on the class numbers of cyclic extensions of prime degree of Q.
On holomorphic maps with only fold singularities
Authors: Ando Yoshifumi
Published: July 2016

Let f : N ≡ P be a holomorphic map between n-dimensional complex manifolds which has only fold singularities. Such a map is called a holomorphic fold map. In the complex 2-jet space J2(n,n;C), let Ω10 denote the space consisting of all 2-jets of regular map germs and fold map germs. In this paper we prove that Ω10 is homotopy equivalent to SU(n + 1). By using this result we prove that if the tangent bundles TN and TP are equipped with SU(n)-structures in addition, then a holomorphic fold map f canonically determines the homotopy class of an SU(n + 1)-bundle map of TN ⊕ θN to TP⊕ θP, where θN and θP are the trivial line bundles.
Asymptotic expansions of recursion coefficients of orthogonal polynomials with truncated exponential weights
Authors: Joung Haewon
Published: July 2016

Let β > 0 and , define and where a2n denotes Mhaskar-Rahmanov-Staff number for Wβ. Let be the leading coefficients of the nth orthonormal polynomial corresponding to Wβ,cn and write . It is shown that if c > 1 and β is a positive even integer then has an asymptotic expansion. Also when 0 < c < 1, asymptotic expansions of recursion coefficients of the truncated Hermite weights are given.
Families of solvable Frobenius subgroups in finite groups
Authors: Lescot Paul
Published: July 2016

We introduce the notion of abelian system on a finite group G, as a particular case of the recently defined notion of kernel system (see this Journal, September 2001). Using a famous result of Suzuki on CN-groups, we determine all finite groups with abelian systems. Except for some degenerate cases, they turn out to be special linear group of rank 2 over fields of characteristic 2 or Suzuki groups. Our ideas were heavily influenced by [1] and [8].
The moduli space of bilevel-6 abelian surfaces
Authors: Sankaran G. K. , Spandaw J. G.
Published: July 2016

We show that the moduli space of abelian surfaces with polarisation of type (1,6) and a bilevel structure has positive Kodaira dimension and indeed pg ≥ 3. To do this we show that three of the Siegel cusp forms with character for the paramodular symplectic group constructed by Gritsenko and Nikulin are cusp forms without character for the modular group associated to this moduli problem. We then calculate the divisors of the corresponding differential forms, using information about the fixed loci of elements of the paramodular group previously obtained by Brasch.
On the rational solutions of q-Painlevé V equation
Authors: Masuda Tetsu
Published: July 2016

We give an explicit determinant formula for a class of rational solutions of a q-analogue of the Painlevé V equation. The entries of the determinant are given by the continuous q-Laguerre polynomials.
Multiplier Hermitian structures on Kähler manifolds
Authors: Mabuchi Toshiki
Published: July 2016

The main purpose of this paper is to make a systematic study of a special type of conformally Kähler manifolds, called multiplier Hermitian manifolds, which we often encounter in the study of Hamiltonian holomorphic group actions on Kähler manifolds. In particular, we obtain a multiplier Hermitian analogue of Myers’ Theorem on diameter bounds with an application (see [M5]) to the uniquness up to biholomorphisms of the “Kähler-Einstein metrics” in the sense of [M1] on a given Fano manifold with nonvanishing Futaki character.
On Osgood-Yang’s conjecture and Mues conjecture
Authors: Yi Hong-Xun , Li Yu-Hua
Published: July 2016

In this paper, we deal with the relation between the characteristic functions of meromorphic functions that share three values CM. As applications of our main results, we shall affirmatively settle two conjectures proposed by Mues and Osgood-Yang.
The Hardy-Littlewood property of flag varieties
Authors: Watanabe Takao
Published: July 2016

We study the asymptotic distribution of rational points on a generalized flag variety which are of bounded height and satisfy some congruence conditions in the formulation analogous to a strongly Hardy-Littlewood variety.
A combinatorial identity for the derivative of a theta series of a finite type root lattice
Authors: Naito Satoshi
Published: July 2016

Let be a (not necessarily simply laced) finite-dimensional complex simple Lie algebra with the Cartan subalgebra and Q ⊂ * the root lattice. Denote by ΘQ(q) the theta series of the root lattice Q of . We prove a curious “combinatorial” identity for the derivative of ΘQ(q), i.e. for by using the representation theory of an affine Lie algebra.
Algebro-geometric version of Nevanlinna’s lemma on logarithmic derivative and applications
Authors: Yamanoi Katsutoshi
Published: July 2016

In this paper we shall establish some generalization of Nevanlinna’s Lemma on Logarithmic Derivative to the case of meromorphic maps from a finite analytic covering space over the m-dimensional complex affine space ℂm to a smooth complex projective variety. Then we shall apply this to “the Second Main Theorem” in Nevanlinna theory in several complex variables.
A global theory of flexes of periodic functions
Authors: Thorbergsson Gudlaugur , Umehara Masaaki
Published: July 2016

For a real valued periodic smooth function u on R, n ≥ 0, one defines the osculating polynomial φs (of order 2n + 1) at a point s ∈ R to be the unique trigonometric polynomial of degree n, whose value and first 2n derivatives at s coincide with those of u at s. We will say that a point s is a clean maximal flex (resp. clean minimal flex) of the function u on S1 if and only if φs ≥ u (resp. φs ≤ u) and the preimage (φ - u)-1(0) is connected. We prove that any smooth periodic function u has at least n + 1 clean maximal flexes of order 2n + 1 and at least n + 1 clean minimal flexes of order 2n + 1. The assertion is clearly reminiscent of Morse theory and generalizes the classical four vertex theorem for convex plane curves.
Modular forms arising from zeta functions in two variables attached to prehomogeneous vector spaces related to quadratic forms
Authors: Ueno Takahiko
Published: July 2016

In this paper, we prove the functional equations for the zeta functions in two variables associated with prehomogeneous vector spaces acted on by maximal parabolic subgroups of orthogonal groups. Moreover, applying the converse theorem of Weil type, we show that elliptic modular forms of integral or half integral weight can be obtained from the zeta functions.
Topological triviality of families of functions on analytic varieties
Authors: Ruas Maria Aparecida Soares , Tomazella João Nivaldo
Published: July 2016

We present in this paper sufficient conditions for the topological triviality of families of germs of functions defined on an analytic variety V. The main result is an infinitesimal criterion based on a convenient weighted inequality, similar to that introduced by T. Fukui and L. Paunescu in [8]. When V is a weighted homogeneous variety, we obtain as a corollary, the topological triviality of deformations by terms of non negative weights of a weighted homogeneous germ consistent with V. Application of the results to deformations of Newton non-degenerate germs with respect to a given variety is also given.
On symplectic fillings of links of rational surface singularities with reduced fundamental cycle
Authors: Bhupal Mohan
Published: July 2016

We prove that every symplectic filling of the link of a rational surface singularity with reduced fundamental cycle admits a rational compactification, possibly after a modification of the filling in a collar neighbourhood of the link.
Bergman completeness of hyperconvex manifolds
Authors: Chen Bo-Yong
Published: July 2016

We proved that any hyperconvex manifold has a complete Bergman metric.
Types of complete Infinitely sheeted Planes
Authors: Nakai Mitsuru
Published: July 2016

We will answer negatively to the question whether the completeness of infinitely sheeted covering surfaces of the extended complex plane have anything to do with their types being parabolic or hyperbolic. This will be accomplished by giving a one parameter family {W[α]: α ∈ A} of complete infinitely sheeted planes W[α] depending on the parameter set A of sequences α = (an)n>1 of real numbers 0 < an ≤ 1/2 (n ≥ 1) such that W[α] is parabolic for ‘small’ α’s and hyperbolic for ‘large’ α’s.
On l-Adic Iterated Integrals, II Functional Equations and l-Adic Polylogarithms
Authors: Wojtkowiak Zdzislaw
Published: July 2016

We continue to study l-adic iterated integrals introduced in the first part. We shall show that the l-adic iterated integrals satisfy essentially the same functional equations as the classical complex iterated integrals. Next we are studying l-adic analogs of classical polylogarithms.
L2Extension for jets of holomorphic sections of a Hermitian line Bundle
Authors: Popovici Dan
Published: July 2016

Let (X, ω) be a weakly pseudoconvex Kähler manifold,Y ⊂ Xa closed submanifold defined by some holomorphic section of a vector bundle overX, andLa Hermitian line bundle satisfying certain positivity conditions. We prove that for any integerk> 0, any section of the jet sheafwhich satisfies a certain L2condition, can be extended into a global holomorphic section ofLoverXwhose L2growth on an arbitrary compact subset ofXis under control. In particular, ifYis merely a point, this gives the existence of a global holomorphic function with an L2norm under control and with prescribed values for all its derivatives up to orderkat that point. This result generalizes the L2extension theorems of Ohsawa-Takegoshi and of Manivel to the case of jets of sections of a line bundle. A technical difficulty is to achieve uniformity in the constant appearing in the final estimate. To this end, we make use of the exponential map and of a Rauch-type comparison theorem for complete Riemannian manifolds.
A Vanishing Theorem
Authors: Laytimi F. , Nahm W.
Published: July 2016

The main result is a general vanishing theorem for the Dolbeault cohomology of an ample vector bundle obtained as a tensor product of exterior powers of some vector bundles. It is also shown that the conditions for the vanishing given by this theorem are optimal for some parameter values.
Two-dimensional symmetric stable distributions and Their projections
Authors: Kojo Katsuya
Published: July 2016

We study the problem whether a given 2-dimensional symmetric stable distribution with index α (0 < α ≤ 1) is determined by its 1-dimensional projections in some specified directions. We give some conditions for the affirmative answer and for the negative answer.
A Mirror Construction for the Totally Nonnegative Part of the Peterson Variety
Authors: Rietsch Konstanze
Published: July 2016

We explain how A. Givental’s mirror symmetric family [14] to the typeAag variety and its proposed generalization [3] to partial ag varieties by Batyrev, Ciocan-Fontanine, Kim and van Straten relate to the Peterson varietyY ⊂ SLn/B. We then use this theory to describe the totally nonnegative part ofY, extending a result from [30].
Carleson measures for weighted Hardy-sobolev spaces
Authors: Cascante Carme , Ortega Joaquin M.
Published: July 2016

We obtain characterizations of positive Borel measures µ on Bn so that some weighted Hardy-Sobolev are imbedded in Lp(dµ), where w is an Ap weight in the unit sphere of Cn.
Infinitesimal Invariant and vector bundles
Authors: Pirola Gian Pietro , Rizzi Cecilia
Published: July 2016

We study the Saito-Ikeda infinitesimal invariant of the cycle defined by curves in their Jacobians using rank k + 1 vector bundles. We give a criterion for which the higher cycle class map is not trivial. When k = 2, this turns out to be strictly linked to the Petri map for vector bundles. In this case we can improve a result of Ikeda: an explicit construction on a curve of genus g ≥ 10 shows the existence of a non trivial element in the higher Griffiths group.
Estimates for the Products of the Green Function and the Martin Kernel
Authors: Hirata Kentaro
Published: July 2016

Let Ω be a proper subdomain of ℝn, n ≥ 2, and let x0∈ Ω be fixed. By GΩ and KΩ we denote the Green function and the Martin kernel for Ω, respectively. Under a certain assumption on Ω near a boundary point ξ, we show that the product GΩ(x, x0)KΩ(x, ξ) is comparable to |x - ξ|2-n for x in a nontangential cone with vertex at ξ. We also give an estimate for the product KΩ(x, ξ)KΩ(x,η) in a uniform domain, where η is another boundary point.
Symmetry on Linear Relations for Multiple Zeta Values
Authors: Ihara Kentaro , Ochiai Hiroyuki
Published: July 2016

We find a symmetry for the reflection groups in the double shuffle space of depth three. The space was introduced by Ihara, Kaneko and Zagier and consists of polynomials in three variables satisfying certain identities which are connected with the double shuffle relations for multiple zeta values. Goncharov has defined a space essentially equivalent to the double shuffle space and has calculated the dimension. In this paper we relate the structure among multiple zeta values of depth three with the invariant theory for the reflection groups and discuss the dimension of the double shuffle space in this view point.
Analytic Jet Parametrization for CR Automorphisms of Some Essentially Finite CR Manifolds
Authors: Kim Sung-Yeon
Published: July 2016

In this paper we construct analytic jet parametrizations for the germs of real analytic CR automorphisms of some essentially finite CR manifolds on their finite jet at a point. As an application we show that the stability groups of such CR manifolds have Lie group structure under composition with the topology induced by uniform convergence on compacta.
Rigidity of Linear Strands and Generic Initial Ideals
Authors: Murai Satoshi , Singla Pooja
Published: July 2016

Let K be a field, S a polynomial ring and E an exterior algebra over K, both in a finite set of variables. We study rigidity properties of the graded Betti numbers of graded ideals in S and E when passing to their generic initial ideals. First, we prove that if the graded Betti numbers for some i > 1 and k ≥ 0, then for all q ≥ i, where I ⊂ S is a graded ideal. Second, we show that if for some i > 1 and k ≥ 0, then for all q ≥ 1, where I ⊂ E is a graded ideal. In addition, it will be shown that the graded Betti numbers for all i ≥ 1 if and only if I(k) and I(k+1) have a linear resolution. Here I(d) is the ideal generated by all homogeneous elements in I of degree d, and R can be either the polynomial ring or the exterior algebra.
Nonrational Weighted Hypersurfaces
Authors: Okada Takuzo
Published: July 2016

The aim of this paper is to construct (i) infinitely many families of nonrational ℚ-Fano varieties of arbitrary dimension ≥ 4 with at most quotient singularities, and (ii) twelve families of nonrational ℚ-Fano threefolds with at most terminal singularities among which two are new and the remaining ten give an alternate proof of nonrationality to known examples. These are constructed as weighted hypersurfaces with the reduction mod p method introduced by Kollár [10].
C∞-Convergence of Circle Patterns to Minimal Surfaces
Authors: Lan Shi-Yi , Dai Dao-Qing
Published: July 2016

Given a smooth minimal surface F: Ω → ℝ3 defined on a simply connected region Ω in the complex plane ℂ, there is a regular SG circle pattern . By the Weierstrass representation of F and the existence theorem of SG circle patterns, there exists an associated SG circle pattern in ℂ with the combinatoric of . Based on the relationship between the circle pattern and the corresponding discrete minimal surface F∊: → ℝ3 defined on the vertex set of the graph of , we show that there exists a family of discrete minimal surface Γ∊: → ℝ3, which converges in C∞(Ω) to the minimal surface F: Ω → ℝ3 as ∊ → 0.
Logarithmic Vector Fields and Hyperbolicity
Authors: Rousseau Erwan
Published: July 2016

Using vector fields on logarithmic jet spaces we obtain some new positive results for the logarithmic Kobayashi conjecture about the hyperbolicity of complements of curves in the complex projective plane. We are interested here in the cases where logarithmic irregularity is strictly smaller than the dimension. In this setting, we study the case of a very generic curve with two components of degrees d1 ≤ d2 and prove the hyperbolicity of the complement if the degrees satisfy either d1 ≥ 4, or d1 = 3 and d2 ≥ 5, or d1 = 2 and d2 ≥ 8, or d1 = 1 and d2 ≥ 11. We also prove that the complement of a very generic curve of degree d at least equal to 14 in the complex projective plane is hyperbolic, improving slightly, with a new proof, the former bound obtained by El Goul.
Truncated Euler Systems over Imaginary Quadratic Fields
Authors: Seo Soogil
Published: July 2016

Let K be an imaginary quadratic field and let F be an abelian extension of K. It is known that the order of the class group ClF of F is equal to the order of the quotient UF/ElF of the group of global units UF by the group of elliptic units ElF of F. We introduce a filtration on UF/ElF made from the so-called truncated Euler systems and conjecture that the associated graded module is isomorphic, as a Galois module, to the class group. We provide evidence for the conjecture using Iwasawa theory.
Characterization of Domains in ℂn by their Noncompact Automorphism Groups
Authors: Thai Do Duc , Thu Ninh Van
Published: July 2016

In this paper, the characterization of domains in ℂn by their noncompact automorphism groups are given.
An Extension of Poincaré Formula in Integral Geometry
Authors: Kurita Minoru
Published: July 2016

A curve c2 of finite length L2 moves on a euclidean plane. Let the number of points of intersection of c2 with the fixed, curve C1 of length Ls1 be n, and the element of kinematic measure of the position of c2 be dK.
A Note on the Differential Forms on Everywhere Normal Varieties
Authors: Kawahara Yûsaku
Published: July 2016

A. Weil proposed in his book “Foundations of algebraic geometry” several problems concerning differential forms on algebraic varieties, S. Koizumi has proved that if ω is a differential form on a complete variety U without multiple point, which is finite at every point of IT, then ω is the differential form of the first kind. The following example shows that on everywhere normal varieties with multiple points this statement holds no more; that is: A differential form on a everywhere normal variety which is finite on every simple point of its variety is not always the differential form of the first kind.
Lefschetz operator and local Langlands modℓ: The regular case
Authors: Dat Jean-François
Published: July 2016

Letpandℓbe two distinct primes. The aim of this paper is to show how, under a certain congruence hypothesis, the modℓcohomology complex of the Lubin-Tate tower, together with a natural Lefschetz operator, provides a geometric interpretation of Vignéras’s local Langlands correspondence moduloℓfor unipotent representations.
Some conjectures on endoscopic representations in odd orthogonal groups
Authors: Ginzburg David , Jiang Dihua
Published: July 2016

In this paper, we introduce two conjectures on characterizations of endoscopy structures of irreducible generic cuspidal automorphic representations of odd special orthogonal groups in terms of nonvanishing of certain period of automorphic forms. We discuss a relation between the two conjectures and prove that a special case of Conjecture 1 (and hence Conjecture 2) is true.
Matrix coefficients of the large discrete series representations of Sp(2; R) as hypergeometric series of two variables
Authors: Oda Takayuki
Published: July 2016

We investigate the radial part of the matrix coefficients with minimal K-types of the large discrete series representations of Sp(2; R). They satisfy certain difference-differential equations derived from Schmid operators. This system is reduced to a holonomic system of rank 4, which is finally found to be equivalent to higher-order hypergeometric series in the sense of Appell and Kampé de Fériet.
The topology of an open manifold with radial curvature bounded from below by a model surface with finite total curvature and examples of model surfaces
Authors: Tanaka Minoru , Kondo Kei
Published: July 2016

We construct distinctive surfaces of revolution with finite total curvature whose Gauss curvatures are not bounded. Such a surface of revolution is employed as a reference surface of comparison theorems in radial curvature geometry. Moreover, we prove that a complete noncompact Riemannian manifold M is homeomorphic to the interior of a compact manifold with boundary if the manifold M is not less curved than a noncompact model surface of revolution and if the total curvature of the model surface is finite and less than 2π. By the first result mentioned above, the second result covers a much wider class of manifolds than that of complete noncompact Riemannian manifolds whose sectional curvatures are bounded from below by a constant.
Nonarchimedean geometry of Witt vectors
Authors: Kedlaya Kiran S.
Published: July 2016

LetRbe a perfect 𝔽-algebra equipped with the trivial norm. LetW(R) be the ring ofp-typical Witt vectors overRequipped with thep-adic norm. At the level of nonarchimedean analytic spaces (in the sense of Berkovich), we demonstrate a close analogy betweenW(R) and the polynomial ringR[T] equipped with the Gauss norm, in which the role of the structure morphism fromRtoR[T] is played by the Teichmüller map. For instance, we show that the analytic space associated toRis a strong deformation retract of the space associated toW(R). We also show that each fiber forms a tree under the relation of pointwise comparison, and we classify the points of fibers in the manner of Berkovich’s classification of points of a nonarchimedean disk. Some results pertain to the study ofp-adic representations of étale fundamental groups of nonarchimedean analytic spaces (i.e., relativep-adic Hodge theory).
An Application of the Path-Space Technique to the Theory of Triads
Authors: Nomura Yasutoshi
Published: July 2016

One of the most powerful tools in homotopy theory is the homotopy groups of a triad introduced by Blakers and Massey in [1]. Our aim here is to develop systematically the formal, elementary aspects of the theory of a generalized triad and the mapping track associated with it. This will be used in §5 to deduce a result (Theorem 5.5) which seems to be closely related to an exact sequence established by Brown [2].
A Criterion for a Set and Its Image under Quasiconformal Mapping to be of α(0 < α ≦ 2)-Dimensional Measure Zero
Authors: Ikoma Kazuo
Published: July 2016

Let w = w(z) be any K-quasiconformai mapping (in the sense of Pfluger-Ahlfors) of a domain D in the z-plane into the w-plane. Since w = w(z) is a measurable mapping (vid. Bers [1]), it transforms any set of Hausdorffs 2-dimensional measure zero in D into such another one. However, A. Mori [5] showed that for 0 < α ≤ 2, any set of -dimensional measure zero in a Jordan domain D is transformed by w = w(z)into a set of α-dimensional measure zero.
A Localization Principle for a Class of Analytic Functions
Authors: Storvick D. A.
Published: July 2016

It has been shown by Kiyoshi Noshiro [8; p. 35] that a bounded analytic function w = f(z) in |z| < 1 having radial limit values of modulus one almost everywhere satisfies a localization principle of the following type. Let (c) be any circular disk: | w − α | < ρ lying inside |w| < 1 whose periphery may be tangent to the circumference |w| = 1. Denote by Δ any component of the inverse image of (c) under w = f(z) and by z = z(ξ) a function which maps |ξ| < 1 onto the simply connected domain Δ in a one-to-one conformal manner. Then, the function

is also a bounded analytic function in | ξ | < 1 with radial limits of modulus one almost everywhere.
Behaviour of Green Lines at Royden’s Boundary of Riemann Surfaces
Authors: Nakai Mitsuru
Published: July 2016

The aim of this paper is to investigate the behaviour of Green lines at Royden’s boundary Γ of a Riemann surface R with the Green function g(z, o) with the fixed pole o in R. We denote by the totality of Green lines L issuing from the fixed point o.
Existence of Linear Connections with Respect to Which Given Tensor Fields are Parallel or Recurrent
Authors: Wong Yung-Chow
Published: July 2016

Let M be an n-dimensional (n≥2) connected C∞-manifold with a linear connection. For simplicity, tensor fields on M will simply be called tensors on M. A tensor S on M is said to be parallel if its covariant derivative is everywhere zero in M, i.e., if ▽S = 0. S is said to be recurrent if its covariant derivative is equal to the tensor product of a covector and S itself, i.e., if ▽S = W⊗S, where W is called the recurrence covector.
Quotients of Pseudo Groups by Invariant Fiberings
Authors: Kuranishi M. , Rodrigues A. M.
Published: July 2016

Let Γ be a continuous pseudo group acting on a manifold M. Denote by (M, M’, ρ) a fibered manifold preserved by transformations in Γ. Then any f in Γ locally induces a local transformation f′ of M′. Denote by Γ/ρ the set of all such f′. Then it might seem natural to expect that Γ/ρ is a continuous pseudo group acting on M′. However the matter is not so simple. For instance, take f′ and g′ in Γ/ρ such that the composition f′°g′ can be defined. Then they can be lifted to local transformations f and g belonging to Γ.
On Feller’s Kernel and the Drichlet Norm
Authors: Fukushima Masatoshi
Published: July 2016

Recently J. L. Doob [2] evaluated the Dirichlet integral of the BLD harmonic funtion on a Green space in terms of its fine boundary values and θ-kernel of L. Naïm.

On the other hand, the general theory of additive functionals of Markov processes enables us to define the concept of the Dirichlet norm of functions with respect to Markov processes.
Time Reversions of Markov Processes
Authors: Nagasawa Masao
Published: July 2016

A time reversion of a Markov process was discussed by Kolmogoroff for Markov chains in 1936 [6] and for a diffusion in 1937 [7l He described it as a process having an adjoint transition probability. Although his treatment is purely analytical, in his case if the process xt has an invariant distribution, the reversed process zt = x-t is the process with the adjoint transition probability. In this discussion, however, it is very restrictive that the initial distribution of the process must be an invariant measure.
On the Distortion and Correspondence under Quasiconformal Mappings in Space
Authors: Ikoma Kazuo
Published: July 2016

Recently many important results on rings and quasiconformal mappings in space have been obtained by B. V. Šabat [9], F. W. Gehring [3], J. Väisälä [11] and others. The modulus of a ring in space can be defined in three apparently different but essentially equivalent ways. (See Gehring [4]). In the theory of quasiconformal mappings in space, some properties for moduli of rings in space play an important role, because the method by means of moduli acts also as a substitute in space for the Riemann mapping theorem which does not hold in space.
On the Double Commutator Algebra of QF-3 Algebras
Authors: Mochizuki H. Y.
Published: July 2016

Introduction and Preliminaries. Nakayama [9] suggested that algebras be classified according to the length of a right projective, injective resolution of the algebra as a left module. Tachikawa [10] showed that an algebra is QF-3 (see [12] for definition) if and only if the length is at least one. He [11] also gave some estimations of the length of the resolution besides relating the length to the size of the double commutator algebra of a faithful projective, injective left ideal.
A New Definition of the n-Dimensional Quasiconformal Mappings
Authors: Caraman Petru
Published: July 2016

In this note we shall extend, for arbitrary n, Pesin’s [11] bidimensional definition for quasiconformal mappings and establish its equivalence with Gehring’s [7] and Väisälä’s [15] definitions.
An Application of the Power Residue Theory to Some Abelian Functions
Authors: Kubota Tomio
Published: July 2016

The aim of this paper is to point out a number-theoretical property of a certain product of values taken by an abelian function at points of finite order of the abelian variety on which the abelian function is considered We use the theory of power residues and the theory of complex multiplication, and the result is somewhat similar to the so-called Stickelberger’s relation in the theory of Gauss sums. A related investigation was previously made by the author in a special case of elliptic curves [2].
Involutory Automorphisms of Groups of odd Order and Their Fixed Point Groups
Authors: Kovács L. G. , Wall G. E.
Published: July 2016

Let G be a finite group of odd order with an automorphism θ of order 2. (We use without further reference the fact, established by W. Feit and J. G. Thompson, that all groups of odd order are soluble.) Let Gθ denote the subgroup of G formed by the elements fixed under θ. It is an elementary result that if Gθ = 1 then G is abelian. But if we merely postulate that Gθ be cyclic, the structure of G may be considerably more complicated—indeed G may have arbitrarily large soluble length.
An Existence Theorem in Potential Theory
Authors: Kishi Masanori
Published: July 2016

1. Concerning a positive lower semicontinuous kernel G on a locally compact Hausdorff space X the following existence theorem was obtained in [3].
Existence of Perfect Picard Sets
Authors: Matsumoto Kikuji
Published: July 2016

LetEbe a totally disconnected compact set in thez-plane and letΩbe its complement with respect to the extended 2-plane. ThenΩis a domain and we can consider a single-valued meromorphic functionf(z) inΩwhich has a transcendental singularity at each point ζ ∊E. Suppose thatEis a null-set of the classWin the sense of Kametani [4] (= the classNBin the sense of Ahlfors and Beurling [1]).
On the Characters of Soluble Groups
Authors: Itô Noboru
Published: July 2016

The theory of representations of finite groups, which was originated by G. Frobenius, has been developed by I. Schur to become popular and studied more and more profoundly by R. Brauer even in the current stage of modern algebra. However, it seems that its applications to the structure theory of finite groups are still far from being satisfactory, partially because these two theories for structure and for representation are not firmly tied up.
On a Hopf Homotopy Classification Theorem
Authors: Uehara Hiroshi
Published: July 2016

There are various generalizations of Hopf’s brilliant theorem, which may be stated, as newly formulated by Alexandroff; all the homotopy classes of the mappings of a compact Hausdorff space X with dim X≦n into an n-sphere Sn are in a (1-1) -correspondence with the elements of the n-dimensional Čech cohomology group Hn(X) with integer coefficients.
A Remark on Finitely Generated Modules
Authors: Nakayama Tadasi
Published: July 2016

Theorem 5 of Azumaya’s recent article can be formulated in the following generalized form:

Let R be a ring. Let m be a finitely generated right-module of R such that mR = m. Assume that m = u1r + ubr + … + umr for every generating system of u1, u2, …, um of m and for every maximal right-ideal r of R. Then m = 0.
Sur l’Existence des Mesures des Condensateurs
Authors: Kishi Masanori
Published: July 2016

Dans l’espace de Dirichlet il existe des mesures des condensateurs et inversement un certain espace de fonctions est léespace de Dirichlet séil y existe des mesures des condensateurs. Dans ce mémoire nous considérons le problème d’existence des mesures des condensateurs par rapport ä un noyau positif et continu au sens large, symétrique ou non.
Corrections to ‘Character Theory of Finite Groups with Trivial Intersection Subsets (Vol 27, 515—524)
Authors: Walter John H.
Published: July 2016

The conditions (TI 1) and (TI 2) are stated for and henceforth in the paper H is understood to be when D is taken to be a T.I. subset of G. Also in the definition of T. I. subset the condition is that D ∩ DG≠ø where ø is the empty set.
Algebraic Deformations of Polarized Varieties
Authors: Matsusaka T.
Published: July 2016

Let V be a projectively embeddable complete non-singular variety of dimension n > 1. Let f be a projective embedding of V, U a non-singular variety, W a non-singular variety and φ a morphism of W onto U such that φ-1(u0) = f(V) for some point u0 of U. Denote by ∑(V) the set of all those complete non-singular fibres φ-1(u), u ∈ U, as we consider all possible (f, U, W). Suppose that we call members of ∑(V) (algebraic) deformations of V and propose to study ∑(V) from the stand point of algebraic geometry, as a generalization of the case of curves. This has been taken up at least locally by Kodaira, Spencer, Kuranishi and others in the case of characteristic 0 from a little more general point of view of complex manifolds (cf. [9] and references given in [16]).
On Osculating Systems of Differential Equations of Type (N, 1, 2)
Authors: Morikawa Hisasi
Published: July 2016

The main subject in the present article has the origin in the following quite primitive question: Linear systems of ordinary differential equations form a nice family. Then, from the projective point of view, what does correspond to linear systems?
On the Singularity of Green functions in Markov Processes
Authors: Kanda Mamoru
Published: July 2016

In the previous paper [6] we have discussed Markov processes in Rd with the Green function G (x, y) satisfying are positive constants), and showed that the regular points of its process are the same as those of α-stable process. The present article is closely related to the previous one.
A Note on Tangential Equivalences
Authors: Shiraiwa Kenichi
Published: July 2016

The main objective of this paper is to prove the following theorem, which generalizes some results of [1], [2], [6]. Our theorem is also suggested by the work of Novikov [5].
On the Hyperelliptic Riemann Surfaces of Infinite Genus with Absolutely Convergent Riemann’s Theta Functions
Authors: Tahara Kenichi
Published: July 2016

The Riemann’s theta functions associated with a closed Riemann surface are absolutely convergent. In the present paper, we shall show an example of an hyperelliptic Riemann surface of infinite genus such that the Riemann’s theta functions associated with are absolutely convergent.
Some Conditions under Which Sequences of Functions are Uniformly Bounded
Authors: Rung D.C.
Published: July 2016

After one introduces the theory of normal families in a course in complex analysis, the usual pattern is to give an example of a non-normal family. One of the simplest, of course, is the sequence fn(z) = nz, n = 1,2, ···. The very devastating effect of multiplying by zero insures the required abnormality!
Existence of Non-trivial Deformations of Inseparable Extension Fields III
Authors: Kimura Hiroshi
Published: July 2016

Let K be an extension of a field k and p denotes the characteristic. In [4] and [5], we proved that if K is inseparable algebraic over k, then considered as an algebra over k, K is not rigid.
Quasi-Flows
Authors: Kubo Izumi
Published: July 2016

The purpose of this paper is to investigate a quasi-flow which is a one-parameter group of non-singular measurable point transformations on a measure space. If, in particular, the transformations are all measure preserving (i.e. a flow is given), the ergodicity together with the mixing property, the spectral or metrical type, increasing partitions of the space and the entropy of the flow are our main interests. Those methods used in the study of a flow are frequently useful for our approach. For example, the concept of a special flow introduced by W. Ambrose [3] plays an important role and the representation of a given flow in terms of a special flow is a powerful tool in the study of flows. L.M. Abramov [1] calculates the entropy of a flow with the help of the representation. As another example we give attention to the work of G. Maruyama [10] and H. Totoki [15] where they discuss a general time-change of flows the basic idea of which was originated by E. Hopf [8]. They discuss the invariant measure of a general time-changed flow and prove that the ergodicity is inherited and the entropy is kept invariant by the time-change. In the study of quasi-flows, we shall use both the repesentation in terms of a special quasi-flow and a time-change. Besides a quasi-flow requires its own methods in the investigation and it gives us some further problems such as the existence of an invariant measure (cf. [4], [5], [6] and [7]) and related topics.
On a Crossed Product of a Division Ring
Authors: Nobusawa Nobuo
Published: July 2016

1. Let R and C be a ring and its center, and G an automorphism group of R of order n. By a factor set {cα,τ}, we mean a system of regular elements cα,τ (α,τ ∈ G) in C such that

(1)
Galois Theory with Infinitely Many Idempotents
Authors: Villamayor O.E. , Zelinsky D.
Published: July 2016

In 1942 Artin proved the linear independence, over a field S, of distinct automorphism of S; in other words if G is a finite group of automorphisms of S and R is the fixed field, then Horn^S, S) is a free S-module with G as basis. Since then, this last condition (“S is G-Galois”) or its equivalents have been used as a postulate in all the Galois theories of rings that are not fields, for example by Dieudonné, Jacobson, Azumaya and Nakayama for noncommutative rings and then in [AG, Appendix] and [CUR] for commutative rings. When S has no idempotents but 0 and 1, [CHR] proves that the ordinary fundamental theorem of Galois theory holds with no real change from the classical, field case.
Monomial Representations and Metabelian Groups
Authors: Basmaji B.G.
Published: July 2016

1. Introduction. In this paper we develop a method to find all the irreducible and inequivalent representations over the complex field C of a family of finite groups that includes the metabelian groups. The outline of the paper is as follows: In §2 we let P be a one-dimensional representation of a subgroup H of a finite group G and find a maximal subgroup K, H ⊆ K ⊆ G, such that an extension P̅ of P to K exists. We show that the induced representation P̅G is irreducible if K is normal in G. In §3 we give all the irreducible and inequivalent representations of the “generalized metabelian group” G, and in particular of the metabelian group, and decompose the group ring CG into its simple components. The convenience of this method is shown in §4 where we determine the representations of the metacyclic group and a metabelian group of order 2sp2, p an odd prime and s|p — l. The algorithm in §5 is supplementary and can be used to find representations of more general groups than the two in §4.
On Boundary Value Problems for Elliptic Equations in a Singular Domain
Authors: Hayashida Kazunari
Published: July 2016

1. Let Ω be a bounded domain in the plane and denotes its closure and boundary by Ω̅ and ∂Ω, respectively. We shall say that the domain Ω is regular, if every point P ∈ ∂û has an 2-dimensional neighborhood U such that dΩ ∩ U can be mapped in a one-to-one way onto a portion of the tangent line through P by a mapping T which together with its inverse is infinitely differentiable. Let L be an elliptic operator of order 2m defined in Ω̅ and let be a normal set of boundary operators of orders mf <2m. If f is a given function in Ω, the boundary value problem II(L,f,Bj) will be to find a solution u of

satisfying

Bju = 0 on ∂Ω, j = 1, …, m.
Note on the Behavior of Solutions of Parabolic Equations with Unbounded Coefficients
Authors: Chen Lu-San
Published: July 2016

Let

be a parabolic differential operator defined in Ω = Rn + (0, ∞), where Rn is the n-dimensional Euclidean space, the point x ∈ Rn is represented by its coordinates (x1,...,xn) and aij(=aji), bi and c are functions in (x,t)∈Ω.
On Some Doubly Transitive Permutation Groups of Degree N And Order 6n(n – 1)
Authors: Iwasaki Shiro , Kimura Hiroshi
Published: July 2016

Let Ω be the set of symbols 1,2,..., n. Let be a doubly transitive group on Ω of order 6n(n — 1) not containing a regular normal subgroup and let be the stabilizer of the set of symbols 1 and 2.
Sur le Principe de Majoration de K. Yosida
Authors: Kishi Masanori
Published: July 2016

Soit X un espace séparé localement compact et dénombrable à l’infini. Désignons par l’espace des fonctions numériques réelles continues sur X et à support compact et par l’espace complété de par la norme uniforme, et par et les sous-ensembles de et constitués par des fonctions non-négatives.
Sur les Directions de Julia des Fonctions Algébroïdes Dans |z| < ∞
Authors: Toda Nobushige
Published: July 2016

L’étude sur les directions de Julia des fonctions méromorphes dans le plan fini est fait présque complètement par Ostrowski [5] et après Rauch [6] etc. l’ont développé.
Units and Class Numbers of Real Quadratic Fields
Authors: Yokoi Hideo
Published: July 2016

The aim of this paper is to prove the following main theorem:

THEOREM. For the discriminant d>0 of a real quadratic field let (x,y) = (t,u) be the least positive integral solution of Pell’s equation x2 — dy2 = 4 and put and denote by hd the ideal class number.
Formal Foundation of Analytical Dynamics Based on the Contact Structure
Authors: Kurita Minoru
Published: July 2016

A systematic treatment of analytical dynamics was given by E. Cartan in [1], where the 1-form plays the fundamental role. We give here a further investigation. One of our main purposes is to clarify relations between dynamical systems and Finsler spaces and the other is to formulate an intrinsic bundle structure of the systems. This paper is closely related to my previous papers [4] [5].
On the Singularity of Green Functions in Markov Processes II
Authors: Kanda Mamoru
Published: July 2016

In the previous paper [3] we have studied Green functions with singularity φ ∈ Φ, especially in connection with regular points.
Stochastic Integrals Based on Martingales Taking Values in Hilbert Space
Authors: Kunita Hiroshi
Published: July 2016

Let H be a separable Hilbert space with inner product (,) and norm ║ ║. We denote by K the set of all linear operators on H. Let be a probability space and suppose we are given a family of σ-fields t≥O such that for O ≤ s ≤ t and .
On a Homology Theory Associated to Foliations
Authors: Shikata Yoshihiro
Published: July 2016

In this note, we associate a foliated singular homology theory to a foliation on a compact manifold X and construct a spectral sequence which relates the foliated homology to the ordinary homology of X. Since the foliated homology is so constructed as to be related closely to a certain topological behavior of the foliation, we may expect that further study of the spectral sequence reveals some information on topology of foliation. The study and applications will be given in a sequel.
A Determinate Logic
Authors: Takeuti Gaisi
Published: July 2016

Let L be a fixed language and K be a set of structures related to L. A sentence in L is said to be K-valid if and only if for every structure in K,
Sample Properties of Weakly Stationary Processes
Authors: Kawata T. , Kubo I.
Published: July 2016

Let X(t) = X(t,ω), – ∞ < t < ∞, be a stationary stochastic process with

and the continuous covariance function

where F(x) is the spectral distribution function.
Evans-Kuramochi Exhaustion Functions on Non-Algebroid Riemann Surfaces
Authors: Skeath J.E.
Published: July 2016

Let denote a non-compact parabolic Riemann surface, and let be compact and such that each frontier point of D is contained in a continuum that is also contained in D.