bluuebunny/crossref_metadata_2025 huggingface dataset:
On Everywhere Dense Imbedding of Free Groups in Lie Groups
Authors: Kuranishi Masatake
Published: July 2016

In this note it will be proved that some kinds of Lie groups (including semi-simple Lie groups) have an everywhere dense subgroup which is algebraically isomorphic to the free group generated by two elements (Theorem 8),

In § 1 characterizations of Lie groups which are approximated by discrete subgroups’ are given. This section is closely connected with a part of the results of Malcev [4] and Matsushima [5], and some theorems are slight modifications of them (Theorems 2 and 3).
On Waring’s problem: Three cubes and a minicube
Authors: Brüdern Jörg , Wooley Trevor D.
Published: July 2016

We establish that almost all natural numbersnare the sum of four cubes of positive integers, one of which is no larger thann5/36. The proof makes use of an estimate for a certain eighth moment of cubic exponential sums, restricted to minor arcs only, of independent interest.
Quasi-socle ideals in Buchsbaum rings
Authors: Goto Shiro , Horiuchi Jun , Sakurai Hideto
Published: July 2016

Quasi-socle ideals, that is, ideals of the formI = Q: mq(q≥ 2), withQparameter ideals in a Buchsbaum local ring (A,m), are explored in connection to the question of whenIis integral overQand when the associated graded ring G(I) ⊕n≥0In/In+1ofIis Buchsbaum. The assertions obtained by Wang in the Cohen-Macaulay case hold true after necessary modifications of the conditions on parameter idealsQand integersq. Examples are explored.
On the residue class distribution of the number of prime divisors of an integer
Authors: Coons Michael , Dahmen Sander R.
Published: July 2016

Let Ω(n) denote the number of prime divisors ofncounting multiplicity. One can show that for any positive integermand allj= 0,1,…,m– 1, we have

withα= 1. Building on work of Kubota and Yoshida, we show that form> 2 and anyj= 0,1,…,m– 1, the error term is noto(xα) for anyα< 1.
Locally conformally Kähler metrics on Kato surfaces
Authors: Brunella Marco
Published: July 2016

We show that every Kato surface admits a locally conformally Kähler metric.
Normality of orbit closures in the enhanced nilpotent cone
Authors: Achar Pramod N. , Henderson Anthony , Jones Benjamin F.
Published: July 2016

We continue the study of the closures of GL(V)-orbits in the enhanced nilpotent coneV × Nbegun by the first two authors. We prove that each closure is an invariant-theoretic quotient of a suitably defined enhanced quiver variety. We conjecture, and prove in special cases, that these enhanced quiver varieties are normal complete intersections, implying that the enhanced nilpotent orbit closures are also normal.
On self-injective algebras of stable dimension zero
Authors: Yoshiwaki Michio
Published: July 2016

LetAbe a self-injective algebra over an algebraically closed field. We study the stable dimension ofA, which is the dimension of the stable module category ofAin the sense of Rouquier. Then we prove thatAis representation-finite if the stable dimension ofAis zero.
Notes on boundedness of spectral multipliers on Hardy spaces associated to operators
Authors: Anh Bui The
Published: July 2016

LetLbe a nonnegative self-adjoint operator onL2(X), whereXis a space of homogeneous type. Assume thatLgenerates an analytic semigroupe–tlwhose kernel satisfies the standard Gaussian upper bounds. We prove that the spectral multiplierF(L) is bounded onfor 0< p< 1, the Hardy space associated to operatorL, whenFis a suitable function.
Isoparametric hypersurfaces with four principal curvatures, II
Authors: Chi Quo-Shin
Published: July 2016

In this sequel to an earlier article, employing more commutative algebra than previously, we show that an isoparametric hypersurface with four principal curvatures and multiplicities (3,4) inS15is one constructed by Ozeki and Takeuchi and Ferus, Karcher, and Münzner, referred to collectively asof OT-FKM type. In fact, this new approach also gives a considerably simpler proof, both structurally and technically, that an isoparametric hypersurface with four principal curvatures in spheres with the multiplicity constraintm2≥2m1-1 is of OT-FKM type, which left unsettled exactly the four anomalous multiplicity pairs (4,5),(3,4),(7,8), and (6, 9), where the last three are closely tied, respectively, with the quaternion algebra, the octonion algebra, and the complexified octonion algebra, whereas the first stands alone in that it cannot be of OT-FKM type. A by-product of this new approach is that we see that Condition B, introduced by Ozeki and Takeuchi in their construction of inhomogeneous isoparametric hypersurfaces, naturally arises. The cases for the multiplicity pairs (4,5), (6, 9), and (7,8) remain open now.
Schatten p-class property of pseudodifferential operators with symbols in modulation spaces
Authors: Kobayashi Masaharu , Miyachi Akihiko
Published: July 2016

It is proved that the pseudodifferential operatorsσt(X, D) belong to the Schattenp-classCp, 0< p≤ 2, if the symbolσ(x,ω) is in certain modulation spaces on
Bounds on the Hilbert-Kunz multiplicity
Authors: Celikbas Olgur , Dao Hailong , Huneke Craig , Zhang Yi
Published: July 2016

In this paper we give new lower bounds on the Hilbert-Kunz multiplicity of unmixed nonregular local rings, bounding them uniformly away from 1. Our results improve previous work of Aberbach and Enescu.
Lowest weights in cohomology of variations of Hodge structure
Authors: Peters Chris , Saito Morihiko
Published: July 2016

LetXbe an irreducible complex analytic space withj:U ↪ Xan immersion of a smooth Zariski-open subset, and let 𝕍 be a variation of Hodge structure of weightnoverU. Assume thatXis compact Kähler. Then, provided that the local monodromy operators at infinity are quasi-unipotent,IHk(X, 𝕍) is known to carry a pure Hodge structure of weightk+n, whileHk(U, 𝕍) carries a mixed Hodge structure of weight at leastk+n. In this note it is shown that the image of the natural mapIHk(X, 𝕍) →Hk(U, 𝕍) is the lowest-weight part of this mixed Hodge structure. In the algebraic case this easily follows from the formalism of mixed sheaves, but the analytic case is rather complicated, in particular when the complementX — Uis not a hypersurface.
On low-dimensional Ricci limit spaces
Authors: Honda Shouhei
Published: July 2016

We call a Gromov–Hausdorff limit of complete Riemannian manifolds with a lower bound of Ricci curvature a Ricci limit space. Furthermore, we prove that any Ricci limit space has integral Hausdorff dimension, provided that its Hausdorff dimension is not greater than 2. We also classify 1-dimensional Ricci limit spaces.
On the uniform spread of almost simple linear groups
Authors: Burness Timothy C. , Guest Simon
Published: July 2016

Let G be a finite group, and let k be a nonnegative integer. We say that G has uniform spread k if there exists a fixed conjugacy class C in G with the property that for any k nontrivial elements x1,…,xk in G there exists y ∊ C such that G = ‹xi,y› for all i. Further, the exact uniform spread of G, denoted by u(G), is the largest k such that G has the uniform spread k property. By a theorem of Breuer, Guralnick, and Kantor, u(G) ≥ 2 for every finite simple group G. Here we consider the uniform spread of almost simple linear groups. Our main theorem states that if G = ‹PSLn (q),g› is almost simple, then u(G) ≥ 2 (unless G ≅ S6), and we determine precisely when u(G) tends to infinity as |G| tends to infinity.
The Brauer–Manin pairing, class field theory, and motivic homology
Authors: Yamazaki Takao
Published: July 2016

For a smooth proper variety over ap-adic field, its Brauer group and abelian fundamental group are related to higher Chow groups by the Brauer–Manin pairing and class field theory. We generalize this relation to smooth (possibly nonproper) varieties, using motivic homology and a variant of Wiesend’s ideal class group. Several examples are discussed.
Logarithmic abelian varieties, III: Logarithmic elliptic curves and modular curves
Authors: Kajiwara Takeshi , Kato Kazuya , Nakayama Chikara
Published: July 2016

We illustrate the theory of log abelian varieties and their moduli in the case of log elliptic curves.
Generic formal fibers and analytically ramified stable rings
Authors: Olberding Bruce
Published: July 2016

LetAbe a local Noetherian domain of Krull dimensiond. Heinzer, Rotthaus, and Sally have shown that if the generic formal fiber ofAhas dimensiond– 1, thenAis birationally dominated by a 1-dimensional analytically ramified local Noetherian ring having residue field finite over the residue field ofA. We explore further this correspondence between prime ideals in the generic formal fiber and 1-dimensional analytically ramified local rings. Our main focus is on the case where the analytically ramified local rings are stable, and we show that in this case the embedding dimension of the stable ring reflects the embedding dimension of a prime ideal maximal in the generic formal fiber, thus providing a measure of how far the generic formal fiber deviates from regularity. A number of characterizations of analytically ramified local stable domains are also given.
Differential operators on quantized flag manifolds at roots of unity, II
Authors: Tanisaki Toshiyuki
Published: July 2016

We formulate a Beilinson-Bernstein-type derived equivalence for a quantized enveloping algebra at a root of 1 as a conjecture. It says that there exists a derived equivalence between the category of modules over a quantized enveloping algebra at a root of 1 with fixed regular Harish-Chandra central character and the category of certain twistedD-modules on the corresponding quantized flag manifold. We show that the proof is reduced to a statement about the (derived) global sections of the ring of differential operators on the quantized flag manifold. We also give a reformulation of the conjecture in terms of the (derived) induction functor.
Simple normal crossing Fano varieties and log Fano manifolds
Authors: Fujita Kento
Published: July 2016

A projective log variety (X, D) is called alog Fano manifoldifXis smooth and ifDis a reduced simple normal crossing divisor onΧwith − (KΧ+D) ample. Then-dimensional log Fano manifolds (X, D) with nonzeroDare classified in this article when the log Fano indexrof (X, D) satisfies eitherr≥n/2withρ(X) ≥ 2 orr≥n− 2. This result is a partial generalization of the classification of logarithmic Fano 3-folds by Maeda.
Modular forms of half-integral weights on SL(2, ℤ)
Authors: Yang Yifan
Published: July 2016

In this paper, we prove that, for an integerrwith (r, 6) = 1 and 0< r <24 and a nonnegative even integers, the set

is isomorphic to

as Hecke modules under the Shimura correspondence. HereMs(1) denotes the space of modular forms of weightis the space of newforms of weight 2kon Γ0(6) that are eigenfunctions with eigenvalues€2and€3for Atkin-Lehner involutionsW2andW3, respectively, and the notation ⊕(12/.) means the twist by the quadratic character (12/-). There is also an analogous result for the cases (r, 6) = 3.
On operator-valued monotone independence
Authors: Hasebe Takahiro , Saigo Hayato
Published: July 2016

We investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant formula. As an application, one can obtain an easy proof of the central limit theorem for the operator-valued case. Moreover, we prove a generalization of Muraki’s formula for the sum of independent random variables and a relation between generating functions of moments and cumulants.
Polarized pairs, log minimal models, and Zariski decompositions
Authors: Birkar Caucher , Hu Zhengyu
Published: July 2016

We continue our study of the relation between log minimal models and various types of Zariski decompositions. Let (X,B) be a projective log canonical pair. We will show that (X,B) has a log minimal model if eitherKX+Bbirationally has a Nakayama–Zariski decomposition with nef positive part, or ifKX+Bis big and birationally has a Fujita–Zariski or Cutkosky–Kawamata–Moriwaki–Zariski decomposition. Along the way we introduce polarized pairs (X,B+P), where (X,B) is a usual projective pair and wherePis nef, and we study the birational geometry of such pairs.
Representations of Algebraic Groups
Authors: Steinberg Robert
Published: July 2016

Our purpose here is to study the irreducible representations of semisimple algebraic groups of characteristic p 0, in particular the rational representations, and to determine all of the representations of corresponding finite simple groups. (Each algebraic group is assumed to be defined over a universal field which is algebraically closed and of infinite degree of transcendence over the prime field, and all of its representations are assumed to take place on vector spaces over this field.)
Invariants of Finite Reflection Groups
Authors: Solomon Louis
Published: July 2016

Let K be a field of characteristic zero. Let V be an n-dimensional vector space over K and let S be the graded ring of polynomial functions on V. If G is a group of linear transformations of V, then G acts naturally as a group of automorphisms of S if we define

The elements of S invariant under all γ ∈ G constitute a homogeneous subring I(S) of S called the ring of polynomial invariants of G.
Homological Invariants of Local Rings
Authors: Uehara Hiroshi
Published: July 2016

In this paper R is a commutative noetherian local ring with unit element 1 and M is its maximal ideal. Let K be the residue field R/M and let {t1,t2,…, tn) be a minimal system of generators for M. By a complex R we mean an R-algebra* obtained by the adjunction of the variables T1. . ., Tp of degree 1 which kill t1,…, tp. The main purpose of this paper is, among other things, to construct an R-algebra resolution of the field K, so that we can investigate the relationship between the homology algebra H (R < T1,…, Tn>) and the homological invariants of R such as the algebra TorR(K, K) and the Betti numbers Bp = dimk TorR(K, K) of the local ring R. The relationship was initially studied by Serre [5].
Classification of Locally Euclidean Spaces
Authors: Sario Leo
Published: July 2016

The classification of Riemann surfaces has largely reached its completion. The purpose of the present paper is to lay the foundation for a new intriguing field in the classification theory: Riemannian spaces with Euclidean metrics. The paper is self-contained, both for the Riemann surface expert and the reader whose main interest is with higher dimensions.
An Operational Calculus for Meromorphic Functions
Authors: Gindler Herbert A.
Published: July 2016

Consider a linear transformation T whose domain D(T) and range R(T) lie in a complex Banach space X. We denote by [X] the class of all linear transformations T for which D(T) = X and T is continuous (bounded). Also, we denote the resolvent set of T by ρ(T) and the spectrum of T by σ(T).
Rings with Ascending Condition on Annihilators
Authors: Faith Carl
Published: July 2016

Quasi-frobenius (= QF) rings have many interesting characterizations. One such, due to Ikeda [17] is that these rings are right (left) artinian and right (left) self-injective. Thus, if R is QF, then R is right (left) noetherian, so each direct sum of injective right R-modules is injective: in particular, each free, hence, each projective, R-module is injective. One object of this paper is to report that this property characterizes QF-rings:
Remarks on a Theorem of Bourbaki
Authors: Auslander M.
Published: July 2016

Bourbaki has established the following theorem which we state without proof as

THEOREM A ([3, Theorem 6, §4]). Let R be a noetherian integrally closed domain and M a finitely generated torsion free R-module. Then there exists a free submodule F of M such that M/F is isomorphic to an ideal in R.

It is our purpose in this note to present a few consequences of this theorem. Before giving these results we briefly review some terminology and known results.
Subnormale Lösungen der Differentialgleichung: w” + p(ez)w’ + q(ez) w + 0
Authors: In Karlsruhe Von H. Wittich
Published: July 2016

In der Differentialgleichung w″+a1(z)w‣w‣+a0(z)w=0 seien die Koeffizienten aj(z) ganze Funktionen. Dann ist jede Lösung w(z) eine ganze Funktion und genau dann von endlicher Ordnung, wenn die Koeffizienten Polynome sind. In diesem Fall gilt für die Ordnung

die Beziehung λ(w)= m/2, m ≧ 0 ganzzahlig.
On Local Maximality for the Coefficient a6
Authors: Jenkins James A. , Ozawa Mitsuru
Published: July 2016

Recently a number of authors have studied the application of Grunsky’s coefficient inequalities to the study of the Bieberbach conjecture for the class of normalized regular univalent functions f(z) in the unit circle |z|< 1

Charzynski and Schiffer [2] applied this result to give an elementary proof of the inequality | a4 | Ȧ 4. One of the present authors [8] proved that if a2 is real non-negative then A natural first step in the study of the inequality for a coefficient is to prove local maximality for a2 near to 2.
On the Boundary Behavior of Conformal Maps
Authors: Warschawski S.E.
Published: July 2016

Suppose Ω is a simply connected domain which is mapped conformally onto a disk. A much studied problem is the behavior of the mapping function at an accessible boundary point P of Ω, in particular the question, under what conditions the map is ‘ “conformai” at such a point (a) in the sense that angles are preserved as P is approached from Ω (“semi-conformality” at P) and (b) the dilatation at P is finite and positive. In his fundamental paper [8] in 1936, A. Ostrowski established a necessary and sufficient condition (depending on the geometry of the domain only) for the validity of the first property which subsumes all previous results and establishes a definitive solution of this problem.
On Self-Intersection Number of a Section on a Ruled Surface
Authors: Nagata Masayoshi
Published: July 2016

Let E be a non-singular projective curve of genus g ≥ 0, P the projective line and let F be the surface E×P. Then it is well known that a ruled surface F* which is birational to F is biregular to a surface which is obtained by successive elementary transformations from F (for the notion of an elementary transformation, see [3]).
On Permutation Groups of Prime Degree p Which Contain at Least Two Classes of Conjugate Subgroups of Index p. II
Authors: Ito Noboru
Published: July 2016

Let p be a prime and let Ω be the set of p symbols 1,2, ..., p, called points. Let be a transitive permutation group on Ω such that

(I) contains a subgroup of index p which is not the stabilizer of a point.
On Principal Function Problem
Authors: Nakai Mitsuru
Published: July 2016

Sario’s theory of principal functions fully discussed in his research monograph [3] with Rodin stems from the principal function problem which is to find a harmonic function p on an open Riemann surface R imitating the ideal boundary behavior of the given harmonic function s in a neighborhood A of the ideal boundary δ of R.
On a Space of Some Theta Functions
Authors: Kitaoka Yoshiyuki
Published: July 2016

In the theory of modular forms there is an interesting problem whether every modular form can be expressed as a linear comination of theta functions. For this Eichler proved in [1] that for a sufficiently large prime q all modular forms of degree — 2m(m = 1,2, · · ·) for Γ0(q) can be represented by linear combinations of theta functios of degree — 2m with level 1 and q. We prove this theorem for q = 2, 3, 5 and 11 by using a theorem of Siegel for q = 2, 3, 5 and a general result of Eichler for q = 11. The former method is shown in Schoeneberg [2].
Characteristic Classes for Spherical Fiber Spaces
Authors: Tsuchiya Akihiro
Published: July 2016

Let SF = SG denote the space , and BSF be the classifying space of SF. Our purpose is to determine H*(BSF: Zp) as a Hopf algebra over Zp where p is an odd prime number. We have announced the main result in [14].
Some Integral Formulas for Hyper-Surfaces in Euclidean Spaces
Authors: Chen Bang-Yen
Published: July 2016

Let M be an oriented hypersurface differentiably immersed in a Euclidean space of n + 1 ≥: 3 dimensions. The r-th mean curvature Kr of M at the point P of M is defined by the following equation:
On Holomorphic Maps into a Taut Complex Space
Authors: Fujimoto Hirotaka
Published: July 2016

The purpose of this paper is to study the extension problem of holomorphic maps of a complex manifold into a taut complex space, which is defined by analogy with a taut complex manifold given by H. Wu ([11]).
The Fields of Moduli for Polarized Abelian Varieties and for Curves
Authors: Koizumi Shoji
Published: July 2016

In the study of moduli of polarized abelian varieties and of curves as well as in the theory of complex multiplications, the notion of fields of moduli for structures plays an essential role. This notion was first introduced by Matsusaka [7] for polarized varieties with some pleasing properties and later was given a more comprehensible treatment by Shimura [10] in the case of polarized abelian varieties or polarized abelian varieties with some further structures. Both authors discussed fields of moduli not only in algebraic geometry of characteristic zero but also in that of positive characteristic, but in the latter case the definition of fields of moduli seems somewhat artificial and there have been no essential applications of them so far.
The First Monsky-Washnitzer Cohomology Group
Authors: Meredith David
Published: July 2016

Throughout this paper, k is a perfect field of characteristic p > 0, R is a complete discrete valuation ring with residue field k and quotient field of characteristic zero, and Z is a connected smooth prescheme of finite type over k.
On Class Field Towers and the Rank of Ideal Class Groups
Authors: Furuta Yoshiomi
Published: July 2016

The following theorem on infinite class field towers is well-known.
Some Examples of one Dimensional Gorenstein Domains
Authors: Watanabe Keiichi
Published: July 2016

In this paper, I will prove the following theorems;

For given integers n and m such that m ≧ 2n, there exist 1-dimensional local domains which are complete intersections and have embedding dimension n + 1 and multiplicity m.
Manifolds which do not Admit Anosov Diffeomorphisms
Authors: Shiraiwa Kenichi
Published: July 2016

In [3], M. W. Hirsch obtained some necessary conditions for the existence of an Anosov diffeomorphism on a differentiable manifold. As an application, he constructed many manifolds which do not admit Anosov diffeomorphisms.
Note on Galois Cohomology
Authors: Nakayama Tadasi
Published: July 2016

Let K/k be a Galois extension. Formerly the writer studied, in [3], [4], a certain correlation of factor sets in K/k with the norm class group of K/k, and extended it, in [5.], to 3-dimensional cocycles. The present note is to study the same relationship for general n-cocycles. As a matter of fact, the constructions which underlie the relationship have become common places in cohomology theory, through the works of French and American authors, and indeed the construction to bring certain (non-Galois) cocycles into the ground field k has been discussed by Baer [1, Theorem C] for general dimensions n under the setting of general group cohomology.
Multiplicity of some classes of Gaussian processes
Authors: Hitsuda Masuyuki
Published: July 2016

The aim of this paper is to discuss the multiplicity of the sum of two independent Gaussian processes

where x1(t) is a Wiener process and is a simple Markov process.
On the zeros of a conformal vector field
Authors: Blair David E.
Published: July 2016

In [1] S. Kobayashi showed that the connected components of the set of zeros of a Killing vector field on a Riemannian manifold (Mn,g) are totally geodesic submanifolds of (Mn,g) of even codimension including the case of isolated singular points. The purpose of this short note is to give a simple proof of the corresponding result for conformal vector fields on compact Riemannian manifolds. In particular we prove the following
On a classification of the function fields of algebraic tori
Authors: Endo Shizuo , Miyata Takehiko
Published: July 2016

Let II be a finite group and denote by MII the class of all (finitely generated Z-free) II-modules. In the previous paper [3] we defined an equivalence relation in MII and constructed the abelian semigroup T(II) by giving an addition to the set of all equivalence classes in MII. The investigation of the semigroup T(II) seems interesting and important, because this gives a classification of the function fields of algebraic tori defined over a field k which split over a Galois extension of k with group II.
The uniqueness problem of meromorphic maps into the complex projective space
Authors: Fujimoto Hirotaka
Published: July 2016

In 1921, G. Pólya showed that non-constant meromorphic functions ϕ and ψ of finite genera on the complex plane C are necessarily equal if there are distinct five values ai(1 ≦ i ≦ 5) such that ϕ(z) — ai and ψ(z) — ai have the same zeros of the same multiplicities for each i ([8]). Afterwards, R. Nevanlinna obtained the same conclusion for arbitrary ϕp and ψ satisfying ϕ— 1(ai) = ψ— 1(1 ≦ i ≦ 5) regardless of multiplicities. And, some other results relating to this were given by H. Cartan ([2], [3]), E. M. Schmid ([9]) and others. The purpose of this paper is to give some types of generalizations of these results to the case of meromorphic maps into the N-dimensional complex projective space PN(C).
On construction of holomorphic cusp forms of half integral weight
Authors: Shintani Takuro
Published: July 2016

In [10], G.Shimura gave a method of constructing holomorphic cusp forms of even integral weight from given forms of half integral weight. In this paper, we try to present an inverse construction. To state our main result, some notational preliminaries are necessary. We denote by the complex upper half plane.
Symmetry and separation of variables for the Helmholtz and Laplace equations
Authors: Boyer C. P. , Kalnins E. G. , Miller W.
Published: July 2016

This paper is one of a series relating the symmetry groups of the principal linear partial differential equations of mathematical physics and the coordinate systems in which variables separate for these equations. In particular, we mention [1] and paper [2] which is a survey of and introduction to the series. Here we apply group-theoretic methods to study the separable coordinate systems for the Helmholtz equation.
Involutions in Chevalley groups over fields of even order
Authors: Aschbacher Michael , Seitz Gary M.
Published: July 2016

LetG=G(q)be a Chevalley group defined over a fieldFqof characteristic 2. In this paper we determine the conjugacy classes of involutions in Aut(G) and the centralizers of these involutions. This study was begun in the context of a different problem.
Boundedness and convergence of solutions of Duffing’s equation
Authors: Shiraiwa Kenichi
Published: July 2016

In this paper, we shall discuss boundedness of solutions of the equation

under suitable conditions. And we shall discuss asymptotic stability of a periodic solution and convergence of solutions for the equation

for a positive constant cand a periodic function e(t)under some restricted conditions.
Eigenfunction expansion of generalized functions
Authors: Pandey J. N. , Pathak R. S.
Published: July 2016

Expansions of generalized functions have been investigated by many authors. Korevaar [11], Widlund [20], Giertz [8], Walter [19] developed procedures for expanding generalized functions of Korevaar [12], Temple [17], and Lighthill [13], Expansions of certain Schwartz distributions [15] into series of orthonormal functions were given by Zemanian [23] (see also Zemanian [24]) and thereby he extended a number of integral transforms to distributions. The method involved in his work is very much related to the Hilbert space technique and is of somewhat different character from those used in most of the works on integral transforms such as [24, chapters 1-8]. Other works that discuss orthogonal series expansions involving generalized functions are by Bouix [1, chapter 7], Braga and Schönberg [2], Gelfand and Shilov [7, vol. 3, chapter 4] and Warmbrod [21].
Projective invariant metrics for Einstein spaces
Authors: Kobayashi Shoshichi
Published: July 2016

In my recent paper [1], I associated a projectively invariant pseudo-distance dM to every affinely connected manifold M and proved the following

Theorem 1. Let M be a Riemannian manifold with metric and Ricci tensor RicM such that RicM ≤–c2. Let δM be the Riemannian distance defined by .
Hyperbolic nonwandering sets without dense periodic points
Authors: Kurata Masahiro
Published: July 2016

In this paper we give a negative answer to the problem which is suggested in [3]: if a nonwandering set Ω is hyperbolic, are the periodic points dense in Ω?

Newhouse and Palis proved that on two dimensional closed manifolds the answer is positive ([1], [2]).
Zeta functions of Selberg’s type for some noncompact quotients of symmetric spaces of rank one
Authors: Gangolli Ramesh , Warner Garth
Published: July 2016

In a previous paper [5], one of the present authors has worked out a theory of zeta functions of Selberg’s type for compact quotients of symmetric spaces of rank one. In the present paper, we consider the analogues of those results when G/K is a noncompact symmetric space of rank one and Γ is a discrete subgroup of G such that G/Γ is not compact but such that vol(G/Γ)<∞. Thus, Γ is a non-uniform lattice. Certain mild restrictions, which are fulfilled in many arithmetic cases, will be put on Γ, and we shall consider how one can define a zeta function ZΓ of Selberg’s type attached to the data (G, K, Γ).
Seminormal rings and weakly normal varieties
Authors: Leahy John V. , Vitulli Marie A.
Published: July 2016

In the late sixties and early seventies the operation of weak normalization was formally introduced first in the case of analytic spaces and later in the abstract scheme setting (cf. [6] & [4]). The notion arose from a classification problem. An unfortunate phenomenon in this area occurs when one tries to parametrize algebraic objects associated with a space by an algebraic variety; the resulting variety is, in general, not uniquely determined and may, for example, depend on the choice of coordinates. Under certain conditions one does know that the normalization of the parameter variety is unique. The price one pays for passing to the normalization is that often this variety no longer parametrizes what it was intended to; one point on the original parameter variety may split into several in the normalization. This problem is avoided if one passes instead to the weak normalization of the original variety. One then obtains a variety homeomorphic to the original variety with universal mapping properties that guarantee uniqueness.
When is a regular sequence super regular?
Authors: Herzog J.
Published: July 2016

Let (=,F) be a filtered, noetherian ring. A sequence x = x1 …, xn in B is called super regular if the sequence of initial forms

ξ = L(x1, …, ξn = L(xn)

is a regular sequence in grF(B).
Riemannian homogeneous foliations without holonomy
Authors: Blumenthal Robert A.
Published: July 2016

Let M be a compact connected C∞ manifold with a smooth Riemannian foliation ℱ. That is, (M, ℱ) admits a bundle-like metric in the sense of [7]. In [4] it is shown that if all leaves of ℱ are closed without holonomy, then the space of leaves M/ℱ of the foliation is a manifold and the natural projection M → M/ℱ is a locally trivial fibre space. In the present work we show that for certain of the Riemannian homogeneous foliations, holonomy is the only obstruction to the foliation being a fibration.
Boundary behavior of positive harmonic functions in balls of Rn
Authors: Renteln Michael Von
Published: July 2016

Let Rn be the real n-dimensional euclidean space. Elements of Rn are denoted by x = (xl • • •, xn), and ‖ x ‖ denotes the euclidean norm of x.

The open ball B(x, r) with center x and radius r is defined by
Quasilinear wave equations and related nonlinear evolution equations
Authors: Yamada Yoshio
Published: July 2016

In this paper we consider the relations between quasilinear wave equations
Smoothness of solutions of parabolic equations in regions with edges
Authors: Azzam A. , Kreyszig E.
Published: July 2016

We consider the mixed initial-boundary value problem for the parabolic equation

in a region Ω × (0, T], where x = (x1, x2) and Ω ⊂ R2 is a simply-connected bounded domain having corners.
On lacunary series
Authors: Murai Takafumi
Published: July 2016

We are concerned with the behaviour of Fourier series in an interval [0,2K) and, in particular, interested in that of so-called lacunary series. The spectrum of a Taylor seriesis defined by Spec (F) =, whereZ+denotes the semi-group of positive integers.
The stability theorems for discrete dynamical systems on two-dimensional manifolds
Authors: Sannami Atsuro
Published: July 2016

One of the basic problems in the theory of dynamical systems is the characterization of stable systems.

Let M be a closed (i.e. compact without boundary) connected smooth manifold with a smooth Riemannian metric and Diffr (M) (r ≥ 1) denote the space of Cr diffeomorphisms on M with the uniform Cr topology.
On the Niwa-Shintani theta-kernel lifting of modular forms
Authors: Cipra Barry A.
Published: July 2016

Modular forms of half-integral weight are of intrinsic interest: many of the functions of classical number theory transform under a matrix group with half-integral weight. The aim of this paper is to refine some results and techniques which have been introduced to study these functions and the arithmetic information which they contain.
Representation of spinor exceptional integers by ternary quadratic forms
Authors: Earnest A. G.
Published: July 2016

The existence and basic properties of what are now referred to as spinor exceptional integers for a genus of integral ternary quadratic forms were first observed in the 1950’s by Jones and Watson [7] and Kneser [8] in the context of indefinite forms. The study of these integers and their generalizations has been undertaken by a number of authors in recent years, and has contributed significantly to the understanding of representation properties unique to ternary forms. In this direction, the present author proved in a previous paper [4] that if c is a primitive spinor exceptional integer for a genus of integral ternary quadratic forms and f is some form in this genus, then a form in the spinor genus of f primitively represents c if and only if f primitively represents an integer of the type ct2, for some odd positive integer t, relatively prime to the discriminant d, which satisfies the condition that the Jacobi symbol (–cd/t) equals 1.
The Hodge cohomology and cubic equivalences
Authors: Saito Hiroshi
Published: July 2016

In 1969, Mumford [8] proved that, for a complete non-singular algebraic surface F over the complex number field C, the dimension of the Chow group of zero-cycles on F is infinite if the geometric genus of F is positive. To this end, he defined a regular 2-form ηf on a non-singular variety S for a regular 2-form η on F and for a morphism f: S → SnF, where SnF is the 72-th symmetric product of F, and he showed that ηf vanishes if all 0-cycles f(s), s ∈ S, are rationally equivalent. Roitman [9] later generalized this to a higher dimensional smooth projective variety V.
Cusp forms of weight one, quartic reciprocity and elliptic curves
Authors: Ishii Noburo
Published: July 2016

Let m be a non-square positive integer. Let K be the Galois extension over the rational number field Q generated by and . Then its Galois group over Q is the dihedral group D4 of order 8 and has the unique two-dimensional irreducible complex representation ψ. In view of the theory of Hecke-Weil-Langlands, we know that ψ defines a cusp form of weight one (cf. Serre [6]).
Projective Connections and Projective Transformations
Authors: Tanaka Noboru
Published: July 2016

The main purpose of the present paper is to establish a theorem concerning the relation between the group of all projective transformations on an affinely connected manifold and the group of all affine transformations.
Existence of extremal Beltrami coefficients with nonconstant modulus
Authors: Yao Guowu
Published: July 2016

Suppose that [μ]T(Δ)is a point of the universal Teichmüller spaceT(Δ). In 1998, Božin, Lakic, Marković, and Mateljević showed that there existsμsuch thatμis uniquely extremal in [μ]T(Δ)and has a nonconstant modulus. It is a natural problem whether there is always an extremal Beltrami coefficient of constant modulus in [μ]T(Δ)if [μ]T(Δ)admits infinitely many extremal Beltrami coefficients; the purpose of this paper is to show that the answer is negative. An infinitesimal version is also obtained. Extremal sets of extremal Beltrami coefficients are considered, and an open problem is proposed. The key tool of our argument is Reich’s construction theorem.
Buchsbaumness in local rings possessing constant first Hilbert coefficients of parameters
Authors: Goto Shiro , Ozeki Kazuho
Published: July 2016

Let (A,m) be a Noetherian local ring withd= dimA≥ 2. Then, ifAis a Buchsbaum ring, the first Hilbert coefficientsofAfor parameter idealsQare constant and equal towherehi(A)denotes the length of theith local cohomology moduleofAwith respect to the maximal ideal m. This paper studies the question of whether the converse of the assertion holds true, and proves thatAis a Buchsbaum ring ifAis unmixed and the valuesare constant, which are independent of the choice of parameter idealsQinA. Hence, a conjecture raised by [GhGHOPV] is settled affirmatively.
Topological uniqueness of negatively curved surfaces
Authors: Chan Hsungrow
Published: July 2016

In this paper we consider complete, noncompact, negatively curved surfaces that are twice continuously differentiably embedded in Euclidean three-space, showing that if such surfaces have square integrable second fundamental form, then their topology must, by the index method, be an annulus. We then show how this relates to some minimal surface theorems and has a corollary on minimal surfaces with finite total curvature. In addition, we discuss, by the index method, the relation between the topology and asymptotic curves. Finally, we apply the results yielded to the problem of isometrical immersions into Euclidean three-space of black hole models.
Generators for modules of vector-valued Picard modular forms
Authors: Cléry Fabien , Geer Gerard Van Der
Published: July 2016

We construct generators for modules of vector-valued Picard modular forms on a unitary group of type (2, 1) over the Eisenstein integers. We also calculate eigenvalues of Hecke operators acting on cusp forms.
A note on thick subcategories of stable derived categories
Authors: Krause Henning , Stevenson Greg
Published: July 2016

For an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection, we classify thick subcategories of finitely generated modules over strict local complete intersections and produce generators for the category of coherent sheaves on a separated Noetherian scheme with an ample family of line bundles.
Musielak–Orlicz Hardy Spaces Associated with Divergence Form Elliptic Operators Without Weight Assumptions
Authors: Tran Tri Dung
Published: July 2016

LetLbe a divergence form elliptic operator with complex bounded measurable coefficients, letωbe a positive Musielak-Orlicz function on (0, ∞) of uniformly strictly critical lower-typepω∈ (0, 1], and letρ(x,t) = t−1/ω−1(x,t−1) forx∈ ℝn, t∊ (0, ∞). In this paper, we study the Musielak-Orlicz Hardy spaceHω,L(ℝn) and its dual space BMOρ,L* (ℝn), whereL*denotes the adjoint operator ofLinL2(ℝn). Theρ-Carleson measure characterization and the John-Nirenberg inequality for the space BMOρ,L(ℝn) are also established. Finally, as applications, we show that the Riesz transform ∇L−1/2and the Littlewood–Paleyg-functiongLmapHω,L(ℝn) continuously intoL(ω).
Strong Regularity in Arbitrary Rings
Authors: Kandô Tetsuo
Published: July 2016

An element a of a ring R is called regular, if there exists an element x of R such that a×a = a, and a two-sided ideal a in R is said to be regular if each of its elements is regular B. Brown and N. H. McCoy [1] has recently proved that every ring R has a unique maximal regular two-sided ideal M(R), and that M(R) has the following radical-like property: (i) M(R/M(R)) = 0; (ii) if a is a two-sided ideal of R, then M(a) = a ∩ M(R); (iii) M(Rn) = (M(R))n, where Rn denotes a full matrix ring of order n over R. Arens and Kaplansky [2] has defined an element a of R to be strongly regular when there exists an element x of R such that a2x = a. We shall prove in this note that replacing “regularity” by “strong regularity,” we have also a unique maximal strongly regular ideal N(R), and shall investigate some of its properties.
On Some Asymptotic Properties Concerning Brownian Motion
Authors: Sirao Tunekiti , Nisida Tosio
Published: July 2016

About the behavior of brownian motion at time point oo, there are many results by P. Lévy, A. Khintchine etc. P. Lévy cited a theorem by A. Kolmogoroff as the most precise result in his famous book “Processus stochastiques et mouvement brownian” without proof. In this paper we shall prove this theorem, using the similar result about the random sequence by W. Feller, and then, applying the theorem of projective invariance by P. Lévy, we shall find also the behavior of brownian motion at time point 0 from the above theorem.
On the Uniform Continuity of Wiener Process with a Multidimensional Parameter
Authors: Hida Takeyuki
Published: July 2016

Let X(A, ω), ω∈Ω, be Wiener process on the probability space (Ω, B, P) depending on a point A of an N dimensional Euclidean space EN.
Dirichletsche Abbildungen
Authors: Constantinescu C.
Published: July 2016

Für jede Riemannsche Fläche R bezeichnen wir mit M(R) die Algebra von Royden auf R und mit R* (bzw. ΔR)- die Kompaktifizierung (bzw. den idealen Rand) von Royden von R ([5]). Für jede Funktion ξ ∊ M(R) sei Jξ
das kompakte Segment und X(R) der kompakte Raum . Laut der Definition von R* ist jede Funktion ξ∊M(R) auf R* (in eindeutiger Weise) stetig fortsetzbar. Bezeichnet man ebenfalls mit ξ die so fortgesetzte Funktion und mit φR
die Abbildung von R*→X(R), so ist φR
ein Homeomorphismus von R* auf φR(R*).
Multiply Harmonic Functions
Authors: Gowrisankaran Kohur
Published: July 2016

Let Ω and Ω′ be two locally compact, connected Hausdorff spaces having countable bases. On each of the spaces is defined a system of harmonic functions satisfying the axioms of M. Brelot [2]. The following is the description of such a system. To each open set of Ω is assigned a vector space of finite continuous functions, called the harmonic functions, on this set.
A Formalism for the Classical Sentence-Logic
Authors: Ono Katuzi
Published: July 2016

I have introduced in my paper [1] a formalism for lower order predicate logics in which any sequence of variables and brackets (‘[’ and ‘]’) can be regarded as a meaningful (well-formed) sentence. Also, in my paper [2], I have introduced another formalism of the same kind for a certain kind of predicate logics of higher order. Can we introduce a formalism of the same kind properly for sentence logics too? Since sentence logics can be regarded as a sub-system of predicate logics, we are apt to consider that our device introduced in [1] works well for sentence logics too.
A Theorem on Valuation Rings and its Applications
Authors: Nagata Masayoshi
Published: July 2016

In the present paper, we first prove the following

THEOREM 1. Let K be a field, x a transcendental element over K, and V* a valuation ring of K(x). Set V= V* ∩ K. Denote by p* and p the maximal ideals of V* and V respectively. If (i) V*/p* is not algebraic over V/p and (ii) the value group of V* is isomorphic to Zn (Z=the module of rational integers), i.e., V* is of rank n and discrete in the generalized sense, then V*/p* is a simple transcendental extension of a finite algebraic extension of V/p.
Finite Dimensional Approximation to Band Limited White Noise
Authors: Hida Takeyuki , Nomoto Hisao
Published: July 2016

One of the authors discussed finite dimensional approximations to a white noise and a periodic Brownian motion with period 2 π on the projective limit space of spheres ([2]). The group of unitary operators derived from the periodic white noise has a pure point spectrum which consists of all integers with countably infinite multiplicity. We also have much interest in the investigation of a band limited white noise which is another typical example having quite different spectral type. Indeed, the corresponding group of unitary operators has a continuous spectrum with countably infinite multiplicity.
Contraction Groups and Equivalent Norms
Authors: Vogt William G. , Eisen Martin M. , Buis Gabe R.
Published: July 2016

Using the notation in [1], the Lumer-Phillips theorem (3. 1 of [2]) is refined to single parameter groups in real Banach space and real Hilbert space. The theory can be extended to complex spaces.
Abelian varieties attached to cycles of intermediate dimension
Authors: Saito Hiroshi
Published: July 2016

The group of cycles of codimension one algebraically equivalent to zero of a nonsingular projective variety modulo rational equivalence forms an abelian variety, i.e., the Picard variety. To the group of cycles of dimension zero and of degree zero, there corresponds an abelian variety, the Albanese variety. Similarly, Weil, Lieberman and Griffiths have attached complex tori to the cycles of intermediate dimension in the classical case. The aim of this article is to give a purely algebraic construction of such “intermediate Jacobian varieties.”
Quasi-homeomorphisms of Dirichlet forms
Authors: Chen Zhen-Qing , Ma Zhi-Ming , Röckner Michael
Published: July 2016

Extending fundamental work of M. Fukushima, M. L. Silverstein, S. Carrillo Menendez, and Y. Le Jan (cf. [F71a, 80], [Si74], [Ca-Me75], [Le77]) it was recently discovered that there is a one-to-one correspondence between (equivalent classes of) all pairs of sectorial right processes and quasi-regular Dirichlet forms (see [AM91], [AM92], [AMR90], [AMR92a], [AMR92b], [MR92]). Based on the potential theory for quasi-regular Dirichlet forms, it was shown that any quasi-regular Dirichlet form on a general state space can be considered as a regular Dirichlet form on a locally compact separable metric space by “local compactification”. There are several ways to implement this local compactification. One relies on h-transformation which was mentioned in [AMR90, Remark 1.4]. A direct way using a modified Ray-Knight compactification was announced on the “5th French-German meeting: Bielefeld Encounters in Mathematics and Physics IX. Dynamics in Complex and Irregular Systems”, Bielefeld, December 16 to 21, 1991, and the “Third European Symposium on Analysis and Probability”, Paris, January 3-10, 1992, and appeared in [MR92, Chap. VI] and [AMR92b] (see also the proof of Theorem 3.7 below). One can also do this by Gelfand-transform. This way was found by the first named author independetly and announced in the “12th Seminar on Stochastic Processes”, Seattle, March 26-28, 1992. It will be discussed in Section 4.
On the structure of local cohomology modules for monomial curves in
Authors: Bresinsky H. , Curtis F. , Fiorentini M. , Hoa L. T.
Published: July 2016

Our setting for this paper is projective 3-spaceover an algebraically closed fieldK. By a curveC⊂is meant a 1-dimensional, equidimensional projective algebraic set, which is locally Cohen-Macaulay. Letbe the Hartshorne-Rao module of finite length (cf. [R]). HereZis the set of integers andℐcthe ideal sheaf ofC. In [GMV] it is shown that, whereis the homogeneous ideal ofC,is the first local cohomology module of theR-moduleMwith respect to. Thus there exists a smallest nonnegative integerk∊Nsuch that, (see also the discussion on the 1-st local cohomology module in [GW]). Also in [GMV] it is shown thatk= 0 if and only ifCis arithmetically Cohen-Macaulay andCis arithmetically Buchsbaum if and only ifk≤ 1. We therefore have the following natural definition.