bluuebunny/crossref_metadata_2025 huggingface dataset:
Differentiable Structures on the 15-Sphere and Pontrjagin Classes of Certain Manifolds
Authors: Shimada Nobuo
Published: July 2016

No manifold had been known which can carry two distinct differentiable structures until the recent important contribution due to J. Milnor [7] concerning the 7-sphere appeared.

In connection with his work, there are several problems, for example, about the existence of any other manifold with such property, about the topological invariance of the Pontrjagin classes of manifolds, etc.; some of them will be discussed in the present note.
On the asymptotic boundary behavior of functions analytic in the unit disk
Authors: Choike James R.
Published: July 2016

In [8] a necessary and sufficient condition was given for determining the equivalence of two asymptotic boundary paths for an analytic function w = f(p) on a Riemann surface F. In this paper we give a necessary and sufficient condition for determining the nonequivalence of two asymptotic boundary paths for f(z) analytic in |z| < R, 0 < R ≤ + ∞. We shall, also, illustrate some applications of the main result and examine a class of functions introduced by Valiron.
Scalar extension of quadratic lattices II
Authors: Kitaoka Yoshiyuki
Published: July 2016

Let k be a totally real algebraic number field, the maximal order of k, and let L (resp. M) be a Z-lattice of a positive definite quadratic space U (resp. V) over the field Q of rational numbers. Suppose that there is an isometry σ from L onto M. We have shown that the assumption implies σ(L) = M in some cases in [2]. Our aim in this paper is to improve the results of [2]. In § 1 we introduce the notion of E-type: Let L be a positive definite quadratic lattice over Z.
Remarks on regular sequences
Authors: Eisenbud David , Hermann Manfred , Vogel Wolfgang
Published: July 2016

In this note we exhibit a condition under which a sequence of elements a1, …, an in a commutative noetherian local ring A form an A-sequence, and derive a number of corollaries.
Galois groups of number fields generated by torsion points of elliptic curves
Authors: Wingberg Kay
Published: July 2016

Coates and Wiles [1] and B. Perrin-Riou (see [2]) study the arithmetic of an elliptic curve E defined over a number field F with complex multiplication by an imaginary quadratic field K by using p-adic techniques, which combine the classical descent of Mordell and Weil with ideas of Iwasawa’s theory of Zp-extensions of number fields. In a special case they consider a non-cyclotomic Zp-extension F∞ defined via torsion points of E and a certain Iwasawa module attached to E/F, which can be interpreted as an abelian Galois group of an extension of F∞. We are interested in the corresponding non-abelian Galois group and we want to show that the whole situation is quite analogous to the case of the cyclotomic Zp-extension (which is generated by torsion points of Gm).
Mixed periodic Jacobi continued fractions
Authors: Kato Yoshifumi
Published: July 2016

Let b0 be a positive real number and

be a Jacobi matrix. We can associate with them a Jacobi continued fraction, which will be abbreviated to a J fraction from the next section, as follows

where An(z)/Bn(z) is the n-th Padé approximant of φ(z).
On Continuous Isomorphisms of Topological Groups
Authors: Gotô Morikuni , Yamabe Hidehiko
Published: July 2016

Let G be a locally compact connected group, and let A (G) be the group of all continuous automorphisms of G. We shall introduce a natural topology into A(G) as previously (i.e. the topology of uniform convergence in the wider sense.) When the component of the identity of A(G) coincides with the group of inner automorphisms, we shall call G complete. The purpose of this note is to prove the following theorem and give some applications of it.
Riemann Space with Two-Parametric Homogeneous Holonomy Group
Authors: Kurita Minoru
Published: July 2016

The rotational part of the holonomy group of a Riemann space is called its homogeneous holonomy group. A Riemann space, whose homogeneous holonomy group is one-parametric, was investigated by Liber and an alternative treatment of the same problem was given by S. Sasaki [1]. I will treat here a Riemann space with two-parametric homogeneous holonomy group and prove the following theorem by the method analogous to that of [1]. I thank Prof. T. Ootuki for his kind advice.
On the Differential Forms on Algebraic Varieties
Authors: Kawahara Yûsaku
Published: July 2016

In the book “Foundations of algebraic geometry” A. Weil proposed the following problem ; does every differential form of the first kind on a complete variety U determine on every subvariety V of U a differential form of the first kind? This problem was solved affirmatively by S. Koizumi when U is a complete variety without multiple point. In this note we answer this problem in affirmative in the case where V is a simple subvariety of a complete variety U (in §1). When the characteristic is 0 we may extend our result to a more general case but this does not hold for the case characteristic p≠0 (in §2).
Sur une Conjecture de Krull en Theorie des Valuations
Authors: Ribenboim P.
Published: July 2016

Dans cette note, nous étudions les anneaux d’intégrité primaires et complètement intégralement clos. Krull [1] a posé la question suivante: est-ce qu’un anneau d’intégrité primaire et complètemente intégralement clos est nécessairement un anneau de valuation?
On the Derivations in Maximal Orders of Simple Algebras
Authors: Kawahara Yûsaku
Published: July 2016

The theory of derivations and differents in the algebraic number fields or Dedekind rings has been developped by A. Weil [1], Y. Kawada [2] and M. Moriya [4]. Further Y. Kawada [3] has investigated the derivations in maximal orders of simple algebras over number fields. This note is concerned with the derivations in the simple algebras over fields which are quotient fields of Dedekind rings; the commutative rings in which the fundamental theorem of multiplicative ideal theory holds. The auther gives his hearty thanks to Prof. M. Moriya who gave him valuable remarks.
An Investigation on the Logical Structure of Mathematics (III): Fundamental Deductions
Authors: Kuroda Sigekatu
Published: July 2016

In this Part (III) the proofs in UL are given for fundamental formulas concerning the following dependent variables:

Elementary set {a1, … , an};

Ordered pair ‹a, b›;

Image by σ of aσ‘a;

Image by σ of elements of aσ“a;

Domain of operator Dσ;

Range of operator Wσ;

Uniqueness Un;

Bi-uniqueness Un2;

Inverse operator σ-1;

One-to-one mapping Map2a, b;

Composition of operators σ o τ;

Restriction of operator

Identical mapping ℓ
On the Dimension of Modules and Algebras IX: Direct Limits
Authors: Berstein Israel
Published: July 2016

Let J be a directed set and let {Λj, φij} be a direct system of rings indexed by J and with limit Λ. Let {Aj, φij} be a direct system of groups indexed by J. Assume that each Aj is a left Λj-module and that φij(λa) = φij(λ) φij(a) for each λ ∈ Λj, a ∈ Aj. Then the limit A of (Aj, φij) is a left Λ-module.
On the Existence of Unramified Separable Infinite Solvable Extensions of Function Fields over Finite Fields
Authors: Morikawa Hisasi
Published: July 2016

In the present note, using the results in the previous paper, we shall prove the following existence theorem:

THEOREM. Let k be a finite field with q elements and K/k be a regular extension of dimension one over k. Then, if q ≧ 11 and the genus gK of K/k is greater than one, there exists an unramified separable infinite solvable extension of K ivhich is regular over k.
Über Geschlossene Geodätische auf Geschlossenen Mannigfaltigkeiten
Authors: Shizuma Ryoji
Published: July 2016

In der vorliegenden Arbeit beschäftigen wir uns mit dem Problem der geschlossenen Geodätischen auf geschlossenen Mannigfaltigkeiten. Dieses Problem geht bekanntlich auf Morse ([4], [5]) zurück. Wir machen aber von seinem Kunstgriff des “zyklischen” Produktes [4] keinen Gebrauch; vielmehr kommt es uns hier darauf an, den Funktionalraum unseres Variations-problems direkt in Betracht zu ziehen, wie es Morse beim analogen Problem der geodätischen Linien mit festen Randpunkte herausgearbeitet hat. Es wird sich im folgenden zeigen, wie sich sein Verfahren auf den Fall der geschlossenen Geodätischen übertragen lässt.
An Investigation on the Logical Structure of Mathematics (IV): Compendium for Deductions
Authors: Kuroda Sigekatu
Published: July 2016

In § 1 the usage and conventions which are used in the deductions in UL are explained. In §§ 2-4 some metatheorems concerning the deductions are proved. Namely, in § 2 the order of proof constituents in a proof is investigated; in § 3 the applicability of composite proof constituents are proved on the basis of § 2; in §4 the place of the “ordinarily used” principle of extensionality in a proof is specified. In §5 a sufficient condition of the mechanization of mathematics is given in such a manner that the mechanical and non-mechanical parts in solving mathematical problems are separated in accord with the usual way of thinking in mathematics.
Sur Le Groupe D’automorphismes D’un Espace Fibré Principal Analytique Complexe
Authors: Morimoto Akihiko
Published: July 2016

Dans ce mémoir nous démontrons que le groupe d’automorphismes d’un espace fibre principal analytique complexe à base compacte est un groupe de Lie complexe par la topologie de la convergence compacte et ensuite nous étudierons quelques relations entre le groupe d’automorphismes d’un espace fibre principal analytique complexe et le groupe d’homéomorphisme analytiques de sa base.
A Maximal Riemann Surface
Authors: Jurchescu Martin
Published: July 2016

We let the notations be as in [3]. Then, in the category 6 of all bordered Riemann surfaces, the following inclusion diagram holds [3, Theorem 9]:
On the Boundary Behavior of Holomorphic Functions in the Unit Disk
Authors: Faust Claude Marie
Published: July 2016

Let f(z) be a holomorphic function defined in the unit disk |z|<1, which we shall denote by D. Let Σ be a subset of D, whose closure has at least one point in common with C, the circumference of the unit disk. The set of all values a such that the equation f(z) = a has infinitely many solutions in Σ is called the range of f(z) in Σ, and is denoted by R(f, Σ). Let τ be a point of C, and let {zn
) be a sequence of points in D with the properties: . The non-Euclidean (hyperbolic) distance ρ(zn, zn+1
) between two points zn
and z

n+1 of the sequence is defined to be equal to

(cf.[3], Ch. II).
On a Practical Way of Describing Formal Deductions
Authors: Ono Katuzi
Published: July 2016

Introduction

Even though the logical structure of any formal deduction can be nicely expressed in a tree-form diagram, it is more practical to write it down in a series of propositions. In each step of inference, we usually deduce a proposition on basis of some foregoing propositions. However, global aspects of mathematical theories show us that this is not always the case. For, in mathematical theories, theorems are usually stated before their proofs. In fact, also in proofs of theorems, it is often practical that we prove propositions after stating them. Accordingly, in our real way of thinking, we arrange propositions going back and forth in the logical order.
Reinforced Logics
Authors: Ono Katuzi
Published: July 2016

The device of representing a predicate by a universal sentence gives rise to logics of higher order. To represent an object constructed by a series of certain steps, we usually use terms. To represent a predicate constructed by a series of certain steps, we now use sentences in general. We can now substitute special predicates represented by sentences for predicate variables of a sentence just as we have been able to substitute special objects represented by terms for object variables. It is remarkable that we can always distinguish predicates from objects, proceeding in this way.
On the Characters of the Prolonged Differential System
Authors: Hayashi Isao
Published: July 2016

Let M = M(D π) be a (real analytic) fibered manifold of dimension n over a manifold D of dimension p, with projection π. We denote by M′ (D, α) the prolonged fibered manifold of M(D, π). Every point of M′ is a p-dimensional contact element of M, and a p-dimensional contact element X of M belongs to M′ if and only if π*X = Tπ(x)(D), where x is the origin of X. We write x = β(X) and α = π°β. We also denote by M″(D, α′) the prolonged fibered manifold of M′(D, α), where α′ = α°β′ and β′ is the projection of each X′ ∈ M″ to its origin in M′.
On the Asymptotic Behavior of Functions Harmonic in a Disc
Authors: Mcmillan J. E.
Published: July 2016

Let D be the open unit disc, and let C be the unit circle in the complex plane. Let f be a (real-valued) function that is harmonic in D. A simple continuous curve β: z(t) (0≦t<1) contained in D such that |z(t)|→1 as t→1 is a boundary path with end (the bar denotes closure).
Characterizations of Supports of Balayaged Measures
Authors: Itô Masayuki
Published: July 2016

Beurling and Deny [1], [2] introduced Dirichlet spaces by generalizing the notion of“energy”in potential theory. They showed the existences of balayaged measures and condensor measures in the theory of Dirichlet spaces. The purpose of this paper is to characterize the supports of those measures. First we obtain the following result.
Perfect Picard Set of Positive Capacity
Authors: Matsumoto Kikuji
Published: July 2016

In our previous paper [1], we proved that any Cantor set E with successive ratios ξn satisfying the condition

is a Picard set, that is, each single-valued meromorphic function with E as the set of essential singularities takes on every value infinitely often in any neighborhood of each singularity with the possible exception of two values.
The Theorem of Identity for Coherent Analytic Modules
Authors: Fujimoto Hirotaka
Published: July 2016

The theorem of identity for analytic subsets of a reduced complex space is stated as follows;

Let V and V′ be two analytic subsets of a reduced complex space. If V is irreducible and there exists a point x ∊ V such that the germ Vx of V at x is included in V′x, then V is included in V′.
On q-th Derivative of Vector Bundles
Authors: Kato Akikuni
Published: July 2016

In the present note we shall be concerned with the improvement of fundamental definitions in higher order enumerative geometry which has been recently given by W. F. Pohl. Pohl’s definition of q-th derivative of vector bundle is very complicated. We shall give a simpler and more reasonable definition of the q-th derivative of vector bundle in terms of sheaf theory and simplify the proofs in [P]. We shall also give a definition of higher order singularity of map.
Singular Sets of Some Kleinian Groups (II)
Authors: Akaza Tohru
Published: July 2016

In the theory of automorphic functions it is important to investigate the properties of the singular sets of the properly discontinuous groups. But we seem to know nothing about the size or structure of the singular sets of Kleinian groups except the results due to Myrberg and Akaza [1], which state that the singular set has positive capacity and there exist Kleinian groups whose singular sets have positive 1-dimensional measure. In our recent paper [2], we proved the existence of Kleinian groups with fundamental domains bounded by five circles whose singular sets have positive 1-dimensional measure and presented the problem whether there exist or not such groups in the case of four circles. The purpose of this paper is to solve this problem. Here we note that, by Schottky’s condition [4], the 1-dimensional measure of the singular set is always zero in the case of three circles.
A Boundary Theorem for Tsuji Functions
Authors: Collingwood E. F.
Published: July 2016

Let D denote the unit disc | z | <1, C the unit circle | z | = 1 and Cr the circle | z| = r. Corresponding to any function w(z) meromorphic in D we denote by w*(z) the spherical derivative
Remark on the Dual EHP Sequence
Authors: Nomura Yasutoshi
Published: July 2016

In this note we will improve the dual EHP sequence which has been constructed in [6] by showing that that can be extended by one term. We then observe that this can be used to deduce a result which has been announced by T. Ganea in [4]. As another application we will establish a theorem which asserts that, under certain conditions, a principal fibration with a loop-space as fibre is principally equivalent to the one induced by some map.
On the Eisenstein Series for the Principal Congruence Subgroups
Authors: Orihara Akio
Published: July 2016

Let Γ be a Fuchsian group (of finite type) acting on the upper half plane. To each parabolic cusp Ki (i = 1, …, h), corresponds a Eisenstein serie
On a class of non-elliptic boundary problems
Authors: Kato Yoshio
Published: July 2016

Let Ω be a bounded domain in Rl (l ≥ 2) with, C∞ boundary Γ of dimension l — 1 and let there be given a second order elliptic differential equation

(1) in Ω,

where ∂j = ∂/∂xi and all coefficients are assumed, for the sake of simplicity, to be real-valued and C∞ on .
Reducing towers of principal fibrations
Authors: McClendon J. F.
Published: July 2016

Consider a tower of principal fibrations

That is, Ei+1 is the pullback of Ei→Ri and the path fibration PRi → Ri. The question arises as to whether or not the tower can be shortened, that is, whether or not En+1→ B is fiber homotopically equivalent to a nice fibration E → B. If “nice” is taken to mean “principal” then sufficient conditions are known. They involve connectivity assumptions on the Ei. In this paper “nice” is taken to mean “D-relatively principal” for some space D.
On nilpotent factors of congruent ideal class groups of Galois extensions
Authors: Furuta Yoshiomi
Published: July 2016

Let K be a Galois extension of an algebraic number field k of finite degree with Galois group g. Then g acts on a congruent ideal class group of K as a group of automorphisms, when the class field M over K corresponding to is normal over K. Let Ig be the augmentation ideal of the group ring Zg over the ring of integers Z, namely Ig be the ideal of Zg generated by σ − 1, σ running over all elements of g. Then is the group of all elements aσ-1 where a and σ belong to and g respectively.
Les pseudo-groupes intransitifs et le probleme d’equivalence
Authors: Higa Tatsuo
Published: July 2016

Dans les travaux célèbres [1], [2], [3], E. Cartan a fait des recherches sur les pseudo-groupes, sans distinguer entre les deux cas, transitif ou intransitif. Tout d’abord, Cartan a abouti au théorème qu’il a considéré comme la base de la théorie des pseudo-groupes continus, c’est-à-dire le premier théorème fondamental: Tout pseudo-groupe de Lie admet un prolongement holoédrique opérant sur un certain nombre r de variables xi et défini comme l’ensemble des transformations qui laissent invariants

1° un certain nombre de fonctions des xi;

2° r formes de Pfaff wi(x, y, dx) linéairement indépendantes par rapport aux différentielles dxi et dont les coefficients peuvent dépendre d’autres variables auxiliaires yj; enfin le prolongement considéré a ses équations de définition du premier ordre (voir [5]). Puis, il a introduit l’équation structurale de manière à caractériser le pseudo-groupe.
Local deformations of isolated singularities associated with negative line bundles over abelian varieties
Authors: Omoto Hideo , Nakano Shigeo
Published: July 2016

Let V be an analytic space with an isolated singularity p. In [1] M. Kuranishi approached the problem of deformations of isolated singularities (c.f. [2] and [3]) as follows; Let M be a real hypersurface in the complex manifold V − {p}. Then one has the induced CR-structure °T″(M) on M by the inclusion map i: M→ V − {p} (c.f. Def. 1.6). Then deformations of the isolated singularity (V, p) give rise to ones of the induced CR-structure °T″(M). He established in §9 in [1] the universality theorem for deformations of the induced CR-structure °T″(M)9 when M is compact strongly pseudo-convex (Def. 1.5) of dim M ≧ 5. Form this theorem we can know CR-structures on M which appear in deformations of °T″(M).
On the radius of convergence of the p-adic L-function
Authors: Morita Yasuo
Published: July 2016

In their paper [11], Kubota-Leopoldt constructed the p-adic L-function Lp(s; χ) for each Dirichlet character χ. This function Lp(s; χ) is a mero-morphic function on the open dies {|s − 1| < |<q-1 p1/(p-1)|} with a possible simple pole at s = 1.
Complexes of Cousin type and modules of generalized fractions
Authors: Chung Sang-Cho
Published: July 2016

Let R be a commutative (Noetherian) ring, M an R-module and let ℱ = (Fi)i≥0 be a filtration of Spec(R) which admits M.

A complex of R-modules is said to be of Cousin type if it satisfies the four conditions of ([GO], 3.2) which are reproduced below (Definition (1.5)). In ([RSZ], 3.4), Riley, Sharp and Zakeri proved that the complex, which is constructed from a chain of special triangular subsets defined in terms of ℱ (Example (1.3)(3)), is of Cousin type for M with respect to ℱ (Corollary (3.5)(2)). Gibson and O’carroll ([GO], 3.6) showed that the complex, which is obtained by means of a chain = (Ui)i≥1 of saturated triangular subsets and the filtration = (Gi)i≥0 induced by and M, is of Cousin type for M with respect to (Corollary (3.5)(3)).
Defining ideals of Buchsbaum semigroup rings
Authors: Kamoi Yuuji
Published: July 2016

Let H be a simplicial semigroup. We consider the semigroup ring k[H] and its defining ideal IH. For definition see the first paragraph of Section 1.

When dim(k[H]) = 1, the defining ideal IH of k[H] has been studied by many authors (e.g. [1], [2], [8], [11], [3]). In this paper, we study the ideal IH using the notion of Gröbner bases for arbitrary dimension.
The existence of symmetric Riemann surfaces determined by cyclic groups
Authors: Nakamura Gou
Published: July 2016

Let n > 1, m ≥ 1, g ≥ 3 and γ be given integers. The purpose of this paper is to determine the relations of n, m, g and γ for the existence of the symmetric Riemann surfaces S of type (n, m) with genus g and species γ. If n is an odd prime, the relations are known in [3]. In the case that n is odd, we shall show the analogous result when E(S) is isomorphic to a cyclic group Z2n and when the quotient space S/E(S) is orientable.
The existence of periodic solutions for systems of ordinary differential equations
Authors: Lee Yong-Hoon
Published: July 2016

We prove a multiplicity result of 2π-periodic solutions for certain weakly coupled system of ordinary differential equations with real parameters. The proofs are based on differential inequalities and coincidence degree.
Sur l’incomplétude de la série linéaire caractéristique d’une famille de courbes planes à nœuds et à cusps
Authors: Guffroy Sébastien
Published: July 2016

Since J.Wahl ([27]), it is known that degreedplane curves having some fixed numbers of nodes and cusps as its only singularities can be represented by a scheme, let sayH, which can be singular. In Wahl’s example,His singular along a subschemeFbut the induced reduced schemeHredis smooth alongF. In this work, we construct explicitly a family of plane curves with nodes and cusps which are represented by singular points ofHred.

To this end, we begin to show that the Hilbert scheme of smooth and connected space curves of degree 12 and genus 15 is irreducible and generically smooth. It follows that it is singular along a hypersurface (3.10). This example is minimal in the sense that the Hilbert scheme of smooth and connected space curves is regular in codimension 1 ford< 12 (B.2). Finally we construct our plane curves from the space curves represented by points of this hypersurface (4.7).
Invariant theory for linear differential systems modeled after the grassmannian Gr(n, 2n)
Authors: Sasaki Takeshi , Yoshida Masaaki
Published: July 2016

We find invariants for the differential systems of rank 2n in n2 variables with n unknowns under the linear changes of the unknowns with variable coefficients. We look for a set of coefficients that determines the other coefficients, and give transformation rules under the linear changes above and coordinate changes. These can be considered as a generalization of the Schwarzian derivative, which is the invariant for second order ordinary differential equations under the change of the unknown by multiplying a non-zero function. Special treatment is done when n = 2: the conformal structure obtained through the Plücker embedding is studied, and a relation with line congruences is discussed.
On a Theorem of P. Fong
Authors: Korchagina Inna
Published: July 2016

This paper is a contribution to the “revision” project of Gorenstein, Lyons and Solomon, whose goal is to produce a unified proof of the Classification of Finite Simple Groups.
Convolution Dirichlet Series and a Kronecker Limit Formula for Second-Order Eisenstein Series
Authors: Jorgenson Jay , O’Sullivan Cormac
Published: July 2016

In this article we derive analytic and Fourier aspects of a Kronecker limit formula for second-order Eisenstein series. Let Γ be any Fuchsian group of the first kind which acts on the hyperbolic upper half-space H such that the quotient Γ\H has finite volume yet is non-compact. Associated to each cusp of Γ\H, there is a classically studiedfirst-ordernon-holomorphic Eisenstein seriesE(s, z) which is defined by a generalized Dirichlet series that converges for Re(s) > 1. The Eisenstein seriesE(s, z) admits a meromorphic continuation with a simple pole ats= 1. Classically, Kronecker’s limit formula is the study of the constant term1(z) in the Laurent expansion ofE(s, z) ats= 1. A number of authors recently have studied what is known as thesecond-orderEisenstein seriesE*(s, z), which is formed by twisting the Dirichlet series that defines the seriesE(s, z) by periods of a given cusp formf. In the work we present here, we study an analogue of Kronecker’s limit formula in the setting of the second-order Eisenstein seriesE* (s, z), meaning we determine the constant term2(z) in the Laurent expansion ofE*(s, z) at its first pole, which is also ats= 1. To begin our investigation, we prove a bound for the Fourier coefficients associated to the first-order Kronecker limit function1. We then define two families of convolution Dirichlet series, denoted byandwithm∈ ℕ, which are formed by using the Fourier coefficients of1and the weight two cusp formf. We prove that for allm,andadmit a meromorphic continuation and are holomorphic ats= 1. Turning our attention to the second-order Kronecker limit function2, we first express2as a solution to various differential equations. Then we obtain its complete Fourier expansion in terms of the cusp formf, the Fourier coefficients of the first-order Kronecker limit function1, and special values(1) and(1) of the convolution Dirichlet series. Finally, we prove a bound for the special values(1) and(1) which then implies a bound for the Fourier coefficients of2. Our analysis leads to certain natural questions concerning the holomorphic projection operator, and we conclude this paper by examining certain numerical examples and posing questions for future study.
Classification of Möbius Isoparametric Hypersurfaces in 4
Authors: Hu Zejun , Li Haizhong
Published: July 2016

Let Mn be an immersed umbilic-free hypersurface in the (n + 1)-dimensional unit sphere n+1, then Mn is associated with a so-called Möbius metric g, a Möbius second fundamental form B and a Möbius form Φ which are invariants of Mn under the Möbius transformation group of n+1. A classical theorem of Möbius geometry states that Mn (n ≥ 3) is in fact characterized by g and B up to Möbius equivalence. A Möbius isoparametric hypersurface is defined by satisfying two conditions: (1) Φ ≡ 0; (2) All the eigenvalues of B with respect to g are constants. Note that Euclidean isoparametric hyper-surfaces are automatically Möbius isoparametric, whereas the latter are Dupin hypersurfaces.

In this paper, we prove that a Möbius isoparametric hypersurface in 4 is either of parallel Möbius second fundamental form or Möbius equivalent to a tube of constant radius over a standard Veronese embedding of ℝP2 into 4. The classification of hypersurfaces in n+1 (n ≥ 2) with parallel Möbius second fundamental form has been accomplished in our previous paper [6]. The present result is a counterpart of Pinkall’s classification for Dupin hypersurfaces in 4 up to Lie equivalence.
Positive Toeplitz Operators of Schatten–Herz Type
Authors: Choe Boorim , Koo Hyungwoon , Na Kyunguk
Published: July 2016

Motivated by a recent work of Loaiza et al. for the holomorphic case on the disk, we introduce and study the notion of Schatten-Herz type Toeplitz operators acting on the harmonic Bergman space of the ball. We obtain characterizations of positive Toeplitz operators of Schatten-Herz type in terms of averaging functions and Berezin transforms of symbol functions. Our characterization in terms of Berezin transforms settles a question posed by Loaiza et al.
Truncated Microsupport and Hyperbolic Inequalities
Authors: Martins Ana Rita , Fernandes Teresa Monteiro
Published: July 2016

We prove that the k-truncated microsupport of the specialization of a complex of sheaves F along a submanifold is contained in the normal cone to the conormal bundle along the k-truncated microsupport of F. In the complex case, applying our estimates to , where is a coherent -module, we obtain new estimates for the truncated microsupport of real analytic and hyperfunction solutions. When is regular along Y we also obtain estimates for the truncated microsupport of the holomorphic solutions of the induced system along Y as well as for the nearby-cycle sheaf of when Y is a hypersurface.
Some Results on Finite Groups Whose Order Contains a Prime to the First Power
Authors: Brauer Richard
Published: July 2016

In a previous investigation [1], the author has studied finite groups of an order g = pg0 where p is a prime and g0 an integer not divisible by p. This work has been continued by H. F. Tuan [5]. Let t denote the number of conjugate classes of which consist of element of order p. Tuan dealt with the groups for which t≦2 and which have a faithful representation of degree less than p - 1. We shall assume here that t≧3. We shall also suppose that does not have a normal subgroup of order p. We state here two results. We shall show (Corollary, Theorem 1) that if / is a faithful irreducible character of of degree n which has T>1 conjugates over the field of the g0-th roots of unity, then
A Theorem on Analytic Mappings of Complex Manifolds
Authors: Kurita Minoru
Published: July 2016

We prove in this paper a theorem on analytic mappings of the complex space Cn into the complex projective space Pn. The theorem is closely related to that of S. S. Chern in [1], and the main idea of the proof is the same with the latter, though the calculations are rather different. The background of our calculation is the normal contact metric structure which was found by S. Sasaki and Y. Hatakeyama [4].
Note on Schiffer’s Variation in the Class of Univalent Functions in the Unit Disc
Authors: Matsumoto Kikuji
Published: July 2016

Let S denote the class of univalent functions f(z) in the unit disc D: | z | < 1 with the following expansion:

(1) f(z) = z + a2z2 + a3z3 + · · · · anzn + · ··.

We denote by fn(z) the extremal function in S which gives the maximum value of the real part of an and by Dn the image of D under w = fn(z).
Approximation of Uniform Transport Process on a Finite Interval to Brownian Motion
Authors: Watanabe Toitsu
Published: July 2016

Let us consider a finite closed interval [− a, a] which will be thought of as being a medium capable of transporting particles. These particles may move only to the right or to the left with the constant speed c, and each particle changes the moving-direction during the time Δ with probability kΔ + o(Δ). If a right- (left-) moving particle hits the boundary point a (— a), then either it turns to the left (right) with probability 1 — q1(1 − q-1) or dies with probability q1(q-1).
Note sur L’ensemble D’Adhérence Fine des Fonctions Algébroïdes
Authors: Toda Nobushige
Published: July 2016

Soit f(z) une fonction algébroïde dans | z | < ∞ définie par

où cette équation est irréducible dans | z | < ∞. Rf est la surface de Riemann définie par f(z) comme surface de recouvrement de | z | < ∞.
On Formal Theories
Authors: Ono Katuzi
Published: July 2016

The main purpose of the present paper is to introduce a new understanding of formal theories.

It has been a traditional pattern of formal theories to presuppose a logic and an axiom system for each formal theory. The axiom system of any formal theory consists of a finite number of axiom schemata in general, but occasionally it can be regarded as consisting of a finite number of axioms. I will call any formal theory of this kind an axiomatic theory or an axiom-schematic theory according as its axiom system is regarded as consisting of a finite number of axioms or as consisting of a finite number of axiom schemata.
On Homogeneous Spaces, Holonomy, and Non-Associative Algebras
Authors: Sagle Arthur A.
Published: July 2016

Let G be a connected Lie group and H a closed subgroup. The homogeneous space M = G/H is called reductive if in the Lie algebra g of G there exists a subspace m such that (subspace direct sum) and where is the Lie algebra of H, see [8].
The role of language in the dual process theory of thinking
Authors: Evans Jonathan St. B. T. , Over David E.
Published: July 2016

Carruthers’proposals would seem to implicate language in what is known as System 2 thinking (explicit) rather than System 1 thinking (implicit) in contemporary dual process theories of thinking and reasoning. We provide outline description of these theories and show that while Carruthers’characterization of non-verbal processes as domain-specific identifies one critical feature of System 1 thinking, he appears to overlook the fact that much cognition of this type results from domain-general learning processes. We also review cognitive psychological evidence that shows that language and the explicit representations it supports are heavily involved in supporting System 1 thinking, but falls short of supporting his claim that it is the medium in which domain-general thinking occurs.
An assessment of the value of plasma urea nitrogen and albumin concentrations as monitors of the protein status of sheep
Authors: Sykes A.R.
Published: July 2016

There are two basic aspects of protein metabolism the measurement of which may assist in improving sheep management, first, the extent to which the daily requirement of the animal is met and secondly, the extent of depletion of body reserves. The need for the latter assessment arises because in some situations in which nutrient requirement and supply are not in phase it is often desirable for economic reasons to utilize the capacity of the animal to deplete and replete its body reserves.

Of the major nutrients, the prediction of energy metabolism from plasma parameters has received most attention. Thus the work of Annison (1960), Reid and Hinks (1962), West and Annison (1964) relating Free Fatty Acid (FFA) concentration to rate of fat mobilization allowed the prediction not only of energy balance but also rate of energy reserve mobilisation in controlled nutritional situations (Russel, Doney and Reid, 1967; Russel and Honey, 1969; Robinson, Fraser and Bennett, 1971).
Blood profiles as a guide to nutritional status in the field
Authors: Wilson P.N. , Medd R.K.
Published: July 2016

The object of this paper is to discuss the practical application of blood profiles and the value of blood profiles as an advisory aid in the field. For this purpose, an attempt has been made to quantify the ‘success rate’ of blood profiles on a case study basis. It is hoped that the paper will serve to stimulate discussion by being as objective as possible. It is not presented as an original scientific paper and should not be interpreted as such.

The productivity of the dairy herd is primarily dependent on the metabolic and nutritional status of each dairy cow. All too frequently, there is a tendency for high output demands - milk and calves - to be associated with inadequate feed inputs, resulting in imbalances of body metabolites, which, if sustained, eventually become clinically apparent as ‘production diseases’ such as hypocalcaemia and hypomagnesaemia.
Cattle Identification
Authors: Street M.J.
Published: July 2016

The livestock industry is looking for are liable means of regularly identifying individual animals for a variety of reasons, all of which stem from an economic requirement to reduce costs or improve efficiency.
The Effect of Mechanization and Automation on Machine Milking Performance in Milking Parlours
Authors: Clough P.A.
Published: July 2016

Machine milking performance is measured in terms of cows milked per person per hour and is influenced by the duration of the routine work of the milker associated with each cow milked, the milk yield per cow at a milking, and the type and size of milking parlour installation (Clough and Dodd, 1959).
Control, Data Recording and Retrieval - Farmers' Requirements
Authors: Bacon J.K.
Published: July 2016

The basic requirements of any automated system for collecting and processing data for a diary herd are that:-

- it must present the information required for day-to-day management in an easy and readily available form.

- it will be justified only if the system provides useful management data that would be more costly to produce in other ways or be impractical to obtain manually

- it should be built from a simple base with add-on units to a complete system, to allow for various sizes of herd, levels of technical development and cost. (Inputs could be either from manual records or automatic recorders)

- it should provide information on a visual display unit, with lists printed when required

- accurate identification is essential especially if automatic identification is used

- it should be developed to a fully computerized farm recording system.
1.2 Sociological implications of intensifying animal production in developing countries: the case of the african pastoralists
Authors: Baker P. R.
Published: July 2016

In the early part of the last decade the World Bank identified the livestock sector as the principal area for investment in several countries in Africa, upon which continent this paper concentrates. Since that time very considerable amounts of time and scarce development capital have been directed into improving and “modernising” the production and marketing of, particularly, cattle from the traditional sector. However, the success rate of projects has been extremely low, leading one writer to comment: “There are few fields of economic development characterized by greater or more destructive blunders than those involving attempts to improve the productivity of grazing lands and the animals depending on them” (Dasmann, Milton and Freeman, 1973).
3.3 The use of by-products for intensive animal production
Authors: Preston T. R.
Published: July 2016

In the majority of developing countries, there is increasing competition for land use. This is due, on the one hand, to increasing population pressure and, on the other hand, to the need to earn/save foreign exchange by growing crops for export and also for human consumption at home. In this situation, it becomes increasingly difficult to justify the utilization of land for animal production only, as is the case in grazing systems.
5.2 The potential contribution of indigenous pigs to intensive pig production in Southern Africa
Authors: Chigaru P. R. N. , Holness D. H.
Published: July 2016

Populations of domestic pigs, very different in appearance and size to recently imported exotic breeds, are found in many countries in Africa. Although often referred to as indigenous or native, in East and Southern Africa at least, they may be descended from stock originally introduced by Europeans, probably in the nineteenth century (Mason and Maule, 1960). Diverse phenotypes have developed in different parts of the continent (e.g. Jollans, 1959; Joubert, Combrinck and Bonsma, 1960), and reports generally refer to their poor conformation, slow growth rates and low productivity. To some extent this is probably a reflection of their environment and diet, since they largely subsist by foraging around human habitations and cultivations (Epstein, 1971).
5.3 Peri-urban piggeries in Papua New Guinea
Authors: Walters J. R.
Published: July 2016

The pig is by far the most important domestic animal in Papua New Guinea, having been introduced to the island from Asia as domestic stock more than 5 000 years ago (Purdy, 1971; Harris, 1975; Brown, 1978).
5.7 Integrated fish farming in developing countries
Authors: Muir J. F.
Published: July 2016

The production of food through fish-farming or aquaculture has become an area of increasing interest in the developing world, as the potential of unused water resources is realised and the spread of appropriate techniques for suitable fish species is encouraged. From a production through aquaculture of 6 million tonnes or approximately 10% of current captive fisheries in 1976 (Pillay 1976), estimates of as high as 4O% by the year 2000 have been given (Bardach, Rhyther and McLarney, 1972), a great part of which will be from developing countries. Where resources are limited, techniques Of aquaculture which are integrated with conventional agricultural or industrial activities by using their wastes, or which provide useful by-products, are especially to be encouraged.
6.3 Intensive milk production in Sri Lanka
Authors: Thangarajah P.
Published: July 2016

Sri Lanka is an island within the tropics between the northern latitudes 5°55′ and 9°50′ and the eastern longitudes 79°42′ and 80°51′. The island covers an area of 65 000 km2 (25 332 sq. miles). The human population of the island is estimated at 14.6 million.
6.6 Intensive beef production in Zimbabwe, based on sugar cane by-products
Authors: De La Hunt T. E.
Published: July 2016

Animal feeds based on sugar cane by-products play a major part in intensive beef production in Zimbabwe. Molasses and bagasse are widely used in factory-produced diets for complete and full feeding of slaughter cattle in confinement and also in concentrates for supplementary feeding on pasture. Feed dry matter to carcass gain conversion ratios vary from 1:12.3 on diets containing 55% molasses and zero maize, to 1:10 on diets containing 14% molasses and 52% maize.
Changes in the marketing chain
Authors: Harrington Geoff
Published: July 2016

Anyone called upon to describe change has to decide how far to go back in history, because recent developments are usually part of a much longer-term trend. For this audience, I am sure I do not need to go back as far as the drove roads or to the Shambles around the big livestock market called Smithfield. But many of us can remember the structure of our meat industry when it was built around a distribution system for imported meat, particularly to the consumers in the major conurbations, with home-produced meat being concentrated into rural areas and some of the higherclass shops in the towns.
National and international policies and legislation
Authors: Revell Brian J.
Published: July 2016

In considering markets for meat, it is important to distinguish between what a market may want and what it can have. The objectives and operation of national and international policies and legislation are frequently at variance with those of the marketplace. Policies have been designed either to modify market signals or to offset some of their effects, principally on production, but also on consumption and trade. They usually place constraints on availability and/or radically alter price signals to producers. In a recent report (OECD, 1982), it was observed that

‘Government intervention in domestic and international meat markets is increasing. All major beef importing countries now control beef imports in some way or another. The introduction of the EEC Sheepmeat Regime could in the future have a major impact on the pattern of sheepmeat trade flows. The importation of meat by many of the newly developed markets is controlled by state trading institutions.’
Tissue quality in lean pigs
Authors: Wood J. D. , Brown A. J. , Enser M. , Jones R. C. D.
Published: July 2016

Pig carcasses have become progressively leaner over the last 10 years, a necessary trend to satisfy consumer requirements for lean meat. However, this trend has not always been welcomed by the meat trade. For instance, the headline “No to Further Fat Reduction” appeared in the Meat Trades Journal of September 2, 1982. Concern has been expressed over lack of eating quality in very lean pork and certain aspects of lean carcasses as follows:

— soft, floppy backfat

— carcasses do not set after chilling, making cutting or slicing difficult

— separation occurs between backfat layers, between backfat and muscle and between intermuscular fat and muscle.
Variation in the retail value of beef carcasses as affected by fatness, conformation and different butchery techniques
Authors: Fisher A. V. , Brown A. J.
Published: July 2016

There are several aspects of carcass composition and quality which, as an integrated whole, determine carcass value. However, it is convenient, and informative, to restrict the study to quantitative (gravimetric) data and to remove the effect of carcass weight. If this is done, and if requirements to meet standard joints or cuts are imposed, there are only two factors which affect value: (a) the proportion of saleable meat in the carcass and (b) its distribution amongst joints of different value. There is an overriding importance of (a) in this context and the commercial significance of carcass classification schemes is dependent on the accuracy with which the proportion of saleable meat in carcasses can be predicted.
Food-borne pathogens: limiting the spread
Authors: Cooke E. M.
Published: July 2016

There are several sources of information on food-borne illness in the United Kingdom. These include laboratory and clinical reports and the results of special studies and surveys.

The data are collected, analysed and published, amongst other places, in the Communicable Disease Report and the Public Health Laboratory Service/State Veterinary Service (PHLS/SVS) Salmonella Update. In the latter, animal and human data are brought together. Reported cases of food poisoning represent a small proportion of the total load of disease but are valuable as an indication of trends. The data produced from these sources in relation to salmonellosis, listeriosis, campylobacter and E. coli 0157 infection are described, as are some data about the costs of human salmonellosis. Possible approaches to the reduction of these economically important human diseases are described against a background of the existing advisory and legal structures.