bluuebunny/crossref_metadata_2025 huggingface dataset:
The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime
Authors: Kato Ryo , Shimomura Katsumi
Published: July 2016

The chromatic spectral sequence was introduced by Miller, Ravenel, and Wilson to compute the E2-term of the Adams-Novikov spectral sequence for computing the stable homotopy groups of spheres. The E1-term of the spectral sequence is an Ext group of BP*BP-comodules. There is a sequence of Ext groups for nonnegative integers n with and there are Bockstein spectral sequences computing a module (n – s) from So far, a small number of the E1-terms are determined. Here, we determine the for p > 2 and n > 3 by computing the Bockstein spectral sequence with E1-term for s = 1, 2. As an application, we study the nontriviality of the action of α1 and β1 in the homotopy groups of the second Smith-Toda spectrum V(2).
New estimates of Hilbert–Kunz multiplicities for local rings of fixed dimension
Authors: Aberbach Ian M. , Enescu Florian
Published: July 2016

We present results on the Watanabe–Yoshida conjecture for the Hilbert–Kunz multiplicity of a local ring of positive characteristic. By improving on a “volume estimate” giving a lower bound for Hilbert–Kunz multiplicity, we obtain the conjecture when the ring has either Hilbert–Samuel multiplicity less than or equal to 5 or dimension less than or equal to 6. For nonregular rings with fixed dimension, a new lower bound for the Hilbert–Kunz multiplicity is obtained.
Triangulation of the map of a G-manifold to its orbit space
Authors: Murayama Mitsutaka , Shiota Masahiro
Published: July 2016

LetGbe a Lie group, and letMbe a smooth properG-manifold. LetM/Gdenote the orbit space, and letπ:M → M/Gbe the natural map. It is known thatM/Gis homeomorphic to a polyhedron. In the present paper we show that there exist a piecewise linear (PL) manifoldP,a polyhedronL, and homeomorphismsτ:P → Mandσ:M/G → Lsuch thatσ o π o τis PL. This is an application of the theory of subanalytic sets and subanalytic maps of Shiota. IfMand theG-action are, moreover, subanalytic, then we can chooseτandσsubanalytic andPandLunique up to PL homeomorphisms.
Erratum: Linear Projections and Successive Minima
Authors: Soulé Christophe
Published: July 2016

The proof of Proposition 1 and Theorem 2 in [3] is incorrect. Indeed, Sections 2.5 and 2.7 in [3] contain a vicious circle: the definition of the filtrationVi, 1 ≤i≤n, in Section 2.5 of that article depends on the choice of the integersni, when the definition of the integersniin Section 2.7 depends on the choice of the filtration(Vi). Thus, only Theorem 1 and Corollary 1 in [3] are proved. In the following we will prove another result instead of [3, Proposition 1].
Gluing Silting Objects
Authors: Liu Qunhua , Vitória Jorge , Yang Dong
Published: July 2016

Recent results by Keller and Nicolás and by Koenig and Yang have shown bijective correspondences between suitable classes of t-structures and cot-structures with certain objects of the derived category: silting objects. On the other hand, the techniques of gluing (co-)t-structures along a recollement play an important role in the understanding of derived module categories. Using the above correspondence with silting objects, we present explicit constructions of gluing of silting objects, and, furthermore, we answer the question of when the glued silting is tilting.
Centrally Symmetric Configurations of Integer Matrices
Authors: Ohsugi Hidefumi , Hibi Takayuki
Published: July 2016

The concept of centrally symmetric configurations of integer matrices is introduced. We study the problem when the toric ring of a centrally symmetric configuration is normal and when it is Gorenstein. In addition, Gröbner bases of toric ideals of centrally symmetric configurations are discussed. Special attention is given to centrally symmetric configurations of unimodular matrices and to those of incidence matrices of finite graphs.
Singular Del Pezzo surfaces and analytic compactifications of 3-dimensional complex affine space C3
Authors: Furushima Mikio
Published: July 2016

Let X be an n-dimensional connected compact complex manifold and A be an analytic subset of X. We say that the pair (X, A) is a complex analytic compactification of Cn if X − A is biholomorphic to Cn. If X admits a Kähler metric, we shall say that (X, A) is a (non-singular) Kähler compactification of Cn. For n = 1, it is easy to see that (X, A) ≃ (P1, ∞). For n = 2, Remmert-Van de Ven [17] proved that (X, A) ≃ (P2, P1) if A is irreducible, where A = P1 is linearly embedded in P2. Morrow [15] gave more detailed classifications of complex analytic compactifications of C2 For n = 3, Brenton-Morrow showed the following

THEOREM ([5]). Let (X, A) be a non-singular Kähler complex analytic compactification of C3such that the analytic subset A has only isolated singular points. Then X is projective algebraic and A is birationally equivalent to a ruled surface over an algebraic curve of genus g = b3(X)/2.

Further, Brenton [3] classified the possible types of singular points of A in the case that the canonical line bundle KA of A is not trivial.
General Néron desingularization and approximation
Authors: Popescu Dorin
Published: July 2016

LetAbe a noetherian ring (all the rings are supposed here to be commutative with identity),a⊂Aa proper ideal andÂthe completion ofAin theα-adic topology. We consider the following conditions

(WAP) Every finite system of polynomial equations overAhas a solution inAiff it has one inÂ.
Über die Klassenzahlen algebraischer Zahlkörper
Authors: Kuroda Sigekatu
Published: July 2016

Seit Herr Artin seine allgemeinen L-Funktionen, die mit Frobeniusschen Gruppencharakteren gebildet sind, entdeckt hat [1], sind die multiplikativen Relationen Dedekindscher ζ-Funktionen als additive Relationen zwischen den Frobeniusschen Gruppencharakteren mit Erfolg untersucht worden. Durch diese Methode sind gewisse Klassenzahlrelationen in den folgenden Zeilen zu betrachten.
Stochastic Differential Equations in a Differentiable Manifold
Authors: Itô Kiyosi
Published: July 2016

The theory of stochastic differential equations in a differentiate manifold has been established by many authors from different view-points, especially by R Lévy [2], F. Perrin [1], A. Kolmogoroff [1] [2] and K. Yosida [1] [2]. It is the purpose of the present paper to discuss it by making use of stochastic integrals.
On Titchmarsh-Kodaira’s Formula concerning Weyl-Stone’s Eigenfunction Expansion
Authors: Yosida Kôsaku
Published: July 2016

Let q (x) be real and continuous in the infinite open interval (- ∞, ∞) and let y1(x, λ), y2(x, λ) be the solutions of

(1.1)

with the initial conditions

(1.2) .
A Theorem on the Cluster Sets of Pseudo-Analytic Functions
Authors: Noshiro Kiyoshi
Published: July 2016

Let D be an arbitrary connected domain and w = f(z) = u(x,y) + iv(x,y), z = x + iy, be an interior transformation in the sense of Stoïlow in D. Denote by γ a set, in D, such that D and the derived set γ′ of γ have no point in common.
Corrections and Supplementaries to My Paper concerning Krull-Remak-Schmidt’s Theorem
Authors: Azumaya Gorô
Published: July 2016

It has recently been found that my previous paper “On generalized semi-primary rings and Krull-Remak-Schmidt’s theorem” Jap. Journ. Math. 19 (1949) — referred to as S. K. — contained in its Theorems 19 and 20 some errors. Nevertheless the writer has been able to correct them in suitable forms so that most parts of both theorems hold, even under a weaker assumption, and also subsequent theorems remain valid. These will be, together with some supplementary remarks, shown in the present note.
Some Remarks on the Exceptional Simple Lie Group
Authors: Matsushima Yozô
Published: July 2016

Let be the Cayley algebra of dimension 8 over the field R of real numbers and let be the set of all 3 × 3 Hermitian matrices
On the Inner Automorphisms of a Compact Group
Authors: Murakami Shingo , Gotô Morikumi
Published: July 2016

In this note, we give a characterization of inner automorphisms in the set of automorphisms of a compact connected group, and then apply it to give a proof of a theorem due to K. Iwasawa on the group of automorphisms of a compact group.
Kleine Studie zur Kombinatorischen Geometrie der Sphäre
Authors: Hadwiger von H.
Published: July 2016

Es bezeichne Sn die n-dimensionale Sphäre, Eine solche ist der Rand einer (n + 1)-dimensionalen euklidischen Vollkugel vom Radius 1.
On a Problem of Chevalley
Authors: Masuda Katsuhiko
Published: July 2016

Recently Prof. Chevalley in Nagoya suggested to the author the following problem: Let k be a field, K5 = k(x1, x2, x3, x4, x5) be a purely transcendental extension field (of transcendental degree 5) of k, s5 be the cyclic permutation of x: S5X1 = x2s5x2 = x3s5x3 = x4s5x4 = x5s5x5 = x1, and let L5 be the field of invariants of s5 in K5. Is L5 then purely transcendental over k or not? When the characteristic p of k is not equal to 5, it is answered in the following positively. When the characteristic p of k is equal to 5, it is answered also positively by Mr. Kuniyoshi’s result in [2].
On a Problem of Chevalley
Authors: Kuniyoshi Hideo
Published: July 2016

In the present note we wish to deal with the same problem as the preceding paper [1] for the case of modular fields.

Let k be a ñeiá of characteristic and K = k(x1 …, xp) a purely-transcendental extension of k, Let S be the automorphism of K which is induced by the cyclic permutation (x1., .., xp) and L the fixed subfield of S. Then L is a purely transcendental extension field over k.
Note on the Group of Affine Transformations of an Affinely Connected Manifold
Authors: Hano Jun-Ichi , Morimoto Akihiko
Published: July 2016

The purpose of the present note is to reform Mr. K. Nomizu’s result on the group of all affine transformations of an affinely connected manifold. We shall prove the following.

THEOREM. The group of all affine transformations of an affinely connected manifold is a Lie group.
On the Holonomy Group of the Conformally Flat Riemannian Manifold
Authors: Kurita Minoru
Published: July 2016

The main purpose of the present paper is to show that the local homogeneous holonomy group of the conformally flat Riemannian manifold is the full rotation group with some exceptions.
On the Dimension of Modules and Algebras, X: A Right Hereditary Ring which is not left Hereditary
Authors: Kaplansky Irving
Published: July 2016

A ring R is said to be right (left) hereditary if every right (left) ideal in R is projective, that is, a direct summand of a free R-module. Cartan and Eilenberg [3, p. 15] ask whether there exists a right hereditary ring which is not left hereditary. The answer: yes.
Note on Relative Homological Dimension
Authors: Hochschild G.
Published: July 2016

Let R be a ring with identity element 1, and let S be a subring of R containing 1. We consider R-modules on which 1 acts as the identity map, and we shall simultaneously regard such R-modules as S-modules in the natural way. In [4], we have defined the relative analogues of the functors of Cartan-Eilenberg [1], and we have briefly treated the corresponding relative analogues of module dimension and global ring dimension.
Über den Idealen Rand und Einige Seiner Anwendungen bei der Klassifikation der Riemannschen Flächen
Authors: Constantinescu Corneliu , Cornea Aurel
Published: July 2016

Ein gewöhnliches Verfahren bei dem Studium der Riemannschen Flächen besteht darin, dass man die für die komplexe Ebene benutzten Methoden auf allgemeine Riemannsche Flächen überführt und die bekannten Satze fur schlichtartige Gebiete auf den Riemannschen Flachen verallgemeinert. Dises Verfahren schlägt zuweilen fehl, da manche Sätze, welche im Falle der schlichtartigen Gebiete richtig sind, im Falle beliebiger Riemannscher Flächen nicht mehr wahr bleiben.
On a Class of Conformal Metrics
Authors: Heins Maurice
Published: July 2016

Last year when I was preparing for course lectures the work of Ahlfors [1] which establishes that the Bloch constant is at least as large as it appeared to me that the resources of the theory of metrics of negative curvature offered rich possibilities from a function-theoretic point of view. The parallelism between certain properties of subharmonic functions and those of the metrics introduced by Ahlfors [1] is so striking that we are led to ask whether one can introduce a class of metrics including the metrics of Ahlfors for which not only does a Schwarz-Pick-Ahlfors lemma hold, but also requirements of differentiability disappear, as in the modern theory of subharmonic functions.
Problemes d’Universalite s’Introduisant dans l’Algébrisation de la Logique Mathématique II
Authors: Ponasse Daniel
Published: July 2016

Nous définirons la structure d’ensemble individualisé au moyen des données suivantes:

—un ensemble non vide A, éléments notés u, v, w,…

—un ensemble infini I, éléments notés a, b, c,… i, j, k,… et appelés individus.

—une application s de I2 dans l’ensemble des applications de A dans lui-même; une fonction telle que s(a, b) sera dite “substitution de a à b”, et lorsque aucune confusion ne sera à craindre, on la notera simplement (a/b), sa valeur pour u ∈ A sera alors notée (a/b)u. Si l’on est en présence de plusieurs individualisations différentes, on pourra préciser en disant que A est s-individualisé sur I.
A Property of Weak Solutions for Some Parabolic Equations of Higher Order
Authors: Chen Lu-San
Published: July 2016

Recently Aronson [1] proved the uniqueness property of weak solutions of the initial boundary value problem for second order parabolic equations with discontinuous coefficients. An analogous result to Aronson’s was proved by Kuroda M in the case of some parabolic equations of higher order, where the method due to Aronson [2] plays an essential role. In this paper, under the same idea we shall be concerned with the asymptotic behavior of weak solutions for parabolic equations of higher order of the divergence form, when the data are prescribed on a portion of a time-like surface.
Some Remarks in the Fourier Analysis
Authors: Tatuzawa Tikao
Published: July 2016

In this paper, I should like to add some remarks to my previous note titled “Some results in the Fourier analysis” (Nagoya Math. Journal, Vol. 27, 1966). At first, we shall show that the orthnormal set exp [2 πi(m1x1+ … mnxn is complete in the Hilbert space L2 over the unit cube E = {(x1, …, xn); 0≧xj≦1 (1≦j≦n)}, where the inner product ‹f, g› for f, g ∊ L2 over E is defined by
Normal Bases in Galois Extensions of Number Fields
Authors: Ullom S.
Published: July 2016

The notion of module together with many other concepts in abstract algebra we owe to Dedekind [2]. He recognized that the ring of integersOKof a number field was a freeZ-module. When the extensionK/Fis Galois, it is known thatKhas an algebraic normal basis overF. A fractional ideal ofKis a Galois module if and only if it is an ambiguous ideal. Hilbert [4, §§105-112] used the existence of a normal basis for certain rings of integers to develop the theory of root numbers — their decomposition already having been studied by Kummer.
On a canonical Lie algebra sl(2r + 2)-bundle over grass (n, r)
Authors: Morikawa Hisasi
Published: July 2016

In the present note we shall construct a Lie algebra sl (2r + 2)-bundle over Grass (n, r), canonically, which may be useful for theory of holomorphic vector bundles probably.
On classification of quasi-symmetric domains
Authors: Satake I.
Published: July 2016

The notion of “Siegel domains” was introduced by [8]. It was then shown that every homogeneous bounded domain is holomorphically equivalent to a Siegel domain (of the second kind) determined uniquely up to an affine isomorphism ([15], cf. also [2], [4], [9b]). In a recent note [10b], I have shown that among (homogeneous) Siegel domains the symmetric domains can be characterized by three conditions (i), (ii), (iii) on the data (U, V, Ω, F) defining the Siegel domain (see Theorem in § 2 of this paper). The class of homogeneous Siegel domains satisfying partial conditions (i), (ii), which we propose to call “quasi-symmetric”, seems to be of some interest, since for instance the fibers appearing in the expressions of symmetric domains as Siegel domains of the third kind fall in this class ([10b], [16]).
A generalized principal ideal theorem
Authors: Eisenbud David , Evans E. Graham
Published: July 2016

Krull’s principal ideal theorm [Krull] states thatqelements in the maximal ideal of a local noetherian ring generate an ideal whose minimal components are all of height at mostq. WritingRfor the ring, we may consider theqelements,x1,· · ·,xqsay, as coordinates of an elementx ∈ Rq.
Non-degenerate real hypersurfaces in complex manifolds admitting large groups of pseudo-conformal transformations. I
Authors: Yamaguchi Keizo
Published: July 2016

Let S (resp. S′) be a (real) hypersurface (i.e. a real analytic sub-manifold of codimension 1) of an n-dimensional complex manifold M (resp. M′). A homeomorphism f of S onto S′ is called a pseudo-conformal homeomorphism if it can be extended to a holomorphic homeomorphism of a neighborhood of S in M onto a neighborhood of S′ in M. In case such an f exists, we say that S and S′ are pseudo-conformally equivalent. A hypersurface S is called non-degenerate (index r) if its Levi-form is non-degenerate (and its index is equal to r) at each point of S.
Remarks to the uniqueness problem of meromorphic maps into PN(C), III
Authors: Fujimoto Hirotaka
Published: July 2016

In the previous papers [3], [4], [5] the author gave some results on the uniqueness of meromorphic maps of Cn into the N-dimensional complex projective space PN(C) which have the pre-assigned inverse images for some hyperplanes in PN(C). Relating to these results, we attempt in this paper to generalize the following Cartan-Nevanlinna’s theorem to the case of meromorphic maps into PN(C).
On homeomorphisms of the unit circle preserving orientation
Authors: Hara Masaru
Published: July 2016

Let Γ denote the unit circle in the complex plane C, C(Γ) the set of complex valued continuous functions on Γ which is a Banach space by the sup-norm ‖·‖, A(z) the uniform closure of all polynomials in z on Γ, H(Γ) the set of homeomorphisms of Γ, H+(Γ) the set of direction-preserving homeomorphisms and H−(Γ) the set of direction-reversing homeomorphisms. For ψ ∈ H(Γ), let A(ψ) denote the uniform closure of all polynomials in ψ on Γ.
On augmented Schottky spaces and automorphic forms, I
Authors: Sato Hiroki
Published: July 2016

With respect to Teichmüller spaces, many beautiful results are obtained by TeichmüUer, Ahlfors, Bers, Maskit, Kra, Earle, Abikoff, and others. For example, the boundary consists of b-groups, and the augmented Teichmüller space is defined by attaching a part of the boundary to the Teichmüller space. By using the augmented Teichmüller space, a compactification of the moduli space of Riemann surfaces is accomplished (cf. Abikoff [1], Bers [2]).
Projective surfaces with K-very ample line bundles of degree ≤ 4K + 4
Authors: Ballico Edoardo , Sommese Andrew J.
Published: July 2016

A line bundle, L, on a smooth, connected projective surface, S, is defined [7] to be k-very ample for a non-negative integer, k, if given any 0-dimensional sub-scheme with length , it follows that the restriction map is onto. L is 1-very ample (respectively 0-very ample) if and only if L is very ample (respectively spanned at all points by global sections). For a smooth surface, S, embedded in projective space by | L | where L is very ample, L being k-very ample is equivalent to there being no k-secant Pk−1 to S containing ≥ k + 1 points of S.
A volume estimate for strong subharmonicity and maximum principle on complete Riemannian manifolds
Authors: Takegoshi Kensho
Published: July 2016

A generalized maximum principle on a complete Riemannian manifold (M, g) is shown under a certain volume growth condition of (M, g) and its geometric applications are given.
One dimensional fibering over q-complete spaces
Authors: Vâjâitu Viorel
Published: July 2016

We show that if E → X is a locally trivial holomorphic fibrations whose fiber is an open Riemann surface and X is a q-complete space, then E is q-complete.
Some notes on the moduli of stable sheaves on elliptic surfaces
Authors: Yoshioka Kōta
Published: July 2016

In this paper, we shall consider the birational structure of moduli of stable sheaves on elliptic surfaces, which is a generalization of Friedman’s results to higher rank cases. As applications, we show that some moduli spaces of stable sheaves on ℙ2 are rational. We also compute the Picard groups of those on Abelian surfaces.
Adapted complex structures and geometric quantization
Authors: Szőke Róbert
Published: July 2016

A compact Riemannian symmetric space admits a canonical complexification. This so called adapted complex manifold structureJAis defined on the tangent bundle. For compact rank-one symmetric spaces another complex structureJSis defined on the punctured tangent bundle. This latter is used to quantize the geodesic flow for such manifolds. We show that the limit of the push forward ofJAunder an appropriate family of diffeomorphisms exists and agrees withJS.
A hybrid mean value of the inversion of L-functions and general quadratic Gauss sums
Authors: Zhang Wenpeng , Deng Yuping
Published: July 2016

The main purpose of this paper is, using the estimates for character sums and the analytic method, to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums, and give two interesting asymptotic formulas.
On classification of ℚ-fano 3-folds of Gorenstein index 2. II
Authors: Takagi Hiromichi
Published: July 2016

In the previous paper, we obtained a list of numerical possibilities of ℚ-Fano 3-folds X with Pic X = ℤ(−2KX) and h0(−KX) ≥ 4 containing index 2 points P such that (X, P) ≃ ({xy + z2 + ua = 0}/ℤ2(1, 1, 1, 0), o) for some a ∈ ℕ. Moreover we showed that such an X is birational to a simpler Mori fiber space. In this paper, we prove their existence except for a few cases by constructing a Mori fiber space with desired properties and reconstructing X from it.
On the dimension and multiplicity of local cohomology modules
Authors: Brodmann Markus P. , Sharp Rodney Y.
Published: July 2016

This paper is concerned with a finitely generated module M over a (commutative Noetherian) local ring R. In the case when R is a homomorphic image of a Gorenstein local ring, one can use the well-known associativity formula for multiplicities, together with local duality and Matlis duality, to produce analogous associativity formulae for the local cohomology modules of M with respect to the maximal ideal. The main purpose of this paper is to show that these formulae also hold in the case when R is universally catenary and such that all its formal fibres are Cohen–Macaulay.

These formulae involve certain subsets of the spectrum of R called the pseudosupports of M; these pseudo-supports are closed in the Zariski topology when R is universally catenary and has the property that all its formal fibres are Cohen–Macaulay. However, examples are provided to show that, in general, these pseudo-supports need not be closed. We are able to conclude that the above-mentioned associativity formulae for local cohomology modules do not hold over all local rings.
On modularity of rigid and nonrigid Calabi-Yau varieties associated to the Root Lattice A4
Authors: Hulek Klaus , Verrill Helena
Published: July 2016

We prove the modularity of four rigid and three nonrigid Calabi-Yau threefolds associated with the A4 root lattice.
On the K-Theory of the Coordinate Axes in the Plane
Authors: Hesselholt Lars
Published: July 2016

Let k a regular noetherian p-algebra, let A = k[x, y]/(xy) be the coordinate ring of the coordinate axes in the affine k-plane, and let I = (x,y) be the ideal that defines the intersection point. We evaluate the relative K-groups Kq(A, I) completely in terms of the big de Rham-Witt groups of k. This generalizes a formula for K1(A, I) and K2(A, I) by Dennis and Krusemeyer.
Even-Relative-Dimensional Vanishing Cycles in Bivariant Intersection Theory
Authors: Saito Hiroshi
Published: July 2016

For a smooth variety proper over a curve having a fibre with isolated ordinary quadratic singularities, it is well-known that we have the vanishing cycles associated to the singularities in the étale cohomology of the geometric generic fibre. The base-change by a double cover of the base curve ramified at the image of the singular fibre has singularities corresponding to the singularities in the fibre. In this note, we show that in the even relative-dimensional case, there exist elements of the bivariant Chow group of the base-change with supports in the singularities and hence their images in the bivariant Chow group with supports in the special fibre and that the usual cohomological vanishing cycles are obtained as their images by a natural map, a kind of “cycle map” so that the elements in the bivariant Chow groups can be regarded as the vanishing cycles. The bivariant Chow group with supports in the special fibre has a ring structure and the natural map is a ring homomorphism to the cohomology ring of the geometric generic fibre. Also discussed is the relation of the bivariant Chow group with supports in the special fibre to the specialization map of Chow groups.
Some Families of Componentwise Linear Monomial Ideals
Authors: Francisco Christopher A. , Tuyl Adam Van
Published: July 2016

Let R = k[x1,…,xn] be a polynomial ring over a field k. Let J = {j1,…,jt} be a subset of {1,…, n}, and let mJ ⊂ R denote the ideal (xj1,…,xjt). Given subsets J1,…,Js of {1,…, n} and positive integers a1,…,as, we study ideals of the form These ideals arise naturally, for example, in the study of fat points, tetrahedral curves, and Alexander duality of squarefree monomial ideals. Our main focus is determining when ideals of this form are componentwise linear. Using polymatroidality, we prove that I is always componentwise linear when s ≤ 3 or when Ji ∪ Jj = [n] for all i ≠ j. When s ≥ 4, we give examples to show that I may or may not be componentwise linear. We apply these results to ideals of small sets of general fat points in multiprojective space, and we extend work of Fatabbi, Lorenzini, Valla, and the first author by computing the graded Betti numbers in the s = 2 case. Since componentwise linear ideals satisfy the Multiplicity Conjecture of Herzog, Huneke, and Srinivasan when char(k) = 0, our work also yields new cases in which this conjecture holds.
Integral Springer Theorem for Quaternionic Forms
Authors: Arenas-Carmona Luis
Published: July 2016

J. S. Hsia has conjectured an arithmetical version of Springer Theorem, which states that no two spinor genera in the same genus of integral quadratic forms become identified over an odd degree extension. In this paper we prove by examples that the corresponding result for quaternionic skew-hermitian forms does not hold in full generality. We prove that it does hold for unimodular skew-hermitian lattices under all extensions and for lattices whose discriminant is relatively prime to 2 under Galois extensions.
Moduli Space of Brody Curves, Energy and Mean Dimension
Authors: Tsukamoto Masaki
Published: July 2016

A Brody curve is a holomorphic map from the complex plane ℂ to a Hermitian manifold with bounded derivative. In this paper we study the value distribution of Brody curves from the viewpoint of moduli theory. The moduli space of Brody curves becomes infinite dimensional in general, and we study its “mean dimension”. We introduce the notion of “mean energy” and show that this can be used to estimate the mean dimension.
On Generalized Modular forms and their Applications
Authors: Kohnen Winfried , Mason Geoffrey
Published: July 2016

We study the Fourier coefficients of generalized modular forms f(τ) of integral weight k on subgroups Γ of finite index in the modular group. We establish two Theorems asserting that f(τ) is constant if k = 0, f(τ) has empty divisor, and the Fourier coefficients have certain rationality properties. (The result is false if the rationality assumptions are dropped.) These results are applied to the case that f(τ) has a cuspidal divisor, k is arbitrary, and Γ = Γ0(N), where we show that f(τ) is modular, indeed an eta-quotient, under natural rationality assumptions on the Fourier coefficients. We also explain how these results apply to the theory of orbifold vertex operator algebras.
Sharp Exponential Integrability for Traces of Monotone Sobolev Functions
Authors: Pankka Pekka , Poggi-Corradini Pietro , Rajala Kai
Published: July 2016

We answer a question posed in [12] on exponential integrability of functions of restricted n-energy. We use geometric methods to obtain a sharp exponential integrability result for boundary traces of monotone Sobolev functions defined on the unit ball.
Cohen-Macaulay edge ideal whose height is half of the number of vertices
Authors: Crupi Marilena , Rinaldo Giancarlo , Terai Naoki
Published: July 2016

We consider a class of graphsGsuch that the height of the edge idealI(G) is half of the number#V(G) of the vertices. We give Cohen-Macaulay criteria for such graphs.
On Eells-Sampson’s existence theorem for harmonic maps via exponentially harmonic maps
Authors: Omori Toshiaki
Published: July 2016

In this note, we introduce an approximation of harmonic maps via a sequence of exponentially harmonic maps. We then reestablish the existence theorem of harmonic maps due to Eells and Sampson.
The binomial edge ideal of a pair of graphs
Authors: Ene Viviana , Herzog Jürgen , Hibi Takayuki , Qureshi Ayesha Asloob
Published: July 2016

We introduce a class of ideals generated by a set of 2-minors of an (m×n)-matrix of indeterminates indexed by a pair of graphs. This class of ideals is a natural common generalization of binomial edge ideals and ideals generated by adjacent minors. We determine the minimal prime ideals of such ideals and give a lower bound for their degree of nilpotency. In some special cases we compute their Gröbner basis and characterize unmixedness and Cohen–Macaulayness.
On the k-Buchsbaum property of powers of Stanley–Reisner ideals
Authors: Minh Nguyên Công , Nakamura Yukio
Published: July 2016

LetS=K[x1,x2,…,xn] be a polynomial ring over a fieldK. Let Δ be a simplicial complex whose vertex set is contained in {1, 2,…,n}. For an integerk≥ 0, we investigate thek-Buchsbaum property of residue class ringsS/I(t); andS/Itfor the Stanley-Reisner idealI=IΔ. We characterize thek-Buchsbaumness of such rings in terms of the simplicial complex Δ and the powert. We also give a characterization in the case whereIis the edge ideal of a simple graph.
Twisted orbifold Gromov–Witten invariants
Authors: Tonita Valentin
Published: July 2016

Letχbe a smooth proper Deligne–Mumford stack over ℂ. One can define twisted orbifold Gromov–Witten invariants ofχby considering multiplicative invertible characteristic classes of various bundles on the moduli spaces of stable mapsχg,n,d, cupping them with evaluation and cotangent line classes, and then integrating against the virtual fundamental class. These are more general than the twisted invariants introduced by Tseng. We express the generating series of the twisted invariants in terms of the generating series of the untwisted ones. We derive the corollaries which are used in a paper with Givental about the quantumK-theory of a complex compact manifoldX.
On q-Galois Extensions of Simple Rings
Authors: Tominaga Hisao
Published: July 2016

In 1952, the late Professor T. Nakayama succeeded in constructing the Galois theory for finite dimensional simple ring extensions [7]. And, we believe, the theory was essentially due to the following proposition: If a simple ring A is Galois and finite over a simple subring B then A is B′-A-completely reducible for any simple intermediate ring B′ of A/B [7, Lemmas 1.1 and 1.2]. Moreover, as was established in [5], Nakayama’s idea was still efficient in considering the infinite dimensional Galois theory of simple rings.
On Meromorphisms of Algebraic Systems
Authors: Hashimoto Junji
Published: July 2016

In the present paper by an algebraic system (algebra) A we shall mean a system with a set F of operations fλ: (x1,…, xn) ∈ A × · · · × A → fλ(x1,…, xn) ∈ A. A polynomial p(x1, …, xr) is a function of variables x1,…, xr which is either one of the xi, or (recursively) a result of some operation fλ(p1,…, pn) performed on other polynomials pi. An algebra A may satisfy a set R of identities p(x1,…, xr) = q(x1,…, xs), and then A shall be called an (F, R)-algebra.
Radical Modules over a Dedekind Domain
Authors: Fröhlich A.
Published: July 2016

A radical of a fieldKis a non zero element of a given algebraic closure some positive power of which lies inK. The groupR(K) of radicals reflects properties of the fieldKand is in turn easily determined as an extension of the multiplicative groupK*of non zero elements ofK. The elements of the quotient groupR(K)/K* are then conveniently identified with certain subspaces of the algebraic closure, the radical spaces ofK(cf. §1). What we are here concerned with is the corresponding arithmetic situation, in which we start with a Dedekind domain o with quotient fieldK. The role of the radicals is taken over by the radical modules. These form a group(o) which contains the group of fractional ideals of o (cf. §4).
On S-Rings in the Sense of F. Kasch
Authors: Morita Kiiti
Published: July 2016

The notion of S-rings was introduced by F. Kasch [4] in establishing a theory of Frobenius extensions. S-rings possess several remarkable properties, although they have been shown to be not indispensable to the theory of Frobenius extensions. The purpose of this paper is to give some characteristic properties of S-rings.
Automorphism Groups of Jordan Algebras
Authors: Bobo E. Ray
Published: July 2016

In his development of a structure theory for Jordan algebras of characteristic two, E.C. Paige [1] introduces an important class of central simple Jordan algebras S[2n], It is the purpose of this paper to completely determine the automorphism groups of the algebras S[2n]. The automorphisms will be represented as matrices operating on a natural basis for the underlying vector space of the algebra. Using this characterization, generators and relations will be obtained for each of the automorphism groups. In this way, we will produce an infinite family of finite 2-groups.
Existence of Non-Trivial Deformations of Inseparable Algebraic Extension Fields II
Authors: Kimura Hiroshi
Published: July 2016

Let K be an extension of a field k, and p denotes the characteristic. It was proved by M. Gerstenhaber ([1]) that if K is separable over k, then it is rigid and it was conjectured in [1] that, if K is not separable over k, then it is not rigid. We studied in [4] the above conjecture in certain special case. In this note we shall extend the results of [4] to inseparable algebraic extension fields.
Upper Bounds on Homological Dimensions
Authors: Osofsky B. L.
Published: July 2016

The homological dimension of a module MR is often related to the cardinality of a set of generators for M or for right ideals of R. In this note, upper bounds for this homological dimension are obtained in two situations.
A Survey of the Work of George Lusztig
Authors: Carter R. W.
Published: July 2016

It is an honour to be invited to contribute a survey article on the work of George Lusztig in celebration of his 60th birthday.
Verma Modules and Preprojective Algebras
Authors: Geiss Christof , Leclerc Bernard , Schröer Jan
Published: July 2016

We give a geometric construction of the Verma modules of a symmetric Kac-Moody Lie algebra g in terms of constructible functions on the varieties of nilpotent finite-dimensional modules of the corresponding preprojective algebra Λ.
Some Groups of Type E7
Authors: Springer T. A.
Published: July 2016

An algebraic group of type E7 over an algebraically closed field has an irreducible representation in a vector space of dimension 56 and is, in fact, the identity component of the automorphism group of a quartic form on the space. This paper describes the construction of the quartic form if the characteristic is ≠ 2, 3, taking into account a field of definition F. Certain F-forms of E7 appear in the automorphism groups of quartic forms over F, as well as forms of E6. Many of the results of the paper are known, but are perhaps not easily accessible in the literature.
Le Groupe GLn Tordu, Sur un Corps Fini
Authors: Waldspurger J.-L.
Published: July 2016

Let q be a finite field, G = GLn(q), θ be the outer automorphism of G, suitably normalized. Consider the non-connected group G ⋊ {1, θ} and its connected component = Gθ. We know two ways to produce functions on , with complex values and invariant by conjugation by G: on one hand, let π be an irreducible representation of G we can and do extend to a representation π+ of G ⋊ {1, θ}, then the restriction trace to of the character of π+ is such a function; on the other hand, Lusztig define character-sheaves a, whose characteristic functions ϕ(a) are such functions too. We consider only “quadratic-unipotent” representations. For all such representation π, we define a suitable extension π+, a character-sheave f(π) and we prove an identity trace = γ(π)ϕ(f(π)) with an explicit complex number γ(π).
de Rham cohomology of local cohomology modules: The graded case
Authors: Puthenpurakal Tony J.
Published: July 2016

LetKbe a field of characteristic zero, and letR = K[X1,… ,Xn]. Let An(K) = K⟨X1,… ,Xn,∂1,… ,∂n⟩ be thenth Weyl algebra overK. We consider the case whenRandAn(K) are graded by giving degXi= ωiand deg∂i=–ωifori= 1,…,n(hereωiare positive integers). Set. LetIbe a graded ideal inR. By a result due to Lyubeznik the local cohomology modulesare holonomic (An(K))-modules for eachi≥0. In this article we prove that the de Rham cohomology modulesare concentrated in degree —ω; that is,forj ≠ –ω. As an application whenA = R/(f) is an isolated singularity, we relatetoHn-1(∂(f);A), the (n –1)th Koszul cohomology ofAwith respect to∂1(f),…,∂n(f).
Projective geometry in characteristic one and the epicyclic category
Authors: Connes Alain , Consani Caterina
Published: July 2016

We show that the cyclic and epicyclic categories which play a key role in the encoding of cyclic homology and the lambda operations, are obtained from projective geometry in characteristic one over the infinite semifield ofmax-plus integersℤmax. Finite-dimensional vector spaces are replaced by modules defined by restriction of scalars from the one-dimensional free module, using the Frobenius endomorphisms of ℤmax. The associated projective spaces arefiniteand provide a mathematically consistent interpretation of Tits's original idea of a geometry over the absolute point. The self-duality of the cyclic category and the cyclic descent number of permutations both acquire a geometric meaning.
Deformations with constant Lê numbers and multiplicity of nonisolated hypersurface singularities
Authors: Eyral Christophe , Soares Ruas Maria Aparecida
Published: July 2016

We show that the possible jump of the order in an 1-parameter deformation family of (possibly nonisolated) hypersurface singularities, with constant Lê numbers, is controlled by the powers of the deformation parameter. In particular, this applies to families of aligned singularities with constant topological type—a class for which the Lê numbers are “almost” constant. In the special case of families withisolatedsingularities—a case for which the constancy of the Lê numbers is equivalent to the constancy of the Milnor number—the result was proved by Greuel, Plénat, and Trotman.

As an application, we prove equimultiplicity for new families of nonisolated hypersurface singularities with constant topological type, answering partially the Zariski multiplicity conjecture.
Spherical functors on the Kummer surface
Authors: Krug Andreas , Meachan Ciaran
Published: July 2016

We find two natural spherical functors associated to the Kummer surface and analyze how their induced twists fit with Bridgeland's conjecture on the derived autoequivalence group of a complex algebraic K3 surface.
A McShane-type identity for closed surfaces
Authors: Huang Yi
Published: July 2016

We prove a McShane-type identity: a series, expressed in terms of geodesic lengths, that sums to 2π for any closed hyperbolic surface with one distinguished point. To do so, we prove a generalized Birman-Series theorem showing that the set of complete geodesics on a hyperbolic surface with large cone angles is sparse.
Torsion in tensor powers of modules
Authors: Celikbas Olgur , Iyengar Srikanth B. , Piepmeyer Greg , Wiegand Roger
Published: July 2016

Tensor products usually have nonzero torsion. This is a central theme of Auslander's 1961 paper; the theme continues in the work of Huneke and Wiegand in the 1990s. The main focus in this article is on tensor powers of a finitely generated module over a local ring. Also, we study torsion-free modulesNwith the property thatM ⊗RNhas nonzero torsion unlessMis very special. An important example of such a moduleNis the Frobenius powerpeRover a complete intersection domainRof characteristicp> 0.
Semiclassical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromy
Authors: Witte N. S.
Published: July 2016

A 𝔻-semiclassical weight is one which satisfies a particular linear, first-order homogeneous equation in a divided-difference operator 𝔻. It is known that the system of polynomials, orthogonal with respect to this weight, and the associated functions satisfy a linear, first-order homogeneous matrix equation in the divided-difference operator termed thespectral equation. Attached to the spectral equation is a structure which constitutes a number of relations such as those arising from compatibility with the three-term recurrence relation. Here this structure is elucidated in the general case of quadratic lattices. The simplest examples of the 𝔻-semiclassical orthogonal polynomial systems are precisely those in the Askey table of hypergeometric and basic hypergeometric orthogonal polynomials. However within the 𝔻-semiclassical class it is entirely natural to define a generalization of the Askey table weights which involve a deformation with respect to new deformation variables. We completely construct the analogous structures arising from such deformations and their relations with the other elements of the theory. As an example we treat the first nontrivial deformation of the Askey–Wilson orthogonal polynomial system defined by the q-quadratic divided-difference operator, the Askey–Wilson operator, and derive the coupled first-order divided-difference equations characterizing its evolution in the deformation variable. We show that this system is a member of a sequence of classical solutions to theq-Painlevé system.
Instability of periodic traveling waves for the symmetric regularized long wave equation
Authors: Pava Jaime Angulo , Brango Carlos Alberto Banquet
Published: July 2016

We prove the linear and nonlinear instability of periodic traveling wave solutions for a generalized version of the symmetric regularized long wave (SRLW) equation. Using analytic and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so the linear instability of periodic profiles is obtained. An application of this approach is made to obtain the linear/nonlinear instability of cnoidal wave solutions for the modified SRLW (mSRLW) equation. We also prove the stability of dnoidal wave solutions associated to the equation just mentioned.
Some constructions of modular forms for the Weil representation of SL2(ℤ)
Authors: Scheithauer Nils R.
Published: July 2016

Modular forms for the Weil representation of SL2(ℤ) play an important role in the theory of automorphic forms on orthogonal groups. In this paper we give some explicit constructions of these functions. As an application, we construct new examples of generalized Kac-Moody algebras whose denominator identities are holomorphic automorphic products of singular weight. They correspond naturally to the Niemeier lattices with root systemsand to the Leech lattice.
Democracy, society and truth: an exploration of Catholic social teaching
Authors: Bretherton Luke
Published: July 2016

This article maintains that modern Catholic social teaching took shape by positioning itself between revolutionary ideologies that sought to destroy the church and reactionary forces that sought to instrumentalise it. Among the factors that contributed to this development were the emergence of a theologyical and socio-political conception of the laity, reflection on the question of how humans participate in Christ's rule, the development of a consociational vision of sovereignty in distinction from top-down or monistic views, the importance of labour to a proper understanding of human dignity, and the discovery of ‘society’, as distinct from the market and the state. Appreciation of these factors resulted in the magisterial defence of democratic politics as a necessary condition for telling the truth about what it means to be human.
Changes in plasma concentrations of glucose, free fatty acids, ketone bodies, thyroxine and insulin of lactating beef cows in relation to time of feeding and energy status
Authors: Coggins C.R.E. , Field A.C.
Published: July 2016

The economic implications of sub-standard performance in animal production which result from the increased incidence of metabolic disorders such as bovine ketosis and ovine pregnancy toxaemia, and accompanying reduced reproductive performance, plus the detrimental effects of undernutrition, are well known. Together they pinpoint the desirability of being able to assess the adequacy of rations in supplying nutrients, particularly energy, to provide an appropriate diet. The assessment of nutritional status is becoming increasingly important as farmers attempt to maintain enterprise profitability by either reducing feed costs and maintaining production, or by maintaining feed costs and increasing overall production, or by a combination of these two procedures.
Calcium, magnesium and phosphorus in lactation and the dry period
Authors: Pickard D.W.
Published: July 2016

This paper will deal with the relevance of calcium, phosphorus and magnesium intakes to the variations which are seen in the plasma levels of these elements in dairy cows during lactation and the dry period.

Calcium

There is to my knowledge no report of any consistent effect of age, milk yield, season or level of calcium intake on the level of calcium in the blood of dairy cows. Changes do, however, take place in the blood level of calcium and it is the factors which influence the extent of such changes which I will discuss, particularly those relating to milk fever.
The effect of feeding pattern and sampling procedure on blood parameters
Authors: Lindsay D.B.
Published: July 2016

I am not sure what the organisers had in mind when they selected the title for this talk. To me it suggests that two components may contribute to the concentration of a metabolite - one determined by the flow of nutrients, derived either exogenously or endogenously, while a second is derived from what I propose to call ‘transitory phenomena’, that is, produced from some fleeting or transitory response - stress, human/animal interaction or a response to feeding as distinct from food. Presumably it is the first component which we would hope to relate in some way to animal production, and I propose to begin by seeing to what extent we find a close relation between flow and concentration for several blood constituents. I have used the term ‘flux’ to encompass conveniently what has variously been called ‘entry rate’, ‘turnover rate’ and ‘irreversible’ loss. These terms are not synonymous, but for the present discussion the distinctions are not important.