bluuebunny/crossref_metadata_2025 huggingface dataset:
Normalized potentials of minimal surfaces in spheres
Authors: Chi Quo-Shin , Fernández Luis , Wu Hongyou
Published: July 2016

We determine explicitly the normalized potential, a Weierstrass-type representation, of a superconformal surface in an even-dimensional sphere S2n in terms of certain normal curvatures of the surface. When the Hopf differential is zero the potential embodies a system of first order equations governing the directrix curve of a superminimal surface in the twistor space of the sphere. We construct a birational map from the twistor space of S2n into ℂPn(n+1)/2. In general, birational geometry does not preserve the degree of an algebraic curve. However, we prove that the birational map preserves the degree, up to a factor 2, of the twistor lift of a superminimal surface in S6 as long as the surface does not pass through the north pole. Our approach, which is algebro-geometric in nature, accounts in a rather simple way for the aforementioned first order equations, and as a consequence for the particularly interesting class of superminimal almost complex curves in S6. It also yields, in a constructive way, that a generic superminimal surface in S6 is not almost complex and can achieve, by the above degree property, arbitrarily large area.
Some remarks on complex Lie groups
Authors: Kazama H. , Kim D. K. , Oh C. Y.
Published: July 2016

First we show that any complex Lie group is complete Kähler. Moreover we obtain a plurisubharmonic exhaustion function on a complex Lie group as follows. Let the real Lie algebra of a maximal compact real Lie subgroup K of a complex Lie group G. Put q := dimC Then we obtain that there exists a plurisubharmonic, strongly (q + 1)-pseudoconvex in the sense of Andreotti-Grauert and K-invariant exhaustion function on G.
The joint universality and the functional independence for Lerch zeta-functions
Authors: Laurinčikas Antanas , Matsumoto Kohji
Published: July 2016

The joint universality theorem for Lerch zeta-functions L(λl,αl, s) (1 ≤ l ≤ n) isproved, in the case when λls are rational numbers andαlsare transcendental numbers. The casen= 1 was known before ([12]); the rationality of λls is used to establish the theorem for the “joint” casen≥ 2. As a corollary, the joint functional independence for those functions is shown.
Conformally flat hypersurfaces in Euclidean 4-space
Authors: Suyama Yoshihiko
Published: July 2016

We study generic and conformally flat hypersurfaces in Euclidean four-space. What kind of conformally flat three manifolds are really immersed generically and conformally in Euclidean space as hypersurfaces? According to the theorem due to Cartan [1], there exists an orthogonal curvature-line coordinate system at each point of such hypersurfaces. This fact is the first step of our study. We classify such hypersurfaces in terms of the first fundamental form. In this paper, we consider hypersurfaces with the first fundamental forms of certain specific types. Then, we give a precise representation of the first and the second fundamental forms of such hypersurfaces, and give exact shapes in Euclidean space of them.
Tangent loci and certain linear sections of adjoint varieties
Authors: Kaji Hajime , Yasukura Osami
Published: July 2016

An adjoint variety X(g)associated to a complex simple Lie algebra is by definition a projective variety in ℙ*(g) obtained as the projectivization of the (unique) non-zero, minimal nilpotent orbit in g. We first describe the tangent loci of X(g) in terms of triples. Secondly for a graded decomposition of contact type we show that the intersection of X(g) and the linear subspace ℙ*(g1) in ℙ*(g) coincides with the cubic Veronese variety associated to g.
Fixed point theorems of discontinuous increasing operators and applications to nonlinear integro-differential equations
Authors: Zhang Jinqing
Published: July 2016

In this paper, we obtain some new existence theorems of the maximal and minimal fixed points for discontinuous increasing operators in C[I,E], where E is a Banach space. As applications, we consider the maximal and minimal solutions of nonlinear integro-differential equations with discontinuous terms in Banach spaces.
Two-weighted inequalities for the derivatives of holomorphic functions and Carleson measures on the unit ball
Authors: Kang Hyeonbae , Koo Hyungwoon
Published: July 2016

We characterize those positive measure µ’s on the higher dimensional unit ball such that “two-weighted inequalities” hold for holomorphic functions and their derivatives. Characterizations are given in terms of the Carleson measure conditions. The results of this paper also distinguish between the fractional and the tangential derivatives.
Distribution of units of real quadratic number fields
Authors: Chen Yen-Mei J. , Kitaoka Yoshiyuki , Yu Jing
Published: July 2016

Let k be a real quadratic field and k, E the ring of integers and the group of units in k. Denoting by E() the subgroup represented by E of (k/)× for a prime ideal , we show that prime ideals for which the order of E() is theoretically maximal have a positive density under the Generalized Riemann Hypothesis.
On separable A1-forms
Authors: Dutta Amartya Kumar
Published: July 2016

We show that for any field k, separable A1-forms over commutative k-algebras are trivial.
Hecke structure of spaces of half-integral weight cusp forms
Authors: Frechette Sharon M.
Published: July 2016

We investigate the connection between integral weight and half-integral weight modular forms. Building on results of Ueda [14], we obtain structure theorems for spaces of half-integral weight cusp formsSk/2(4N,χ) wherekandNare odd nonnegative integers withk≥ 3, andχis an even quadratic Dirichlet character modulo 4N. We give complete results in the case whereNis a power of a single prime, and partial results in the more general case. Using these structure results, we give a classical reformulation of the representation-theoretic conditions given by Flicker [5] and Waldspurger [17] in results regarding the Shimura correspondence. Our version characterizes, in classical terms, the largest possible image of the Shimura lift given our restrictions onNandχ, by giving conditions under which a newform has an equivalent cusp form inSk/2(4N, χ). We give examples (computed using tables of Cremona [4]) of newforms which have no equivalent half-integral weight cusp forms for any suchNandχ. In addition, we compare our structure results to Ueda’s [14] decompositions of the Kohnen subspace, illustrating more precisely how the Kohnen subspace sits inside the full space of cusp forms.
On the Hecke-Landau L-Series
Authors: Tatuzawa Tikao
Published: July 2016

Let k be an algebraic number field of degree n = r1 + 2r2 with r1 real conjugates k(l) (1 ≦ l ≦ r1) and r2 pairs of complex conjugates k(m), k(m+r2)) (r1 + 1 ≦ m ≦ r1 + r2). Let o be the integral domain consisting of all integers in k.
Relation Between Higher Obstructions and Postnikov Invariants
Authors: Shiraiwa Kenichi
Published: July 2016

The problem of extending a continuous map is one of the most important problems in algebraic topology. Many topologists have contributed for the solution of this problem. One of the most powerful methods in the extension problem is the obstruction theory defined first by S. Eilenberg [1] and developed by many others. N. E. Steenrod worked on the primary obstruction and showed that there is a strong connection between obstruction theory and cohomology operations [7].
Ordered Semigroups
Authors: Conrad Paul
Published: July 2016

1. Introduction. In this paper order will always mean linear or total order, and, unless otherwise stated, the composition of any semigroup will be denoted by +. A semigroup S is an ordered semigroup (notation o.s.) if S is an ordered set and for all a, b, c in S
Values of zeta functions and class number 1 criterion for the simplest cubic fields
Authors: Kim Hyun Kwang , Hwang Hyung Ju
Published: July 2016

Let K be the simplest cubic field defined by the irreducible polynomial

where m is a nonnegative rational integer such that m2 + 3m + 9 is square-free. We estimate the value of the Dedekind zeta function ζK(s) at s = −1 and get class number 1 criterion for the simplest cubic fields.
The 2-Ideal Class Groups of ℚ(ζl)
Authors: Cornacchia Pietro
Published: July 2016

For prime l we study the structure of the 2-part of the ideal class group Cl of ℚ(ζl). We prove that Cl ⊗ ℤ2) is a cyclic Galois module for all l < 10000 with one exception and compute the explicit structure in several cases.
Vector Field Energies and Critical Metrics on Kähler Manifolds
Authors: Mabuchi Toshiki
Published: July 2016

Associated with a Hamiltonian holomorphic vector field on a compact Kähler manifold, a nice functional on a space of Kähler metrics will be constructed as an integration of the bilinear pairing in [FM] contracted with the Hamiltonian holomorphic vector field. As applications, we have functionals whose critical points are extremal Kähler metrics or “Kähler-Einstein metrics” in the sense of [M4], respectively. Finally, the same method as used by [G1] allows us to obtain, from the convexity of , the uniqueness of “Kähler-Einstein metrics” on nonsingular toric Fano varieties possibly with nonvanishing Futaki character.
Positive Solutions of Nonresonant Singular Boundary Value Problem of Second Order Differential Equations
Authors: Wei Zhongli , Pang Changci
Published: July 2016

This paper investigates the existence of positive solutions of nonresonant singular boundary value problem of second order differential equations. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as well as C1[0, 1] positive solutions is given by means of the method of lower and upper solutions with the fixed point theorems.
Solutions of a Certain Nonlinear Elliptic Equation on Riemannian Manifolds
Authors: Lee Yong Hah
Published: July 2016

In this paper, we prove that if a complete Riemannian manifold M has finitely many ends, each of which is a Harnack end, then the set of all energy finite bounded A-harmonic functions on M is one to one corresponding to Rl, where A is a nonlinear elliptic operator of type p on M and l is the number of p-nonparabolic ends of M. We also prove that if a complete Riemannian manifold M is roughly isometric to a complete Riemannian manifold with finitely many ends, each of which satisfies the volume doubling condition, the Poincaré inequality and the finite covering condition near infinity, then the set of all energy finite bounded A-harmonic functions on M is finite dimensional. This result generalizes those of Yau, of Donnelly, of Grigor’yan, of Li and Tam, of Holopainen, and of Kim and the present author, but with a barrier argument at infinity that the peculiarity of nonlinearity demands.
On Waring’s problem: Three cubes and a sixth power
Authors: Brüdern Jörg , Wooley Trevor D.
Published: July 2016

We establish that almost all natural numbers not congruent to 5 modulo 9 are the sum of three cubes and a sixth power of natural numbers, and show, moreover, that the number of such representations is almost always of the expected order of magnitude. As a corollary, the number of representations of a large integer as the sum of six cubes and two sixth powers has the expected order of magnitude. Our results depend on a certain seventh moment of cubic Weyl sums restricted to minor arcs, the latest developments in the theory of exponential sums over smooth numbers, and recent technology for controlling the major arcs in the Hardy-Littlewood method, together with the use of a novel quasi-smooth set of integers.
Twistor spaces and the adiabatic limits of Dirac operators
Authors: Nagase Masayoshi
Published: July 2016

We show that a (Spinq-style) twistor space admits a canonical Spin structure. The adiabatic limits of η-invariants of the associated Dirac operator and of an intrinsically twisted Dirac operator are then investigated.
On modification of the q-L-series and its applications
Authors: Tsumura Hirofumi
Published: July 2016

We slightly modify the definitions of q-Hurwitz ζ-functions and q-L-series constructed by J. Satoh. By using these modified functions, we give some relations for the ordinary Dirichlet L-series. Especially we give an elementary proof of Katsurada’s formula on the values of Dirichlet L-series at positive integers.
Nilpotency and triviality of mod p Morita-Mumford classes of mapping class groups of surfaces
Authors: Akita Toshiyuki
Published: July 2016

This paper is concerned with mod p Morita-Mumford classes of the mapping class group Γg of a closed oriented surface of genus g ≥ 2, especially triviality and nontriviality of them. It is proved that is nilpotent if n ≡ − 1 (mod p − 1), while the stable mod p Morita-Mumford class is proved to be nontrivial and not nilpotent if n ≢ −1 (mod p − 1). With these results in mind, we conjecture that vanishes whenever n ≡ − 1 (mod p − 1), and obtain a few pieces of supporting evidence.
On a generalized divisor problem I
Authors: Lau Yuk-Kam
Published: July 2016

We give a discussion on the properties of Δa(x) (− 1 < a < 0), which is a generalization of the error term Δ(x) in the Dirichlet divisor problem. In particular, we study its oscillatory nature and investigate the gaps between its sign-changes for −½ ≤ a < 0.
On the theta divisor of SU(r; 1)
Authors: Brivio Sonia , Verra Alessandro
Published: July 2016

Let SU(r; 1) be the moduli space of stable vector bundles, on a smooth curve C of genus g ≥ 2, with rank r ≥ 3 and determinant OC(p), p ∈ C; let L be the generalized theta divisor on SU(r; 1). In this paper we prove that the map øL, defined by L, is a morphism and has degree 1.
Numerical criteria for certain fiber spaces to be birationally trivial
Authors: Cai Jin-Xing
Published: July 2016

Let f: X → B be a fiber space over a curve B whose general fiber F belongs to one of the following type: 1) F is of general type and satisfying some mild conditions, 2) F is with trivial canonical sheaf. In this note, a numerical characterization for f: X → B to be birationally trivial is given.
On the cohomological completeness of q-complete domains with corners
Authors: Matsumoto Kazuko
Published: July 2016

We prove the vanishing and non-vanishing theorems for an intersection of a finite number of q-complete domains in a complex manifold of dimension n. When q does not divide n, it is stronger than the result naturally obtained by combining the approximation theorem of Diederich-Fornaess for q-convex functions with corners and the vanishing theorem of Andreotti-Grauert for q-complete domains. We also give an example which implies our result is best possible.
Modification of balayage spaces by transitions with application to coupling of PDE’s
Authors: Hansen Wolfhard
Published: July 2016

Modifications of balayage spaces are studied which, in probabilistic terms, correspond to killing and transitions (creation of mass combined with jumps). This is achieved by a modification of harmonic kernels for sufficiently small open sets. Applications to coupling of elliptic and parabolic partial differential equations of second order are discussed.
Algebraic dependence of meromorphic mappings in value distribution theory
Authors: Aihara Yoshihiro
Published: July 2016

In this paper we first prove some criteria for the propagation of algebraic dependence of dominant meromorphic mappings from an analytic finite covering space X over the complex m-space into a projective algebraic manifold. We study this problem under a condition on the existence of meromorphic mappings separating the generic fibers of X. We next give applications of these criteria to the uniqueness problem of meromorphic mappings. We deduce unicity theorems for meromorphic mappings and also give some other applications. In particular, we study holomorphic mappings into a smooth elliptic curve E and give conditions under which two holomorphic mappings from X into E are algebraically related.
Invariant Kähler structures on the cotangent bundles of compact symmetric spaces
Authors: Mykytyuk Ihor V.
Published: July 2016

For rank-one symmetric spacesMof the compact type all Kähler structuresFλ, defined on their punctured tangent bundlesT0Mand invariant with respect to the normalized geodesic flow onT0M, are constructed. It is shown that this class {Fλ} of Kähler structures is stable under the reduction procedure.
Character sheaves and generalized Springer correspondence
Authors: Aubert Anne-Marie
Published: July 2016

LetGbe a connected reductive algebraic group over an algebraic closure of a finite field of characteristicp. Under the assumption thatpis good forG, we prove that for each character sheafAonGwhich has nonzero restriction to the unipotent variety ofG, there exists a unipotent classCAcanonically attached toA, such thatAhas non-zero restriction onCA, and any unipotent classCinGon whichAhas non-zero restriction has dimension strictly smaller than that ofCA.
The transcendence degree of an integral domain over a subfield and the dimension of the domain
Authors: Tanimoto Hiroshi
Published: July 2016

For a domain A containing a field k with tr.degkA < ∞, we define a new transcendence degree of A with respect to k, which is denoted by tdkA. By using this, we generalize the theorem that for every affine domain A over a field k it holds that dim A = tr.degkA. For example, we show that if A is a quasi-local domain containing a field k with dim A = tdkA < ∞, then for every Noetherian local k-subalgebra R of A it holds that dim R = tdkR. Moreover we also generalize the theorem due to Gilmer, Nashier and Nichols.
Lp extension of holomorphic functions from submanifolds to strictly pseudoconvex domains with non-smooth boundary
Authors: Adachi Kenzō
Published: July 2016

Let D be a bounded strictly pseudoconvex domain in ℂn (with not necessarily smooth boundary) and let X be a submanifold in a neighborhood of . Then any Lp (1 ≥ p < ∞) holomorphic function in X ∩ D can be extended to an Lp holomorphic function in D.
Liouville sequences
Authors: Hančl Jaroslav
Published: July 2016

The new concept of a Liouville sequence is introduced in this paper by mean of the related Liouville series. Main results are two criteria for when certain sequences are Liouville. Several applications are presented. A counterexample is included for the case that we substantially weaken the hypotheses in the main results.
Harder–Narasimhan reduction of a principal bundle
Authors: Biswas Indranil , Holla Yogish I.
Published: July 2016

Let E be a principal G–bundle over a smooth projective curve over an algebraically closed field k, where G is a reductive linear algebraic group over k. We construct a canonical reduction of E. The uniqueness of canonical reduction is proved under the assumption that the characteristic of k is zero. Under a mild assumption on the characteristic, the uniqueness is also proved when the characteristic of k is positive.
Homology and residues of adiabatic pseudodifferential operators
Authors: Moroianu Sergiu
Published: July 2016

We compute the Hochschild homology groups of the adiabatic algebra Ψa(X), a deformation of the algebra of pseudodifferential operators Ψ(X) when X is the total space of a fibration of closed manifolds. We deduce the existence and uniqueness of traces on Ψa(X) and some of its ideals and quotients, in the spirit of the noncommutative residue of Wodzicki and Guillemin. We introduce certain higher homological versions of the residue trace. When the base of the fibration is S1, these functionals are related to the η function of Atiyah-Patodi-Singer.
Tight Closure and Plus Closure for Cones Over Elliptic Curves
Authors: Brenner Holger
Published: July 2016

We characterize the tight closure of a homogeneous primary ideal in a normal homogeneous coordinate ring over an elliptic curve by a numerical condition and we show that it is in positive characteristic the same as the plus closure.
On Weighted Polynomial Approximation With Gaps
Authors: Deng Guantie
Published: July 2016

Let α be a nonnegative continuous function on ℝ. In this paper, the author obtains a necessary and sufficient condition for polynomials with gaps to be dense in Cα, where Cα is the weighted Banach space of complex continuous functions ƒ on ℝ with ƒ(t) exp(−α(t)) vanishing at infinity.
A 7-Local Identification of the Monster
Authors: Parker C. W. , Wiedorn C. B.
Published: July 2016

We identify the monster from two of its 7-constrained maximal 7-local subgroups.
Geometric Quantities of Manifolds with grassmann structure
Authors: Bokan N. , Matzeu P. , Rakić Z.
Published: July 2016

We study geometry of manifolds endowed with a Grassmann structure which depends on symmetries of their curvature. Due to this reason a complete decomposition of the space of curvature tensors over tensor product vector spaces into simple modules under the action of the group G = GL(p, ℝ) ⊗ GL(q, ℝ) is given. The dimensions of the simple submodules, the highest weights and some projections are determined. New torsion-free connections on Grassmann manifolds apart from previously known examples are given. We use algebraic results to reveal obstructions to the existence of corresponding connections compatible with some type of normalizations and to enlighten previously known results from another point of view.
Equivalence Classes of Ideals in the Nilradical of a Borel Subalgebra
Authors: Sommers Eric N.
Published: July 2016

An equivalence relation is defined and studied on the set of B-stable ideals in the nilradical of the Lie algebra of a Borel subgroup B. Techniques are developed to compute the equivalence relation and these are carried out in the exceptional groups. There is a natural partial order on equivalence classes coming from inclusion of one ideal in another. A main theorem is that this partial order is a refinement of the closure ordering on nilpotent orbits.
Direct Summands of Syzygy Modules of the Residue Class Field
Authors: Takahashi Ryo
Published: July 2016

LetRbe a commutative Noetherian local ring. This paper deals with the problem asking whetherRis Gorenstein if thenth syzygy module of the residue class field ofRhas a non-trivial direct summand of finite G-dimension for somen. It is proved that ifnis at most two then it is true, and moreover, the structure of the ringRis determined essentially uniquely.
Logarithmic Abelian Varieties
Authors: Kajiwara Takeshi , Kato Kazuya , Nakayama Chikara
Published: July 2016

We develop the algebraic theory of log abelian varieties. This is Part II of our series of papers on log abelian varieties, and is an algebraic counterpart of the previous Part I ([6]), where we developed the analytic theory of log abelian varieties.
The Centralizer of a Nilpotent Section
Authors: McNinch George J.
Published: July 2016

Let F be an algebraically closed field and let G be a semisimple F-algebraic group for which the characteristic of F is very good. If X ∈ Lie(G) = Lie(G)(F) is a nilpotent element in the Lie algebra of G, and if C is the centralizer in G of X, we show that (i) the root datum of a Levi factor of C, and (ii) the component group C/C° both depend only on the Bala-Carter label of X; i.e. both are independent of very good characteristic. The result in case (ii) depends on the known case when G is (simple and) of adjoint type.

The proofs are achieved by studying the centralizer of a nilpotent section X in the Lie algebra of a suitable semisimple group scheme over a Noetherian, normal, local ring . When the centralizer of X is equidimensional on Spec(), a crucial result is that locally in the étale topology there is a smooth -subgroup scheme L of such that Lt is a Levi factor of for each t ∈ Spec ().
Vector Semi-Fredholm Toeplitz Operators and Mean Winding Numbers
Authors: Yakubovich Dmitry
Published: July 2016

For a continuous nonvanishing complex-valued function g on the real line, several notions of a mean winding number are introduced. We give necessary conditions for a Toeplitz operator with matrix-valued symbol G to be semi-Fredholm in terms of mean winding numbers of det G. The matrix function G is assumed to be continuous on the real line, and no other apriori assumptions on it are made.
A Compactification of 3 via K3 Surfaces
Authors: Artebani Michela
Published: July 2016

S. Kondō defined a birational period map between the moduli space of genus three curves and a moduli space of polarized K3 surfaces. In this paper we give a resolution of the period map, providing a surjective morphism from a suitable compactification of 3 to the Baily-Borel compactification of a six dimensional ball quotient.
The One-Dimensional Stratum in the Boundary of the Moduli Stack of Stable Curves
Authors: Zintl Jörg
Published: July 2016

It is well-known that the moduli space of Deligne-Mumford stable curves of genus g admits a stratification by the loci of stable curves with a fixed number i of nodes, where 0 ≤ i ≤ 3g - 3. There is an analogous stratification of the associated moduli stack .
Intuitionistische Untersuchungen der formalistischen Logik
Authors: Kuroda Sigekatu
Published: July 2016

Der. Umschwung, welchen die mathematischen Grundlagenforschungen in diesem Jahrhundert erfuhren, teilte früher einmal die Untersuchungen in drei Hauptrichtungen ab, nämlich in die intuitionistische, logistische und formalistische Auffassung der Mathematik, wonach die lebhafte Polemik über das Wesen der Mathematik sowie das Verhältnis der Logik zur Mathematik aufblütete, und zwar am heftigsten in den zwanziger Jahren dieses Jahrhunderts. Nicht in den prinzipiellen Einsichten, sondern in der Methode der Forschungen hatten doch diese drei Standpunkte viele Berührungspunkte. Erstens entlehnt der Hilbertsche Formalismus dem Logizismus das Hilfsmittel zur Formalisierung der Mathematik. Zweitens ragt die Beweisführung in der Metamathematik, welche die formalisierte Mathematik als ihren eigenen Gegenstand der Untersuchungen betrachtet, insofern nicht aus der intuitionistischen Mathematik hervor, als man die formalisierte Mathematik nur als Zeichenkombinationen ansieht. Ferner sind die formalen Regeln, welche in der intuitionistischen Denktätigkeit erfindlich sind, zuerst von Herrn Heyting formalisiert, danach von Herren Gödel, Gentzen u. a, der logistischen Untersuchungen unterworfen worden. Überdies haben diese drei Richtungen der Grundlagenforschungen heutzutage, wozu gemeinsam der erste Anstoss durch die Cantorsche Mengenlehre gegeben worden ist, auch ihre Absicht in Gemeinschaft, welche dar in besteht, die Logik in bezug auf das Unendliche zu verdeutlichen und damit der Mathematik sichere Stellung zu liefern.
On the Discrete Subgroups and Homogeneous Spaces of Nilpotent Lie Groups
Authors: Matsushima Yozô
Published: July 2016

Recently A, Malcev has shown that the homogeneous space of a connected nilpotent Lie group G is the direct product of a compact space and an Euclidean-space and that the compact space of this direct decomposition is also a homogeneous space of a connected subgroup of G. Any compact homogeneous space M of a connected nilpotent Lie group is of the form where is a connected simply connected nilpotent group whose structure constants are rational numbers in a suitable coordinate system and D is a discrete subgroup of G.
Log-canonical thresholds on del Pezzo surfaces of degrees ≥ 2
Authors: Park Jihun , Won Joonyeong
Published: July 2016

We compute the global log-canonical thresholds (lct) of del Pezzo surfaces of degrees ≥ 2 with du Val singularities.
Derived equivalences and stable equivalences of Morita type, I
Authors: Hu Wei , Xi Changchang
Published: July 2016

For self-injective algebras, Rickard proved that each derived equivalence induces a stable equivalence of Morita type. For general algebras, it is unknown when a derived equivalence implies a stable equivalence of Morita type. In this article, we first show that each derived equivalenceFbetween the derived categories of Artin algebrasAandBarises naturally as a functorbetween their stable module categories, which can be used to compare certain homological dimensions ofAwith that ofB. We then give a sufficient condition for the functorto be an equivalence. Moreover, if we work with finite-dimensional algebras over a field, then the sufficient condition guarantees the existence of a stable equivalence of Morita type. In this way, we extend the classical result of Rickard. Furthermore, we provide several inductive methods for constructing those derived equivalences that induce stable equivalences of Morita type. It turns out that we may produce a lot of (usually not self-injective) finite-dimensional algebras that are both derived-equivalent and stably equivalent of Morita type; thus, they share many common invariants.
Dilogarithm identities for conformal field theories and cluster algebras: Simply laced case
Authors: Nakanishi Tomoki
Published: July 2016

The dilogarithm identities for the central charges of conformal field theories of simply laced type were conjectured by Bazhanov, Kirillov, and Reshetikhin. Their functional generalizations were conjectured by Gliozzi and Tateo. They have been partly proved by various authors. We prove these identities in full generality for any pair of Dynkin diagrams of simply laced type based on the cluster algebra formulation of the Y-systems.
A cohomological Tamagawa number formula
Authors: Huber Annette , Kings Guido
Published: July 2016

For smooth linear group schemes over ℤ, we give a cohomological interpretation of the local Tamagawa measures as cohomological periods. This is in the spirit of the Tamagawa measures for motives defined by Bloch and Kato. We show that in the case of tori, the cohomological and the motivic Tamagawa measures coincide, which proves again the Bloch-Kato conjecture for motives associated to tori.
The rationality problem for norm one tori
Authors: Endo Shizuo
Published: July 2016

We consider the problem of whether the norm one torus defined by a finite separable field extensionK/kis stably (or retract) rational overk. This has already been solved for the case whereK/kis a Galois extension. In this paper, we solve the problem for the case whereK/kis a non-Galois extension such that the Galois group of the Galois closure ofK/kis nilpotent or metacyclic.
Harmonic morphisms applied to classical potential theory
Authors: Fuglede Bent
Published: July 2016

It is shown that ifϕdenotes a harmonic morphism of type Bl between suitable Brelot harmonic spacesXandY, then a functionf, defined on an open setV ⊂ Y, is superharmonic if and only iff ∘ ϕis superharmonic onϕ–1(V) ⊂ X. The “only if” part is due to Constantinescu and Cornea, withϕdenoting any harmonic morphism between two Brelot spaces. A similar result is obtained for finely superharmonic functions defined on finely open sets. These results apply, for example, to the case whereϕis the projection from ℝNto ℝn(N > n ≥1) or whereϕis the radial projection from ℝN\ {0} to the unit sphere in ℝN(N≥ 2).
Geometry of G2 orbits and isoparametric hypersurfaces
Authors: Miyaoka Reiko
Published: July 2016

We characterize the adjointG2orbits in the Lie algebragofG2as fibered spaces overS6with fibers given by the complex Cartan hypersurfaces. This combines the isoparametric hypersurfaces of case (g,m) = (6,2) with case (3,2). The fibrations on two singular orbits turn out to be diffeomorphic to the twistor fibrations ofS6andG2/SO(4). From the symplectic point of view, we show that there exists a 2-parameter family of Lagrangian submanifolds on every orbit.
Variation formulas for principal functions, II: Applications to variation for harmonic spans
Authors: Hamano Sachiko , Maitani Fumio , Yamaguchi Hiroshi
Published: July 2016

A domainD⊂ Czadmits the circular slit mappingP(z) fora, b∈Dsuch thatP(z) – 1/(z–a) is regular ataandP(b) = 0. We callp(z) =log|P(z)|theLi-principal functionandα= log |P′(b)| theL1-constant, and similarly, the radial slit mappingQ(z) implies theL0-principal functionq(z) and theL0-constantβ. We calls=α–βtheharmonic spanfor (D, a, b). We show the geometric meaning ofs. Hamano showed the variation formula for theL1-constantα(t) for the moving domainD(t) in Czwitht∈B:= {t∈ C: |t| <ρ}. We show the corresponding formula for theL0-constantβ(t) forD(t) and combine these to prove that, if the total spaceD =∪t∈B(t, D(t)) is pseudoconvex inB× Cz, thens(t) is subharmonic onB. As a direct application, we have the subharmonicity of log coshd(t) onB, whered(t) is the Poincaré distance betweenaandbonD(t).
Ordinary varieties and the comparison between multiplier ideals and test ideals
Authors: Mustaţă Mircea , Srinivas Vasudevan
Published: July 2016

We consider the following conjecture: ifXis a smooth and irreduciblen-dimensional projective variety over a fieldkof characteristic zero, then there is a dense set of reductionsXsto positive characteristic such that the action of the Frobenius morphism onHn(Xs, OXs) is bijective. There is another conjecture relating certain invariants of singularities in characteristic zero (the multiplier ideals) with invariants in positive characteristic (the test ideals). We prove that the former conjecture implies the latter one in the case of ambient nonsingular varieties.
Products of pairs of Dehn twists and maximal real Lefschetz fibrations
Authors: Degtyarev Alex , Salepci Nermin
Published: July 2016

We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz fibration is algebraic.
Sally’s question and a conjecture of shimoda
Authors: Goto Shiro , O’carroll Liam , Planas-Vilanova Francesc
Published: July 2016

In 2007, Shimoda, in connection with a long-standing question of Sally, asked whether a Noetherian local ring, such that all its prime ideals different from the maximal ideal are complete intersections, has Krull dimension at most 2. In this paper, having reduced the conjecture to the case of dimension 3, if the ring is regular and local of dimension 3, we explicitly describe a family of prime ideals of height 2 minimally generated by three elements. Weakening the hypothesis of regularity, we find that, to achieve the same end, we need to add extra hypotheses, such as completeness, infiniteness of the residue field, and the multiplicity of the ring being at most 3. In the second part of the paper, we turn our attention to the category of standard graded algebras. A geometrical approach via a double use of a Bertini theorem, together with a result of Simis, Ulrich, and Vasconcelos, allows us to obtain a definitive answer in this setting. Finally, by adapting work of Miller on prime Bourbaki ideals in local rings, we detail some more technical results concerning the existence in standard graded algebras of homogeneous prime ideals with an (as it were) excessive number of generators.
Toric degenerations of integrable systems on Grassmannians and polygon spaces
Authors: Nohara Yuichi , Ueda Kazushi
Published: July 2016

We introduce a completely integrable system on the Grassmannian of 2-planes in ann-space associated with any triangulation of a polygon withnsides, and we compute the potential function for its Lagrangian torus fiber. The moment polytopes of this system for different triangulations are related by an integral piecewise-linear transformation, and the corresponding potential functions are related by its geometric lift in the sense of Berenstein and Zelevinsky.
Generalized Lyubeznik numbers
Authors: Núñez-Betancourt Luis , Witt Emily E.
Published: July 2016

Given a local ring containing a field, we define and investigate a family of invariants that includes the Lyubeznik numbers but captures finer information. Thesegeneralized Lyubeznik numbersare defined in terms ofD-modules and are proved well defined using a generalization of the classical version of Kashiwara’s equivalence for smooth varieties; we also give a definition for finitely generatedK-algebras. These new invariants are indicators ofF-singularities in characteristicp >0 and have close connections with characteristic cycle multiplicities in characteristic zero. We characterize the generalized Lyubeznik numbers associated to monomial ideals and compute examples of those associated to determinantal ideals.
Two remarks on polynomially bounded reducts of the restricted analytic field with exponentiation
Authors: Randriambololona Serge
Published: July 2016

This article presents two constructions motivated by a conjecture of van den Dries and Miller concerning the restricted analytic field with exponentiation. The first construction provides an example of two o-minimal expansions of a real closed field that possess the same field of germs at infinity of one-variable functions and yet define different global one-variable functions. The second construction gives an example of a family of infinitely many distinct maximal polynomially bounded reducts (all this in the sense of definability) of the restricted analytic field with exponentiation.
On Languages Which are Based on Non-Standard Arithmetic
Authors: Robinson Abraham
Published: July 2016

The natural numbers play a part in the formulation of logical syntax inasmuch as they are used to count the symbols in a sentence, or the sentences in a proof, etc. In the present paper, we shall study an infinitary logical calculus which is based on replacing the ordinary natural numbers in the capacity just mentioned, by a non-standard model of arithmetic. (Compare refs. 3, 5, 6 for some other logical calculi of infinitary nature). Thus, our calculus will include formulae of length n for any natural number n, finite or infinite, in the chosen non-standard model of arithmetic. Evidently, the study of such formulae can be of interest only if we introduce concepts which are beyond the power of expression of the notions borrowed from the standard case. It turns out that the concept of truth in a model, when defined by means of Skolem functions has this character and involves a curious phenomenon which is analogous to one first pointed out by H. Steinhaus and J. Mycielski for another kind of infinitary language. Thus, while in the standard predicate calculus the negation of a sentence in prenex normal form is reduced to prenex normal form by changing the type of the quantifiers and by shifting the sign of negation, this procedure is not legitimate when truth is defined in this way in our calculus.
A Stronger System of Object Theory as a Prototype of Set Theory
Authors: Ono Katuzi
Published: July 2016

We have introduced in our former work [1] a theory of mathematical objects which can be regarded as a prototype of set theory. We have been successful to imbed the Zermelo set-theory [3] without the axiom of choice in our system. However, it seems impossible to imbed the Fraenkel set-theory [4] in our system even without the axiom of choice. In this work, we introduce another system of object theory in which we can imbed the Fraenkel set-theory without the axiom of choice. We shall denote our former system by OZ (object theory in the manner of the Zermelo set-theory) and the new system we are going to introduce in this work by OF (object theory in the manner of the Fraenkel set-theory). We shall also denote the Zermelo set-theory without the axiom of choice by SZ and the Fraenkel set-theory without the axiom of choice by SF.
On the Exponential Maps and the Triangular 2-Chomology of Graded Lie Rings of Length Three
Authors: Morikawa Hisasi
Published: July 2016

Let H be a group. We mean by an Af-series in H a decreasing series of subgroups H1 = H, H2…,Hn+1 = {e} such that the commutator xyx-1y-1 of two elements x and y respectively in Hi and Hj belongs to Hi+j, where Hs = {e} for s≥n + 1. We call n the length of the N-series (Hi). We mean by a graded Lie ring of length n a Lie ring which is a direct sum A1 + … + -An of additive subgroups A1…, An such that [Ai, Aj]⊂Ai+j, where As = {0} for s≥n + 1.
On the Fundamental Existence Theorem of Kishi
Authors: Nakai Mitsuru
Published: July 2016

Let Ω be a locally compact Hausdorff space and G(x, y) be a strictly positive lower semicontinuous function on the product space Ω×Ω of Ω. Such a function G(x, y) is called a kernel on Ω. The adjoint kernel Ğ(x, y) of G(x, y) is defined by Ğ(x, y) =G(y, x). Whenever we say a measure on Ω, we mean a positive regular Borel measure on Ω. The potential Gμ(x) and the adjoint potential Ğμ(x) of a measure μ relative to the kernel G(x, y) is defined by

respectively. These are also strictly positive lower semicontinuous functions on Ω provided μ≠0.
Faithfully Exact Functors and Their Applications to Projective Modules and Injective Modules
Authors: Ishikawa Takeshi
Published: July 2016

The aim of this paper is to study a property of a special kind of exact functors and give some applications to projective modules and injective modules.

In section 1 we introduce the notion of faithfully exact functors [Definition 1] as a generalization of the functor T(X) = X⊗M, where M is a faithfully flat module, and give a property of this class of functors [Theorem 1.1]. Next, applying this general theory to functors ⊗ and Horn, we define the notion of faithfully projective modules [Definition 2] and faithfully injective modules [Definition 3]. In the commutative case “faithfully projective” means, however, simply “projective and faithfully flat” [Proposition 2.3]. In section 2, equivalent conditions for a projective module P to be faithfully projective are given [Theorem 2.2, Proposition 2. 3 and 2.4]. And a simpler proof is given to Y. Hinohara’s result [6] asserting that projective modules over an indecomposable weakly noetherian ring are faithfully flat [Proposition 2.5]. In section 3, we consider faithfully injective modules.
Poincaré Theta Series and Singular Sets of Schottky Groups
Authors: Akaza Tohru
Published: July 2016

In the theory of automorphic functions for a properly discontinuous groupGof linear transformations, the Poincaré theta series plays an essential role, since the convergence problem of the series occupies an important part of the theory. This problem was treated by many mathematicians such as Poincaré, Burnside [2], Fricke [4], Myrberg [6], [7] and others. Poincaré proved that the (-2m)-dimensional Poincaré theta series always converges ifmis a positive integer greater than 2, and Burnside treated the problem and conjectured that ( -2)-dimensional Poincaré theta series always converges if G is a Schottky group. This conjecture was solved negatively by Myrberg. As is shown later (Theorem A), the convergence of Poincaré theta series gives an information on a metrical property of the singular set of the group.
A Certain Kind of Formal Theories
Authors: Ono Katuzi
Published: July 2016

A common feature of formal theories is that each theory has its own system of axioms described in terms of some symbols for its primitive notions together with logical symbols. Each of these theories is developed by deduction from its axiom system in a certain logical system which is usually the classical logic of the first order.
Über den Quasinormalteiler der regulären p-Gruppe von der Klasse 2
Authors: Nakamura Kirio
Published: July 2016

In der vorliegenden Arbeit wird untersucht, was für eine Struktur eine Untergruppe von endlicher p-Gruppe habe, wenn mit jeder Untergruppe von als ganzes vertauschbar ist. In diesen tritt natürlich ein nicht nur aus E bestehender Normalteiler von auf und er enthält ein Zentrumselement von der Ordnung p. Wir fragen: Gilt das Ähnliche auch, falls kein Normalteiler ist? Die gestellte Frage läßt sich für regülare beantworten, deren Klasse 2 ist, aber für andere bleibt sie noch offen. Bevor wir diese Frage untersuchen, stellen wir einige Definitionen und nötige Sätze und Hilfssätze zusammen.
Relative Cohomology of Algebraic Linear Groups, II
Authors: Kimura Hiroshi
Published: July 2016

Let G be an algebraic linear group over a field F of characteristic 0, and let H be an algebraic subgroup of G. Let A, M be rational G-modules. In [4], we defined (A, M), and, in particular, relative cohomology groups Hn(G, H, M) were defined as (F, M).
On Multiply Transitive Groups I
Authors: Nagao Hirosi
Published: July 2016

The purpose of this paper is to prove the following three theorems which were announced in [2].
Some Results in the Fourier Analysis
Authors: Tatuzawa Tikao
Published: July 2016

There are many uses of Fourier analysis in the analytic number theory. In this paper we shall derive two fundamental theorems using Cramer’s method (Mathematical methods of statistics, 1946). Let E, E* be unit cubes in the whole n-dimensional Euclidean space X such that
Hereditary Local Rings
Authors: Cohn P. M.
Published: July 2016

Many questions about free ideal rings ( = firs, cf. [5] and §2 below) which at present seem difficult become much easier when one restricts attention to local rings. One is then dealing with hereditary local rings, and any such ring is in fact a fir (§2). Our object thus is to describe hereditary local rings. The results on firs in [5] show that such a ring must be a unique factorization domain; in §3 we prove that it must also be rigid (cf. the definition in [3] and §3 below). More precisely, for a semifir R with prime factorization rigidity is necessary and sufficient for R to be a local ring.
A Note on Ideal Class Groups
Authors: Iwasawa Kenkichi
Published: July 2016

In the first part of the present paper, we shall make some simple observations on the ideal class groups of algebraic number fields, following the group-theoretical method of Tschebotarew. The applications on cyclotomic fields (Theorems 5, 6) may be of some interest. In the last section, we shall give a proof to a theorem of Kummer on the ideal class group of a cyclotomic field.
On Universal Character of the Primitive Logic
Authors: Ono Katuzi
Published: July 2016

The PRIMITIVE LOGIC LO introduced in my former work is a logic having only two logical constants IMPLICATION → and UNIVERSAL QUANTIFICATION ( ) with their usual inference rules which are admitted even in the INTUITIONISTIC PREDICATE LOGIC LJ. LO is really a very simple logic, maybe the simplest possible logic as one can imagine, but it is very important because of its universal character. In fact, popular logics such as the LOWER CLASSICAL PREDICATE LOGIC LK, the INTUITIONISTIC PREDICATE LOGIC LJ, the MINIMAL PREDICATE .LOGIC LM, etc. can be faithfully interpreted in it. Speaking frankly, I am further expecting that all the important logics would be interpreted faithfully in it and would disclose their intrinsic characteristics by being interpreted in it. Main purpose of this paper is to show the universal character of the primitive logic LO by pointing out that a series of typical logics are faithfully interpretable in LO.
Open Riemann Surface with Null Boundary
Authors: Noshiro Kiyoshi
Published: July 2016

Recently the writer has obtained some results concerning meromorphic or algebroidal functions with the set of essential singularities of capacity zero, with an aid of a theorem of Evans. In the present paper, suggested from recent interesting papers of Sario and Pfluger, the writer will extend his results to single-valued analytic functions defined on open abstract Riemann surfaces with null boundary in the sense of Nevanlinna, using a lemma instead of Evans’ theorem.
Dirichlet Problems on Riemann Surfaces and Conformal Mappings
Authors: Ohtsuka Makoto
Published: July 2016

The object of this paper is an investigation of existence problems and Dirichlet problems on an abstract Riemann surface in the sense of Weyl-Radó or on a covering surface over it, and of boundary correspondence in the conformal mapping of the surface.
Condensor Principle and the Unit Contraction
Authors: Itô Masayuki
Published: July 2016

Deny introduced in [4] the notion of functional spaces by generalizing Dirichlet spaces. In this paper, we shall give the following necessary and sufficient conditions for a functional space to be a real Dirichlet space.

Let be a regular functional space with respect to a locally compact Hausdorff space X and a positive measure ξ in X. The following four conditions are equivalent.