bluuebunny/crossref_metadata_2025 huggingface dataset:
Proper Holomorphic self-maps of quasi-circular domains in C2
Authors: Coupet B. , Pan Y. , Sukhov A.
Published: July 2016

In this paper, we prove that every proper holomorphic self-map of a smoothly bounded pseudoconvex circular or Hartogs domain of finite type in C2 is biholomorphic.
An example concerning Bergman completeness
Authors: Zwonek Włodzimierz
Published: July 2016

We construct a bounded plane domain which is Bergman complete but for which the Bergman kernel does not tend to infinity as the point approaches the boundary.
Oscillation results for n-th order linear differential equations with meromorphic periodic coefficients
Authors: Shimomura Shun
Published: July 2016

Consider n-th order linear differential equations with meromorphic periodic coefficients of the form w(n) + Rn-1(ez)w(n-1) + … + R1(ez)w′ + R0(ez)w = 0, n ≥ 2, where Rv(t) (0 ≤ ν ≤ n – 1) are rational functions of t. Under certain assumptions, we prove oscillation theorems concerning meromorphic solutions, which contain necessary conditions for the existence of a meromorphic solution with finite exponent of convergence of the zero-sequence. We also discuss meromorphic or entire solutions whose zero-sequences have an infinite exponent of convergence, and give a new zero-density estimate for such solutions.
Monogenesis of the rings of integers in certain imaginary abelian fields
Authors: Shah Syed Inayat Ali , Nakahara Toru
Published: July 2016

In this paper we consider a subfield K in a cyclotomic field km of conductor m such that [km: K] = 2 in the cases of m = lpn with a prime p, where l = 4 or p > l = 3. Then the theme is to know whether the ring of integers in K has a power basis or does not.
Special rays in the Mori cone of a projective variety
Authors: Andreatta Marco , Occhetta Gianluca
Published: July 2016

Let X be a smooth n-dimensional projective variety over an algebraically closed field k such that KX is not nef. We give a characterization of non nef extremal rays of X of maximal length (i.e of length n – 1); in the case of Char(k) = 0 we also characterize non nef rays of length n – 2.
Structure of solutions to Fuchsian systems of partial differential equations
Authors: Mandai Takeshi , Tahara Hidetoshi
Published: July 2016

To a certain Volevič system of singular partial differential equations, called a Fuchsian system, all the solutions of the homogeneous equation in a complex domain are constructed and parametrized in a good way, without any assumption on the characteristic exponents.
Convergence of the zeta functions of prehomogeneous vector spaces
Authors: Saito Hiroshi
Published: July 2016

Let (G, ρ, X) be a prehomogeneous vector space with singular set S over an algebraic number field F. The main result of this paper is a proof for the convergence of the zeta fucntions Z(Φ, s) associated with (G, ρ, X) for large Re s under the assumption that S is a hypersurface. This condition is satisfied if G is reductive and (G, ρ, X) is regular. When the connected component of the stabilizer of a generic point x is semisimple and the group Πx of connected components of Gx is abelian, a clear estimate of the domain of convergence is given.

Moreover when S is a hypersurface and the Hasse principle holds for G, it is shown that the zeta fucntions are sums of (usually infinite) Euler products, the local components of which are orbital local zeta functions. This result has been proved in a previous paper by the author under the more restrictive condition that (G, ρ, X) is irreducible, regular, and reduced, and the zeta function is absolutely convergent.
On uniqueness polynomials for meromorphic functions
Authors: Fujimoto Hirotaka
Published: July 2016

A polynomialP(w)is called a uniqueness polynomial (or a uiqueness polynomial in a broad sense) ifP(f) = cP(g)(orP(f) = P(g))impliesf=gfor any nonzero constantcand nonconstant meromorphic functionsfandgonC. We consider a monic polynomialP(w)without multiple zero whose derivative has mutually distinctkzerosejwith multiplicitiesqj.Under the assumption thatP(el) ≠ P(em)for all distinctlandm,we prove thatP(w)is a uniqueness polynomial in a broad sense if and only if ∑l ∑lql. We also give some sufficient conditions for uniqueness polynomials.
On the commutators of singular integrals related to block spaces
Authors: Lu Shanzhen , Wu Huoxiong
Published: July 2016

In this paper, the commutators of singular integrals with rough kernels are considered. By the method of block decomposition for kernel function and Fourier transform estimates, some new results about the Lp(ℝn) boundedness for these commutators are obtained.
Application of theτ-function theory of Painlevé equations to random matrices:PVI, the JUE, CyUE, cJUE and scaled limits
Authors: Forrester P. J. , Witte N. S.
Published: July 2016

Okamoto has obtained a sequence ofτ-functions for the PVIsystem expressed as a double Wronskian determinant based on a solution of the Gauss hypergeometric equation. Starting with integral solutions of the Gauss hypergeometric equation, we show that the determinant can be re-expressed as multidimensional integrals, and these in turn can be identified with averages over the eigenvalue probability density function for the Jacobi unitary ensemble (JUE), and the Cauchy unitary ensemble (CyUE) (the latter being equivalent to the circular Jacobi unitary ensemble (cJUE)). Hence these averages, which depend on four continuous parameters and the discrete parameterN, can be characterised as the solution of the second order second degree equation satisfied by the Hamiltonian in the PVItheory. We show that the Hamiltonian also satisfies an equation related to the discrete PVequation, thus providing an alternative characterisation in terms of a difference equation. In the case of the cJUE, the spectrum singularity scaled limit is considered, and the evaluation of a certain four parameter average is given in terms of the general PVtranscendent inσform. Applications are given to the evaluation of the spacing distribution for the circular unitary ensemble (CUE) and its scaled counterpart, giving formulas more succinct than those known previously; to expressions for the hard edge gap probability in the scaled Laguerre orthogonal ensemble (LOE) (parameteraa non-negative integer) and Laguerre symplectic ensemble (LSE) (parameteraan even non-negative integer) as finite dimensional combinatorial integrals over the symplectic and orthogonal groups respectively; to the evaluation of the cumulative distribution function for the last passage time in certain models of directed percolation; to theτ-function evaluation of the largest eigenvalue in the finite LOE and LSE with parametera =0; and to the characterisation of the diagonal-diagonal spin-spin correlation in the two-dimensional Ising model.
Solutions in Morrey spaces of some semilinear heat equations with time-dependent external forces
Authors: Zhou Xiaofang
Published: July 2016

In this paper, we consider the Cauchy problem for some semilinear heat equations with time-dependent external forces. Both the external force and the initial data are assumed to be small in some Morrey spaces. We first prove the unique existence of a small time-global solution. We next show the stability of that solution by proving the time-global sovability of perturbation problems.
Wiman-Valiron method for difference equations
Authors: Ishizaki K. , Yanagihara N.
Published: July 2016

Let f(z) be an entire function of order less than 1/2. We consider an analogue of the Wiman-Valiron theory rewriting power series of f(z) into binomial series. As an application, it is shown that if a transcendental entire solution f(z) of a linear difference equation is of order χ < 1/2, then we have log M (r, f) = Lrχ(1 + o(1)) with a constant L > 0.
Formation and construction of a shock wave for 3-D compressible Euler equations with the spherical initial data
Authors: Yin Huicheng
Published: July 2016

In this paper, the problem on formation and construction of a shock wave for three dimensional compressible Euler equations with the small perturbed spherical initial data is studied. If the given smooth initial data satisfy certain nondegeneracy conditions, then from the results in [22], we know that there exists a unique blowup point at the blowup time such that the first order derivatives of a smooth solution blow up, while the solution itself is still continuous at the blowup point. From the blowup point, we construct a weak entropy solution which is not uniformly Lipschitz continuous on two sides of a shock curve. Moreover the strength of the constructed shock is zero at the blowup point and then gradually increases. Additionally, some detailed and precise estimates on the solution are obtained in a neighbourhood of the blowup point.
On Elliptic Curves in SL2(ℂ)/Γ.., Schanuel’s Conjecture and Geodesic Lengths
Authors: Winkelmann Jörg
Published: July 2016

Let Γ be a discrete cocompact subgroup of SL2(ℂ). We conjecture that the quotient manifold X = SL2(ℂ) / Γ contains infinitely many non-isogenous elliptic curves and prove this is indeed the case if Schanuel’s conjecture holds. We also prove it in the special case where Γ ∩ SL2(∝) is cocompact in SL2(ℝ).

Furthermore, we deduce some consequences for the geodesic length spectra of real hyperbolic 2- and 3-folds.
Bergman completeness of unbounded hartogs Domains
Authors: Pflug Peter , Zwonek Włodzimierz
Published: July 2016

Some results for the Bergman functions in unbounded domains are shown. In particular, a class of unbounded Hartogs domains, which are Bergman complete and Bergman exhaustive, is given.
Endomorphisms of Deligne-Lusztig Varieties
Authors: Digne F. , Michel J.
Published: July 2016

We study some conjectures on the endomorphism algebras of the co-homology of Deligne-Lusztig varieties which are a refinement of those of [BMi].
The Theorem of Bo Chen and Hall Polynomials
Authors: Ringel Claus Michael
Published: July 2016

Let Λ be the path algebra of a Dynkin quiver. A recent result of Bo Chen asserts that Hom(X; Y/X) = 0 for any Gabriel-Roiter inclusion X ⊆ Y. The aim of the present note is to give an interpretation of this result in terms of Hall polynomials, and to extend it in this way to representation-directed split algebras. We further show its relevance when dealing with arbitrary representation-finite split algebras.
Singular Localization and Intertwining Functors for Reductive Lie Algebras in Prime Characteristic
Authors: Bezrukavnikov Roman , Mirković Ivan , Rumynin Dmitriy
Published: July 2016

In [BMR] we observed that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of finite characteristic with a given (generalized) regular central character can be identified with coherent sheaves on the formal neighborhood of the corresponding (generalized) Springer fiber. In the present paper we treat singular central characters.

The basic step is the Beilinson-Bernstein localization of modules with a fixed (generalized) central character λ as sheaves on the partial flag variety corresponding to the singularity of λ. These sheaves are modules over a sheaf of algebras which is a version of twisted crystalline differential operators. We discuss translation functors and intertwining functors. The latter generate an action of the affine braid group on the derived category of modules with a regular (generalized) central character, which intertwines different localization functors. We also describe the standard duality on Lie algebra modules in terms of D-modules and coherent sheaves.
Some Examples of Hecke Algebras for Two-Dimensional Local Fields
Authors: Braverman Alexander , Kazhdan David
Published: July 2016

Let K be a local non-archimedian field, F = K((t)) and let G be a split semi-simple group. The purpose of this paper is to study certain analogs of spherical and Iwahori Hecke algebras for representations of the group G = G(F) and its central extension Ĝ. For instance our spherical Hecke algebra corresponds to the subgroup G (A) ⊂ G(F) where A ⊂ F is the subring OK((t)) where OK ⊂ K is the ring of integers. It turns out that for generic level (cf. [4]) the spherical Hecke algebra is trivial; however, on the critical level it is quite large. On the other hand we expect that the size of the corresponding Iwahori-Hecke algebra does not depend on a choice of a level (details will be considered in another publication).
Level 0 Monomial Crystals
Authors: Hernandez David , Nakajima Hiraku
Published: July 2016

We study the monomial crystal defined by the second author. We show that each component of the monomial crystal can be embedded into a crystal of an extremal weight module introduced by Kashiwara. And we determine all monomials appearing in the components corresponding to all level 0 fundamental representations of quantum affine algebras except for some nodes of. Thus we obtain explicit descriptions of the crystals in these examples. We also give those for the corresponding finite dimensional representations. For classical types, we give them in terms of tableaux. For exceptional types, we list up all monomials.
Averaging formula for Nielsen coincidence numbers
Authors: Kim Seung Won , Lee Jong Bum
Published: July 2016

In this paper we study the averaging formula for Nielsen coincidence numbers of pairs of maps(f,g): M→Nbetween closed smooth manifolds of the same dimension. Suppose that G is a normal subgroup of Π = π1(M) with finite index andHis a normal subgroup of Δ = π1(N) with finite index such thatThen we investigate the conditions for which the following averaging formula holds

whereis any pair of fixed liftings of (f, g). We prove that the averaging formula holds whenMandNare orientable infra-nilmanifolds of the same dimension, and whenM = Nis a non-orientable infra-nilmanifold with holonomy groupℤ2and (f, g) admits a pair of liftingson the nil-coveringofM.
m-Blocks Collections and Castelnuovo-mumford Regularity in multiprojective spaces
Authors: Costa L. , Miró-Roig R. M.
Published: July 2016

The main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on n-dimensional smooth projective varieties X with an n-block collection B which generates the bounded derived category To this end, we use the theory of n-blocks and Beilinson type spectral sequence to define the notion of regularity of a coherent sheaf F on X with respect to the n-block collection B. We show that the basic formal properties of the Castelnuovo-Mumford regularity of coherent sheaves over projective spaces continue to hold in this new setting and we compare our definition of regularity with previous ones. In particular, we show that in case of coherent sheaves on ℙn and for the n-block collection Castelnuovo-Mumford regularity and our new definition of regularity coincide. Finally, we carefully study the regularity of coherent sheaves on a multiprojective space ℙn1x…x ℙnr with respect to a suitable n1 +…+ nr-block collection and we compare it with the multigraded variant of the Castelnuovo-Mumford regularity given by Hoffman and Wang in [14].
On the Kohnen-Zagier Formula in the Case of ‘4 × General Odd’ Level
Authors: Sakata Hiroshi
Published: July 2016

We study the Fourier coefficients of cusp forms of half integral weight and generalize the Kohnen-Zagier formula to the case of ‘4 × general odd’ level by using results of Ueda. As an application, we obtain a generalization of the result of Luo-Ramakrishnan [11] to the case of arbitrary odd level.
Every Curve of Genus not Greater Than Eight Lies on a K3 Surface
Authors: Ide Manabu
Published: July 2016

Let C be a smooth irreducible complete curve of genus g ≥ 2 over an algebraically closed field of characteristic 0. An ample K3 extension of C is a K3 surface with at worst rational double points which contains C in the smooth locus as an ample divisor.

In this paper, we prove that all smooth curve of genera. 2 ≤ g ≤ 8 have ample K3 extensions. We use Bertini type lemmas and double coverings to construct ample K3 extensions.
A Reduction Theorem for Stable sets of Holomorphic Foliations on Complex Tori
Authors: Ohsawa Takeo
Published: July 2016

Some complex n-tori admit holomorphic foliations of codimension one besides the flat ones. It will be shown that such nonlinear foliations, possibly with singularities, can be reduced to those on 2-tori under some topological conditions. A crucial step is an application of the Hodge theory on pseudoconvex manifolds.
Gröbner Bases of Simplicial Toric Ideals
Authors: Hellus Michael , Hoa Lê Tûan , Stückrad Jürgen
Published: July 2016

Bounds for the maximum degree of a minimal Gröbner basis of simplicial toric ideals with respect to the reverse lexicographic order are given. These bounds are close to the bound stated in Eisenbud-Goto’s Conjecture on the Castelnuovo-Mumford regularity.
Averaging Formula for Nielsen Numbers of Maps on Infra-Solvmanifolds of Type (R)
Authors: Lee Jong Bum , Lee Kyung Bai
Published: July 2016

We prove that the averaging formula for Nielsen numbers holds for continuous maps on infra-solvmanifolds of type (R): Let M be such a manifold with holonomy group Ψ and let f: M → M be a continuous map. The averaging formula for Nielsen numbers

is proved. This is a workable formula for the difficult number N(f).
Graded rings of rank 2 Sarkisov links
Authors: Brown Gavin , Zucconi Francesco
Published: July 2016

We compute a class of Sarkisov links from Fano 3-folds embedded in weighted Grassmannians using explicit methods for describing graded rings associated to a variation of geometric invariant theory (GIT) quotient.
Linear projections and successive minima
Authors: Soulé Christophe
Published: July 2016

LetXbe an arithmetic surface, and letLbe a line bundle onX. Choose a metrichon the lattice Λ of sections ofLoverX. When the degree of the generic fiber ofXis large enough, we get lower bounds for the successive minima of (Λ,h) in terms of the normalized height ofX. The proof uses an effective version (due to C. Voisin) of a theorem of Segre on linear projections and Morrison’s proof that smooth projective curves of high degree are Chow semistable.
Periodicities of T-systems and Y-systems
Authors: Inoue Rei , Iyama Osamu , Kuniba Atsuo , Nakanishi Tomoki , Suzuki Junji
Published: July 2016

The unrestricted T-system is a family of relations in the Grothendieck ring of the category of the finite-dimensional modules of Yangian or quantum affine algebra associated with a complex simple Lie algebra. The unrestricted T-system admits a reduction called the restricted T-system. In this paper we formulate the periodicity conjecture for the restricted T-systems, which is the counterpart of the known and partially proved periodicity conjecture for the restricted Y-systems. Then, we partially prove the conjecture by various methods: the cluster algebra and cluster category method for the simply laced case, the determinant method for typesAandC, and the direct method for typesA, D, andB(level 2).
Zeta functions, heat kernels, and spectral asymptotics on degenerating families of discrete tori
Authors: Chinta Gautam , Jorgenson Jay , Karlsson Anders
Published: July 2016

By a discrete torus we mean the Cayley graph associated to a finite product of finite cycle groups with the generating set given by choosing a generator for each cyclic factor. In this article we examine the spectral theory of the combinatorial Laplacian for sequences of discrete tori when the orders of the cyclic factors tend to infinity at comparable rates. First, we show that the sequence of heat kernels corresponding to the degenerating family converges, after rescaling, to the heat kernel on an associated real torus. We then establish an asymptotic expansion, in the degeneration parameter, of the determinant of the combinatorial Laplacian. The zeta-regularized determinant of the Laplacian of the limiting real torus appears as the constant term in this expansion. On the other hand, using a classical theorem by Kirchhoff, the determinant of the combinatorial Laplacian of a finite graph divided by the number of vertices equals the number of spanning trees, called thecomplexity, of the graph. As a result, we establish a precise connection between the complexity of the Cayley graphs of finite abelian groups and heights of real tori. It is also known that spectral determinants on discrete tori can be expressed using trigonometric functions and that spectral determinants on real tori can be expressed using modular forms on general linear groups. Another interpretation of our analysis is thus to establish a link between limiting values of certain products of trigonometric functions and modular forms. The heat kernel analysis which we employ uses a careful study ofI-Bessel functions. Our methods extend to prove the asymptotic behavior of other spectral invariants through degeneration, such as special values of spectral zeta functions and Epstein-Hurwitz–type zeta functions.
Mean representation number of integers as the sum of primes
Authors: Bhowmik Gautami , Schlage-Puchta Jan-Christoph
Published: July 2016

Assuming the Riemann hypothesis, we obtain asymptotic estimates for the mean value of the number of representations of an integer as a sum of two primes. By proving a corresponding Ω-term, we show that our result is essentially the best possible.
On fibrations whose geometric fibers are nonreduced
Authors: Schröer Stefan
Published: July 2016

We give a bound on embedding dimensions of geometric generic fibers in terms of the dimension of the base, for fibrations in positive characteristic. This generalizes the well-known fact that for fibrations over curves, the geometric generic fiber is reduced. We illustrate our results with Fermat hypersurfaces and genus 1 curves.
Kummer surfaces associated to (1, 2)-polarized abelian surfaces
Authors: Mehran Afsaneh
Published: July 2016

The aim of this paper is to describe the geometry of the generic Kummer surface associated to a (1, 2)-polarized abelian surface. We show that it is the double cover of a weak del Pezzo surface and that it inherits from the del Pezzo surface an interesting elliptic fibration with twelve singular fibers of typeI2.
Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero
Authors: Hoshi Yuichiro
Published: July 2016

Letlbe a prime number. In this paper, we prove that the isomorphism class of anl-monodromically full hyperbolic curve of genus zero over a finitely generated extension of the field of rational numbers is completely determined by the kernel of the natural pro-louter Galois representation associated to the hyperbolic curve. This result can be regarded as a genus zero analogue of a result due to Mochizuki which asserts that the isomorphism class of an elliptic curve which does not admit complex multiplication over a number field is completely determined by the kernels of the natural Galois representations on the various finite quotients of its Tate module.
Stickelberger elements and Kolyvagin systems
Authors: Büyükboduk Kâzim
Published: July 2016

In this paper, we construct (many) Kolyvagin systems out of Stickelberger elements utilizing ideas borrowed from our previous work on Kolyvagin systems of Rubin-Stark elements. The applications of our approach are twofold. First, assuming Brumer’s conjecture, we prove results on the odd parts of the ideal class groups of CM fields which are abelian over a totally real field, and we deduce Iwasawa’s main conjecture for totally real fields (for totally odd characters). Although this portion of our results has already been established by Wiles unconditionally (and refined by Kurihara using an Euler system argument, when Wiles’s work is assumed), the approach here fits well in the general framework the author has developed elsewhere to understand Euler/Kolyvagin system machinery when the core Selmer rank isr >1 (in the sense of Mazur and Rubin). As our second application, we establish a rather curious link between the Stickelberger elements and Rubin-Stark elements by using the main constructions of this article hand in hand with the “rigidity” of the collection of Kolyvagin systems proved by Mazur, Rubin, and the author.
Quantum (sln, ∧V n ) link invariant and matrix factorizations
Authors: Yonezawa Yasuyoshi
Published: July 2016

In this paper, we give a generalization of Khovanov-Rozansky homology. We define a homology associated to the quantum (sln, ∧Vn) link invariant, where∧Vnis the set of fundamental representations ofUq(sln). In the case of an oriented link diagram composed of[k, 1]-crossings, we define a homology and prove that the homology is invariant under Reidemeister II and III moves. In the case of an oriented link diagram composed of general[i,j]-crossings, we define a normalized Poincaré polynomial of homology and prove that the normalized Poincaré polynomial is a link invariant.
How not to prove the Alon-Tarsi conjecture
Authors: Stones Douglas S. , Wanless Ian M.
Published: July 2016

The sign of a Latin square is −1 if it has an odd number of rows and columns that are odd permutations; otherwise, it is +1. LetLEnandLonbe, respectively, the number of Latin squares of ordernwith sign +1 and −1. The Alon-Tarsi conjecture asserts thatLEn≠Lonwhennis even. Drisko showed thatLEp+1≢Lop+1(modp3) for primep≥ 3 and asked if similar congruences hold for orders of the formpk+ 1,p+ 3, orpq+ 1. In this article we show that ift≤n, thenLEn+1≢L0n+1(modt3) only ift = nandnis an odd prime, thereby showing that Drisko’s method cannot be extended to encompass any of the three suggested cases. We also extend exact computation ton≤ 9, discuss asymptotics forLo/LE, and propose a generalization of the Alon-Tarsi conjecture.
Supplement to classification of threefold divisorial contractions
Authors: Kawakita Masayuki
Published: July 2016

Every threefold divisorial contraction to a non-Gorenstein point is a weighted blowup.
Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements
Authors: Dimca Alexandru
Published: July 2016

The order of the Milnor fiber monodromy operator of a central hyperplane arrangement is shown to be combinatorially determined. In particular, a necessary and sufficient condition for the triviality of this monodromy operator is given.

It is known that the complement of a complex hyperplane arrangement is cohomologically Tate and, if the arrangement is defined over ℚ, has polynomial count. We show that these properties hold for the corresponding Milnor fibers if the monodromy is trivial.

We construct a hyperplane arrangement defined over ℚ, whose Milnor fiber has a nontrivial monodromy operator, is cohomologically Tate, and has no polynomial count. Such examples are shown not to exist in low dimensions.
Fonctions zêtaℓ-modulaires
Authors: Mínguez Alberto
Published: July 2016

Let F be a non-Archimedean locally compact field, of residual characteristicp,and let D be a finite-dimensional central division F-algebra. Letℓbe a prime number different fromp.In this article, generalizing the results of [GJ], we associate, to eachℓ-modular smooth irreducible representationπof GLm(D), two invariantsL(T,π), ε(T,π,ψ),whereTis an indeterminate andψis a nontrivial character of F.
Kulikov surfaces form a connected component of the moduli space
Authors: Chan Tsz On Mario , Coughlan Stephen
Published: July 2016

We show that the Kulikov surfaces form a connected component of the moduli space of surfaces of general type withpg= 0 andK2= 6. We also give a new description for these surfaces, extending ideas of Inoue. Finally, we calculate the bicanonical degree of Kulikov surfaces and prove that they verify the Bloch conjecture.
Estimates for F-jumping numbers and bounds for Hartshorne–Speiser–Lyubeznik numbers
Authors: Mustaţă Mircea , Zhang Wenliang
Published: July 2016

Given an ideal a on a smooth variety in characteristic zero, we estimate theF-jumping numbers of the reductions of a to positive characteristic in terms of the jumping numbers of a and the characteristic. We apply one of our estimates to bound the Hartshorne–Speiser–Lyubeznik invariant for the reduction to positive characteristic of a hypersurface singularity.
Algebras of acyclic cluster type: Tree type and type Ã
Authors: Amiot Claire , Oppermann Steffen
Published: July 2016

In this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree or of typeÃ.We are particularly interested in their derived equivalence classification. We prove that each algebra which is cluster equivalent to a tree quiver is derived equivalent to the path algebra of this tree. Then we describe explicitly the algebras of cluster typeÃnfor each possible orientation ofÃn.We give an explicit way to read off the derived equivalence class in which such an algebra lies, and we describe the Auslander-Reiten quiver of its derived category. Together, these results in particular provide a complete classification of algebras which are cluster equivalent to tame acyclic quivers.
Stability of tautological bundles on the Hilbert scheme of two points on a surface
Authors: Wandel Malte
Published: July 2016

Let (X, H) be a polarized smooth projective surface satisfyingH1(Χ, OΧ) = 0, and letƑbe either a rank 1 torsion-free sheaf or a rank 2μH-stable vector bundle onΧ. Assume thatc1(Ƒ) ≠ 0. This article shows that the rank 2—respectively, rank 4—tautological sheafƑ[2]associated withƑon the Hilbert squareΧ[2]isμ-stable with respect to a certain polarization.
Almost direct summands
Authors: Bhatt Bhargav
Published: July 2016

We prove new cases of the direct summand conjecture using fundamental theorems inp-adic Hodge theory due to Faltings. The cases tackled include the ones when the ramification locus lies entirely in characteristicp.
Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities
Authors: bona Jerry L. , Cohen Jonathan , Wang Gang
Published: July 2016

In this paper, coupled systems

of Korteweg-de Vries type are considered, whereu=u(x, t),v=v(x, t) are real-valued functions and wherex, t∈R. Here, subscripts connote partial differentiation and

are quadratic polynomials in the variablesuandv. Attention is given to the pure initial-value problem in whichu(x, t) andv(x, t) are both specified att= 0, namely,

forx∈ ℝ. Under suitable conditions onPandQ, global well-posedness of this problem is established for initial data in theL2-based Sobolev spacesHs(ℝ) ×Hs(ℝ) for anys> ‒3/4.
Blocks and Normal Subgroups of Finite Groups
Authors: Reynolds W. F.
Published: July 2016

Let H be a normal subgroup of a finite group G, and let ζ be an (absolutely) irreducible character of H. In [7], Clifford studied the irreducible characters X of G whose restrictions to H contain ζ as a constituent. First he reduced this question to the same question in the so-called inertial subgroup S of ζ in G, and secondly he described the situation in S in terms of certain projective characters of S/H. In section 8 of [10], Mackey generalized these results to the situation where all the characters concerned are projective.
New Formulation of the Axiom of Choice by making use of the Comprehension Operator
Authors: Ono Katuzi
Published: July 2016

We have introduced in our former work [1] and [2] the comprehension operator “{·)”, which maps every binary relation to a binary relation. The definition of this operator

is remarkable in that it can be defined in any formal system having themembershiprelation ∈, which is hereafter called theuniversal systemand is denoted by U. In this work, we would like to point out that theaxiom of choice, in the strong sense as well as in the weak sense, can be formulated in an extremely simple style by making use of the comprehension operator.
General Value Distribution Theory
Authors: Sario Leo
Published: July 2016

We shall introduce the main theorems of value distribution theory in the most general case of complex dimension one: analytic mappings of arbitrary Riemann surfaces into arbitrary Riemann surfaces. The case of mappings of arbitrary Riemann surfaces into closed Riemann surfaces was discussed in [41]. Earlier literature on analytic mappings is listed in the Bibliography.
Compactifications of Harmonic Spaces
Authors: Constantinescu C. , Cornea A.
Published: July 2016

Many results of the theory of Riemann surfaces derive only from the properties of the sheaf of harmonic functions on these surfaces. It is therefore natural to try to extend these results to more comprehensive structures defined by means of a sheaf of continuous functions on a topological space which should possess the main properties of the sheaf of harmonic functions on a Riemann surface. The aim of the present paper is to generalise some known results from the theory of Riemann surfaces to spaces endowed with sheaves satisfying Brelot’s axioms [2], which we call harmonic spaces. In order to do so we had to introduce and to study the maps, associated in a natural way with this structure, called harmonic maps; they replace the analytic maps between Riemann surfaces. In this general frame we reconstruct the whole theory of Wiener compactification as well as the theory of the behaviour of analytic maps at the Wiener boundary.
Singular Sets of Some Kleinian Groups
Authors: Akaza Tohru
Published: July 2016

In our paper Cl] we showed that there exist Schottky groups whose singular sets have positive 1-dimensional measure. Since the example was very complicated, it is natural to seek for simpler examples. Further the problem how about the singular sets of more general groups occurs.
Eleven Nonequivalent Conditions on a Commutative Ring
Authors: Gilmer Robert W.
Published: July 2016

We consider in this paper eleven conditions on a commutative ringR. The first of these is thatRcontains an identity. It is well known that each of the other properties is a consequence of the first condition. This paper considers other relations which exist between these properties. A complete diagram of all simple implications which exist between the eleven properties, together with proof of these implications, is given in section 3. Examples illustrating simple implications which do not hold are presented in section 4.
Generalized Commutative Rings
Authors: Belluce L. P. , Herstein I. N. , Jain S. K.
Published: July 2016

Among his various interests in algebra Nakayama also took part in the various researches, published in the early and middle 1950’s, which dealt with the commutativity of rings. This paper, which studies a problem of a related sort, thus seems appropriate in a Journal honoring his memory.

We shall study a certain class of rings which satisfy a weak form of the commutative law and shall show that the structure of such rings can be determined.
A Characterization of QF-3 Rings
Authors: WU L. E. T. , Mochizuki H. Y. , Jans J. P.
Published: July 2016

A left QF-3 ring R is one in which RR, the ring considered as a left module over itself, can be embedded in a projective infective left R module Q(RR). QF-3 rings were introduced by Thrall [14] and have been studied and characterized by a number of authors [5, 8, 9, 12, 13, 15] usually restricted to the case of algebras over a field. In such a case, the concept of left QF-3 and right QF-3 coincide.

The study of QF-3 rings and algebras and many other such classes of rings had its origin in the now classic papers of Nakayama [10, 11]. He was an outstanding pioneer in algebra for many years, and we acknowledge our great debt to him and to his many excellent papers.
On Galois Extension of Rings
Authors: Kanzaki Teruo
Published: July 2016

Let Λ be a ring and G a finite group of ring automorphisms of Λ. The totality of elements of Λ which are left invariant by G is a subring of Λ. We call it the G-fixed subring of Λ. Let be the crossed product of Λ and G with trivial factor set, i.e. {u0} is a Λ-free basis of Δ and , and let Γ be a subring of the G-fixed subring of Λ which has the same identity as Λ.
Imbedding a Regular Ring in a Regular Ring with Identity
Authors: Funayama Nenosuke
Published: July 2016

In [1] L. Fuchs and I. Halperin have proved that a regular ring R is isomorphic to a two-sided ideal of a regular ring with identity. ([1] Theorem 1). Their methed is to imbed the regular ring R in the ring of all pairs (a, p) with a ∊ R and p from a suitable commutative regular ring S with identity such that R is an algebra over S. Thus S may be seen as the ring of R — R endomorphisms of the additive group of R. The following question is naturally raised: Is it true that the ring of all R-R endomorphisms of a rugular ring is a commutative regular ring? The main purpose of this paper is to answer this question affirmatively. (Theorem 1). After established this theorem we can follow the method in [1] to solve the problem in the title.
The Notion of Restricted Idèles with Application to Some Extension Fields
Authors: Furuta Yoshiomi
Published: July 2016

Letkbe an algebraic number field of finite degree,Kbe its normal extension of degreen, andŝbe the set of those primes ofKwhich have degree 1. Using this setsinstead of the set of all primes ofK, we define an s-restricted idèle ofKby the same way as ordinary idèles. It is known by Bauer that the normal extension of an algebraic number field is determined by the set of all primes of the ground field which are decomposed completely in the extension field. This suggests that if we treat abelian extensions overKwhich are normal overk, the class field theory is expressed by means of the ŝ-restricted idèles (theorem 2). WhenK = k, ŝ is the set of all primes ofK, and we have the ordinary class field theory.
The Homological Dimension of a Quotient Field
Authors: Kaplansky Irving
Published: July 2016

Let R be an integral domain, Q its quotient field. For any R-module A we write d(A) for its homological dimension (minimal length of a projective resolution), or dR(A) if it is necessary to call attention to R.
On Primitive Extensions of Rank 3 of Symmetric Groups
Authors: Tsuzuku Tosiro
Published: July 2016

1. Let Ω be a finite set of arbitrary elements and let (G, Ω) be a permutation group on Ω. (This is also simply denoted by G). Two permutation groups (G, Ω) and (G, Γ) are called isomorphic if there exist an isomorphism σ of G onto H and a one to one mapping τ of Ω onto Γ such that (g(i))τ=gσ(iτ) for g ∊ G and i∊Ω. For a subset Δ of Ω, those elements of G which leave each point of Δ individually fixed form a subgroup GΔ of G which is called a stabilizer of Δ. A subset Γ of Ω is called an orbit of GΔ if Γ is a minimal set on which each element of G induces a permutation. A permutation group (G, Ω) is called a group of rank n if G is transitive on Ω and the number of orbits of a stabilizer Ga of a ∊ Ω, is n. A group of rank 2 is nothing but a doubly transitive group and there exist a few results on structure of groups of rank 3 (cf. H. Wielandt [6], D. G. Higman M).
On Algebraic Groups and Discontinuous Groups
Authors: Ono Takashi
Published: July 2016

Let G be a connected semi-simple algebraic group defined over Q and let Γ be a discrete subgroup of GR (the subgroup of G consisting of points rational over R) such that Γ\GR is compact. The main purpose of the present paper is to prove that for a certain type of group G there exists an invariant algebraic differential from ω on G of highest degree defined over Q such that
Über die Einstufig Nichtkommutativen Ringe
Authors: Ikeda Masatoshi
Published: July 2016

In der Arbeit [2] hat L. Rédei den Begriff des einstufig nichtkommutativen Ringes eingefiihrt, und die alien möglichen Typen der einstufig nichtkommutativen endlichen Ringe aufgezàhlt. Sie bestehen aus drei Grundtypen und ihren homomorphen Bildern. In der oben genannten Arbeit hat Rédei einstufig nichtkommutativen unendlichen Ringes ganz kurz erwähnt, und nur darauf hingewiesen, dass man nicht einmal weiss, ob solche Ringe überhaupt existieren. In der vorliegenden Arbeit handelt es sich um die Nichtexistenz der einstufig nichtkommutativen unendlichen Ringe. Obwohl die Nichtexistenz der allge-meinen unendlichen Ringe vom genannten Charakter hoch glaubwürdig scheint, kann ich doch zur Zeit die Aufgabe in ihrer vollen Allgemeinheit nicht losen, sondem ich kann nur zeigen, dass ein einstufig nichtkommutativer Ring mit einer zusätzlichen Bedingung notwendigerweise endlich wird. Im folgenden soil nämlich der untenbenannte Satz bewiesen werden.
On a Formula Concerning Stochastic Differentials
Authors: Itô Kiyosi
Published: July 2016

In his previous paper [1] the author has stated a formula concering stochastic differentials with the outline of the proof. The aim of this paper is to show this formula in details in a little more general form (Theorem 6).
On the Cohomology of Some Hopf Algebras
Authors: Shimada Nobuo , Iwai Akira
Published: July 2016

In this paper we study certain injective resolutions for some Hopf algebras. An injective resolution for a coalgebra A with augmentation η is defined to be such an exact sequence that

where K is the basic field, Xn are injective A-comodules and δn are morphism of A-comodules.
On Various Definitions of Capacity and Related Notions
Authors: Ohtsuka Makoto
Published: July 2016

The electric capacity of a conductor in the 3-dimensional euclidean space is defined as the ratio of a positive charge given to the conductor and the potential on its surface. The notion of capacity was defined mathematically first by N. Wiener [7] and developed by C. de la Vallée Poussin, O. Frostman and others. For the history we refer to Frostman’s thesis [2]. Recently studies were made on different definitions of capacity and related notions. We refer to M. Ohtsuka [4] and G. Choquet [1], for instance. In the present paper we shall investigate further some relations among various kinds of capacity and related notions. A part of the results was announced in a lecture of the author in 1962.
On the Defining Equations of Abelian Varieties
Authors: Morikawa Hisasi
Published: July 2016

This article is a continuation and completion of our study in the previous one [1] in which we gave the defining equations of abelian varieties projectively embedded by theta functions of level three. These defining equations are nothing else the canonical generators of theta relations for theta functions with ⅓—characteristics. In the present article the canonical generators of 3 theta relations will be given for the wider class of theta functions with rational characteristics.
On Quasi-Linear Parabolic Equations
Authors: Ikeda Yoshiaki
Published: July 2016

In this paper we consider the following quasi-linear parabolic equations

Lu = ut — div A(x, t, u, ux)+B(x, t, u, ux= 0,

where A is a given vector function of the variables x,t,u,uX, and B is a given scalar function of the some variables. We assume that they are difined in the rectangle
On Square Integrable Martingales
Authors: Kunita Hiroshi , Watanabe Shinzo
Published: July 2016

Theory of real and time continuous martingales has been developed recently by P. Meyer [8, 9]. Let be a square integrable martingale on a probability space P. He showed that there exists an increasing process ‹X›t such that
Positively Infinite Singularities of a Superharmonic Function
Authors: Matsumoto Kikuji
Published: July 2016

Let E be a compact set of logarithmic capacity zero in the complex plane. Then the following is well-known as Evans-Selberg’s theorem [1] [8]: there is a measure with support contained in E such that its logarithmic potential is positively infinite at each point of E. But such a potential does not exist for E of logarithmic positive capacity. Now suppose that E is contained in the circumference of the unit disc |z| < 1 and is of linear measure zero.
A Note on Simple Anti-Commutative Algebras Obtained from Reductive Homogeneous Spaces
Authors: Sagle Arthur A.
Published: July 2016

LetGbe a connected Lie group andHa closed subgroup, then the homogeneous spaceM = G/His calledreductiveif there exists a decomposition(subspace direct sum) withwhereg(resp.) is the Lie algebra ofG(resp.H); in this case the pair (g,) is called areductive pair.
On Real Quadratic Fields Containing Units with Norm -1
Authors: Yokoi Hideo
Published: July 2016

LetQbe the rational number field, and letK=(D> 0 a rational integer) be a real quadratic field. Then, throughout this paper, we shall understand by the fundamental unitεDofthe normalized fundamental unitεD> 1.
The Reciprocity of Dedekind Sums and the Factor Set for the Universal Covering Group of SL(2, R)
Authors: Asai Tetsuya
Published: July 2016

By explicit studying on theta-multipliers (i.e. the multipliers which appear in theta-transformation formulas under general modular substitutions), we can naturally get the reciprocity law of Gauss sums or quadratic residue symbols. This remarkable fact, by Cauchy, Kronecker, Hecke and others, is very classical, but its theoretical meaning has not been sufficiently clear yet.
On the Automorphism Group of a Holomorphic Fiber Bundle over A Complex Space
Authors: Fujimoto Hirotaka
Published: July 2016

In [8], A. Morimoto proved that the automorphism group of a holomorphic principal fiber bundle over a compact complex manifold has a structure of a complex Lie group with the compact-open topology. The purpose of this paper is to get similar results on the automorphism groups of more general types of locally trivial fiber spaces over complex spaces. We study automorphisms of a holomorphic fiber bundle over a complex space which has a complex space Y as the fiber and a (not necessarily complex Lie) group G of holomorphic automorphisms of Y as the structure group (see Definition 3. l).
Sur Le Schéma de la Séparation
Authors: Arruda Ayda I. , Da Costa Newton C.A.
Published: July 2016

En continuant l’étude d’un problème soulevé dans [3] et plus tard abordé par un de nous dans [1] et [2], nous avons publié deux “abstracts” (voir [6] et [7]) sur certains calculs propositionnels appellés Jn, 1 ≤ n ≤ 5, et leurs relations avec le postulat de la séparation. On développe maintenant les systèmes Jn, 1 ≤ n ≤ 5, et on esquisse la construction des calculs correspondants de prédicats de premier ordre. Enfin, on démontre la non trivialité des théories correspondantes des ensembles quand on utilise des postulats comme ceux de Zermelo-Fraenkel, mais avec le schéma de la séparation formulé sans les restrictions ad hoc pour éviter les paradoxes.
On a Π01 Set of Positive Measure
Authors: Tanaka Hisao
Published: July 2016

Some basis results for arithmetic, hyperarithmetic (HA) or sets which have positive measure (or which are not meager, i.e., of the second Baire category) have been obtained by several authors. For example, every non-meager set must have a recursive element (Shoenfield-Hinman, Hinman [2]) but there exists a non-meager set (as well as of measure 1) that contains no recursive element (Shoenfield [7]), and every set (i.e., arithmetic set) of positive measure contains an arithmetic element (Sacks [5], and Tanaka [12]).
The Topological Support of Gauss Measure on Hilbert Space
Authors: Ito Kiyosi
Published: July 2016

Let X be a Hilbert space. The topological support of a Radon probability measure P on X is the least closed subset M of X that carries the total measure 1.
A Characterization of the Finite Simple Groups PSp(4,q), G2(q), D42(q), II
Authors: Fong Paul
Published: July 2016

Our object in this paper is to prove the following result.

THEOREM. Let G be a finite group satisfying the following conditions:

(*) G has subgroups L1, L2 such that L1 ≃ SL(2, q1), L2 ≃ SL(2, q2), [L1 L2] = 1, , where j is an involution, and |C(j): L1L2| = 2.

(**) where n2 = 1,
Some Homogeneous Einstein Manifolds
Authors: Sagle Arthur A.
Published: July 2016

Let G be a connected Lie group and H a closed subgroup with Lie algebra such that in the Lie algebra g of G there exists a subspace m with (subspace direct sum) and In this case the corresponding manifold M = G/H is called a reductive homogeneous space and (g,) (or (G,H)) a reductive pair. In this paper we shall show how to construct invariant pseudo-Riemannian connections on suitable reductive homogeneous spaces M which make M into an Einstein manifold.