bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Waring’s problem: Three cubes and a minicube
Authors: Brüdern Jörg , Wooley Trevor D. 
Published: July 2016

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

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

AbstractLet Ω(n) denote the number of prime divisors ofncounting multiplicity. One can show that for any positive integermand allj= 0,1,…,m– 1, we havewithα= 1. Building on work of Kubota and Yoshida, we show that form&gt; 2 and anyj= 0,1,…,m– 1, the error term is noto(xα) for anyα&lt; 1.
Normality of orbit closures in the enhanced nilpotent cone
Authors: Achar Pramod N. , Henderson Anthony , Jones Benjamin F. 
Published: July 2016

AbstractWe continue the study of the closures of GL(V)-orbits in the enhanced nilpotent coneV × Nbegun by the first two authors. We prove that each closure is an invariant-theoretic quotient of a suitably defined enhanced quiver variety. We conjecture, and prove in special cases, that these enhanced quiver varieties are normal complete intersections, implying that the enhanced nilpotent orbit closures are also normal.
Notes on boundedness of spectral multipliers on Hardy spaces associated to operators
Authors: Anh Bui The 
Published: July 2016

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

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

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

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

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

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

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

AbstractFor a smooth proper variety over ap-adic field, its Brauer group and abelian fundamental group are related to higher Chow groups by the Brauer–Manin pairing and class field theory. We generalize this relation to smooth (possibly nonproper) varieties, using motivic homology and a variant of Wiesend’s ideal class group. Several examples are discussed.
Generic formal fibers and analytically ramified stable rings
Authors: Olberding Bruce 
Published: July 2016

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

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

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

AbstractIn this paper, we prove that, for an integerrwith (r, 6) = 1 and 0&lt; r &lt;24 and a nonnegative even integers, the setis isomorphic toas Hecke modules under the Shimura correspondence. HereMs(1) denotes the space of modular forms of weightis the space of newforms of weight 2kon Γ0(6) that are eigenfunctions with eigenvalues€2and€3for Atkin-Lehner involutionsW2andW3, respectively, and the notation ⊕(12/.) means the twist by the quadratic character (12/-). There is also an analogous result for the cases (r, 6) = 3.
On operator-valued monotone independence
Authors: Hasebe Takahiro , Saigo Hayato 
Published: July 2016

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

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

Let K be a field of characteristic zero. Let V be an n-dimensional vector space over K and let S be the graded ring of polynomial functions on V. If G is a group of linear transformations of V, then G acts naturally as a group of automorphisms of S if we defineThe elements of S invariant under all γ ∈ G constitute a homogeneous subring I(S) of S called the ring of polynomial invariants of G.
Remarks on a Theorem of Bourbaki
Authors: Auslander M. 
Published: July 2016

Bourbaki has established the following theorem which we state without proof asTHEOREM A ([3, Theorem 6, §4]). Let R be a noetherian integrally closed domain and M a finitely generated torsion free R-module. Then there exists a free submodule F of M such that M/F is isomorphic to an ideal in R.It is our purpose in this note to present a few consequences of this theorem. Before giving these results we briefly review some terminology and known results.
Subnormale Lösungen der Differentialgleichung: w” + p(ez)w’ + q(ez) w + 0
Authors: In Karlsruhe Von H. Wittich 
Published: July 2016

In der Differentialgleichung w″+a1(z)w‣w‣+a0(z)w=0 seien die Koeffizienten aj(z) ganze Funktionen. Dann ist jede Lösung w(z) eine ganze Funktion und genau dann von endlicher Ordnung, wenn die Koeffizienten Polynome sind. In diesem Fall gilt für die Ordnung die Beziehung λ(w)= m/2, m ≧ 0 ganzzahlig.
On Local Maximality for the Coefficient a6
Authors: Jenkins James A. , Ozawa Mitsuru 
Published: July 2016

Recently a number of authors have studied the application of Grunsky’s coefficient inequalities to the study of the Bieberbach conjecture for the class of normalized regular univalent functions f(z) in the unit circle |z|< 1Charzynski and Schiffer [2] applied this result to give an elementary proof of the inequality | a4 | Ȧ 4. One of the present authors [8] proved that if a2 is real non-negative then A natural first step in the study of the inequality for a coefficient is to prove local maximality for a2 near to 2.
On Permutation Groups of Prime Degree p Which Contain at Least Two Classes of Conjugate Subgroups of Index p. II
Authors: Ito Noboru 
Published: July 2016

Let p be a prime and let Ω be the set of p symbols 1,2, ..., p, called points. Let be a transitive permutation group on Ω such that(I) contains a subgroup of index p which is not the stabilizer of a point.
Projective invariant metrics for Einstein spaces
Authors: Kobayashi Shoshichi 
Published: July 2016

In my recent paper [1], I associated a projectively invariant pseudo-distance dM to every affinely connected manifold M and proved the followingTheorem 1. Let M be a Riemannian manifold with metric and Ricci tensor RicM such that RicM ≤–c2. Let δM be the Riemannian distance defined by .
Boundary behavior of positive harmonic functions in balls of Rn
Authors: Renteln Michael Von 
Published: July 2016

Let Rn be the real n-dimensional euclidean space. Elements of Rn are denoted by x = (xl • • •, xn), and ‖ x ‖ denotes the euclidean norm of x.The open ball B(x, r) with center x and radius r is defined by
The stability theorems for discrete dynamical systems on two-dimensional manifolds
Authors: Sannami Atsuro 
Published: July 2016

One of the basic problems in the theory of dynamical systems is the characterization of stable systems.Let M be a closed (i.e. compact without boundary) connected smooth manifold with a smooth Riemannian metric and Diffr (M) (r ≥ 1) denote the space of Cr diffeomorphisms on M with the uniform Cr topology.
Existence of extremal Beltrami coefficients with nonconstant modulus
Authors: Yao Guowu 
Published: July 2016

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

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

AbstractIn this paper we consider complete, noncompact, negatively curved surfaces that are twice continuously differentiably embedded in Euclidean three-space, showing that if such surfaces have square integrable second fundamental form, then their topology must, by the index method, be an annulus. We then show how this relates to some minimal surface theorems and has a corollary on minimal surfaces with finite total curvature. In addition, we discuss, by the index method, the relation between the topology and asymptotic curves. Finally, we apply the results yielded to the problem of isometrical immersions into Euclidean three-space of black hole models.
A note on thick subcategories of stable derived categories
Authors: Krause Henning , Stevenson Greg 
Published: July 2016

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

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

In the present paper, we first prove the following
THEOREM 1. Let K be a field, x a transcendental element over K, and V* a valuation ring of K(x). Set V= V* ∩ K. Denote by p* and p the maximal ideals of V* and V respectively. If (i) V*/p* is not algebraic over V/p and (ii) the value group of V* is isomorphic to Zn (Z=the module of rational integers), i.e., V* is of rank n and discrete in the generalized sense, then V*/p* is a simple transcendental extension of a finite algebraic extension of V/p.
Moduli spaces of vector bundles over ruled surfaces
Authors: Aprodu Marian , Brînzănescu Vasile 
Published: July 2016

AbstractWe study moduli spacesM(c1,c2,d, r) of isomorphism classes of algebraic 2-vector bundles with fixed numerical invariantsc1,c2,d,rover a ruled surface. These moduli spaces are independent of any ample line bundle on the surface. The main result gives necessary and sufficient conditions for the non-emptiness of the spaceM(c1,c2,d, r) and we apply this result to the moduli spacesML(c1,c2) of stable bundles, whereLis an ample line bundle on the ruled surface.
Sextactic points on a simple closed curve
Authors: Thorbergsson Gudlaugur , Umehara Masaaki 
Published: July 2016

AbstractWe give optimal lower bounds for the number of sextactic points on a simple closed curve in the real projective plane. Sextactic points are after inflection points the simplest projectively invariant singularities on such curves. Our method is axiomatic and can be applied in other situations.
Existence and Boundedness of Parametrized Marcinkiewicz Integral with Rough Kernel on Campanato Spaces
Authors: Ding Yong , Xue Qingying , Yabuta Kôzô 
Published: July 2016

AbstractLet g(f), S(f), g*λ(f) be the Littlewood-Paley g function, Lusin area function, and Littlewood-Paley g*λ(f) function of f, respectively. In 1990 Chen Jiecheng and Wang Silei showed that if, for a BMO function f, one of the above functions is finite for a single point in ℝn, then it is finite a.e. on ℝn, and BMO boundedness holds. Recently, Sun Yongzhong extended this result to the case of Campanato spaces (i.e. Morrey spaces, BMO, and Lipschitz spaces). One of us improved his g*λ(f) result further, and treated parametrized Marcinkiewicz functions with Lipschitz kernel μρ(f), μρs(f) and μλ*,ρ(f). In this paper, we show that the same results hold also in the case of rough kernel satisfying Lp-Dini type condition.
Finiteness of Entire Functions Sharing a Finite Set
Authors: Fujimoto Hirotaka 
Published: July 2016

AbstractFor a finite set S = {a1,…, aq}, consider the polynomial PS(w) = (w – a1)(w – a2) … (w – aq) and assume that has distinct k zeros. Suppose that PS(w) is a uniqueness polynomial for entire functions, namely that, for any nonconstant entire functions ɸ and ψ, the equality PS(ɸ) = cPS(ψ) implies ɸ = ψ, where c is a nonzero constant which possibly depends on ɸ and ψ. Then, under the condition q > k + 2, we prove that, for any given nonconstant entire function g, there exist at most (2q-2)/(q – k – 2) nonconstant entire functions f with f*(S) = g*(S), where f*(S) denotes the pull-back of S considered as a divisor. Moreover, we give some sufficient conditions of uniqueness polynomials for entire functions.
Computing certain Gromov-Witten invariants of the crepant resolution of ℙ(1, 3, 4, 4)
Authors: Boissière Samuel , Mann Étienne , Perroni Fabio 
Published: July 2016

AbstractWe prove a formula computing the Gromov-Witten invariants of genus zero with three marked points of the resolution of the transversalA3-singularity of the weighted projective space ℙ(1,3,4,4) using the theory of deformations of surfaces withAn-singularities. We use this result to check Ruan’s conjecture for the stack ℙ(1,3,4,4).
Distribution of polynomials with cycles of a given multiplier
Authors: Bassanelli Giovanni , Berteloot François 
Published: July 2016

AbstractIn the space of degreedpolynomials, the hypersurfaces defined by the existence of a cycle of periodnand multipliereiθare known to be contained in the bifurcation locus. We prove that these hypersurfaces equidistribute the bifurcation current. This is a new result, even for the space of quadratic polynomials.
Quantum reconstruction for Fano bundles on projective space
Authors: Strangeway Andrew 
Published: July 2016

AbstractWe present a reconstruction theorem for Fano vector bundles on projective space which recovers the small quantum cohomology for the projectivization of the bundle from a small number of low-degree Gromov-Witten invariants. We provide an extended example in which we calculate the quantum cohomology of a certain Fano 9-fold and deduce from this, using the quantum Lefschetz theorem, the quantum period sequence for a Fano 3-fold of Picard rank 2 and degree 24. This example is new, and is important for the Fanosearch program.
Rational points on linear slices of diagonal hypersurfaces
Authors: Brüdern Jörg , Robert Olivier 
Published: July 2016

AbstractAn asymptotic formula is obtained for the number of rational points of bounded height on the class of varieties described in the title line. The formula is proved via the Hardy-Littlewood method, and along the way we establish two new results on Weyl sums that are of some independent interest.