bluuebunny/crossref_metadata_2025_split huggingface dataset:
Normal Functions: Lp Estimates
Authors: Chen Huaihui , Gauthier Paul M. 
Published: December 2010

AbstractFor ameromorphic (or harmonic) function ƒ, let us call the dilation of ƒ at z the ratio of the (spherical)metric at ƒ(z) and the (hyperbolic)metric at z. Inequalities are knownwhich estimate the sup norm of the dilation in terms of its Lp norm, for p > 2, while capitalizing on the symmetries of ƒ. In the present paper we weaken the hypothesis by showing that such estimates persist even if the Lp norms are taken only over the set of z on which ƒ takes values in a fixed spherical disk. Naturally, the bigger the disk, the better the estimate. Also, We give estimates for holomorphic functions without zeros and for harmonic functions in the case that p = 2.
Spectral Theory for the Neumann Laplacian on Planar Domains With Horn-Like Ends
Authors: Edward Julian 
Published: December 2010

AbstractThe spectral theory for the Neumann Laplacian on planar domains with symmetric, horn-like ends is studied. For a large class of such domains, it is proven that the Neumann Laplacian has no singular continuous spectrum, and that the pure point spectrum consists of eigenvalues of finite multiplicity which can accumulate only at 0 or ∞. The proof uses Mourre theory.
Determinantal Forms for Symplectic and Orthogonal Schur Functions
Authors: Hamel A. M. 
Published: December 2010

AbstractSymplectic and orthogonal Schur functions can be defined combinatorially in a manner similar to the classical Schur functions. This paper demonstrates that they can also be expressed as determinants. These determinants are generated using planar decompositions of tableaux into strips and the equivalence of these determinants to symplectic or orthogonal Schur functions is established by Gessel-Viennot lattice path techniques. Results for rational (also called composite) Schur functions are also obtained.
The 2-Rank of the Class Group of Imaginary Bicyclic Biquadratic Fields
Authors: McCall Thomas M. , Parry Charles J. , Ranalli Ramona R. 
Published: December 2010

AbstractA formula is obtained for the rank of the 2-Sylow subgroup of the ideal class group of imaginary bicyclic biquadratic fields. This formula involves the number of primes that ramify in the field, the ranks of the 2-Sylow subgroups of the ideal class groups of the quadratic subfields and the rank of a Z2-matrix determined by Legendre symbols involving pairs of ramified primes. As applications, all subfields with both 2- class and class group Z2×Z2 are determined. The final results assume the completeness of D. A. Buell’s list of imaginary fields with small class numbers.
A Complete Convergence Theorem for Attractive Reversible Nearest Particle Systems
Authors: Mountford T. S. 
Published: December 2010

AbstractIn this paper we prove a complete convergence theorem for attractive, reversible, super-critical nearest particle systems satisfying a natural regularity condition. In particular this implies that under these conditions there exist precisely two extremal invariant measures. The result we prove is relevant to question seven of Liggett (1985), Chapter VII.
Classical Orthogonal Polynomials as Moments
Authors: Ismail Mourad E. H. , Stanton Dennis 
Published: December 2010

AbstractWe show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous q-ultraspherical polynomials and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures.We use this fact to derive bilinear and multilinear generating functions for some of these polynomials. We also comment on the corresponding formulas for the Charlier, Hermite and Laguerre polynomials.
Summing up the Dynamics of Quadratic Hamiltonian Systems With a Center
Authors: Pal Janos , Schlomiuk Dana 
Published: December 2010

AbstractIn this work we study the global geometry of planar quadratic Hamiltonian systems with a center and we sum up the dynamics of these systems in geometrical terms. For this we use the algebro-geometric concept of multiplicity of intersection Ip(P,Q) of two complex projective curves P(x, y, z) = 0, Q(x,y,z) = 0 at a point p of the plane. This is a convenient concept when studying polynomial systems and it could be applied for the analysis of other classes of nonlinear systems.
Sur L'Intégrabilité des Sous–Algèbres de lie en Dimension Infinie
Authors: Robart Thierry 
Published: December 2010

RésuméUne des questions fondamentales de la théorie des groupes de Lie de dimension infinie concerne l’intégrabilitédes sous–algèbres de Lie topologiques H de l’algèbre de Lie G d’un groupe de Lie G de dimension infinie au sens de Milnor. Par contraste avec ce qui se passe en théorie classique il peut exister des sous–algèbres de Lie fermées H de G non–intégrables en un sous–groupe de Lie. C’est le cas des algèbres de Lie de champs de vecteurs C∞ d’une variétécompacte qui ne définissent pas un feuilletage de Stefan. Heureusement cette “imperfection” de la théorie n’est pas partagée par tous les groupes de Lie intéressants. C’est ce que montre cet article en exhibitant une très large classe de groupes de Lie de dimension infinie exempte de cette imperfection. Cela permet de traiter complètement le second problème fondamental de Sophus Lie pour les groupes de jauge de la physique–mathématique et les groupes formels de difféomorphismes lisses de ℝn qui fixent l’origine.
Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity
Authors: Shibata Tetsutaro 
Published: December 2010

AbstractWe consider the multiparameter nonlinear Sturm-Liouville problemwhere are parameters. We assume that1 ≤ q ≤ p1 < p2 < ... ≤ pn < 2q + 3.We shall establish an asymptotic formula of variational eigenvalue λ = λ(μ, α) obtained by using Ljusternik-Schnirelman theory on general level set Nμ, α(α < 0 : parameter of level set). Furthermore,we shall give the optimal condition of {(μ, α)}, under which μi(m + 1 ≤ i ≤ n : fixed) dominates the asymptotic behavior of λ(μ, α).
Pieri’S Formula Via Explicit Rational Equivalence
Authors: Sottile Frank 
Published: December 2010

AbstractPieri’s formula describes the intersection product of a Schubert cycle by a special Schubert cycle on a Grassmannian. We present a new geometric proof, exhibiting an explicit chain of rational equivalences from a suitable sum of distinct Schubert cycles to the intersection of a Schubert cycle with a special Schubert cycle. The geometry of these rational equivalences indicates a link to a combinatorial proof of Pieri’s formula using Schensted insertion.
Green's Functions for Powers of the Invariant Laplacian
Authors: Engliš Miroslav , Peetre Jaak 
Published: December 2010

AbstractThe aim of the present paper is the computation of Green's functions for the powers Δm of the invariant Laplace operator on rank-one Hermitian symmetric spaces. Starting with the noncompact case, the unit ball in ℂd, we obtain a complete result for m= 1, 2 in all dimensions. For m≥ 3 the formulas grow quite complicated so we restrict ourselves to the case of the unit disc (d= 1) where we develop a method, possibly applicable also in other situations, for reducing the number of integrations by half, and use it to give a description of the boundary behaviour of these Green functions and to obtain their (multi-valued) analytic continuation to the entire complex plane. Next we discuss the type of special functions that turn up (hyperlogarithms of Kummer). Finally we treat also the compact case of the complex projective space ℙd (for d= 1, the Riemann sphere) and, as an application of our results, use eigenfunction expansions to obtain some new identities involving sums of Legendre (d= 1) or Jacobi (d > 1) polynomials and the polylogarithm function. The case of Green's functions of powers of weighted (no longer invariant, but only covariant) Laplacians is also briefly discussed.
Aϕ-Invariant Subspaces on the Torus
Authors: Izuchi Keiji , Matsugu Yasuo 
Published: December 2010

AbstractGeneralizing the notion of invariant subspaces on the 2-dimensional torus T2, we study the structure of Aϕ-invariant subspaces of L2(T2). A complete description is given of Aϕ-invariant subspaces that satisfy conditions similar to those studied by Mandrekar, Nakazi, and Takahashi.
Isomorphisms Between Generalized Cartan Type W Lie Algebras in Characteristic 0
Authors: Zhao Kaiming 
Published: December 2010

AbstractIn this paper, we determine when two simple generalized Cartan type W Lie algebras Wd(A, T, φ) are isomorphic, and discuss the relationship between the Jacobian conjecture and the generalized Cartan type W Lie algebras.
Derivations and Invariant Forms of Lie Algebras Graded by Finite Root Systems
Authors: Benkart Georgia 
Published: December 2010

AbstractLie algebras graded by finite reduced root systems have been classified up to isomorphism. In this paper we describe the derivation algebras of these Lie algebras and determine when they possess invariant bilinear forms. The results which we develop to do this are much more general and apply to Lie algebras that are completely reducible with respect to the adjoint action of a finite-dimensional subalgebra.
Shape Fibrations, Multivalued Maps and Shape Groups
Authors: Giraldo Antonio 
Published: December 2010

AbstractThe notion of shape fibration with the near lifting of near multivalued paths property is studied. The relation of thesemaps–which agreewith shape fibrations having totally disconnected fibers–with Hurewicz fibrations with the unique path lifting property is completely settled. Some results concerning homotopy and shape groups are presented for shape fibrations with the near lifting of near multivalued paths property. It is shown that for this class of shape fibrations the existence of liftings of a fine multivalued map is equivalent to an algebraic problem relative to the homotopy, shape or strong shape groups associated.
The Hypercentre and the n-Centre of the Unit Group of an Integral Group Ring
Authors: Li Yuanlin 
Published: December 2010

AbstractIn this paper, we first show that the central height of the unit group of the integral group ring of a periodic group is at most 2. We then give a complete characterization of the n-centre of that unit group. The n-centre of the unit group is either the centre or the second centre (for n ≥ 2).
Nilpotent Orbit Varieties and the Atomic Decomposition of theQ-Kostka Polynomials
Authors: Brockman William , Haiman Mark 
Published: December 2010

AbstractWe study the coordinate rings ofscheme-theoretic intersections of nilpotent orbit closures with the diagonal matrices. Here μ′ gives the Jordan block structure of the nilpotent matrix. de Concini and Procesi [5] proved a conjecture of Kraft [12] that these rings are isomorphic to the cohomology rings of the varieties constructed by Springer [22, 23]. The famousq-Kostka polynomialis the Hilbert series for the multiplicity of the irreducible symmetric group representation indexed by λ in the ring. Lascoux and Schützenberger [15, 13] gave combinatorially a decomposition ofas a sum of “atomic” polynomials with non-negative integer coefficients, and Lascoux proposed a corresponding decomposition in the cohomology model.Our work provides a geometric interpretation of the atomic decomposition. The Frobenius-splitting results of Mehta and van der Kallen [19] imply a direct-sum decomposition of the ideals of nilpotent orbit closures, arising from the inclusions of the corresponding sets. We carry out the restriction to the diagonal using a recent theorem of Broer [3]. This gives a direct-sum decomposition of the ideals yielding the, and a new proof of the atomic decomposition of theq-Kostka polynomials.
Conjugacy Classes and Nilpotent Variety of a Reductive Monoid
Authors: Putcha Mohan S. 
Published: December 2010

AbstractWe continue in this paper our study of conjugacy classes of a reductive monoid M. The main theorems establish a strong connection with the Bruhat-Renner decomposition of M. We use our results to decompose the variety Mnil of nilpotent elements of M into irreducible components. We also identify a class of nilpotent elements that we call standard and prove that the number of conjugacy classes of standard nilpotent elements is always finite.
Lusternik-Schnirelmann Category and Algebraic R-Local Homotopy Theory
Authors: Scheerer H. , Tanré D. 
Published: December 2010

AbstractIn this paper, we define the notion of R*-LS category associated to an increasing system of subrings of ℚ and we relate it to the usual LS-category. We also relate it to the invariant introduced by Félix and Lemaire in tame homotopy theory, in which case we give a description in terms of Lie algebras and of cocommutative coalgebras, extending results of Lemaire-Sigrist and Félix-Halperin.
Compound Invariants and Mixed F-, DF-Power Spaces
Authors: Chalov P. A. , Terzioğlu T. , Zahariuta V. P. 
Published: December 2010

AbstractThe problems on isomorphic classification and quasiequivalence of bases are studied for the class of mixed F-, DF-power series spaces, i.e. the spaces of the following kind where ai (p, q) = exp((p - λiq)ai), p,q ∈ ℕ, and λ = (λi)i∈ℕ, a = (ai)i∈ℕ are some sequences of positive numbers. These spaces, up to isomorphisms, are basis subspaces of tensor products of power series spaces of F- and DF-types, respectively. The mrectangle characteristic of the space G(λ a) is defined as the number of members of the sequence (ïiÒ ai)i2N which are contained in the union of m rectangles Pk = (δk, εk] ✗ (τk, tk], k = 1, 2 , . . . , m. It is shown that each m-rectangle characteristic is an invariant on the considered class under some proper definition of an equivalency relation. The main tool are new compound invariants, which combine some version of the classical approximative dimensions (Kolmogorov, Pełczynski) with appropriate geometrical and interpolational operations under neighborhoods of the origin (taken from a given basis).
L’Invariant de Hasse-Witt de la Forme de Killing
Authors: Morales Jorge 
Published: December 2010

AbstractNous montrons que l’invariant de Hasse-Witt de la forme de Killing d’une algèbre de Lie semi-simple L s’exprime à l’aide de l’invariant de Tits de la représentation irréductible de L de poids dominant ρ = 1/2 (somme des racines positives), et des invariants associés au groupe des symétries du diagramme de Dynkin de L.
Values of the Dedekind Eta Function at Quadratic Irrationalities
Authors: van der Poorten Alfred , Williams Kenneth S. 
Published: December 2010

AbstractLet d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that b2 − 4ac = d, a > 0, gcd(a, b, c) = 1.The value of |η(b + √d)/2a)| is determined explicitly, where η(z) is Dedekind’s eta function
Asymptotic Formulae for the Lattice Point Enumerator
Authors: Betke U. , Böröczky K. 
Published: December 2010

AbstractLet M be a convex body such that the boundary has positive curvature. Then by a well developed theory dating back to Landau and Hlawka for large λ the number of lattice points in λM is given by G(λM) = V(λM) + O(λd−1−ε(d)) for some positive ε(d). Here we give for general convex bodies the weaker estimatewhere SZd (M) denotes the lattice surface area of M. The term SZd is optimal for all convex bodies and o(λd−1) cannot be improved in general. We prove that the same estimate even holds if we allow small deformations of M.Further we deal with families {Pλ} of convex bodies where the only condition is that the inradius tends to infinity. Here we havewhere the convex body K satisfies some simple condition, V(Pλ; K; 1) is some mixed volume and S(Pλ) is the surface area of Pλ.
Association Schemes for Ordered Orthogonal Arrays and (T, M, S)-Nets
Authors: Martin W. J. , Stinson D. R. 
Published: December 2010

AbstractIn an earlier paper [10], we studied a generalized Rao bound for ordered orthogonal arrays and (T, M, S)-nets. In this paper, we extend this to a coding-theoretic approach to ordered orthogonal arrays. Using a certain association scheme, we prove a MacWilliams-type theorem for linear ordered orthogonal arrays and linear ordered codes as well as a linear programming bound for the general case. We include some tables which compare this bound against two previously known bounds for ordered orthogonal arrays. Finally we show that, for even strength, the LP bound is always at least as strong as the generalized Rao bound.
Exceptional Moufang Quadrangles of Type F4
Authors: Mühlherr Bernhard , Van Maldeghem Hendrik 
Published: December 2010

AbstractIn this paper, we present a geometric construction of the Moufang quadrangles discovered by Richard Weiss (see Tits & Weiss [18] or Van Maldeghem [19]). The construction uses fixed point free involutions in certain mixed quadrangles, which are then extended to involutions of certain buildings of type F4. The fixed flags of each such involution constitute a generalized quadrangle. This way, not only the new exceptional quadrangles can be constructed, but also some special type of mixed quadrangles.
Homological Aspects of Semigroup Gradings on Rings and Algebras
Authors: Burgess W. D. , Saorín Manuel 
Published: December 2010

AbstractThis article studies algebras R over a simple artinian ring A, presented by a quiver and relations and graded by a semigroup Σ. Suitable semigroups often arise from a presentation of R. Throughout, the algebras need not be finite dimensional. The graded K0, along with the Σ-graded Cartan endomorphisms and Cartan matrices, is examined. It is used to study homological properties.A test is found for finiteness of the global dimension of a monomial algebra in terms of the invertibility of the Hilbert Σ-series in the associated path incidence ring.The rationality of the Σ-Euler characteristic, the Hilbert Σ-series and the Poincaré-Betti Σ-series is studied when Σ is torsion-free commutative and A is a division ring. These results are then applied to the classical series. Finally, we find new finite dimensional algebras for which the strong no loops conjecture holds.
Strong Converse Inequalities for Averages in Weighted Lp Spaces on [-1,1]
Authors: Felten M. 
Published: December 2010

AbstractAverages in weighted spaces defined by additions on [−1; 1] will be shown to satisfy strong converse inequalities of type A and B with appropriate K-functionals. Results for higher levels of smoothness are achieved by combinations of averages. This yields, in particular, strong converse inequalities of type D between K-functionals and suitable difference operators.
Stable Bi-Period Summation Formula and Transfer Factors
Authors: Flicker Yuval Z. 
Published: December 2010

AbstractThis paper starts by introducing a bi-periodic summation formula for automorphic forms on a group G(E), with periods by a subgroup G(F), where E/F is a quadratic extension of number fields. The split case, where E = F ⊕ F, is that of the standard trace formula. Then it introduces a notion of stable bi-conjugacy, and stabilizes the geometric side of the bi-period summation formula. Thus weighted sums in the stable bi-conjugacy class are expressed in terms of stable bi-orbital integrals. These stable integrals are on the same endoscopic groups H which occur in the case of standard conjugacy.The spectral side of the bi-period summation formula involves periods, namely integrals over the group of F-adele points of G, of cusp forms on the group of E-adele points on the group G. Our stabilization suggests that such cusp forms—with non vanishing periods—and the resulting bi-period distributions associated to “periodic” automorphic forms, are related to analogous bi-period distributions associated to “periodic” automorphic forms on the endoscopic symmetric spaces H(E)/H(F). This offers a sharpening of the theory of liftings, where periods play a key role.The stabilization depends on the “fundamental lemma”, which conjectures that the unit elements of the Hecke algebras on G and H have matching orbital integrals. Even in stating this conjecture, one needs to introduce a “transfer factor”. A generalization of the standard transfer factor to the bi-periodic case is introduced. The generalization depends on a new definition of the factors even in the standard case.Finally, the fundamental lemma is verified for SL(2).
Tensor Algebras, Induced Representations, and the Wold Decomposition
Authors: Muhly Paul S. , Solel Baruch 
Published: December 2010

AbstractOur objective in this sequel to [18] is to develop extensions, to representations of tensor algebras overC*-correspondences, of two fundamental facts about isometries on Hilbert space: The Wold decomposition theorem and Beurling’s theorem, and to apply these to the analysis of the invariant subspace structure of certain subalgebras of Cuntz-Krieger algebras.
An Upper Bound on the Least Inert Prime in a Real Quadratic Field
Authors: Granville Andrew , Mollin R. A. , Williams H. C. 
Published: December 2010

AbstractIt is shown by a combination of analytic and computational techniques that for any positive fundamental discriminant D > 3705, there is always at least one prime p < √D/2 such that the Kronecker symbol (D/p) = −1.
On the Maximum and Minimum Modulus of Rational Functions
Authors: Lubinsky D. S. 
Published: December 2010

AbstractWe show that if m, n ≥ 0, λ > 1, and R is a rational function with numerator, denominator of degree ≤ m, n, respectively, then there exists a set ⊂ [0, 1] of linear measure such that for r ∈ ,Here, one may not replace , for any ε > 0. As our motivating application, we prove a convergence result for diagonal Padé approximants for functions meromorphic in the unit ball.
Higher Order Scattering on Asymptotically Euclidean Manifolds
Authors: Christiansen T. J. , Joshi M. S. 
Published: December 2010

AbstractWe develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at timeπon the boundary. Furthermore, it is shown that onnthe asymptotics of certain short-range perturbations of Δkcan be recovered from the scattering matrix at a finite number of energies.
Perforated Ordered K0-Groups
Authors: Elliott George A. , Villadsen Jesper 
Published: December 2010

AbstractA simple C*-algebra is constructed for which theMurray-von Neumann equivalence classes of projections, with the usual addition—induced by addition of orthogonal projections—form the additive semigroup{0, 2, 3, . . .}.(This is a particularly simple instance of the phenomenon of perforation of the ordered K0-group, which has long been known in the commutative case—for instance, in the case of the four-sphere—and was recently observed by the second author in the case of a simple C*-algebra.)
The Equivariant Grothendieck Groups of the Russell-Koras Threefolds
Authors: Bell J. P. 
Published: December 2010

AbstractThe Russell-Koras contractible threefolds are the smooth affine threefolds having a hyperbolic *-action with quotient isomorphic to the corresponding quotient of the linear action on the tangent space at the unique fixed point. Koras and Russell gave a concrete description of all such threefolds and determined many interesting properties they possess. We use this description and these properties to compute the equivariant Grothendieck groups of these threefolds. In addition, we give certain equivariant invariants of these rings.
Ext and OrderExt Classes of Certain Automorphisms of C*-Algebras Arising from Cantor Minimal Systems
Authors: Matui Hiroki 
Published: December 2010

AbstractGiordano, Putnam and Skau showed that the transformation group C*-algebra arising from a Cantor minimal system is an AT-algebra, and classified it by its K-theory. For approximately inner automorphisms that preserve C(X), we will determine their classes in the Ext and OrderExt groups, and introduce a new invariant for the closure of the topological full group. We will also prove that every automorphism in the kernel of the homomorphism into the Ext group is homotopic to an inner automorphism, which extends Kishimoto’s result.