bluuebunny/crossref_metadata_2025 huggingface dataset:
q-Hermite Polynomials and Classical Orthogonal Polynomials
Authors: Berg Christian , Ismail Mourad E. H.
Published: December 2010

We use generating functions to express orthogonality relations in the form of q-beta. integrals. The integrand of such a q-beta. integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegö and leads naturally to the Al-Salam-Chihara polynomials then to the Askey-Wilson polynomials, the big q-Jacobi polynomials and the biorthogonal rational functions of Al-Salam and Verma, and some recent biorthogonal functions of Al-Salam and Ismail.
Bergman Spaces on Disconnected Domains
Authors: Aleman Alexandru , Richter Stefan , Ross William T.
Published: December 2010

For a bounded region G ⊂ ℂ and a compact set K ⊂ G, with area measure zero, we will characterize the invariant subspaces ℳ (under ƒ → zƒ) of the Bergman space (G \ K), 1 ≤ p < ∞, which contain (G) and with dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K. When G \ K is connected, we will see that dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K and thus in this case we will have a complete description of the invariant subspaces lying between (G) and (G \ K). When p = ∞, we will remark on the structure of the weak-star closed z-invariant subspaces between H∞(G) and H∞(G \ K). When G \ K is not connected, we will show that in general the invariant subspaces between (G) and (G \ K) are fantastically complicated. As an application of these results, we will remark on the complexity of the invariant subspaces (under ƒ → ζƒ) of certain Besov spaces on K. In particular, we shall see that in the harmonic Dirichlet space , there are invariant subspaces ℱ such that the dimension of ζℱ in ℱ is infinite.
A Priori Estimates for Some Classes of Difference Schemes
Authors: Bakaev Nikolai
Published: December 2010

A new approach to the analysis of the well-posedness of difference parabolic problems is proposed, which is based on weaker assumptions than in earlier works. The results are applied to the study of multi-dimensional difference parabolic problems in mesh Lebesgue spaces.
Acyclic Models
Authors: Barr Michael
Published: December 2010

Acyclic models is a powerful technique in algebraic topology and homological algebra in which facts about homology theories are verified by first verifying them on "models" (on which the homology theory is trivial) and then showing that there are enough models to present arbitrary objects. One version of the theorem allows one to conclude that two chain complex functors are naturally homotopic and another that two such functors are object-wise homologous. Neither is entirely satisfactory. The purpose of this paper is to provide a uniform account of these two, fixing what is unsatisfactory and also finding intermediate forms of the theorem.
Bounded Pointwise Approximation of Solutions of Elliptic Equations
Authors: Bonilla A. , Trujillo-González
Published: December 2010

We characterize open subsets U of ℝN in which the bounded solutions of certain elliptic equations can be approximated pointwise by uniformly bounded solutions that are continuous in Ū. This result is established in terms of certain capacities. For closed subsets X, this characterization allows us to approximate bounded solutions in X° uniformly on relatively closed subsets of X° by solutions continuous on certain subsets of the boundary of X.
Generators of Ideals Defining Certain Surfaces in Projective Space
Authors: Holay Sandeep H.
Published: December 2010

We consider the surface obtained from the projective plane by blowing up the points of intersection of two plane curves meeting transversely. We find minimal generating sets of the defining ideals of these surfaces embedded in projective space by the sections of a very ample divisor class. All of the results are proven over an algebraically closed field of arbitrary characteristic.
Rings With Finite Maximal Invariant Subrings
Authors: Lanski Charles
Published: December 2010

We prove that if φ is an (anti-) automorphism of a ringRwith finite orbits onR, or integral over the integers, and ifRcontains a finite maximal φ-invariant subring, thenRmust be finite. Special cases are when φ has finite order or is an involution. Two corollaries are thatRmust be finite whenRcontains only finitely many φ-invariant subrings or has both ascending and descending chain conditions on φ invariant subrings. These generalize results in the literature for the special case when φ = idR.
Reconstruction of Entire Functions From Irregularly Spaced Sample Points
Authors: Grozev Georgi R. , Rahman Qazi I.
Published: December 2010

Let where {λn}n ∈ Ζ is a sequence of real numbers such that |λn — n| ≤ Δ for some Δ > 0 and all n ∈ ℤ . Extending an obvious property of sin πz to which the function G reduces when Δ = 0 we show that is bounded by a constant independent of n. The result is then applied to a problem concerning derivative sampling in one and several variables.
Positive-Defininte Functions on Free Semigroups
Authors: Popescu Gelu
Published: December 2010

An extension of the Naimark dilation theorem [N], [SzF2] to positive-definite functions on free semigroups is given. This is used to extend the operatorial trigonometric moment problem [A] to a non-commutative setting and to characterize the classes 𝐶ρ (ρ > 0) of all n-tuples of operators that have a p-isometric dilation (see [SzF2] for the case n = 1). It is also shown that 𝐶ρ ⊂ 𝐶ρ′ and 𝐶ρ ≠ 𝐶ρ′ for 0 < ρ < ρ′ < ∞.

The von Neumann inequality [vN], [Po2] is extended to the classes 𝐶p. This is used to prove that any element in 𝐶ρ is simultaneously similar to an element in 𝐶1.
Homological Duality and Quasi-Heredity
Authors: Ágoston István , Dlab Vlastimil , Lukács Erzsébet
Published: December 2010

This paper represents a general study of the (Yoneda) Ext-algebra A* of a finite dimensional K-algebra A. Our motivation lies in the problem of establishing conditions under which (i) the species of A* coincides with the dual species of A and (ii) the quasi-heredity of A (or A*) yields the quasi-heredity of A* (or A, respectively). These questions are closely related to the Kazhdan—Lusztig Theory as presented by [CPS2]. The main results include introducing the concept of a solid algebra and the relevant Theorem 4.5 as well as a rather complete description of the situation in the case of monomial algebras in Section 5.
Nonabelian Fully-Ramified Sections
Authors: Lewis Mark L.
Published: December 2010

Let G be a finite group and let K and L be normal subgroups of G such that |K : L| and |G : K| are relatively prime, and assume that |K : L| is odd. Let H be a subgroup of G such that G = HK and H ∩ K = L. Let φ be an irreducible character of L that is invariant under the action of L and is fully ramified with respect to K/L. If χ ∈ Irr(G) is a constituent of φG, then we prove that χH has a unique irreducible constituent having odd multiplicity.
The Modular Group Algebra Problem for Small p-Groups Of Maximal Class
Authors: Salim Mohamed A. M. , Sandling Robert
Published: December 2010

We show that p-groups of maximal class and order p5 are determined by their group algebras over the field of p elements. The most important information requisite for the proof is obtained from a detailed study of the unit group of a quotient algebra of the group algebra, larger than the small group algebra.
Sweeping Out Properties of Operator Sequences
Authors: Akcoglu Mustafa A. , Ha Dzung M. , Jones Roger L.
Published: December 2010

Let Lp = Lp(X, μ), 1 ≤ p ≤ ∞, be the usual Banach Spaces of real valued functions on a complete non-atomic probability space. Let (T1, . . . ,TK) be L2-contractions. Let 0 < ε < δ ≤ 1. Call a function f a δ-spanning function if ‖f‖2 = 1 and if ‖Tkf - Qk-1Tkf‖2 ≥ δ for each k = 1, . . . ,K, where Q0 = 0 and Qk is the orthogonal projection on the subspace spanned by (T1f , . . . ,Tkf). Call a function h a (δ, ε) -sweeping function if ‖h‖∞ ≤ 1, ‖h‖1 < ε, and if max1≤k≤K|Tkh| > δ-ε on a set of measure greater than 1 - ε. The following is the main technical result, which is obtained by elementary estimates. There is an integer K = K(δ, ε) ≥ 1 such that if f is a δ-spanning function, and if the joint distribution of (f , T1f , . . . ,TKf) is normal, then h = ((fΛM)Ꮩ(-M)/M is a (δ, ε)-sweeping function, for some M > 0. Furthermore, if Tks are the averages of operators induced by the iterates of ameasure preserving ergodic transformation, then a similar result is true without requiring that the joint distribution is normal. This gives the following theorem on a sequence (Ti) of these averages.Assume that for each K ≤ 1 there is a subsequence (Ti1 , . . . ,Tik) of length K, and a δ-spanning function fK for this subsequence. Then for each ε > 0 there is a function h, 0 ≥ h ≥ 1, ‖h‖1 < ε, such that lim supi Tih ≤ δ a.e.. Another application of the main result gives a refinement of a part of Bourgain’s “Entropy Theorem”, resulting in a different, self contained proof of that theorem.
Normal Functions: Lp Estimates
Authors: Chen Huaihui , Gauthier Paul M.
Published: December 2010

For 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.
Exterior Powers of the Adjoint Representation
Authors: Reeder Mark
Published: December 2010

Exterior powers of the adjoint representation of a complex semisimple Lie algebra are decomposed into irreducible representations, to varying degrees of satisfaction.
Spectral Theory for the Neumann Laplacian on Planar Domains With Horn-Like Ends
Authors: Edward Julian
Published: December 2010

The 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

Symplectic 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

A 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

In 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.
Gorenstein Witt Rings II
Authors: Fitzgerald Robert W.
Published: December 2010

The abstract Witt rings which are Gorenstein have been classified when the dimension is one and the classification problem for those of dimension zero has been reduced to the case of socle degree three. Here we classify the Gorenstein Witt rings of fields with dimension zero and socle degree three. They are of elementary type.
Classical Orthogonal Polynomials as Moments
Authors: Ismail Mourad E. H. , Stanton Dennis
Published: December 2010

We 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

In 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.
Geodesic Flow on Ideal Polyhedra
Authors: Charitos Charalambos , Tsapogas Georgios
Published: December 2010

In this work we study the geodesic flow on n-dimensional ideal polyhedra and establish classical (for manifolds of negative curvature) results concerning the distribution of closed orbits of the flow.
Sur L'Intégrabilité des Sous–Algèbres de lie en Dimension Infinie
Authors: Robart Thierry
Published: December 2010

Une 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.
Non-Hermitian Solutions of Algebraic Riccati Equations
Authors: Rodman Leiba
Published: December 2010

Non-hermitian solutions of algebraic matrix Riccati equations (of the continuous and discrete types) are studied. Existence is proved of non-hermitian solutions with given upper bounds of the ranks of the skew-hermitian parts, under the sign controllability hypothesis.
Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity
Authors: Shibata Tetsutaro
Published: December 2010

We consider the multiparameter nonlinear Sturm-Liouville problem

where are parameters. We assume that

1 ≤ 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

Pieri’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

The 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

Generalizing 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

In 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

Lie 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

The 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

In 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

We 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

We 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

In 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

The 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).
Totally Real Rigid Elements and Galois Theory
Authors: Engler Antonio José
Published: December 2010

Abelian closed subgroups of the Galois group of the pythagorean closure of a formally real field are described by means of the inertia group of suitable valuation rings.
L’Invariant de Hasse-Witt de la Forme de Killing
Authors: Morales Jorge
Published: December 2010

Nous 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

Let 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

Let 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 estimate

where 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 have

where 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

In 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

In 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.
Uniqueness for a Competing Species Model
Authors: Mytnik Leonid
Published: December 2010

We show that a martingale problem associated with a competing species model has a unique solution. The proof of uniqueness of the solution for the martingale problem is based on duality technique. It requires the construction of dual probability measures.
Homological Aspects of Semigroup Gradings on Rings and Algebras
Authors: Burgess W. D. , Saorín Manuel
Published: December 2010

This 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

Averages 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

This 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

Our 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.
Subregular Nilpotent Elements and Bases in K-Theory
Authors: Lusztig G.
Published: December 2010

In this paper we describe a canonical basis for the equivariant K-theory (with respect to a C*-action) of the variety of Borel subalgebras containing a subregular nilpotent element of a simple complex Lie algebra of type D or E.
Realizations of Regular Toroidal Maps
Authors: Monson B. , Weiss A. Ivić
Published: December 2010

We determine and completely describe all pure realizations of the finite regular toroidal polyhedra of types {3, 6} and {6, 3}.
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

It 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

We 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

We 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

A 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

The 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.
On a Product Related to the Cubic Gauss Sum, III
Authors: Ito Hiroshi
Published: December 2010

We have seen, in the previous works [5], [6], that the argument of a certain product is closely connected to that of the cubic Gauss sum. Here the absolute value of the product will be investigated.
Ext and OrderExt Classes of Certain Automorphisms of C*-Algebras Arising from Cantor Minimal Systems
Authors: Matui Hiroki
Published: December 2010

Giordano, 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.
Building a Stationary Stochastic Process From a Finite-Dimensional Marginal
Authors: Pivato Marcus
Published: December 2010

Ifis a finite alphabet,, andis a probability measure onthat “looks like” the marginal projection of a stationary stochastic process on, then can we “extend”to such a process? Under what conditions can we make this extension ergodic, (quasi)periodic, or (weakly) mixing? After surveying classical work on this problem when D = 1, we provide some sufficient conditions and some necessary conditions forto be extendible for D > 1, and show that, in general, the problem is not formally decidable.
Hyperbolic Polynomials and Convex Analysis
Authors: Bauschke Heinz H. , Güler Osman , Lewis Adrian S. , Sendov Hristo S.
Published: December 2010

A homogeneous real polynomialpishyperbolicwith respect to a given vector d if the univariate polynomial t ⟼ p(x − td) has all real roots for all vectorsx. Motivated by partial differential equations, Gårding proved in 1951 that the largest such root is a convex function ofx, and showed various ways of constructing new hyperbolic polynomials. We present a powerful new such construction, and use it to generalize Gårding’s result to arbitrary symmetric functions of the roots. Many classical and recent inequalities follow easily. We develop various convex-analytic tools for such symmetric functions, of interest in interior-point methods for optimization problems over related cones.
Correction to: Upper Bounds for the Resonance Counting Function of Schrödinger Operators in Odd Dimensions
Authors: Froese Richard
Published: December 2010

The proof of Lemma 3.4 in [F] relies on the incorrect equality μj(AB) = μj(BA) for singular values (for a counterexample, see [S, p. 4]). Thus, Theorem 3.1 as stated has not been proven. However, with minor changes, we can obtain a bound for the counting function in terms of the growth of the Fourier transform of |V|.
Decompositions of the Hilbert Function of a Set of Points in ℙn
Authors: Geramita Anthony V. , Harima Tadahito , Shin Yong Su
Published: December 2010

Let H be the Hilbert function of some set of distinct points in ℙn and let α = α(H) be the least degree of a hypersurface of ℙn containing these points. Write α = ds + ds–1 + … + d1 (where di > 0). We canonically decompose H into s other Hilbert functions and show how to find sets of distinct points , lying on reduced hypersurfaces of degrees ds, …, d1 (respectively) such that the Hilbert function of is and the Hilbert function of is H. Some extremal properties of this canonical decomposition are also explored.
Classification of Certain SimpleC*-Algebras with Torsion inK1
Authors: Mygind Jesper
Published: December 2010

We show that the Elliott invariant is a classifying invariant for the class of${{C}^{*}}$-algebras that are simple unital infinite dimensional inductive limits of finite direct sums of building blocks of the form

$$\left\{ f\in C\left( \mathbb{T} \right)\otimes {{M}_{n}}:f\left( {{x}_{i}} \right)\in {{M}_{{{d}_{i}}}},i=1,2,...,N \right\},$$

where${{x}_{1}},\,{{x}_{2.}},...,{{x}_{N\,}}\in \mathbb{T},{{d}_{1}},{{d}_{2}},.\,.\,.,{{d}_{N}}$are integers dividing$n$, and${{M}_{{{d}_{i}}}}$is embedded unitally into${{M}_{n}}$. Furthermore we prove existence and uniqueness theorems for$*$-homomorphisms between such algebras and we identify the range of the invariant.
Small Prime Solutions of Quadratic Equations
Authors: Choi Kwok-Kwong Stephen , Liu Jianya
Published: December 2010

Let b1,…,b5 be non-zero integers and n any integer. Suppose that b1 + … + b5 ≡ n (mod 24) and (bi, bj) = 1 for 1 ≤ i < j ≤ 5. In this paper we prove that

(i)

if all bj are positive and , then the quadratic equation is soluble in primes pj, and

(ii)

if bj are not all of the same sign, then the above quadratic equation has prime solutions satisfying .
Intégrales orbitales pondérées sur les algèbres de Lie : le cas p-adique
Authors: Chaudouard Pierre-Henri
Published: December 2010

Soit G un groupe réductif connexe défini sur un corps p-adique F et son algèbre de Lie. Les intégrales orbitales pondérées sur (F) sont des distributions JM(X, f)—f est une fonction test— indexées par les sous-groupes de Lévi M de G et les éléments semi-simples réguliers . Leurs analogues sur G sont les principales composantes du côté géométrique des formules des traces locale et globale d’Arthur.

Si M = G, on retrouve les intégrales orbitales invariantes qui, vues comme fonction de X, sont borńees sur : c’est un résultat bien connu de Harish-Chandra. Si M ⊊ G, les intégrales orbitales pondérées explosent au voisinage des éléments singuliers. Nous construisons dans cet article de nouvelles intégrales orbitales pondérées (X, f), égales à JM(X, f) à un terme correctif près, qui tout en conservant les principales propriétés des précédentes (comportement par conjugaison, développement en germes, etc.) restent borńees quand X parcourt . Nous montrons également que les intégrales orbitales pondérées globales, associées à des éléments semi-simples réguliers, se décomposent en produits de ces nouvelles intégrales locales.
Framed Stratified Sets in Morse Theory
Authors: Lebel André
Published: December 2010

In this paper, we present a smooth framework for some aspects of the “geometry of CW complexes”, in the sense of Buoncristiano, Rourke and Sanderson [3]. We then apply these ideas to Morse theory, in order to generalize results of Franks [5] and Iriye-Kono [8].

More precisely, consider a Morse function f on a closed manifold M. We investigate the relations between the attaching maps in a CW complex determined by f, and the moduli spaces of gradient flow lines of f, with respect to some Riemannian metric on M.
Mahler’s Measure and the Dilogarithm (I)
Authors: Boyd David W. , Rodriguez-Villegas Fernando
Published: December 2010

An explicit formula is derived for the logarithmicMahler measurem(P) of P(x, y) = p(x)y− q(x), where p(x) and q(x) are cyclotomic. This is used to find many examples of such polynomials for which m(P) is rationally related to the Dedekind zeta value ζF(2) for certain quadratic and quartic fields.
On the Lusternik-Schnirelmann Category of Maps
Authors: Stanley Donald
Published: December 2010

We give conditions which determine if cat of a map go up when extending over a cofibre. We apply this to reprove a result of Roitberg giving an example of a CW complex Z such that cat(Z) = 2 but every skeleton of Z is of category 1. We also find conditions when cat(f × g) < cat(f) + cat(g). We apply our result to show that under suitable conditions for rational maps f, mcat(f) < cat(f) is equivalent to cat(f) = cat(f × idSn). Many examples with mcat(f) < cat(f) satisfying our conditions are constructed. We also answer a question of Iwase by constructing p-local spaces X such that cat(X × S1) = cat(X) = 2. In fact for our spaces and every Y ≄ *, cat(X × Y) ≤ cat(Y) + 1 < cat(Y) + cat(X). We show that this same X has the property cat(X) = cat(X × X) = cl(X × X) = 2.
Strongly Projective Graphs
Authors: Larose Benoit
Published: December 2010

We introduce the notion of strongly projective graph, and characterise these graphs in terms of their neighbourhood poset. We describe certain exponential graphs associated to complete graphs and odd cycles. We extend and generalise a result of Greenwell and Lovász [6]: if a connected graph G does not admit a homomorphism to K, where K is an odd cycle or a complete graph on at least 3 vertices, then the graph G × Ks admits, up to automorphisms of K, exactly s homomorphisms to K.
On Graded Categorical Groups and Equivariant Group Extensions
Authors: Cegarra A. M. , Garćia-Calcines J. M. , Ortega J. A.
Published: December 2010

In this article we state and prove precise theorems on the homotopy classification of graded categorical groups and their homomorphisms. The results use equivariant group cohomology, and they are applied to show a treatment of the general equivariant group extension problem.
Fully Nonlinear Elliptic Equations on General Domains
Authors: Bao Jiguang
Published: December 2010

By means of the Pucci operator, we construct a function u0, which plays an essential role in our considerations, and give the existence and regularity theorems for the bounded viscosity solutions of the generalized Dirichlet problems of second order fully nonlinear elliptic equations on the general bounded domains, which may be irregular. The approximation method, the accretive operator technique and the Caffarelli's perturbation theory are used.
An Exactly Solved Model for Mutation, Recombination and Selection
Authors: Baake Michael , Baake Ellen
Published: December 2010

It is well known that rather generalmutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of the state space one started from.

Here, we present a relevant subclass of such models, in continuous time, with independent mutation events at the sites, and crossover events between them. It admits a closed solution of the corresponding differential equation on the basis of the original state space, and also closed expressions for the linkage disequilibria, derived by means of Möbius inversion. As an extra benefit, the approach can be extended to a model with selection of additive type across sites. We also derive a necessary and sufficient criterion for the mean fitness to be a Lyapunov function and determine the asymptotic behaviour of the solutions.
Higher Order Tangents to Analytic Varieties along Curves
Authors: Braun Rüdiger W. , Meise Reinhold , Taylor B. A.
Published: December 2010

Let V be an analytic variety in some open set in which contains the origin and which is purely k-dimensional. For a curve γ in , defined by a convergent Puiseux series and satisfying γ(0) = 0, and d ≥ 1, define Vt := t−d(V − (t)). Then the currents defined by Vt converge to a limit current Tγ,d[V] as t tends to zero. Tγ,d[V] is either zero or its support is an algebraic variety of pure dimension k in . Properties of such limit currents and examples are presented. These results will be applied in a forthcoming paper to derive necessary conditions for varieties satisfying the local Phragmén-Lindelöf condition that was used by Hörmander to characterize the constant coefficient partial differential operators which act surjectively on the space of all real analytic functions on .
On the Nonsquare Constants of Orlicz Spaces with Orlicz Norm
Authors: Yan Yaqiang
Published: December 2010

Let lΦ and LΦ(Ω) be the Orlicz sequence space and function space generated by N-function Φ(u) with Orlicz norm. We give equivalent expressions for the nonsquare constants CJ(lΦ), CJ(LΦ(Ω)) in sense of James and CS(lΦ), CS(LΦ(Ω)) in sense of Schäffer. We are devoted to get practical computational formulas giving estimates of these constants and to obtain their exact value in a class of spaces lΦ and LΦ(Ω).
Infinitely Divisible Laws Associated with Hyperbolic Functions
Authors: Pitman Jim , Yor Marc
Published: December 2010

The infinitely divisible distributions onof random variablesCt,StandTtwith Laplace transforms

respectively are characterized for various t > 0 in a number of different ways: by simple relations between their moments and cumulants, by corresponding relations between the distributions and their Lévy measures, by recursions for their Mellin transforms, and by differential equations satisfied by their Laplace transforms. Some of these results are interpreted probabilistically via known appearances of these distributions for t = 1 or 2 in the description of the laws of various functionals of Brownian motion and Bessel processes, such as the heights and lengths of excursions of a one-dimensional Brownian motion. The distributions ofC1andS2are also known to appear in the Mellin representations of two important functions in analytic number theory, the Riemann zeta function and the Dirichlet L-function associated with the quadratic character modulo 4. Related families of infinitely divisible laws, including the gamma, logistic and generalized hyperbolic secant distributions, are derived fromStandCtby operations such as Brownian subordination, exponential tilting, and weak limits, and characterized in various ways.