Property (β) implies normal structure of the dual space

We prove that property (β) of Rolewicz implies normal structure of the dual space and we characterize spaces which are duals of spaces with property (β). Research of the second author was supported in part by the M.U.R.S.T. of Italy.     

Hölder mappings of Carnot groups and intrinsic bases

For classes of Hölder mappings of Carnot groups and the corresponding graph mappings, a method for constructing intrinsic bases is described, which makes it possible to push forward the Hausdorff dimension of preimages to images.     

Gröbner bases and triangulations of the second hypersimplex

The algebraic technique of Gröbner bases is applied to study triangulations of the second hypersimplex (2,n). We present a quadratic Gröbner basis for the associated toric idealK(K _n ). The simplices in the resulting triangulation of (2,n) have unit volume, and they are indexed by subgraphs which are linear thrackles [28] with respect to a circular embedding ofK _n . Forn6 the number of distinct initial ideals ofI(K _n ) exceeds the number of regular triangulations of (2,n); more precisely, the secondary polytope of (2,n) equals the state polytope ofI(K _n ) forn5 but not forn6. We also construct a non-regular triangulation of (2,n) forn9. We determine an explicit universal Gröbner basis ofI(K _n ) forn8. Potential applications in combinatorial optimization and random generation of graphs are indicated.Research partially supported by a doctoral fellowship of the National University of Mexico, the National Science Foundation, the David and Lucile Packard Foundation and the U.S. Army Research Office (through ACSyAM/MSI, Cornell).     

Universal and comprehensive Gröbner bases of the classical determinantal ideal

Let A =(x _ij ), i =1,2,... ,k, j =1,2,... ,l, 1 ≤ k ≤ l, be a matrix of independent variables, G be the set of maximal minors of A, and I = (G) be the classical determinantal ideal. We show that G is a universal Gr?bner basis of I. Also, a sufficient condition for G to be a universal comprehensive Gr?bner basis is proved. Bibliography: 12 titles.     

Graded cellular bases for Temperley–Lieb algebras of type A and B

We show that the Temperley–Lieb algebra of type A and the blob algebra (also known as the Temperley–Lieb algebra of type B) at roots of unity are \(\mathbb{Z}\) -graded algebras. We moreover show that they are graded cellular algebras, thus making their cell modules, or standard modules, graded modules for the algebras.     

Equality of Schur’s Q-functions and Their Skew Analogues

We find a simple criterion for the equality Q _λ = Q _μ/v where Q _λ and Q _μ/v are Schur’s Q-functions on infinitely many variables. Received February 8, 2006     

A Further Study of the System of Matrix Equations over a Skew Field

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On the complexity of the surrogate dual of 0–1 programming

It is shown that the surrogate dual of a 0–1 programming problem can be solved by 0(m ³) knapsack calls, ifm denotes the number of constraints.

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Zusammenfassung Es wird gezeigt, daß das surrogate duale Problem zu einer linearen Optimierungsaufgabe mit binären Variablen durch 0(m ³) Rucksackprobleme gelöst werden kann. Dabei bezeichnetm die Anzahl der Nebenbedingungen.

     

On the dual nature of partial theta functions and Appell–Lerch sums

In recent work, Hickerson and the author demonstrated that it is useful to think of Appell–Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving Appell–Lerch sums. In this sense, Appell–Lerch sums and partial theta functions appear to be dual to each other. This duality theory is not unlike that found by Andrews between various sets of identities of Rogers–Ramanujan type with respect to Baxter's solution to the hard hexagon model of statistical mechanics. As an application we construct bilateral q-series with mixed mock modular behaviour. In subsequent work we see that our bilateral series are well-suited for computing radial limits of Ramanujan's mock theta functions.     

On the existence and the uniqueness of the solution of a fluid–structure interaction scattering problem

The existence and uniqueness of the solution of a fluid–structure interaction problem is investigated. The proposed analysis distinguishes itself from previous studies by employing a weighted Sobolev space framework, the DtN operator properties, and the Fredholm theory. The proposed approach allows to extend the range of validity of the standard existence and uniqueness results to the case where the elastic scatterer is assumed to be only Lipschitz continuous, which is of more practical interest.     

Bézier form of dual bivariate Bernstein polynomials

Dual Bernstein polynomials of one or two variables have proved to be very useful in obtaining Bézier form of the L ₂-solution of the problem of best polynomial approximation of Bézier curve or surface. In this connection, the Bézier coefficients of dual Bernstein polynomials are to be evaluated at a reasonable cost. In this paper, a set of recurrence relations satisfied by the Bézier coefficients of dual bivariate Bernstein polynomials is derived and an efficient algorithm for evaluation of these coefficients is proposed. Applications of this result to some approximation problems of Computer Aided Geometric Design (CAGD) are discussed.     

Interpolating Blaschke products and the ideals of the algebra H∂

To each vector-function f, f H(Z²) one can associate two ideals of the algebra. In the note one characterizes those functions f for which some interpolation Blaschke product is contained in I(f) (or J (f)). One also characterizes those functions u, u H such that if for some f, then u I(f) (in the corona theorem a similar statement is proved for the case u =1).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 196–201, 1983.     

Bijectivity of -endomorphisms of ℬ(H) and the unilateral shift

LetH be a separable infinite-dimensional complex Hilbert space. We prove that if : (H)(H) is a^*-preserving ring homomorphism whose range contains a rank-one operator and an operator with dense range, then is an isometric linear or conjugate-linear algebra automorphism of (H). In particular, if the unilateral shift is contained in the range of a^*-endomorphism of (H), then is bijective.Research partially supported by the Hungarian National Research Science Foundation, Operating Grant Number OTKA 1652 and K&H Bank Ltd., Universitas Foundation.     

The structure of Banach algebras of bounded continuous functions on the open disk that contain H∞, the Hoffman algebra,and nontangential limits

LetH _B ^G be an algebra of bounded continuous functions on an open disk representable in the formH _B G, where andH _B is a closed subalgebra in C(D) consisting of the functions that have nontangential limits almost everywhere on {ie1023-06}, and these limits belong to the Douglas algebraB. In this paper we describe the spaceM(H _B ^G ) of maximal ideals of the algebraH _B ^G and prove thatM(H _B ^G ) =M(B) M(H _B ^G and prove thatM(H ₀ ^G ), whereH ₀ ^G is a closed ideal inG consisting of functions having nontangential limits equal to zero almost everywhere on {ie1023-12}. Moreover, it is established that on the disk. The Chang-Marshall theorem is generalized for the Banach algebrasH _B ^G . We also prove that for any Douglas algebraB, whereI B = {u } _B are inner functions such that on.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 924–931, July, 1993.