The automorphism group of the Toeplitz algebra onH2(T2)

The automorphism group of the C^* -algebra generated by the Toeplitz operatos with symbols being continuous functions on the bicircle is characterized completely. The investigation is based on the analysis of the behaviour of an automorphism of the Toeplitz algebra on itsC* -ideal chains, and the state of the closed ideals in .     

Numerical evaluation of a 2-D Cauchy principal value integral based on quasi-interpolating splines

In this paper the author presents a method for the numerical solution of a 2-D Cauchy principal value of the form where S is a domain with a continuous boundary. By using polar coordinates, the integral is reduced to the form where the finite-part of the integral. We construct the relative product rule based on quasi-inter polating splines. Convergence results are proved and numerical examples are given.     

Bayes and empirical Bayes iteration estimators in two seemingly unrelated regression equations

For a system of two seemingly unrelated regression equations given by (?)(y_1 is an m×1 vector and y_2 is an n×1 vector,m≠n),employ- ing the covariance adjusted technique,we propose the parametric Bayes and empirical Bayes iteration estimator sequences for regression coefficients.We prove that both the covariance matrices converge monotonically and the Bayes iteration estimator squence is consistent as well.Based on the mean square error (MSE) criterion,we elaborate the su- periority of empirical Bayes iteration estimator over the Bayes estimator of single equation when the covariance matrix of errors is unknown.The results obtained in this paper further show the power of the covariance adiusted approach.     

Una dimostrazione del fatto che ogni varietà ammette algebre semplici

Riassunto Si dimostra che se è una struttura algebrica priva di quozienti semplici, allora un’opportuna sottoalgebra di ammette quozienti semplici. Ne segue il risultato del titolo.

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Summary Let be an algebraic structure with no simple quotients. Then there is a subalgebra of which possess simple quotients. Therefore every variety of algebras (=algebraic structures) has simple algebras.

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Lavoro eseguito nell’ambito dell’attività del Comitato Nazionale per le Scienze Matematiche del C.N.R. (anno ’68–’69, programma 8).     

Sistemi di assiomi che definiscono un piano affine di ordinen

Riassunto Un insieme di proprietà soddisfatte da una struttura è detto essere un sistema completo di assiomi se è sufficiente a definire come un piano affine. Un sistema completo è minimo se non possiede alcun sottosistema proprio completo. In questo lavoro sono determinati i possibili sistemi minimi completi di assiomi che definiscono un piano affine di ordinen.

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Summary A set of properties which are satisfied by an incidence structure is said to be a complete system of axioms if such a system is sufficient to define as an affine plane. A complete system is minimal if it does not possess any proper complete subsystem. In this work we find all possible minimal complete systems of axioms which define an affine plane of ordern.

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Lavoro eseguito nell’ambito dell’attività dei contratti di ricerca del Comitato per le Scienze Matematiche del C.N.R.     

Symmetric centres of braided monoidal categories

This paper introduces the concept of ‘symmetric centres’ of braided monoidal categories. LetH be a Hopf algebra with bijective antipode over a fieldk. We address the symmetric centre of the Yetter-Drinfel’d module category: and show that a left Yetter-Drinfel’d moduleM belongs to the symmetric centre of and only ifM is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give a sufficient and necessary condition for the braid of, _Hℳ to induce the braid of , or equivalently, the braid of , whereA is a quantum commutativeH-module algebra     

Weak type inequalities for fractional maximal operator on weighted orlicz spaces

The fractional maximal operator on homogeneous space (X, d, μ) is de fined as . In this paper, the sufficient and necessary conditions for the to be of weak type and extra weak type will be given. In Memory of Professor M. T. Cheng     

Sull’unione di classi filtrali

Riassunto In questo lavoro si cercano condizioni perchè una classe di algebre simili filtrali sia essa stessa filtrale. Si trova che se è una famiglia finita di algebre simili e filtrali, che siano indipendenti (cfr.A. L. Foster [2]), allora anche è filtrale. Introdotto poi il concetto disemi-indipendenza, si arriva a un risultato analogo per le algebre semifiltrali e a una condizione sufficiente per la semifiltralità di un'algebra finita. Infine si osserva che i risultati trovati possono essere estesi alle classi ideali.

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Summary This paper refers to the concept offiltrale class of similar algebras, which has been introduced byR. Magari in [6]. First I observe that a class of similarfiltrale algebras is not generallyfiltrale, not even if is a finite family of finite algebras. However I find that if is a finite family of similarfiltrale algebras, which are also independent (using this term in the sense ofA. L. Foster [2]), then also isfiltrale. Then introducing the notion of independent varieties, one arrives at a generalization of the above mentioned result. Given then a family of similar algebras , we say that these aresemi-indipendenti if for everyJ⊂I there exists an algebraic functionf _J defined in II _i so thatf _J(x, y)=z wherez _i=x_i ifi∈J andz _i=y_i ifi∉J for every . I prove that if is a finite family ofsemifiltrali andsemi-indipendenti algebras, then also issemifiltrale. I also find that a finite algebra, which is simple andsemi-indipendente of itself (in the sense that there exists in a binary algebraic functionf withf(x, y)=<x ₀,y ₁>) issemifiltrale. Then I give the notion ofsemi-indipendente variety, which leads to some further results. Finally I observe that all these results can be extended to ideal classes of similar algebras.

     

μ-average N-widths on the Wiener space

In this paper we investigate the asymptotic behaviour of μ-averagen-widths of integral operatorK on the Wiener space, whereK is the inverse operator of an ordinary linear differential operatorL of orderm. For 1≤p.q<∞ . and forp∈[1, ∞),q∈[2, ∞) . Supported by the Fund. of Dooctoral program of NECC.     

Intersections of curve systems and the crossing number ofC 5 ×C 5

It and are two families of pairwise disjoint simple closed curves in the plane such that each curve in intersects each curve in , then the total number of points of intersection in is at least 2(m−1)n, where , and this bound is best possible. We use this to show that the cartesian product of two 5-cycles has crossing number 15.     

The convergence rate of Euler means sequence

Let denote the Euler means of the Fourier series of the 2π-perodic function f(x). For an integer q>0, setting ℰ _nq (ω)=sup‖f−ℰ _n (q,f)‖, the precise value of is obtained.     

Weak type inequalities for fractional maximal operator on weighted orlicz spaces

The fractional maximal operator on homogeneous space (X, d, μ) is de fined as      

Structures of polyhedra determined by submodular functions on crossing families

The present paper shows that for any submodular functionf on a crossing family with , if the polyhedron is nonempty, then there exist a unique distributive lattice with and a unique submodular function with such thatB(f) coincides with the base polyhedron associated with the submodular system . Here, iff is integer-valued, thenf ₁ is also integer-valued. Based on this fact, we also show the relationship between the independent-flow problem considered by the author and the minimum cost flow problem considered by J. Edmonds and R. Giles.     

On bands in which every finitely generated subband is an endomorphic image

A semigroup S is calledE-semigroup ( -semigroup) if every (finitely generated) subsemigroup of S is an endomorphic image of S and Ē-semigroup ( -semigroup) if every subsemigroup of S is an E-semigroup -semigroup. All classes X ε {Ē, , E, } are distinct even in the case of semilattices. It is established when a free band (semilattice) is an X-semigroup. -, - and Ē-chains and E-chains with identity or zero, Ē-and , X-bands with identity and X-semigroups with identity and zero are found.     

Some intersection theorems on two-valued functions

Let be a family of two-valued functions defined on ann-element set in which each pair of functions in satisfy a given intersection condition. For certain intersection conditions we determine the maximal value of .     

Valuations and polarity

Given a collection of convex polytopes, let() denote the set of all convex transversals of. If and are two such collections, of finite cardinality, then there is a simple, arithmetical condition which holds precisely when ()=(). Another such condition, involving what we call the Sallee-Shephard mapping, characterizes those pairs and for which (())=().As these results are established, several distributive lattices involving convex sets are introduced, and relationships between their valuation modules are determined. In particular, it is proven that the Sallee-Shephard mapping is an isomorphism of the additive, abelian group of simple functions generated by the characteristic functions of the open, convex sets and that generated by those of the closed, convex sets.     

A decomposition of 2-weak vertex-packing polytopes

The 2-weak vertex-packing polytope of a loopless graphG withd vertices is the subset of the unitd-cube satisfyingx _i +x _j ≤1 for every edge (i,j) ofG. The dilation by 2 of this polytope is a polytope with integral vertices. We triangulate with lattice simplices of minimal volume and label the maximal simplices with elements of the hyperoctahedral groupB _d . This labeling gives rise to a shelling of the triangulation of , where theh-vector of (and the Ehrharth ^*-vector of can be computed as a descent statistic on a subset ofB _d defined in terms ofG. A recursive way of computing theh-vector of is also given, and a recursive formula for the volume of . This work was partially supported by grants from the Icelandic Council of Science and the Royal Swedish Academy of Sciences, respectively.     

Formal language theory and the geometry of 3-manifolds

Automatic groups were introduced in connection with geometric problems, in particular with the study of fundamental groups of 3-manifolds. In this article the class of automatic groups is extended to include the fundamental group of every compact 3-manifold which satisfies Thurston's geometrization conjecture. Toward this end, the class of asynchronously groups is introduced and studied, where is an arbitrary full abstract family of languages. For example may be the family of regular languagesReg, context-free languagesCF, or indexed languagesInd. The class consists of precisely those groups which are asynchronously automatic. It is proved that contains all of the above fundamental groups, but that does not. Indeed a virtually nilpotent group belongs to if and only if it is virtually abelian. The first author was partially supported by NSF grant DMS-9203500 and FNRS (Suisse). He also wishes to thank the University of Geneva for its hospitality while this paper was being written. The second author thanks the Institute for Advanced Study for its hospitality while this paper was being written.     

Riesz frames and approximation of the frame coefficients

A frame is a fmaily {f _i } _i=1 ^∞ of elements in a Hilbert space with the property that every element in can be written as a (infinite) linear combination of the frame elements. Frame theory describes how one can choose the corresponding coefficients, which are called frame coefficients. From the mathematical point of view this is gratifying, but for applications it is a problem that the calculation requires inversion of an operator on . The projection method is introduced in order to avoid this problem. The basic idea is to consider finite subfamilies {f _i } _i=1 ⁿ of the frame and the orthogonal projection P_n onto its span. For has a representation as a linear combination of f_i, i=1,2,..., n and the corresponding coefficients can be calculated using finite dimensional methods. We find conditions implying that those coefficients converge to the correct frame coefficients as n→∞, in which case we have avoided the inversion problem. In the same spirit we approximate the solution to a moment problem. It turns out, that the class of “well-behaving frames” are identical for the two problems we consider. The first named author is partially supported by NSF DMS 9201357, Danish NSRC grant 9401958, Missouri Research Board grant C-3-41743, and a Missouri Research Council Summer Fellowship.     

Stochastic dilations of uniformly continuous completely positive semigroups

For an arbitrary uniformly continuous completely positive semigroup ( _t :t0) on the space of bounded operators on a Hilbert space, we construct a family (U(t)t0) of unitary operators on a Hilbert space and a conditional expectation from to, such that, for arbitraryt0,. The unitary operatorsU(t) satisfy a stochastic differential equation involving a noncommutative generalisation of infinite dimensional Brownian motion. They do not form a semigroup.Part of this work was completed when the first author was visiting research associate at the Center for Relativity, Physics Department, The University of Texas at Austin, Austin, TX 78712, U.S.A., supported in part by NSF PHY 81-01381.