Unitary Processes with Independent Increments and Representations of Hilbert Tensor Algebras

The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow.

Only Connect?: Aspects of Intertextuality in Zadie Smith's On Beauty

Tutkielma käsittelee intertekstuaalisuuden eri muotoja Zadie Smithin romaanissa On Beauty (suom. Kauneudesta). Tutkimuksen tarkoitus on osoittaa kuinka oleellisesti intertekstuaalisuuden teoria on vaikuttanut kirjallisuustieteen metodeihin ja postmoderniin kirjallisuuskäsitykseen, sekä käsitellä sen soveltuvuutta nykykirjallisuuden tutkimiseen analysoimalla teorian sisäistä monimuotoisuutta ja ristiriitoja. Tutkimusmateriaalina käytetään Smithin romaanin lisäksi E. M. Forsterin romaania Howards End (suom. Talo jalavan varjossa), johon On Beauty tietoisesti viittaa. Teoreettisena viitekehyksenä tutkielmassa toimii Gérard Genetten teoksessa Palimpsests sekä Roland Barthesin esseessä Tekijän kuolema esille tuodut kirjallisuusteoreettiset käsitykset. Valittu metodologia antaa mahdollisuuden hahmottaa intertekstuaalisuus kahdella eri tavalla: Genetten strukturalistinen lähestymistapa soveltuu teosten välisten viittaussuhteiden tutkimiseen, kun taas Barthesin jälkistrukturalistinen diskurssi auttaa ymmärtämään tekstienvälisyyden osana merkityksen jatkuvaa epävakautta. Tutkielman ensimmäinen osio keskittyy analysoimaan lähiluvun keinoin romaanien On Beauty ja Howards End välistä strukturalistista suhdetta vertailemalla teosten eroja ja yhtäläisyyksiä Genetten intertekstuaalisuusteorian valossa. Vertailussa kiinnetetään erityisesti huomiota teosten juoneen, rakenteeseen, aikaan ja paikkaan, sekä uudelleenkirjoitusten yleiseen tendenssiin päivittää alkuperäistä tarinaa kohdeyleisölle paremmin sopivaksi. Toisessa osiossa tutkimusta esille nousee jälkistrukturalistinen näkemys intertekstuaalisuudesta osana lukijan tuottaman merkityksen tulkinnanvaraisuutta. Osiossa käsitellään Rembrandtin taideteosten roolia Smithin romaanissa ja analysoidaan hahmojen tulkintoja sekä suhtautumista Rembrandtin tuotantoon Barthesin teoreettisten käsitteiden kautta. Keskeiseksi analyysin kohteeksi nousee lukija sekä lukijan tuottamat tulkinnat ja niiden merkitys Smithin romaanin tematiikassa. Tutkielmassa osoitetaan kuinka intertekstuaalisuus ei ole niin yksinkertainen termi kuin sen laaja käyttö niin kirjallisuustieteessä kuin mediassakin antaa ymmärtää, sekä selvitetään intertekstuaalisuuden teorian kehitystä 60-luvulta nykypäivään. Vaikka strukturalistisessa muodossa käsite soveltuu etenkin kahden toisiinsa kytkeytyneen teoksen tutkimiseen, vertaileva analyysi kuitenkin osoittaa, että On Beauty ei ole pelkkä uudelleenkirjoitus, vaan romaanin tulkintaan tarvitaan myös jälkistrukturalistisen dekonstruktion käsitteitä, jotta laajemmat tekstuaalisuuden verkostot aukeavat lukijalle. Romaanissa esiintyvä taitelijakuva myös osoittaa, että Smith itse on hyvin tietoinen kirjallisuusteoreettisesta keskustelusta.

Extended kac-akhiezer formulae and the fredholm determinant of finite section hilbert-schmidt kernels

This paper deals with some results (known as Kac-Akhiezer formulae) on generalized Fredholm determinants for Hilbert-Schmidt operators on L2-spaces, available in the literature for convolution kernels on intervals. The Kac-Akhiezer formulae have been obtained for kernels which are not necessarily of convolution nature and for domains in R(n).

CM defect and Hilbert functions of monomial curves

In this article we consider a semigroup ring R = KGamma] of a numerical semigroup Gamma and study the Cohen- Macaulayness of the associated graded ring G(Gamma) := gr(m), (R) := circle plus(n is an element of N) m(n)/m(n+1) and the behaviour of the Hilbert function H-R of R. We define a certain (finite) subset B(Gamma) subset of F and prove that G(Gamma) is Cohen-Macaulay if and only if B(Gamma) = empty set. Therefore the subset B(Gamma) is called the Cohen-Macaulay defect of G(Gamma). Further, we prove that if the degree sequence of elements of the standard basis of is non-decreasing, then B(F) = empty set and hence G(Gamma) is Cohen-Macaulay. We consider a class of numerical semigroups Gamma = Sigma(3)(i=0) Nm(i) generated by 4 elements m(0), m(1), m(2), m(3) such that m(1) + m(2) = mo m3-so called ``balanced semigroups''. We study the structure of the Cohen-Macaulay defect B(Gamma) of Gamma and particularly we give an estimate on the cardinality |B(Gamma, r)| for every r is an element of N. We use these estimates to prove that the Hilbert function of R is non-decreasing. Further, we prove that every balanced ``unitary'' semigroup Gamma is ``2-good'' and is not ``1-good'', in particular, in this case, c(r) is not Cohen-Macaulay. We consider a certain special subclass of balanced semigroups Gamma. For this subclass we try to determine the Cohen-Macaulay defect B(Gamma) using the explicit description of the standard basis of Gamma; in particular, we prove that these balanced semigroups are 2-good and determine when exactly G(Gamma) is Cohen-Macaulay. (C) 2011 Published by Elsevier B.V.

Proof of a conjecture of Frankl and Furedi

We give a simple linear algebraic proof of the following conjecture of Frankl and Furedi [7, 9, 13]. (Frankl-Furedi Conjecture) if F is a hypergraph on X = {1, 2, 3,..., n} such that 1 less than or equal to /E boolean AND F/ less than or equal to k For All E, F is an element of F, E not equal F, then /F/ less than or equal to (i=0)Sigma(k) ((i) (n-1)). We generalise a method of Palisse and our proof-technique can be viewed as a variant of the technique used by Tverberg to prove a result of Graham and Pollak [10, 11, 14]. Our proof-technique is easily described. First, we derive an identity satisfied by a hypergraph F using its intersection properties. From this identity, we obtain a set of homogeneous linear equations. We then show that this defines the zero subspace of R-/F/. Finally, the desired bound on /F/ is obtained from the bound on the number of linearly independent equations. This proof-technique can also be used to prove a more general theorem (Theorem 2). We conclude by indicating how this technique can be generalised to uniform hypergraphs by proving the uniform Ray-Chaudhuri-Wilson theorem. (C) 1997 Academic Press.

Coherent states on Hilbert modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.

The Herzog-Vasconcelos conjecture for affine semigroup rings

Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.

OOCs, Partial Relative Difference Families and a Conjecture of Golomb

The cyclic difference sets constructed by Singer are also examples of perfect distinct difference sets (DDS). The Bose construction of distinct difference sets, leads to a relative difference set. In this paper we introduce the concept of partial relative DDS and prove that an optical orthogonal code (OOC) construction due to Moreno et. al., is a partial relative DDS. We generalize the concept of ideal matrices previously introduced by Kumar and relate it to the concepts of this paper. Another variation of ideal matrices is introduced in this paper: Welch ideal matrices of dimension n by (n - 1). We prove that Welch ideal matrices exist only for n prime. Finally, we recast an old conjecture of Golomb on the Welch construction of Costas arrays using the concepts of this paper. This connection suggests that our construction of partial relative difference sets is in a sense, unique

Ontheproof of the Poincare´ conjecture

In 2002, Perelman proved the Poincare conjecture, building on the work of Richard Hamilton on the Ricci flow. In this article, we sketch some of the arguments and attempt to place them in a broader dynamical context.

On the proof of the Poincare´ conjecture

In 2002, Perelman proved the Poincare conjecture, building on the work of Richard Hamilton on the Ricci flow. In this article, we sketch some of the arguments and attempt to place them in a broader dynamical context.

Contractive Hilbert modules and their dilations

In this note, we show that a quasi-free Hilbert module R defined over the polydisk algebra with kernel function k(z,w) admits a unique minimal dilation (actually an isometric co-extension) to the Hardy module over the polydisk if and only if S (-1)(z, w)k(z, w) is a positive kernel function, where S(z,w) is the Szego kernel for the polydisk. Moreover, we establish the equivalence of such a factorization of the kernel function and a positivity condition, defined using the hereditary functional calculus, which was introduced earlier by Athavale [8] and Ambrozie, Englis and Muller [2]. An explicit realization of the dilation space is given along with the isometric embedding of the module R in it. The proof works for a wider class of Hilbert modules in which the Hardy module is replaced by more general quasi-free Hilbert modules such as the classical spaces on the polydisk or the unit ball in a'', (m) . Some consequences of this more general result are then explored in the case of several natural function algebras.

Unitary invariants for Hilbert modules of finite rank

We associate a sheaf model to a class of Hilbert modules satisfying a natural finiteness condition. It is obtained as the dual to a linear system of Hermitian vector spaces (in the sense of Grothendieck). A refined notion of curvature is derived from this construction leading to a new unitary invariant for the Hilbert module. A division problem with bounds, originating in Douady's privilege, is related to this framework. A series of concrete computations illustrate the abstract concepts of the paper.

Hilbert W*-modules and coherent states

Hilbert C*-module valued coherent states was introduced earlier by Ali, Bhattacharyya and Shyam Roy. We consider the case when the underlying C*-algebra is a W*-algebra. The construction is similar with a substantial gain. The associated reproducing kernel is now algebra valued, rather than taking values in the space of bounded linear operators between two C*-algebras.