Two weight inequalities for discrete positive operators

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Two weight inequalities for maximal truncations of dyadic Calderón-Zygmund operators

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Coefficients of Drinfeld modular forms and Hecke operators

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The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

Hankel operators on holomorphic Hardy-Orlicz spaces

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Complex and real Hausdorff operators

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Moduli of smoothness and rate of a.e. convergence for some convolution operators

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Reduction theorems for operators on the cones of monotone functions

For a quasilinear operator on the semiaxis a reduction theorem is proved on the cones of monotone functions in Lp - Lq setting for 0 < q < ∞, 1<= p < ∞. The case 0 < p < 1 is also studied for operators with additional properties. In particular, we obtain critera for three-weight inequalities for the Hardy-type operators with Oinarov' kernel on monotone functions in the case 0 < q < p <= 1.

Folner sequences and finite operators

This article analyzes Folner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper Folner sequence (i.e. a Folner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper Folner sequence. Moreover, we show that an operator is finite if and only if it has a proper Folner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no Folner sequence and give examples of them. For this analysis we introduce the notion of strongly non-Folner operators, which are far from finite block reducible operators, in some uniform sense, and show that this class coincides with the class of non-finite operators.

Compact portable biosensor for arsenic detection in aqueous samples with Escherichia coli bioreporter cells.

We present a compact portable biosensor to measure arsenic As(III) concentrations in water using Escherichia coli bioreporter cells. Escherichia coli expresses green fluorescent protein in a linearly dependent manner as a function of the arsenic concentration (between 0 and 100 μg/L). The device accommodates a small polydimethylsiloxane microfluidic chip that holds the agarose-encapsulated bacteria, and a complete optical illumination/collection/detection system for automated quantitative fluorescence measurements. The device is capable of sampling water autonomously, controlling the whole measurement, storing and transmitting data over GSM networks. We demonstrate highly reproducible measurements of arsenic in drinking water at 10 and 50 μg/L within 100 and 80 min, respectively.

Additional compact formulas for vibrational dynamic dipole polarizabilities and hyperpolarizabilities

Compact expressions, complete through second order in electrical and/or mechanical anharmonicity, are given for the dynamic dipole vibrational polarizability and dynamic first and second vibrational hyperpolarizabilities. Certain contributions not previously formulated are now included

Modulaarisen paisunta-astian kehittäminen compact -sarjan teollisuusvaihteeseen

Tämä insinöörityö tehtiin SEW Industrial Gears Oy:lle, joka valmistaa hammasvaihteita teollisuuden eri sovellutuksiin. Työn tavoitteena oli kehittää modulaarinen paisuntaastiasarja compact -sarjan teollisuusvaihteeseen. Työn alkuvaiheessa käytössä oli kahdenlaisia paisunta-astioita: kosteissa oloissa käytettävä suljettu astiamalli ja kuiviin olosuhteisiin soveltuva malli. Koska käytössä oleva suljettu astiamalli oli kallis ja kuivien olosuhteiden mallin käyttö oli rajoitettu, oli uudelle modulaariselle paisunta-astialle selkeä tarve. Uuden astiamallin tuli olla yhteensopiva vaihteen yleisimpien varusteiden ja asennusasentojen kanssa. Lisäksi tavoitteena oli puolittaa uuden konseptin hinta vanhaan verrattuna ja paikata vanhoissa konstruktioissa olleita puutteita. Työ aloitettiin analysoimalla olemassa olevat paisunta-astiatyypit, minkä jälkeen paisuntaastialle ideoitiin uusia ominaisuuksia. Toisessa vaiheessa perehdyttiin modulaariseen järjestelmään sekä öljynpaisunnan teoriaan teollisuusvaihteessa. Viimeisessä vaiheessa tehtiin konseptin varsinainen suunnittelutyö, valittiin astian valmistustapa ja materiaali sekä optimoitiin hinta. Uudesta mallista valmistettiin myös prototyyppi, jotta suunniteltua tuotetta päästiin kokeilemaan myös käytännössä. Näin voitiin varmistaa tuotteen toimivuus. Suunnittelutyön tuloksena saatiin uuden paisunta-astiasarjan piirustukset tarvittavista osista ja kokoonpanoista sekä komponenttistandardi ja myyntiä tukevaa materiaalia. Käytännön osuus antoi tietoa laskelmien oikeellisuudesta sekä öljyn täyttöön ja paisuntaan liittyvistä asioista.