7 resultados para Green-Tao theorem
em Helda - Digital Repository of University of Helsinki
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Environmentally benign and economical methods for the preparation of industrially important hydroxy acids and diacids were developed. The carboxylic acids, used in polyesters, alkyd resins, and polyamides, were obtained by the oxidation of the corresponding alcohols with hydrogen peroxide or air catalyzed by sodium tungstate or supported noble metals. These oxidations were carried out using water as a solvent. The alcohols are also a useful alternative to the conventional reactants, hydroxyaldehydes and cycloalkanes. The oxidation of 2,2-disubstituted propane-1,3-diols with hydrogen peroxide catalyzed by sodium tungstate afforded 2,2-disubstituted 3-hydroxypropanoic acids and 1,1-disubstituted ethane-1,2-diols as products. A computational study of the Baeyer-Villiger rearrangement of the intermediate 2,2-disubstituted 3-hydroxypropanals gave in-depth data of the mechanism of the reaction. Linear primary diols having chain length of at least six carbons were easily oxidized with hydrogen peroxide to linear dicarboxylic acids catalyzed by sodium tungstate. The Pt/C catalyzed air oxidation of 2,2-disubstituted propane-1,3-diols and linear primary diols afforded the highest yield of the corresponding hydroxy acids, while the Pt, Bi/C catalyzed oxidation of the diols afforded the highest yield of the corresponding diacids. The mechanism of the promoted oxidation was best described by the ensemble effect, and by the formation of a complex of the hydroxy and the carboxy groups of the hydroxy acids with bismuth atoms. The Pt, Bi/C catalyzed air oxidation of 2-substituted 2-hydroxymethylpropane-1,3-diols gave 2-substituted malonic acids by the decarboxylation of the corresponding triacids. Activated carbon was the best support and bismuth the most efficient promoter in the air oxidation of 2,2-dialkylpropane-1,3-diols to diacids. In oxidations carried out in organic solvents barium sulfate could be a valuable alternative to activated carbon as a non-flammable support. In the Pt/C catalyzed air oxidation of 2,2-disubstituted propane-1,3-diols to 2,2-disubstituted 3-hydroxypropanoic acids the small size of the 2-substituents enhanced the rate of the oxidation. When the potential of platinum of the catalyst was not controlled, the highest yield of the diacids in the Pt, Bi/C catalyzed air oxidation of 2,2-dialkylpropane-1,3-diols was obtained in the regime of mass transfer. The most favorable pH of the reaction mixture of the promoted oxidation was 10. The reaction temperature of 40°C prevented the decarboxylation of the diacids.
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The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.
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Tiivistelmä
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Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.
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Tässä tutkielmassa tarkastellaan Bolivialaisten naisvankien (alkuperäisväestön) ja globaalin huumesodan ("War on Drugs") välistä yhteyttä. Keskustelu sijoitetaan laajemmin kokan viljelyn politiikkaan ja alkuperäisväestön kulttuuriin. Kokaa viljeleviä köyhiä maalaisia, joista huomattava osa on naisia, on vangittu Boliviassa kiihtyvää tahtia viime vuosikymmeninä. Moni naisista on kokan tuotannossa ja kaupassa mukana, sillä se on monesti ainoa keino taloudelliseen selviämiseen. Yleisesti ottaen naisvangit ja naisrikolliset ovat marginaalinen ilmiö. Kansainvälisesti tarkasteltuna naisvankien suhteellinen osuus koko vankilaväestöstä on noin 5,2 % (keskiarvo). Boliviassa osuus on vaihdellut 6,1 %:n ja 17,1 %:n välillä vuosina 2000-2008. Naisvankien määrä yleisesti ottaen on ollut rajussa kasvussa, suurin syy naisten vangitsemiseen on huumausaineisiin liittyvät rikokset. Näyttää myös siltä että vähemmistöt ja etnisen taustan omaavat henkilöt ovat yliedustettuina vankilaväestössä. Bolivia seuraa tätä kansainvälistä trendiä. Tämä tutkielma on rajattu kysymyksiin Bolivian intiaaniperäisten naisten osuudesta maan huumerikollisuudessa, sekä heidän suhteellisen korkeaa vangitsemisastetta selittäviin yhteiskunnallisiin tekijöihin. Kysymykset sukupuolesta, etnisyydestä ja kokan viljelyn politiikasta ovat keskiössä. Yleisiä kriminologisia teorioita peilataan kriittisesti suhteessa aineistoon ja Bolivian kontekstiin. Huumesodan ja Bolivian ankaran huumelainsäädännön seurauksista keskustellaan kriittisesti, sekä pohditaan köyhän alkuperäisväestön massavangitsemisen tarpeellisuutta. Tutkimuskysymykseni ovat: mitkä tekijät selittävät kohtuullisen korkean intiaaniperäisten naisvankien määrän Boliviassa, ja mikä on heidän asemansa globaalissa huumesodassa? Tutkielmassa on analysoitu kvantitatiivista ja kvalitatiivista aineistoa. Päälähteenä on ollut Bolivian tilastokeskuksen tuottamat rikostilastot. Tutkielman tärkeimpänä löydöksenä voidaan pitää havaintoa, että vastoin tiettyjä olettamuksia, intiaaniperäiset naiset ovat hyvinkin aktiivisia perinteisesti miehisiksi käsitetyillä aloilla kuten rikollisuudessa ja politiikassa. Tutkielmassa osoitetaan myös, että pidätysten määrät ovat moninkertaistuneet muutamassa vuosikymmenessä. Koska kokan viljelyssä on kyse pääasiallisesti taloudellisesta toimeentulosta, tämä tutkielma kysyy, onko hengissä pysyminen rikos?