A Possible and Necessary Consistency Proof

After Gödel's incompleteness theorems and the collapse of Hilbert's programme Gerhard Gentzen continued the quest for consistency proofs of Peano arithmetic. He considered a finitistic or constructive proof still possible and necessary for the foundations of mathematics. For a proof to be meaningful, the principles relied on should be considered more reliable than the doubtful elements of the theory concerned. He worked out a total of four proofs between 1934 and 1939. This thesis examines the consistency proofs for arithmetic by Gentzen from different angles. The consistency of Heyting arithmetic is shown both in a sequent calculus notation and in natural deduction. The former proof includes a cut elimination theorem for the calculus and a syntactical study of the purely arithmetical part of the system. The latter consistency proof in standard natural deduction has been an open problem since the publication of Gentzen's proofs. The solution to this problem for an intuitionistic calculus is based on a normalization proof by Howard. The proof is performed in the manner of Gentzen, by giving a reduction procedure for derivations of falsity. In contrast to Gentzen's proof, the procedure contains a vector assignment. The reduction reduces the first component of the vector and this component can be interpreted as an ordinal less than epsilon_0, thus ordering the derivations by complexity and proving termination of the process.

Pietismin kuva - ikkuna yksityiseen hengellisyyteen : Johann Arndtin opetukset pietistisen embleemin perustana

The image of Pietism a window to personal spirituality. The teachings of Johann Arndt as the basis of Pietist emblems The Pietist effect on spiritual images has to be scrutinised as a continuum initiating from the teachings of Johann Arndt who created a protestant iconography that defended the status of pictures and images as the foundation of divine revelation. Pietist artworks reveal Arndtian part of secret, eternal world, and God. Even though modern scholars do not regarded him as a founding father of Pietism anymore, his works have been essential for the development of iconography, and the themes of the Pietist images are linked with his works. For Arndt, the starting point is in the affecting love for Christ who suffered for the humankind. The reading experience is personal and the words point directly at the reader and thus appear as evidence of the guilt of the reader as well as of the love of God. Arndt uses bounteous and descriptive language which has partially affected promoting and picturing of many themes. Like Arndt, Philipp Jakob Spener also emphasised the heart that believes. The Pietist movement was born to oppose detached faith and the lack of the Holy Ghost. Christians touched by the teachings of Arndt and Spener began to create images out of metaphors presented by Arndt. As those people were part of the intelligentsia, it was natural that the fashionable emblematics of the 17th century was moulded for the personal needs. For Arndt, the human heart is manifested as a symbol of soul, personal faith or unbelief as well as an allegory of the burning love for Jesus. Due to this fact, heart emblems were gradually widely used and linked with the love of Christ. In the Nordic countries, the introduction of emblems emanated from the gentry s connections to the Central Europe where emblems were exploited in order to decorate books, artefacts, interiors, and buildings as well as visual/literal trademarks of the intelligentsia. Emblematic paintings in the churches of the castles of Venngarn (1665) and Läckö (1668), owned by Magnus Gabriel De la Gardie, are one of the most central interior paintings preserved in the Nordic countries, and they emphasise personal righteous life. Nonetheless, it was the books by Arndt and the Poet s Society in Nurnberg that bound the Swedish gentry and the scholars of the Pietist movement together. The Finnish gentry had no castles or castle churches so they supported county churches, both in building and in maintenance. As the churches were not private, their iconography could not be private either. Instead, people used Pietist symbols such as Agnus Dei, Cor ardens, an open book, beams, king David, frankincense, wood themes and Virtues. In the Pietist images made for public spaces, the attention is focused on pedagogical, metaphorical, and meaningful presentation as well as concealed statements.

On Finding the Natural Number of Topics with Latent Dirichlet Allocation: Some Observations

It is important to identify the ``correct'' number of topics in mechanisms like Latent Dirichlet Allocation(LDA) as they determine the quality of features that are presented as features for classifiers like SVM. In this work we propose a measure to identify the correct number of topics and offer empirical evidence in its favor in terms of classification accuracy and the number of topics that are naturally present in the corpus. We show the merit of the measure by applying it on real-world as well as synthetic data sets(both text and images). In proposing this measure, we view LDA as a matrix factorization mechanism, wherein a given corpus C is split into two matrix factors M-1 and M-2 as given by C-d*w = M1(d*t) x Q(t*w).Where d is the number of documents present in the corpus anti w is the size of the vocabulary. The quality of the split depends on ``t'', the right number of topics chosen. The measure is computed in terms of symmetric KL-Divergence of salient distributions that are derived from these matrix factors. We observe that the divergence values are higher for non-optimal number of topics - this is shown by a `dip' at the right value for `t'.

An Eventful Synthetic Approach Towards the Biologically Potent Natural Product Ottelione A: Enantio-, Regio- and Stereoselective Construction of the Bicyclic Core

A novel synthetic approach towards the recently reported anti-tumor and anti-tuberculor natural product ottelione A from the readily available Diels-Alder adduct of cyclopentadiene and p-benzoquinone is delineated. Our short strategy, besides being enantio-, regio- and stereoselective, charts an eventful course and is inherently well-suited for adaptation towards diverse synthetic analogues of this biologically potent natural product.

Super-plasticized natural rubber latex modified concretes

Polymeric admixtures to concrete ingredients modify the properties of the processed concrete. Ductility is one such property modification. This investigation deals with the development of a method of incorporating natural rubber latex into concrete ingredients with only marginal effects on the compressive strength of base plain concrete. This retention of the strength has been effected by reducing the water/cement ratio with the aid of a superplasticizer. The quantity of natural rubber latex is expressed as the dry rubber content by percentage of volume of concrete. The compressive and tensile strengths, as well as post peak ductile behaviour have been the basis for comparison with those of unmodified concrete.

Synthetic studies toward the PPAP natural products, prolifenones A and B and hyperforin: an Effenberger cyclization approach

A synthetic approach toward the geranylated PPAP natural products, prolifenones A and B. employing Effenberger cyclization as the key step, is delineated. The efficacy of this approach is further expanded through access to an advanced precursor of hyperforin. (C) 2010 Elsevier Ltd. All rights reserved.

Diplomatian historiapolitiikka: Historia-argumenttien käyttö Kosovon kysymyksessä 1998-2010

Tutkielmassa tarkastellaan yhtä kansainvälisten suhteiden ja diplomatian lähihistorian pulmallisinta haastetta, kysymystä Kosovon asemasta vuosina 1998–2010. Se oli yksi keskeisimmistä 1990-luvun Jugoslavian hajoamissotien solmukohdista ja suhtautuminen siihen jakaa edelleen kansainvälisen yhteisön rivejä maailmanlaajuisesti. Tapaus on erityisen mielenkiintoinen myös nationalismin ja historiapolitiikan kannalta, sillä Kosovo on sekä albaanien että serbien kansallisen identiteetin ydinaluetta. Varhaishistorian myytit ja etnohistorialliset kertomukset ovat olleet tärkeässä asemassa lukuisissa aluetta koetelleissa konflikteissa. Tutkimuksen lähtökohtana on historiapolitiikan lähestymistavan välttämättömyys kansainvälisesti politisoituneen ”Kosovon kysymyksen” ymmärtämisessä. Historiapolitiikan teoreettisen viitekehyksen soveltuvuuden koettelu diplomatian argumentaation ja kansainvälisten suhteiden analysoinnissa on olennainen osa tutkimuksen tehtävänasettelua, sillä varsinkaan Suomessa ei vastaavaa tutkimusta ole ennen tehty. Samalla tutkimuksen tavoitteena on luokitella, analysoida ja vertailla eri valtioiden diplomaattisten historia-argumenttien käyttöä Kosovon kysymyksen yhteydessä sekä tarkastella näiden argumenttien kautta suhtautumista kansallisiin etnohistorian tulkintoihin ja niiden käyttöön 1990-luvun retoriikassa. Tutkielman tärkeimpiä alkuperäislähteitä ovat YK:n turvallisuusneuvoston Kosovoa käsittelevien istuntojen pöytäkirjat vuosilta 1998–2010 sekä huhti- ja heinäkuussa 2009 YK:n kansainväliselle tuomioistuimelle (ICJ) toimitetut, Kosovon itsenäisyysjulistuksen lainmukaisuutta käsittelevät, kirjalliset lausunnot ja kommentit. Tutkimuskirjallisuuden osalta tutkielman tärkeimpiä lähteitä ovat muun muassa Oliver Jens Schmittin, Marc Wellerin ja Pekka Visurin teokset sekä monet albaanien ja serbien kansallisia historiakäsityksiä ilmentävät teokset. Tutkielman metodologisena apuvälineenä on sovellettu suomalaisessa tutkimuksessa aikaisemmin hyvin vähän käytettyä Karl-Georg Faberin mallia historian poliitisen käytön kategorisoimiseksi. Faberin mallia käytetään paitsi historia-argumenttien luokittelun kehikkona, myös ajattelua ohjaavana historianfilosofisena kolmitasoisena mallina. Sitä on täydennytty Chaïm Perelmanin ja Lucie Olbrechts-Tytecan retoriikan tutkimuksen teorialla. Tutkimuksen tärkeimpiä johtopäätöksiä on historiapolitiikan näkökulman ja Faberin mallin hedelmällisyyden toteaminen diplomatian argumentaation analysoinnissa. Samalla tutkimus osoittaa, että historia-argumenteilla oli (ja on edelleen) Kosovon kysymyksessä oma erityinen roolinsa, joka vaihteli ajallisesti ja teemoittain. Toisaalta kansalliset historiakäsitykset, kuten käsitys omasta kansasta uhrina, näkyivät argumenteissa selvästi, toisaalta pyrkimyksenä oli vältellä nationalistiseksi tulkittavia historia-argumentteja. Lisäksi monissa argumenteissa vaaditiin väkivaltaisen historian jättämistä taakse eurooppalaisen tulevaisuuden toivossa.