Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin con- volution of functions de ned on (0;1), and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-di usion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.

The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements

A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement, which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with the findings in the literature and with physical and SPICE models, the equilateral triangular power pad arrangement is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.

Size Effect and Notch Size Effect in Metal Fatigue

It is a well known phenomenon that the constant amplitude fatigue limit of a large component is lower than the fatigue limit of a small specimen made of the same material. In notched components the opposite occurs: the fatigue limit defined as the maximum stress at the notch is higher than that achieved with smooth specimens. These two effects have been taken into account in most design handbooks with the help of experimental formulas or design curves. The basic idea of this study is that the size effect can mainly be explained by the statistical size effect. A component subjected to an alternating load can be assumed to form a sample of initiated cracks at the end of the crack initiation phase. The size of the sample depends on the size of the specimen in question. The main objective of this study is to develop a statistical model for the estimation of this kind of size effect. It was shown that the size of a sample of initiated cracks shall be based on the stressed surface area of the specimen. In case of varying stress distribution, an effective stress area must be calculated. It is based on the decreasing probability of equally sized initiated cracks at lower stress level. If the distribution function of the parent population of cracks is known, the distribution of the maximum crack size in a sample can be defined. This makes it possible to calculate an estimate of the largest expected crack in any sample size. The estimate of the fatigue limit can now be calculated with the help of the linear elastic fracture mechanics. In notched components another source of size effect has to be taken into account. If we think about two specimens which have similar shape, but the size is different, it can be seen that the stress gradient in the smaller specimen is steeper. If there is an initiated crack in both of them, the stress intensity factor at the crack in the larger specimen is higher. The second goal of this thesis is to create a calculation method for this factor which is called the geometric size effect. The proposed method for the calculation of the geometric size effect is also based on the use of the linear elastic fracture mechanics. It is possible to calculate an accurate value of the stress intensity factor in a non linear stress field using weight functions. The calculated stress intensity factor values at the initiated crack can be compared to the corresponding stress intensity factor due to constant stress. The notch size effect is calculated as the ratio of these stress intensity factors. The presented methods were tested against experimental results taken from three German doctoral works. Two candidates for the parent population of initiated cracks were found: the Weibull distribution and the log normal distribution. Both of them can be used successfully for the prediction of the statistical size effect for smooth specimens. In case of notched components the geometric size effect due to the stress gradient shall be combined with the statistical size effect. The proposed method gives good results as long as the notch in question is blunt enough. For very sharp notches, stress concentration factor about 5 or higher, the method does not give sufficient results. It was shown that the plastic portion of the strain becomes quite high at the root of this kind of notches. The use of the linear elastic fracture mechanics becomes therefore questionable.

New approximation to the third-order density : application to the calculation of correlated multicenter indices

In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro's, Nakatsuji's and Mazziotti's approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation

Approximate solution to the speed of spreading viruses

Recently, it has been shown that the speed of virus infections can be explained by time-delayed reactiondiffusion [J. Fort and V. Me´ndez, Phys. Rev. Lett. 89, 178101 (2002)], but no analytical solutions were found. Here we derive formulas for the front speed, valid in appropriate limits. We also integrate numerically the evolution equations of the system. There is good agreement with both numerical and experimental speeds

A linguagem química e o ensino da química orgânica

The importance of chemical language and specifically of molecular models and their representations in the development of chemistry is discussed. Structural formulas are projections of molecular models used as a specific language by chemists. The meaningful learning of chemistry requires knowledge of this language. The use of these analogical symbols without the necessary understanding engenders difficulties for the learning of chemistry.

Development of Color Difference Equations Matching to Human Vision System

Research on color difference evaluation has been active in recent thirty years. Several color difference formulas were developed for industrial applications. The aims of this thesis are to develop the color density which is denoted by comb g and to propose the color density based chromaticity difference formulas. Color density is derived from the discrimination ellipse parameters and color positions in the xy , xyY and CIELAB color spaces, and the color based chromaticity difference formulas are compared with the line element formulas and CIE 2000 color difference formulas. As a result of the thesis, color density represents the perceived color difference accurately, and it could be used to characterize a color by the attribute of perceived color difference from this color.

L’altre Segon Quintet : anàlisi formal i rítmic de l’evolució de la interpretació del repertori en els concerts en directe del Segon Quintet de Miles Davis

“L’altre Segon Quintet. Anàlisi formal i rítmic de l’evolució de la interpretació del repertori en els concerts en directe del Segon Quintet de Miles Davis” és un estudi històric i analític de la música de Miles Davis i el seu famós “Segon Quintet”. A diferència de la majoria de publicacions sobre aquesta banda, es centra únicament en els concerts en directe i el repertori que hi tocaven. Per treure a la llum la “màgia” que hi havia, he fet unes transcripcions amb un mètode propi de diverses versions de les mateixes peces al llarg dels anys i he anotat tots els fets rellevants en aspectes d’arranjaments, plantejaments estètics i interacció entre solistes i secció rítmica. Finalment he comprovat que aquesta “màgia” és fruit d’unes fórmules pautades i no és tan espontània com sembla en una primera escolta. Per altra banda, tots els músics de la banda contribueixen al so del grup, demostrant així la seva condició d’indispensables per la banda.

A importância da lei de Gay-Lussac para a classificação dos compostos orgânicos

This article shows the genesis of the law of volumes of combining gases, formulated by Gay-Lussac in 1808, and how it allowed the expression of the composition of organic compounds in terms of whole numbers of volumes, thus leading to the first classification of organic compounds, formulated by Dumas and Boullay in 1828. It was from this work that Organic Chemistry began to shed its purely taxonomic nature, analogous to what prevailed in Natural History, and to then develop in a vigorous and continuous process, initiating what may be the most significant historical phenomenon in the History of Chemistry of the nineteenth century.

Elintarvikekelpoisten painovärien vertailu offsetpainatuksessa

Tässä diplomityössä tutkittiin kolmen eri painovärivalmistajan elintarvikekelpoisia arkkioffsetpainovärisarjoja ja verrattiin niitä keskenään. Tavoitteena oli löytää optimaalinen elintarvikekartonkipakkausten painamiseen soveltuva arkkioffsetpainoväri. Työn kirjallisessa osassa selvitettiin yleisesti offsetpainatusprosessia, painovärien koostumusta ja elintarvikekelpoisten painovärien eroavaisuutta verrattuna perinteisiin offsetpainoväreihin. Kirjallisuusosassa tuotiin esille myös niitä tekijöitä, joilla elintarvikekelpoisuus määritellään. Näistä yksi tärkeä osa-alue on migraatio-ongelmat, joka on lainsäädännön kannalta ajankohtainen. Kokeellista osaa varten koepainovärejä painettiin taivekartongille arkkioffsetpainokoneella. Painetuista arkeista tehtiin mittauksia, joissa käytettiin densitometrisia, kolorimetrisia, kromatografisia ja aistinvaraisia menetelmiä. Näillä pyrittiin tuomaan esille eroavaisuuksia tutkittavana olleiden painovärien välille. Koeajojen ja mittausten perusteella analysoitiin painatuksen laatua, painettavuutta, painovärien elintarvikekelpoisuutta ja kestävyyttä. Työn tulosten perusteella ei voida suoraan osoittaa, että jokin painovärisarja olisi toimivampi kuin toinen. Yksi johtopäätös olikin, että painovärien koostumusta ja painatusprosessia on mahdollista modifioida monella tavalla, jolloin voidaan parantaa joitakin painovärin ominaisuuksia. Yleisesti kokeet osoittivat, että perinteinen aistinvarainen tapa testata painovärin elintarvikekelpoisuutta on hyvin subjektiivinen ja antaa arveluttavia tuloksia. Koetuloksista oli kuitenkin havaittavissa, että uuden sukupolven vähemmän migraatiota aiheuttavat painovärit ovat elintarvikekelpoisempia kuin aikaisempien kehitysasteiden painovärisarjat.

Teaching mathematics and programming : new approaches with empirical evaluation

Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

Työntömastotrukkien tuotannon optimointi

Tutkimuksessa luodaan Tuko Logistics Oy:n työntömastotrukkien toimintaa opti-moivia toimintaehdotuksia varastonohjausjärjestelmästä saatavan työntömastotruk-kidatan pohjalta. Tutkimus on toteutettu haastattelututkimuksena ja käyttäen apuna tieteellisiä julkaisuja. Tehtävien lomittamistutkimuksen ja loogiseen päättelyn tulok-sena on luotu kaksi toimintaehdotusta: A ja B. Toimintaehdotusten vaikutuksia van-haan järjestelmään verrataan mittareilla, joista osa on tehty jonoteorian jonomallien laskukaavojen pohjalta. Mittareita ovat: tehdyt tehtävät tunnissa, tuottamattoman ajon suhde tuottavaan, normaalitehtäväjonon pituus ja normaalitehtäväjonon koko-naisodotusaika. Toimintaehdotus B osoittautuu tehokkaammaksi ehdotukseksi, mutta Toimintaehdotus A:lla voi varmistaa tehtävien riittämisen työntömastotrukeille. Tut-kimuksessa ehdotetaan myös muita työntömastotrukkien toimintaa optimoivia muu-toksia, jotka voidaan ottaa käyttöön jokaisessa toimintamallissa.

Hitsauksen aiheuttamat muodonmuutokset ja niiden hallinta alumiiniveneiden rakenteissa

Alumiiniveneissä hitsauksen aiheuttamat muodonmuutokset ovat usein erittäin haitallisia, koska niiden aiheuttamat mittamuutokset ja ulkonäölliset haitat alentavat tuotteen laatua sekä arvoa. Monissa tapauksissa myös hitsausliitoksen suorituskyky heikentyy ja lisäksi hitsausmuodonmuutokset voivat aiheuttaa toiminnallisia ongelmia alumiiniveneiden runkorakenteisiin. Tästä johtuen hitsausmuodonmuutosten hallinta ja minimointi ovat erityisen tärkeitä tekijöitä pyrittäessä parantamaan alumiiniveneiden laatua ja kustannustehokkuutta sekä kasvattamaan alumiinivenealan kilpailukykyä. Tässä diplomityössä tutkittiin robotisoidun kaasukaarihitsauksen aiheuttamia muodonmuutoksia sekä niiden hallintaa alumiinista valmistettujen työ- ja huviveneiden runkorakenteissa. Työssä perehdyttiin nykyaikaiseen alumiinivenevalmistukseen sekä hitsattujen rakenteiden yleisiin lujuusopin teorioihin ja käyttäytymismalleihin. Alumiinin hitsausmuodonmuutosten tutkimuksissa suoritettiin käytännön hitsauskokeita, joiden kohteina olivat alumiiniveneissä käytetyt rakenneratkaisut ja liitostyypit. Työn tavoitteena oli määrittää alumiinin hitsauksessa syntyviin muodonmuutoksiin keskeisesti vaikuttavia tekijöitä ja parametreja. Tutkimustulosten perusteella pyrittiin esittämään ratkaisuja alumiiniveneiden rakenteisiin aiheutuvien hitsausmuodonmuutosten vähentämiseksi ja hallitsemiseksi. Alumiinirakenteissa hitsausmuodonmuutokset ovat hyvin tapauskohtaisia, koska usein niiden syntyminen määräytyy monen tekijän yhteisvaikutuksesta. Teräsrakenteille käytetyt yleiset analyyttiset laskentakaavat ja käyttäytymismallit eivät sovellu suoraan alumiinirakenteille, mikä johtuu alumiinin erilaisista materiaaliominaisuuksista ja käyttäytymisestä hitsauksen aikana. Tulevaisuudessa empiiristen koejärjestelyiden ja analyyttisten mallien lisäksi sovellettavan numeerisen elementtimenetelmän avulla voidaan parantaa alumiinin hitsauksessa aiheutuvien muodonmuutosten kokonaisvaltaista hallintaa.

High-speed solid-rotor induction machine – calculation program

The aim of this thesis is to utilize the technology developed at LUT and to provide an easy tool for high-speed solid-rotor induction machine preliminary design. Computer aided design tool MathCAD has been chosen as the environment for realizing the calculation program. Four versions of the design program have been made depending on the motor rotor type. The first rotor type is an axially slitted solid-rotor with steel end rings. The next one is an axially slitted solid-rotor with copper end rings. The third machine type is a solid rotor with deep, rectangular copper bars and end rings (squirrel cage). And the last one is a solid-rotor with round copper bars and end rings (squirrel cage). Each type of rotor has its own specialties but a general thread of design is common. This paper follows the structure of the calculating program and explains some features and formulas. The attention is concentrated on the difference between laminated and solid-rotor machine design principles. There is no deep analysis of the calculation ways are presented. References for all solution methods appearing during the design procedure are given for more detailed studying. This thesis pays respect to the latest innovations in solid-rotor machines theory. Rotor ends’ analytical calculation follows the latest knowledge in this field. Correction factor for adjusting the rotor impedance is implemented. The purpose of the created design program is to calculate the preliminary dimensions of the machine according to initial data. Obtained results are not recommended for exact machine development. Further more detailed design should be done in a finite element method application. Hence, this thesis is a practical tool for the prior evaluating of the high-speed machine with different solid-rotor types parameters.

Nettipohjainen voimalaitosratkaisujen hinta-arviojärjestelmä

Työn tarkoitus on suunnitella ja toteuttaa nettipohjainen voimalaitosratkaisujen hinta-arviojärjestelmä Savonia Power Oy:n käyttöön. Järjestelmän tarkoitus on automatisoida voimalaitosratkaisujen tunnuslukujen laskeminen asiakkaan antamien alkuarvojen pohjalta ja tallentaa mahdollinen yhteydenottopyyntö. Järjestelmän vaatimuksina ovat laskentakaavojen helppo päivitettävyys, kaavojen automaattinen hakeminen Excel 2007–muotoisesta tiedostosta ja asiakasrajapinnan nettipohjaisuus. Työ jakaantuu kahteen osaan. Teoriaosassa selvitetään työssä käytettyjen tekniikoiden taustaa ja selvitetään Microsoftin OOXML-tiedostomuodon rakenne työssä vaadittavin osin. Käytännön osassa suunnitellaan ja osin toteutetaan valmis järjestelmä käyttäen PHP-kieltä, XML-määrittelykieltä ja MySQL-tietokantaa. Suurimmat haasteet järjestelmän toteutuksessa ovat laskentakaavojen parsiminen Excel-tiedostosta ilman sen sisällön tiukkaa rajoittamista tiettyihin raameihin ja järjestelmän helppo päivitys saaduilla laskentakaavoilla. Työn lopputuloksena on toimiva, muttei viimeistelty järjestelmä sekä tämä dokumentti. Työn suurin merkitys tulee olemaan edellä mainittujen suunnitteluhaasteiden selvittäminen, sekä valmis ohjelmarunko yleiseen käyttöön otetulle järjestelmälle.