Γ\Gamma-Conformal Algebras

$\Gamma$-conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points. We classify these algebras and their representations in terms of Lie algebras and their representations with an action of the group $\Gamma$. To every $\Gamma$-conformal algebra and a character of $\Gamma$ we associate a Lie algebra generated by fields with the OPE with simple poles. Examples include twisted affine Kac-Moody algebras, the sin algebra (which is a ``$\Gamma$-conformal'' analodue of the general linear algebra) and its analogues, the algebra of pseudodifferential operators on the circle, etc.Comment: 23 pages, AMSLatex Repotr-no: ITEP-TH-28/9

Liiketoimintasuunnitelma autokorjaamolle.

Tämän opinnäytetyön tarkoituksena oli laatia liiketoimintasuunnitelma toimeksiantona toimintansa aloittavalle autokorjaamolle. Tavoitteena oli, että toimeksiantaja voisi hyödyntää liiketoimintasuunnitelmaa yrityksen perustamisessa ja rahoitusta haettaessa ja samalla saisi liiketoimintasuunnitelmasta hyödyllisen oppaan omalle liiketoiminnalle. Lisäksi työn tarkoituksena oli selvittää korjaamon kannattavuutta. Opinnäytetyö on toiminnallinen opinnäytetyö ja muodostuu liiketoimintasuunnitelman laatimiseen liittyvistä asioista, eli teoriaosuudesta ja varsinaisesta liiketoimintasuunnitelmasta. Tietoperustan aineisto haettiin kirjallisuudesta ja internetistä. Toisena empiirisenä osana on yrityksen varsinainen liiketoimintasuunnitelma ja siihen kuuluvat keskeisimmät osa-alueet. Empiirisenä aineistona on käytetty toimeksiantajan haastatteluja ja omia tietoja. Liikeidean kannattavuuden tutkimista varten laadittiin rahoitus-, kannattavuus- ja myyntilaskelmat sekä tulossuunnitelma kolmelle ensimmäiselle toimintavuodelle. Opinnäytetyön tuloksena syntyi liiketoimintasuunnitelma, jota voidaan käyttää yrityksen perustamisessa ja suunnittelussa ja tarvittaessa se on päivitettävissä. Laskelmat perustuivat arvioihin ja niiden tuloksista saa suuntaa antavan kuvan yrityksen kannattavuudesta. Laadittua liiketoimintasuunnitelmaa käytetään liikeidean edelleen kehittämisessä ja tukena yritystoiminnan käynnistämiseen sekä apuna haettaessa lainaa ja vakuutuksia.The main idea of this thesis was to create a business plan for a start-up company specializing in car service and repair. The objective was that the entrepreneur could use the business plan when founding his company and applying for funding. Moreover, he would also get a useful guidebook for his business. In addition, the idea was to determine the company’s profitability. The thesis is practice-based and consists of several aspects of a business plan, its theoretical basis and the actual plan compiled for the client company. Information for the theoretical basis was collected from relevant print and internet sources. The second part presents the business plan and its main areas. Empirical data for the second part is based on a client interview and the author’s own experience and knowledge of the subject. To analyse the profitability of the business idea, financial, profitability and sales calculations were prepared. Additionally, a profit plan for the first three financial years was developed. The thesis resulted in a business plan, which can be used for planning and establishing the company. Moreover, the plan can be updated when necessary. The calculations were based on estimates and are, therefore, indicative of the profitability of the company. The business plan will be used for the future development of the business idea

TRANSLATION NUMBERS DEFINE GENERATORS OF F-k(+) -> Homeo(+) (S-1)

We consider a minimal action of a finitely generated semigroup by homeomorphisms of the circle, and show that the collection of translation numbers of individual elements completely determines the set of generators (up to a common continuous change of coordinates). One of the main tools used in the proof is the synchronization properties of random dynamics of circle homeomorphisms: Antonov’s theorem and its corollaries

Translation numbers define generators of Fk+→Homeo+(S1)F_k^+\to {\text{\rm Homeo}_+}(\mathbb{S}^1)

We consider a minimal action of a finitely generated semigroup by homeomorphisms of a circle, and show that the collection of translation numbers of individual elements completely determines the set of generators (up to a common continuous change of coordinates). One of the main tools used in the proof is the synchronization properties of random dynamics of circle homeomorphisms: Antonov's theorem and its corollaries.Comment: 15 pages, 1 figure, submitte

Minimality and ergodicity of a generic analytic foliation of 2

It is well known that a generic polynomial foliation of 2 is minimal and ergodic. In this paper we prove an analogous result for analytic foliation

Application of TiO2-based photocatalysts to antibiotics degradation: cases of sulfamethoxazole, trimethoprim and ciprofloxacin

peer-reviewedThe extensive application of antibiotics in human and veterinary medicine has led to their widespread occurrence in a natural aquatic environment. Global health crisis is associated with the fast development of antimicrobial resistance, as more and more infectious diseases cannot be treated more than once. Sulfamethoxazole, trimethoprim and ciprofloxacin are the most commonly detected antibiotics in water systems worldwide. The persistent and toxic nature of these antibiotics makes their elimination by conventional treatment methods at wastewater treatment plants almost impossible. The application of advanced oxidation processes and heterogeneous photocatalysis over TiO2 -based materials is a promising solution. This highly efficient technology has the potential to be sustainable, cost-efficient and energy-efficient. A comprehensive review on the application of various TiO2 -based photocatalysts for the degradation of sulfamethoxazole, trimethoprim and ciprofloxacin is focused on highlighting their photocatalytic performance under various reaction conditions (different amounts of pollutant and photocatalyst, pH, light source, reaction media, presence of inorganic ions, natural organic matter, oxidants). Mineralization efficiency and ecotoxicity of final products have been also considered. Further research needs have been presented based on the literature findings. Among them, design and development of highly efficient under sunlight, stable, recyclable and cost-effective TiO2 -based materials; usage of real wastewaters for photocatalytic tests; and compulsory assessment of products ecotoxicity are the most important research tasks in order to meet requirements for industrial application