Indutseeritud 3-Lie superalgebrad ja nende rakendused superruumis

Väitekirja elektrooniline versioon ei sisalda publikatsiooneKäesoleva doktoritöö eesmärk on uurida selliste n-Lie superalgerbrate omadusi, mis on konstrueeritud kasutades (n-1)-Lie superalgebra aluseks olevat (n-1)-aarset tehet, seda eriti juhul n=3. Tavalise Lie algebra mõistet on võimalik super- (või Z_2-gradueeritud) struktuuridele üle kanda kui toome sisse Lie superalgebra mõiste. Sarnaselt on võimalik n-Lie algebra, kus binaarne tehe on asendatud n-aarse tehtega, üldistada superstruktuuridele, kui kasutame Filippov-Jacobi samasuse gradueeritud analoogi, saades n-Lie superalgebra. Väitekirjas on esitatud madaladimensionaalsete 3-Lie superalgebrate klassifikatsioon. Lisaks näitame, et n-Lie superalgebra abil, mille tehtele leidub superjälg, saab konstrueerida (n+1)-Lie superalgebra, mida me nimetame indutseeritud (n+1)-Lie superalgebraks. Enamgi veel, on tõestatud, et kommutatiivse superalgebra korral on võimalik indutseerida erinevad 3-Lie superalgebra struktuurid kasutades involutsiooni, derivatsiooni või neid mõlemad korraga. Dissertatsioonis on toodud Nambu-Hamiltoni võrrandi üldistus superruumis jaoks, ja on näidatud, et selle abil on võimalik indutseerida ternaarsete Nambu-Poissoni sulgude pere superruumi paarisfunktsioonide jaoks. Järgnevalt on konstrueeritud indutseeritud 3-Lie superalgebrate indutseeritud esitused, kasutades selleks vastavalt kas esialgset binaarset Lie algebrat koos jäljega või Lie superalgebrat koos superjäljega. Töös on näidatud, et 3-Lie algebra indutseeritud esitus on sisestatav jäljeta maatriksite Lie algebrasse sl(V), kus sümboliga V on tähistatud esituse ruum. Kahedimensionaalse indutseeritud esituse korral on esitatud tingimused, mida vastav esitus peab rahuldama, et ta oleks taandumatu.The aim of the present thesis is to study the properties and characteristics of n-Lie superalgebras that are constructed using an operation from (n-1)-Lie superalgebras, especially in the case n=3. A regular Lie algebra can be extended to super- (or Z_2-graded) structures by introducing the notion of Lie superalgebra. Similarly n-Lie algebra, where binary operation is replcaed with n-ary multiplication law, can be extended to superstructures by making use of a graded Filippov-Jacobi identity, giving a notion of n-Lie superalgebra. In the dissertation a classification of low dimensional 3-Lie superalgebras is presented. We show that an n-Lie superalgebra equipped with a supertrace can be used to construct a (n+1)-Lie superalgebra, which is referred to as the induced (n+1)-Lie superalgebra. It is proved that one can construct induced 3-Lie superalgebras from commutative superalgebras by using involution, even degree derivation, or combination of both of them together. In the thesis a generalization of Nambu-Hamilton equation to a superspace is proposed, and it is shown that it induces a family of ternary Nambu-Poisson brackets of even degree functions on a superspace. Finally a representations of induced 3-Lie algebras and Lie superalgebras are constructed by means of a representation of the initial binary Lie algebra and trace or Lie superalgebra and supertrace, respectively. It is shown that the constructed induced representation of 3-Lie algebra is a representation by traceless matrices, that is, lies in the Lie algebra sl(V), where V is a representation space. For 2-dimensional representations the irreduciblility condition of the induced representation of induced 3-Lie algebra is found.https://www.ester.ee/record=b536058

Eestis on valminud uus 2. tüüpi diabeedi ravijuhend

Eesti Arst 2016; 95(5):337–33

Singulaarsed murrulised diferentsiaalvõrrandid ja südamlikud Volterra integraaloperaatorid

Murrulist järku tuletised (st tuletised, mille järk ei ole naturaalarv) on teadlastele huvi pakkunud juba sajandeid. Kuna kaua aega ei olnud näha, millised võiksid olla murruliste tuletiste rakendusvõimalused, siis käsitleti nendega seotud küsimusi tavaliselt vaid teoreetilisest vaatepunktist ja sellest huvitusid enamasti ainult matemaatikud. Viimastel aastakümnetel on aga leitud, et murrulist järku tuletisi sisaldavad diferentsiaalvõrrandid võimaldavad suurepäraselt kirjeldada mitmesuguste materjalide käitumist ja paljude protsesside modelleerimist. Võib öelda, et viimase paarikümne aasta jooksul on murruliste tuletiste populaarsus hüppeliselt kasvanud tänu uutele rakendustele füüsikas, bioloogias, keemias ja paljudes teistes valdkondades. Rakendustes omavad suurt tähtsust ka võrrandid, mis sisaldavad hajuvaid integraale (st integraale, mis klassikalises mõttes hajuvad). Üks tähtsamaid käsitusi hajuvate integraalide puhul on olnud nende lõpliku osa defineerimine. Käesoleva väitekirja peamisteks eesmärkideks on teatavat klassi singulaarsete murrulist järku tuletistega diferentsiaalvõrrandite ühese lahenduvuse analüüsimine ning logaritmilise teguriga hajuvate integraalide Hadamard’i lõpliku osa leidmine. Singulaarsete murruliste diferentsiaalvõrrandite uurimiseks kasutatakse südamlike Volterra integraaloperaatorite teooriat.The concept of fractional derivatives (i.e. derivatives of non-integer order) has interested scientists since at least the seventeenth century. For a long time considerations regarding these type of derivatives were purely theoretical in nature interesting mainly mathematicians. Recently however, fractional derivatives have seen a remarkable growth in popularity because of interesting new applications in physics, chemistry, mechanics, biology, economics, aerodynamics, etc. Equations containing divergent integrals (i.e. integrals that diverge under normal conditions) arise in applications quite often. One of the main concepts under discussion has been the summability, i.e. finding the finite part, of divergent integrals. The present thesis is devoted to the analysis of some classes of singular differential equations involving fractional order derivatives of an unknown function. Also finding the Hadamard finite part of a class of divergent integrals with a logarithmic factor is under consideration. The method for the analysis of singular fractional differential equations is based upon the theory of cordial Volterra integral operators

Kalciumomsättning och kalciumreglering

Kalciumbrist är ett kostsamt tillstånd för produktionen. När värphöns drabbas av kalcium-brist försämras skalkvaliteten på äggen och tillslut avtar äggproduktionen. Mjölkkor drabbas oftast av akut kalciumbrist före eller efter kalvning, vilket ofta leder till höga veterinärkost-nader och kan även orsaka andra sjukdomar. I den här litteraturstudien är syftet att jämföra och granska likheter samt olikheter i kalci-umomsättning och kalciumreglering mellan värphöns och mjölkkor. Det totala kalciumbe-hovet per kg kroppsvikt för värphöns ligger på 1,36 g Ca. För en mjölkko varierar det om hon är dräktig (0,18 g Ca per kg kroppsvikt) eller i laktation (0,081 g Ca per kg kroppsvikt). Kalciumomsättningen i kroppen regleras främst av tre olika hormoner, parathormon, 1,25-dihydroxyvitamin D3 och kalcitonin, som stimuleras av en förändring i kalciumkoncentrat-ionen i blodet. Fåglar har ett unikt ben, medullärbenet, som bidrar med kalcium vid skalbild-ningen. Förebyggande åtgärder för kalciumbrist är en viktig uppgift. För värphöns kan exempelvis partikelstorleken förbättra absorptionen av kalcium från tarmen. Det finns även faktorer hos individen som kan behövas ta hänsyn till som till exempel olika raser, ålder och produkt-ionsmängd. Mjölkkor i åldern 7–10 år löper högre risk att drabbas av kalciumbrist än yngre kor. Slutsatsen kunde dras att det finns olika typer av kalciumbrist. Värphönsens unika medullärben är med och buffrar kalciumhalten i blodet, till den grad att muskelfunktionen inte påverkas i samma utsträckning som mjölkkornas muskelfunktion, vid akut hypo-kalcemi. För att förebygga kalciumbrist bör värphöns bli utfodrade med en kalksten med partikelstorlek på 2–5 mm i diameter. Mjölkkor bör utfodras med ett foder med ett lågt DCAD-värde före kalvning för att minska risken för uppkomst av kalvningsförlamning.Hypocalcaemia is an expensive disease for the production. During hypocalcaemia, the laying hens’ eggshell and bone quality decreases and eventually the egg production cease. Around calving the dairy cow have extreme pressure on the calcium homeostasis and can come into calcium deficiency, also called milk fever. This can lead to high veterinary costs and it can also lead to other diseases. The purpose of this review is to compare and examine similarities and differences in cal-cium metabolism and calcium regulation between laying hens and dairy cows. The total calcium requirement per kg bodyweight, for a laying hen is approximant 1.36 g Ca. For a dairy cow, it varies if she undergoes gestation (0,081 g Ca per kg bodyweight) or lactation (0,18 g Ca per kg bodyweight). The calcium metabolism is regulated by three different hormones, parathormone, 1,25-dihydroxyvitamin D3 and calcitonin, in the body and are stimulated by an alteration in the calcium in the plasma. Birds have a unique type of bone, the medullary bone, which con-tributes with calcium for eggshell formation. Prevention for hypocalcaemia is an important task. For example, different particle size of the limestone can affect the absorption of calcium in the digestive tract of laying hens. There are also some aspects in the individual itself to considerate such as, breed, age and produc-tion volume. Dairy cows at the age of 7-10 years, are in higher risk of developing calcium deficiency than younger cows. It was concluded that there are different types of calcium deficiency. The unique medul-lary bone of the laying hen helps to buffer the calcium concentration in the blood during acute hypocalcaemia. The medullary bone contributes in that extent that the muscle function does not get affected in the same amount as the muscle function in dairy cows. To prevent hypocalcaemia, laying hens should be fed limestones with a particle size of 2-5 mm diame-ters. To minimize the rise of milk fever, dairy cows should get a feed containing a low DCAD value before expecting calving

Minkowski aegruumi geomeetriast

We consider a four-dimensional real vector space in which three coordinates describe the space, and the fourth coordinate describes time. Such a vector space, equipped with Minkowski metric, is said to be a Minkowski spacetime, denotedM and sometimes referred just as Minkowski space. In the beginning of 20th century it emerged from the works of Hermann Minkowski and Henry Poincar e that this mathematical tool can be really useful in areas like the theory of special relativity. The rst objective of this thesis is to introduce the classical properties of Minkowski spacetime in a way that doesn't get into the details about the physical meaning of the topic. The main focus is on the elements of the spacetime and the orthogonal maps that describe the transformations of these elements. As this topic, the Minkowski spacetime, has many applications in physics, most of the literature on it originates from physics, rather than mathematics. In the books that are written by physicists, strict proofs are not given properly or they are avoided entirely. Sometimes physical discussion is considered as a proof, but as shown in proposition 3.1 for example, things are not so obvious after all in a mathematical point of view. In contrary, the aim of this thesis is to ll this gap by giving rigorous proof to all the statements that are made. The last part of the thesis takes a new course and tries to introduce tools from branch of mathematics called di erential geometry. Apparatus described there can be useful not just describing the structure of Minkowski spacetime, but also wide areas of theoretical physics. At last, we generalize classical spacetime and present the Minkowski superspace { a space with anticommuting coordinates that has become a useful tool in the eld theory. This is all done in a bit less formal way. This thesis consists of four sections. In the rst section we recall such topics that are not strictly connected to the thesis but have great impact on further understanding of the paper. For example Gram{Schmidt orthogonalization process is reminded and we prove one of the fundamental results related to dot product, the Cauchy{Schwartz{Bunjakowski inequality. We also describe the rules of the multipication of block matrices as 42 well as nding the inverse of block matrix. Map called matrix exponential is introduced as it plays a key role in the nal part of the thesis. Considered the geometrical meaning of the paper we nd ourselves stopping for a bit longer to study the idea of topological manifold. Second section sets an objective to describe the elements or events of the Minkowski spacetime. For that we give a strict de nition of dot product and move on to the concept of pseudoeucleidic space. After that we describe the dot product in Minkowski spacetime, which gives us the metric. It appears that by the metric we can factorize the elements of spacetime into three distinct classes, these are spacelike, timelike and nullvectors. The last subsection is there to describe the orthogonal transformations of Minkowski space, referred as Lorentz transformations. We show how these transformations can be represented in both coordinates and matrix form and what is the connection between the transformations and the metric of M. Finally we prove that the set of all Lorentz transformatioins has a very natural group structure, the Lorentz group. In the third section we continue with the observation of Lorentz transformations. In the rts subsection we take a closer look at the properties of such transformations and concentrate on the most important of them. As a result we nd a rotation subgroup of Lorentz group. We proceed with noting that Lorentz transformations remain the distances invariant. That encourages us to look for other such transformations that share the same property. As it happens translations are of this kind and by observing translations with Lorentz transformations together, we get the symmetry group of Minkowski spacetime, the Poincar e group. The fourth section takes another course. In this section the objective is to introduce, via more popular approach, the connections between Minkowski spacetime and di erential geometry, and to uncover the term superspace with the surrounding mathematics. In the part of di erential geometry we de ne Lie algebra with its representation and give examples to clear the topic. As expected we then nd ourselves de ning Lie group which we later connect with Lie algebra by giving an informal description. The section, as well as the paper is then nished with the introduction of Minkowski superspace. For that we de ne terms such as superalgebra and give a well known example, the Grassmann algebra. By avoiding strict mathematical formalism, we show what are functions on superspace and how to nd integral or derivative of such functions

Mineralämnen i klöver- och gräsvall i Sverige

Minerals are essential elements for all living organisms. Plants and animals need minerals to function and maintain a balanced physiological state. Minerals are also important in the ecological cycle. The minerals originate in the soil and makes the foundation of the plants nutritional value for the animals. The minerals can later re-circulate to the soil in form of manure. Forage is the main feed giving to ruminants and knowledge about the mineral content in the forage is important to avoid deficiencies or toxicities and to get a good under-standing about the mineral balance of the farm. This study aimed to map the contents of calcium, phosphorus, magnesium, potas-sium, sodium, chlorine, sulphur, iron, manganese, zinc, copper, cobalt, selenium, iodine and molybdenum in clover- and grass forage in Sweden and to correlate those with the content of minerals in the soil of Sweden. The results generated 15 different maps showing the content of each mineral in samples of forages from all over Sweden. The results from the regression analysis between minerals in soil and feed, showed a varied relation, where calcium, phospho-rus, copper and molybdenum had the strongest determinations coefficient of 50% - 65%. It was concluded that this study showed mean concentration of calcium, phosphorus, magnesium, potassium, sulphur and copper comparable, to previously reported for Swedish forage. The mean contents of zinc, manganese and selenium, were however higher than those reported earlier and should therefore be the new refrence values for Swedish forage. This study also showed a difference in the phosphorus concentration between the northern and southern Sweden, which contradicts previously reported values of phosphorus in Swedish forage.Mineraler är livsnödvändiga för alla levande organismer. Växter och djur behöver mineraler för att fungera och upprätthålla ett normalt biologiskt tillstånd. Mineraler är också viktiga i det ekologiska kretsloppet. Mineraler kommer ursprungligen från jorden och är grunden till växtens näringsinnehåll för djuren. Näringsämnena kan sedan återvända till jorden i form av gödsel. Vall är den huvudsakliga födokällan till idisslare i Sverige och kunskap om vallens mineralinnehåll är därför viktig att känna till för att undvika brister eller förgiftningar hos djuren och ha en god kännedom om gårdens mineralbalans. Syftet med denna studie var att kartlägga innehållet av, kalcium, fosfor, magne-sium, kalium, natrium, klor, svavel, järn, mangan, zink, koppar, kobolt, selen, jod och molybden i svensk gräs- och klövervall och att korrelera dessa data med motsvarande mineraler i jorden. Resultatet genererade 15 olika kartor, som visade variationen av innehållet för varje mineral i svensk vall. Resultatet för determinationskoefficienten mellan mine-raler i jorden och fodret, visade en varierad regressionsanalys, där kalcium, fosfor, koppar och molybden hade det tydligaste sambandet mellan 50%-65%. I denna studien drogs slutsatsen att medelvärden i vallen för kalcium, fosfor, mag-nesium, kalium, svavel och koppar, var jämförbara med tidigare tabellvärden för svensk vall. Innehållet av zink, mangan och selen, visade dock högre medelvärden i vallen, än tidigare visat och borde därför bli de nya tabellvärdena för svensk vall. Den här studien visade även skillnader i fosforkoncentrationen i vallen mellan norra och södra Sverige, vilket motsäger tidigare tabellvärden för fosfor i svensk vall

Regional bicycleplanning : a study of power and structures in transport planning

Den skånska cykelplaneringen lämnar mycket att önska. I ett gytter av olika aktörer och oklara ansvarsförhållanden har denna viktiga del av trafikplaneringen ofta hamnat mellan stolarna. Detta innebär i praktiken ett osammanhängande, knapphändigt regionalt cykelnät med långa, ineffektiva planeringsprocesser och misslyckade projekt. I denna uppsats analyseras en svensk regions arbete med regional cykelplanering utifrån teorier om hur olika maktstrukturer påverkar transportplaneringen. En av de grundläggande byggstenarna för en ökad cykling identifieras som en tillgänglig, säker, trafikseparerad cykelinfrastruktur som i den studerade regionen visar vara en bristvara. Orsakerna till denna brist härleds till svårrubbliga strukturer inom bl.a. Trafikverket på nationell nivå vilket i sin tur leder till en bristande finansiering i de regionala projekten. Ett resonemang förs även kring huruvida den neoliberala ideologin och andra politiska och ekonomiska strukturer sätter sin prägel på den samtida transportplaneringen och försvårar en övergång mot ett hållbart mobilitetssystem.The Scania bicycle planning leaves you with much to ask. In a hot mess of different stakeholders and unclear areas of responsibilities, this very crucial part of the traffic planning has often been neglected. In reality this has resulted in a disconnected, poorly sustained regional bicycle road network where long and inefficient planning processes has become commonplace. In this paper the bicycle planning in the Swedish region of Scania is analyzed through the lens of different power structures and how these tend to affect the transport planning itself. One of the cornerstones in working for an increased cycling is identified as in creating, safe, available and traffic separated bicycle infrastructure. This kind of infrastructure is inadequate in the region. The causes of the inadequacy is led to cemented structures, in for instance The Swedish transport agency (Trafikverket), which lead to budget decisions tilted towards unsustainable modes of transport. A further argument is made about whether the neoliberal ideology, among other political and economic structures, is actually influencing these decisions on an abstract level and if that is complicating the transition towards a sustainable mobility system

n-Lie superalgebrad

Käesolevas magistritöös tuletame meelde mõned Lie algebrate teooria põhitõed ja vaatame selle klassikalise struktuuri üldistusi. Filippov konstrueeris artiklis [7] n-Lie algebra, kus binaarne kommutaator on asendatud n-aarse analoogiga. Meie kombineerime viimase Lie superalgebra struktuuriga, mis üldistab Lie algebraid kasutades Z2 -gradueeritud vektorruumi ning gradueeringu iseärasusi kommutaatoril tavalise vektorruumi asemel, et saada n-Lie superalgebra, nagu seda on tehtud artiklis [1]. Me uurime n-Lie superalgebra, ehk n-aarse gradueeritud Filippovi samasust rahuldava tehtega superalgebra omadusi, ning rakendades ideid artiklitest [1, 3] indutseerime n-Lie superalgebratest (n +1)-Lie superalgebrad. Viimaks uurime me ternaarseid Lie superalgebraid üle C, kus algebra aluseks oleva supervektorruumi dimensioon on m|n, m + n ≤ 4. Me teeme kindlaks kui palju on erinevaid võimalikke kommutatsioonieeskirju, mida neile tingimustele vastavad 3-Lie superalgebrad omada võivad

Duloksetiin (CYMBALTA) – efektiivne ravim depressiooni emotsionaalsete ja somaatiliste sümptomite raviks

Depressioon on väga sage ja üks peamistest haigestumise ning töövõimetuse põhjustajast maailmas. Maailma Terviseorganisatsiooni andmetel oli 2000. aastal haigestumus depressiooni sagedaim 15 kuni 44 a inimeste haigestumise põhjus. Depressiooni puhul kannatab inimene tavaliselt alanenud meeleolu, huvi ja elurõõmu kadumise ning energia vähenemise all, mis toob kaasa suurenenud väsimuse ja vähenenud aktiivsuse. Eesti Arst 2005; 84 (2): 133-13