Resolution of degree ≤ 6 algebraic equations by genus two theta constants

We adjoin complete first kind Abelian integrals of genus two to solve the general degree six algebraic equation a 0 z 6 + a 1 z 5 + ... + a 6 = 0 by genus two theta constants. Using the same formulas, later we resolve degree five, four and three algebraic equations. We study the monodromy group, which permutes the roots of degree six polynomials

Mass-spin relation of black holes obtained by twin high-frequency quasi-periodic oscillations

The paper studies the uniqueness and the monotonicity of the mass-spin relation of black holes the X-ray power density spectra of which contain twin high-frequency quasi-periodic oscillations in 3:2 ratio. It is found that for geodesic models the properties of the mass-spin relation are independent of the observed frequencies, i.e. they are independent of the particular object. Some results are valid for all geodesic models. For concreteness two of the most commonly used models are studied here: the 3 : 1 nonlinear epicyclic resonance model and its Keplerian version

Stability of stochastic pricing models under volatility fluctuations

The standard theory of the stochastic models used to value financial derivatives contracts involves models whose input parameters are deterministic functions and often constants. Because of the random nature of the changes in the market prices of the financial instruments, the coefficients of these models are inevitably susceptible to random perturbation from their initial estimates. In this paper we will investigate the behavior of some of the most widely used models when small changes are applied to their volatility component. Starting with the Black-Scholes model for the price of a European call option, we will continue our analysis of the traditional models for pricing American options, Asian options, Barrier options, as well as some of the models for the short term rate of interest. In addition to obtaining convergence results for all of the models, we will examine a method of controlling the deviations in the volatility parameter of the Black-Scholes model and the resulting estimate can be used for further extensions on the topic. Moreover, we will present an example of how to calculate probabilities of unlikely events, using a technique called importance sampling. We will concentrate only on the case of discrete random variables but the same algorithm can be applied to estimate the probabilities of the deviations of the pricing functions of the models under question. The latter is left for future research

On the dynamics of the four‐dimensional rigid body in a quadratic potential field

This is the published version, also available here: http://dx.doi.org/10.1063/1.531285.We study the nondegenerated solutions of the rotation of a four‐dimensional rigid body in a quadratic potential field. This problem has 6 degrees of freedom. We obtain 143 topologically different solutions and explicit formulas in Prym theta‐functions

Galaktikate ja neid ümbritsevate parvede ühisevolutsioon

Väitekirja elektrooniline versioon ei sisalda publikatsiooneGalaktikad pole ruumis ühtlaselt jaotunud. Pidevalt mõjuva gravitatsioonilise tõmbe tõttu moodustavad nad erineva tihedusega struktuure: hiiglaslikke, väga väheste galaktikatega tühikuid; tühikuid ääristavaid “seinu”; seinte lõikumisjoont markeerivaid filamente; filamentide ristumiskohtades paiknevaid galaktikaparvi. Galaktikaparved võivad omakorda moodustada superparvi – suurimaid struktuure Universumis. Selles struktuuride võrgustikus toimub pidev areng, mille käigus galaktikagrupid ja väiksemad parved ühinevad suurematega. Omavahel võivad ühineda ka suured galaktikaparved. Vaatlusandmed näitavad, et erinevate struktuuride galaktiline koostis on erinev. Kõige hõredamates keskkondades domineerivad aktiivse tähetekkega spiraalgalaktikad, kuid suurte parvede siseosasid asustavad valdavalt tähetekketa elliptilised galaktikad. Seni ei ole täielikku selgust, milliste mehhanismide toimel on galaktikate tüüp ning tähetekke kiirus seotud keskkonnatihedusega. Käesolevas väitekirjas otsimegi seoseid galaktikate ja neid ümbritseva keskkonna arenemise vahel. Selleks analüüsime galaktikate tähetekke aktiivsust ühes kokkupõrkefaasis olevas galaktikaparves. Samuti uurime külma, tähetekkeks vajaliku gaasi sisaldust galaktikates, mis paiknevad ühes ebatavaliselt rohke tähetekkega galaktikaparves. Lõpuks võrdleme neid kaht parve suurema parvevalimiga, mille liikmed paiknevad meist ligikaudu samal kaugusel. Jõuame järeldusele, et sarnase massiga parvede põrkumise tagajärjel tähetekkeaktiivsus kahaneb. Samas võib põrke algfaasis tähetekkeaktiivsus lühiajaliselt ka suureneda. Näeme, et 2,5 miljardit aastat nooremana paistvate galaktikaparvede gaasisisaldus on sarnane praeguse Universumi parvede omaga, ning et aktiivse tähetekkega galaktikate suurem osakaal kaugetes galaktikaparvedes on tõenäoliselt seotud parvedest väljaspool toimuvate protsessidega.Galaxies, are not uniformly distributed throughout space. Due to the continuous pull of gravity they form structures which range in densities from giant voids, almost completely devoid of galaxies, through sheets which surround the voids, filaments where sheets intersect and clusters which are forming at the crossing of filaments. Clusters of galaxies are often found in conglomerates called super-clusters which are the largest structures in the universe. This network of structures is continuously evolving with groups and smaller clusters of galaxies being accreted onto larger clusters. Sometimes large clusters also collide. It is observed that throughout this network the mixture of galaxies varies. The more rarefied environments are dominated by star forming, spiral galaxies while the interiors of large clusters are dominated by elliptical galaxies, devoid of star formation. The exact physical mechanisms that determines this connection between environment and morphology and activity of galaxies is not yet fully understood. In this thesis we search for a link between the evolution of galaxies and the evolution of the structures within which they are embedded. We analyse the star formation activity in galaxies which are members of a merging cluster of galaxies. We also analyse the cold gas content (fuel for star formation) of galaxies residing in a cluster with unusually high fraction of star forming galaxies. Finally we compare the galaxies found in these two clusters with a sample of other clusters at similar distance from us. We conclude that mergers of clusters of similar mass tend to quench star formation. We find indications that during the initial phase of the merger the star formation can be enhanced briefly. We find the gas content in cluster galaxies observed 2.5 Gyrs ago to be similar to that of local cluster-members, and that the increased fraction of star forming galaxies in distant clusters is likely related to processes working outside these clusters.https://www.ester.ee/record=b522304

Advantages of laparoscopic surgical techniques in the treatment of rectal prolapse

The authors reviewed the problems in the treatment of rectal prolapse and compared the results of the monitoring of a group of 124 patients over a period of 16 years. Based on the application of different surgical techniques and follow-up of short-term and long-term results, they suggested the use of laparoscopic surgical techniques in patients with high surgical risk and advanced stage of rectal prolapse

DE QUERVAIN'S DISEASE - MODERN TRENDS IN TREATMENT

The most popular surgical procedure for treatment of the De Quervain's disease onsists of a longitudinal incision, exposition of the first osteofibrous channel (the first compartment) and releasing the compression over the M. abductor pollicis longus and M. extensor pollicis brevis tendons. This technique has some disadvantages such as rough skin scar and possible dislocation of the tendons after releasing. Seven patients with De Quervain1 s disease were presented. They underwent D. Viet's surgical procedure (1992). The rough skin cicatrices and possible tendon dislocations were avoided because of their fixing with a capsular flap. The good results encouraged the application of this new method