Quantum L∞L_\infty Algebras and the Homological Perturbation Lemma

Quantum $L_\infty$ algebras are a generalization of $L_\infty$ algebras with a scalar product and with operations corresponding to higher genus graphs. We construct a minimal model of a given quantum $L_\infty$ algebra via the homological perturbation lemma and show that it's given by a Feynman diagram expansion, computing the effective action in the finite-dimensional Batalin-Vilkovisky formalism. We also construct a homotopy between the original and this effective quantum $L_\infty$ algebra.Comment: 27 pages, fixed typos and the section 4.

Twisted Quantum Lax Equations

We give the construction of twisted quantum Lax equations associated with quantum groups. We solve these equations using factorization properties of the corresponding quantum groups. Our construction generalizes in many respects the Adler-Kostant-Symes construction for Lie groups and the construction of M. A. Semenov Tian-Shansky for the Lie-Poisson case.Comment: 23 pages, late

Microcomputer Control System with DSP TMS 320F28335

Import 05/08/2014Tato diplomová práce se zabývá popisem řídicího systému se signálovým procesorem TMS320F28335, pro využití ve výukové a výzkumné činnosti katedry Elektroniky. V hlavní části je popsán signálový procesor z hlediska jeho vnitřní struktury a dále jsou podrobněji popsány principy funkce nejvyužívanějších periferií. V přílohách je pak popsán reálný vývojový kit, který byl vyroben katedrou Elektroniky a osazený právě tímto procesorem. Jedná se o popis částí, konkrétních konektorů a pinů. Dále je k této práci přiloženo DVD s potřebným softwarovým vybavením pro obsluhu vývojového kitu. V ostatních přílohách jsou pak manuály pro práci s veškerým softwarovým vybavením. Po nastudování této práce by měla být dotyčná osoba schopna samostatně pracovat a vyvíjet řídící systém za pomoci vývojového kitu s tím, že podrobnější popis musí pak již samostatně studovat z dokumentace výrobce.This thesis deals with the description of the control system with digital signal processor TMS320F28335, for use in teaching and research activities of the Department of Electronic. The main part of the thesis are described signal processor, in terms of its internal structure, and are further described in detail the principles functions of the most used peripherals. The appendix is then described real developmental kit that was made by the Department of Electronics and fitted just this processor. This is the description of parts specific connectors and pins. This work is accompanied by a DVD with the necessary software for operate with the developmental kit. In other annexes are then manuals to work with all software. After finishing of study this work should be the person able to work independently and develop control system with using the developmental kit, but the more detailed description must study in the manufacturer's documentation.430 - Katedra elektronikyvelmi dobř

Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map

We use the Seiberg-Witten map (SW map) to expand noncommutative gravity coupled to fermions in terms of ordinary commuting fields. The action is invariant under general coordinate transformations and local Lorentz rotations, and has the same degrees of freedom as the commutative gravity action. The expansion is given up to second order in the noncommutativity parameter {\theta}. A geometric reformulation and generalization of the SW map is presented that applies to any abelian twist. Compatibility of the map with hermiticity and charge conjugation conditions is proven. The action is shown to be real and invariant under charge conjugation at all orders in {\theta}. This implies the bosonic part of the action to be even in {\theta}, while the fermionic part is even in {\theta} for Majorana fermions.Comment: 27 pages, LaTeX. Revised version with proof of charge conjugation symmetry of the NC action and its parity under theta --> - theta (see new sect. 2.6, sect. 6 and app. B). References added. arXiv admin note: substantial text overlap with arXiv:0902.381

Nambu-Poisson Gauge Theory

We generalize noncommutative gauge theory using Nambu-Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg-Witten map. We construct a covariant Nambu-Poisson gauge theory action, give its first order expansion in the Nambu-Poisson tensor and relate it to a Nambu-Poisson matrix model

Gauge theories of quantum groups

We find two different q-generalizations of Yang-Mills theories. The corresponding lagrangians are invariant under the q-analogue of infinitesimal gauge transformations. We explicitly give the lagrangian and the transformation rules for the bicovariant q-deformation of $SU(2) \times U(1)$. The gauge potentials satisfy q-commutations, as one expects from the differential geometry of quantum groups. However, in one of the two schemes we present, the field strengths do commute.Comment: 12 pages, DFTT-19/9

A C*-Algebraic Model for Locally Noncommutative Spacetimes

Locally noncommutative spacetimes provide a refined notion of noncommutative spacetimes where the noncommutativity is present only for small distances. Here we discuss a non-perturbative approach based on Rieffel's strict deformation quantization. To this end, we extend the usual C*-algebraic results to a pro-C*-algebraic framework.Comment: 13 pages, LaTeX 2e, no figure

R matrix and bicovariant calculus for the inhomogeneous quantum groups IGL_q(n)

We find the R matrix for the inhomogeneous quantum groups whose homogeneous part is $GL_q(n)$, or its restrictions to $SL_q(n)$,$U_q(n)$ and $SU_q(n)$. The quantum Yang-Baxter equation for R holds because of the Hecke relation for the braiding matrix of the homogeneous subgroup. A bicovariant differential calculus on $IGL_q(n)$ is constructed, and its application to the $D=4$ Poincar\'e group ISL_q(2,\Cb) is discussed.Comment: 8 pp., LaTeX, DFTT-59/9

Náhodné měřitelné množiny a procesy částic

Náhodné měřitelné množiny a procesy částic Adam Jurčo Abstrakt V této práci se budeme zabývat procesy částic na obecnějších prostorech. Nejprve vyjdeme z prostoru Lebesgueovsky měřitelných množin reprezentovaných jejich indiká- tory s topologií danou L1 loc konvergencí. Dále se zabýváme topologickými vlastnostmi tohoto prostoru a jeho podprostorů množin konečného a lokálně konečného perimetru. Protože tyto prostory nesplňují obvykle kladené topologické předpoklady potřebné ke kon- strukci bodových procesů, použijeme jiný postup založený na předpokladech z teorie míry. To nám umožní definovat bodové procesy určené pomocí konečně rozměrných projekcí na měřitelných podmnožinách prostoru Lebesgueovsky měřitelných množin. Poté odvodíme vzorec pro objemový podíl takto zobecněného Booleova procesu. Dále se zaměříme na Booleův proces s částicemi konečného perimetru a odvodíme vzorec pro výpočet speci- fického perimetru tohoto procesu. 1Random measurable sets and particle processes Adam Jurčo Abstract In this thesis we deal with particle processes on more general spaces. First we in- troduce the space of Lebesgue measurable sets represented by indicator functions with topology given by L1 loc convergence. We the explore the topological properties of this space and its subspaces of sets of finite and locally finite perimeter. As these spaces do not satisfy the usual topological assumptions needed for construction of point processes we use another approach based on measure-theoretic assumptions. This will allow us to define point processes given by finite dimensional distributions on measurable subsets of the space of Lebesgue-measurable sets. Then we will derive a formula for a volume fraction of a Boolean process defined in this more general setting. Further we introduce a Boolean process with particles of finite perimeter and derive a formula for its specific perimeter. 1Mathematical Institute of Charles UniversityMatematický ústav UKMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

The Use of Linear Programming for Optimization of Advertising Cost

Bakalárska práca sa zaoberá procesmi, ktoré prebiehajú v podniku pri optimalizácii nákladov na reklamu. V teoretickej časti budú definované teoretické východiská, základné pojmy, metódy, postupy a lineárne programovanie, ktoré sa pri optimalizácii využívajú. Následne bude predstavený prvok Riešiteľ, ako podporný prvok Microsoft Excel. V analytickej časti bude predstavená spoločnosť, jej hlavná podnikateľská činnosť a problém s ktorým sa spoločnosť stretáva. V ďalšej časti budú predstavené mnou vytvorené modely, vlastné návrhy riešenia a výsledky budú interpretované pomocou doplnku Riešiteľ.The aim of this thesis is to analyse processes, which take place in the company in relation to optimization of advertising costs. Theoretical basis, basic concepts, methods, procedures and linear programming used for optimization will be defined in the theoretical part of the work. Subsequently, the Reporter element will be presented as a Microsoft Excel support element. The company, its main business targets and the problems that occur in the enterprise will be introduced in the analytical part. The last part will consist of models created by myself, my own suggestions of solutions and the results will be interpreted by the tool Solver.