Modular operads and the quantum open-closed homotopy algebra

We verify that certain algebras appearing in string field theory are algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are explained from the operadic point of view.Comment: 56 pages, v2: substantially revised expositio

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.

Operadické resolventy diagramů

doktorské disertační práce Operadické resolventy diagramů Martin Doubek Zkoumáme resolventy operády AC popisující diagramy daného tvaru C v kat- egorii algeber daného typu A. Za jistých předpokladů dokážeme domněnku M. Markla o konstrukci této resolventy pomocí daných resolvent operád A a C. V případě asociativních algeber dostaneme explicitní popis kohomologické teorie pro příslušné diagramy, která se shoduje s teorií vymyšlenou Gersten- haberem a Schackem. Obecně také ukážeme, že operadickou kohomologii lze popsat pomocí Extu v abelovské kategorii operadických modulů. 1of the Doctoral Thesis Operadic Resolutions of Diagrams by Martin Doubek We study resolutions of the operad AC describing diagrams of a given shape C in the category of algebras of a given type A. We prove the conjecture by Markl on constructing the resolution out of resolutions of A and C, at least in a certain restricted setting. For associative algebras, we make explicit the cohomology theory for the diagrams and recover Gerstenhaber-Schack diagram cohomology. In general, we show that the operadic cohomology is Ext in the category of operadic modules. 1Matematicko-fyzikální fakultaFaculty of Mathematics and Physic

Analysis of construction sub-processes for the evaluation of the real performance of tower cranes

The productivity of work performed at construction sites is primarily dependent on the effective deployment and use of construction machinery. Nevertheless, manufacturers do not state the actual performance of their machinery because it is difficult to determine due to its dependence on the specific conditions present at each construction site. One of the most important machines used in the construction of buildings is the tower crane, which provides secondary transport of material onsite. In order to evaluate the effectiveness of the use of such machines using a deterministic or stochastic approach, a relatively extensive and exact set of data describing the activities of a given tower crane needs to be prepared. These data describe the real requirements of ongoing construction sub-processes with regard to the utilisation of tower cranes. This contribution concerns the analysis of key construction sub-processes during the building of monolithic reinforced concrete structures in connection with secondary transport at the construction site; in particular, it describes the preparation and processing of this data for the evaluation of real time requirements placed on tower cranes

L∞L_\infty-interpretation of a classification of deformations of Poisson structures in dimension three

We give an $L_\infty$-interpretation of the classification, obtained in [AP2], of the formal deformations of a family of exact Poisson structures in dimension three. We indeed obtain again the explicit formulas for all the formal deformations of these Poisson structures, together with a classification in the generic case, by constructing a suitable quasi-isomorphism between two $L_\infty$-algebras, which are associated to these Poisson structures.Comment: 31 pages, Added references, minor change