Institute of Mathematics AS CR, v. v. i.
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On the differential geometry of some classes of infinite dimensional manifolds
Get PDFsummary:Albeverio, Kondratiev, and Röckner have introduced a type of differential geometry, which we call lifted geometry, for the configuration space of any manifold . The name comes from the fact that various elements of the geometry of are constructed via lifting of the corresponding elements of the geometry of . In this note, we construct a general algebraic framework for lifted geometry which can be applied to various “infinite dimensional spaces” associated to . In order to define a lifted geometry for a “space”, one dose not need any topology or local coordinate system on the space. As example and application, lifted geometry for spaces of Radon measures on , mappings into , embedded submanifolds of , and tilings on , are considered. The gradient operator in the lifted geometry of Radon measures is considered. Also, the construction of a natural Dirichlet form associated to a random measure is discussed. It is shown that Stokes’ Theorem appears as “differentiability” of “boundary operator” in the lifted geometry of spaces of submanifolds. It is shown that (generalized) action functionals associated with Lagrangian densities on form the algebra of smooth functions in a specific lifted geometry for the path-space of
Some properties of generalized distance eigenvalues of graphs
No full textsummary:Let be a simple connected graph with vertex set and edge set , and let be the degree of the vertex . Let be the distance matrix and let be the diagonal matrix of the vertex transmissions of . The generalized distance matrix of is defined as , where . Let be the generalized distance eigenvalues of , and let be an integer with . We denote by the sum of the largest generalized distance eigenvalues. The generalized distance spread of a graph is defined as . We obtain some bounds on and of graph , respectively
Parametric representations of BiHom-Hopf algebras
No full textsummary:The main purpose of the present paper is to study representations of BiHom-Hopf algebras. We first introduce the notion of BiHom-Hopf algebras, and then discuss BiHom-type modules, Yetter-Dinfeld modules and Drinfeld doubles with parameters. We get some new -monoidal categories via the category of BiHom-(co)modules and the category of BiHom-Yetter-Drinfeld modules. Finally, we obtain a center construction type theorem on BiHom-Hopf algebras
Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source
No full textsummary:We study the chemotaxis system with singular sensitivity and logistic-type source: , under the non-flux boundary conditions in a smooth bounded domain , , and . It is shown with that the system possesses a global generalized solution for which is bounded when is suitably small related to and the initial datum is properly small, and a global bounded classical solution for
The clean elements of the ring
No full textsummary:We characterize clean elements of and show that is clean if and only if there exists a clopen sublocale in such that . Also, we prove that is clean if and only if has a clean prime ideal. Then, according to the results about we immediately get results about $\mathcal C_{c}(L).
Green-Liouville approximation and correct solvability in of the general Sturm-Liouville equation
No full textsummary:We consider the equation where , and For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions and under which the above equation is correctly solvable in the space $p\in (1,\infty ).
Polyanalytic Besov spaces and approximation by dilatations
No full textsummary:Using partial derivatives and , we introduce Besov spaces of polyanalytic functions in the open unit disk, as well as in the upper half-plane. We then prove that the dilatations of functions in certain weighted polyanalytic Besov spaces converge to the same functions in norm. When restricted to the open unit disk, we prove that each polyanalytic function of degree can be approximated in norm by polyanalytic polynomials of degree at most
The Plato–Galileo Problem
No full textsummary:Edice Fontes Scientiae zpřístupnila významná díla novověké vědy. Jde o soubor pěti knih obsahujících autentické a komentované překlady z děl evropské vědy 17. století. V článku je věnována zvláštní pozornost dopisům Isaaca Newtona, v nichž odpovídá na kosmologické otázky teologa Richarda Bentleyho. Všímáme si nastolené otázky, zda Newtonova fyzika umožňuje vysvětlení souvislosti oběžných rychlostí a poloměrů drah planet, což je úloha, kterou se zabýval i Galilei na základě Platónova popisu vzniku světa. Ptáme se, zda by Galileova hypotéza mohla platit při odlišné podobě gravitačního zákona a mohla tak v "alternativní historii" dovést Galilea k návrhu jeho matematického vyjádření
