20181115 12:39 
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20181002 14:38 
Neglected gravitational redshift in detections of gravitational waves
Křížek, Michal ; Somer, L.
In 2016, the letter [1] about the first detection of gravitational waves was published. They were generated by two merging black holes that had approximately 36 and 29 Sun’s masses. However, the authors have not taken into account a large gravitational redshift of this binary system, which is a direct consequence of time dilation in a strong gravitational field. Thus the proposed masses are overestimated. In our paper we also give other arguments for this statement.
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20181002 14:38 
Classification of distances in cosmology
Křížek, Michal ; Mészáros, A.
In cosmology many different distances are defined: angular, comoving, Euclidean, Hubble, lightyear, luminosity, Minkowski, parallax, proper motion, redshift, ... distance. There is not one single natural distance, since the universe is expanding, curved, and we look back in time. In this survey paper we will concentrate on geometrical interpretations of the abovementioned distances.
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20180316 15:47 
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20180309 13:20 
Genus two prime form formula for vertex operator characters
Zuevsky, Alexander
We find an expression for the selfsewn genus two Riemann surface counterpart of the torus formula for for an $n$vertex operator character for the Heisenberg vertex operator algebra an $n$point correlation function for a vertex operator algebra module with complex parameterization of corresponding states.
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20180309 13:20 
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20180309 13:20 
Courant algebroid connections and string effective actions
Jurčo, B. ; Vysoký, Jan
Courant algebroids are a natural generalization of quadratic Lie algebras, appearing in various contexts in mathematical physics. A connection on a Courant algebroid gives an analogue of a covariant derivative compatible with a given fiberwise metric. Imposing further conditions resembling standard LeviCivita connections, one obtains a class of connections whose curvature tensor in certain cases gives a new geometrical description of equations of motion of low energy effective action of string theory. Two examples are given. One is the so called symplectic gravity, the second one is an application to the the so called heterotic reduction. All necessary definitions, propositions and theorems are given in a detailed and selfcontained way.
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20180309 13:20 
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20180309 13:20 
CrandallRabinowitz type bifurcation for nondifferentiable perturbations of smooth mappings
Recke, L. ; Väth, Martin ; Kučera, Milan ; Navrátil, J.
We consider abstract equations of the type ..., where lambda is a bifurcation parameter and tau is a perturbation parameter. We suppose that ... for all lambda and tau, F is smooth and the unperturbed equation ... describes a CrandallRabinowitz bifurcation in lambda=0, that is, two halfbranches of nontrivial solutions bifurcate from the trivial solution in lambda=0. Concerning G, we suppose only a certain Lipschitz condition; in particular, G is allowed to be nondifferentiable. We show that for fixed small ... there exist also two halfbranches of nontrivial solutions to the perturbed equation, but they bifurcate from the trivial solution in two bifurcation points, which are different, in general. Moreover, we determine the bifurcation directions of those two halfbranches, and we describe, asymptotically as ..., how the bifurcation points depend on tau. Finally, we present applications to boundary value problems for quasilinear elliptic equations and...
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20180309 13:19 
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