We compare the forcing-related properties of a complete Boolean algebra ${\mathbb B}$ with the properties of the convergences $\lambda _{\mathrm s}$ (the algebraic convergence) and $\lambda _{\mathrm {ls}}$ on ${\mathbb B}$ generalizing the convergence on the Cantor and Aleksandrov cube, respectively. In particular, we show that $\lambda _{\mathrm {ls}}$ is a topological convergence iff forcing by ${\mathbb B}$ does not produce new reals and that $\lambda _{\mathrm {ls}}$ is weakly topological if ${\mathbb B}$ satisfies condition $(\hbar )$ (implied by the ${\mathfrak t}$-cc). On the other hand, if $\lambda _{\mathrm {ls}}$ is a weakly topological convergence, then ${\mathbb B}$ is a $2^{\mathfrak h}$-cc algebra or in some generic extension the distributivity number of the ground model is greater than or equal to the tower number of the extension. So, the statement “The convergence $\lambda _{\mathrm {ls}}$ on the collapsing algebra ${\mathbb B}=\mathop {\mathrm {ro}} (^{<\omega }\omega _2)$ is weakly topological“ is independent of ZFC.
We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence, and we present a complete overview of bivariate test spaces for all possible situations. The practical use will be illustrated by means of a numerical application based on an illustrative portfolio containing the S&P 500 Composite Index, the JP Morgan Government Bond Index and the NAREIT All index.
According to the standard cosmological model, 27 % of the Universe consists of some mysterious dark matter, 68 % consists of even more mysterious dark energy, whereas only less than 5 % corresponds to baryonic matter composed from known elementary particles. The main purpose of this paper is to show that the proposed ratio 27 : 5 between the amount of dark matter and baryonic matter is considerably overestimated. Dark matter and partly also dark energy might result from inordinate extrapolations, since reality is identified with its mathematical model. Especially, we should not apply results that were verified on the scale of the Solar System during several hundreds of years to the whole Universe and extremely long time intervals without any bound of the modeling error.
We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold "a harmonic manifold is locally symmetric" and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a slightly more general setting., Yunhee Euh, Jeong Hyeong Park, Kouei Sekigawa., and Obsahuje bibliografii
A workable nonstandard definition of the Kurzweil-Henstock integral is given via a Daniell integral approach. This allows us to study the HL class of functions from . The theory is recovered together with a few new results.
A special case of a combinatorial theorem of De Bruijn and Erdős asserts that every noncollinear set of $n$ points in the plane determines at least $n$ distinct lines. Chen and Chvátal suggested a possible generalization of this assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces where each nonzero distance equals $1$ or $2$.
A version of Dieudonné theorem is proved for lattice group-valued modular measures on lattice ordered effect algebras. In this way we generalize some results proved in the real-valued case.
This paper presented a new image encryption algorithm. The algorithm includes two steps: first, by using Cubic map and wavelet function to produce the 2D chaotic sequences to scramble the location of pixel points from the image, then using DNA sequence and chaotic sequence produced by Logistic chaotic map to disturb the gray of the pixel points from image. The experimental results and security analysis show that our algorithm can get good encryption effect, has widest secret key's space, strong sensitivity to secret key, and has the ability of resisting exhaustive attack and statistic attack.
We give a new proof of the Weiss conjecture for analytic semigroups. Our approach does not make any recourse to the bounded
$H^{\infty }$-calculus and is based on elementary analysis.
BL-algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that BL-algebras are the duals of bounded representable DRl-monoids. This duality enables us to describe some structure properties of BL-algebras.