If (M,∇) is a manifold with a symmetric linear connection, then T*M can be endowed with the natural Riemann extension g¯ (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to g¯g¯ initiated by C. L.Bejan and O.Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure PP on (T*M, g¯) and prove that P is harmonic (in the sense of E.Garciá-Río, L.Vanhecke and M. E.Vázquez-Abal (1997)) if and only if g¯ reduces to the classical Riemann extension introduced by E.M. Patterson and A.G. Walker (1952)., Cornelia-Livia Bejan, Şemsi Eken., and Obsahuje bibliografii
We give a characterization of totally $\eta $-umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form in terms of totally umbilical condition for the holomorphic distribution on real hypersurfaces. We prove that if the shape operator $A$ of a real hypersurface $M$ of a complex space form $M^n(c)$, $c\neq 0$, $n\geq 3$, satisfies $g(AX,Y)=ag(X,Y)$ for any $X,Y\in T_0(x)$, $a$ being a function, where $T_0$ is the holomorphic distribution on $M$, then $M$ is a totally $\eta $-umbilical real hypersurface or locally congruent to a ruled real hypersurface. This condition for the shape operator is a generalization of the notion of $\eta $-umbilical real hypersurfaces.
We characterize when weighted $(LB)$-spaces of holomorphic functions have the dual density condition, when the weights are radial and grow logarithmically.
Given a domain $\Omega $ of class $C^{k,1}$, $k\in \Bbb N $, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of $\Omega $ in the sense that $(\partial- {\partial x_n})\alpha (x',0)= - N(x')$ and that still is of class $C^{k,1}$. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to $k$ on domains of class $C^{k,1}$. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.
The Triangle cemetery in Prague-Střešovice was the only preserved part of the great burial site from the 9th–10th century AD; this site was partially destroyed beginning in the 18th century by the extraction of clay for the Strahov brick factory. A total of 49 graves, all dated to the 10th century, were uncovered in the preserved part of the cemetery in 2012. Children’s grave no. 16 was the richest of the children’s graves and the second richest of all graves in the cemetery. A total of 19 silver jewels were found in the grave: kaptorga – amulet container, beads, hollow spherical pendants – gombiks. A technical study was performed to describe the construction of the different types of jewels and identify the material used to manufacture them. The artefacts were examined with a stereomicroscope, subjected to X-ray radiography and observed and analysed with scanning electron microscopy coupled with energy-dispersive X-ray spectrometry (SEM/EDS). A replica provided practical information about the time of realisation of each type of jewel. Analogies from the technical and thematic points of view were further searched. The set of jewellery comes from the production of the Prague workshop which enriched the tradition of Great Moravian jewellery with new elements inspired by cultural influences from the west, east and south. and Pohřebiště Triangl bylo jedinou zachovanou částí velkého středohradištního pohřebiště ničeného od 18. století těžbou hlíny pro strahovskou cihelnu. V poloze Triangl bylo v roce 2012 prozkoumáno 49 číslovaných hrobů s výbavou datující je do 10. století. Dětský hrob 16 byl nejbohatší z dětských pohřbů a druhý nejbohatší celkově, bylo v něm nalezeno 19 kusů stříbrných šperků – kaptorga, korálky a gombíky. Technologický rozbor šperků má za cíl poznat způsob výroby jednotlivých typů a určit suroviny použité při jejich výrobě. Předměty byly zkoumány pomocí optické stereomikroskopie, rentgenografie a elektronové rastrovací mikroskopie ve spojení s energiově disperzní spektroskopií (SEM/EDS). Byly vyhledány analogie, co se týče technologie výroby i použitých výzdobných motivů. Replika poskytuje představu o čase potřebném k výrobě každého jednotlivého typu šperku. Soubor šperků pochází z produkce pražské dílny, která tradici velkomoravského šperkařství obohatila o nové prvky inspirované kulturními vlivy ze západu, východu i jihu.
Starting from flare models of Karličky (Solar Phys. 130, 1990, 347), we present the timedependent numerical simulations of hydrogen plasma excitation and ionization on subsecond time scales. These scales are consistent with the spiky behaviour of the kinetic temperature produced by non-thermal electron beam pulses of very short duration. Self-consistent numerical solution of
time-dependent, NLTE problem for a three-level plus continuum hydrogen atom allows us to predict theoretically the behaviour of
the Hα line intensity variations on subsecond time intervals. We present the Hα temporal profiles, evaluated at the line center and in the wing, which can be qualitatively compared with some recent flare observations obtained with very high (0.1 sec) temporal resolution. and Full version of this contribution was published in Solar Phys. 135 (1991), 65.
Hagler and the first named author introduced a class of hereditarily $l_1$ Banach spaces which do not possess the Schur property. Then the first author extended these spaces to a class of hereditarily $l_p$ Banach spaces for $1\leq p<\infty $. Here we use these spaces to introduce a new class of hereditarily $l_p(c_0)$ Banach spaces analogous of the space of Popov. In particular, for $p=1$ the spaces are further examples of hereditarily $l_1$ Banach spaces failing the Schur property.
In [5] and [10], statistical-conservative and $\sigma $-conservative matrices were characterized. In this note we have determined a class of statistical and $\sigma $-conservative matrices studying some inequalities which are analogous to Knopp’s Core Theorem.
In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system are established. Some results obtained are extended.