A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.
Let $G\subset {\bf SU}(2,1)$ be a non-elementary complex hyperbolic Kleinian group. If $G$ preserves a complex line, then $G $ is $\mathbb {C}$-Fuchsian; if $ G $ preserves a Lagrangian plane, then $ G $ is $\mathbb {R}$-Fuchsian; $ G $ is Fuchsian if $ G $ is either $\mathbb {C}$-Fuchsian or $\mathbb {R}$-Fuchsian. In this paper, we prove that if the traces of all elements in $ G $ are real, then $ G $ is Fuchsian. This is an analogous result of Theorem V.G. 18 of B. Maskit, Kleinian Groups, Springer-Verlag, Berlin, 1988, in the setting of complex hyperbolic isometric groups. As an application of our main result, we show that $ G $ is conjugate to a subgroup of ${\bf S}(U(1)\times U(1,1))$ or ${\bf SO}(2,1)$ if each loxodromic element in $G $ is hyperbolic. Moreover, we show that the converse of our main result does not hold by giving a $\mathbb {C}$-Fuchsian group.
By the interval function of a finite connected graph we mean the interval function in the sense of H. M. Mulder. This function is very important for studying properties of a finite connected graph which depend on the distance between vertices. The interval function of a finite connected graph was characterized by the present author. The interval function of an infinite connected graph can be defined similarly to that of a finite one. In the present paper we give a characterization of the interval function of each connected graph.
Let $G$ be a finite group and $\pi _{e}(G)$ be the set of element orders of $G$. Let $k \in \pi _{e}(G)$ and $m_{k}$ be the number of elements of order $k$ in $G$. Set ${\rm nse}(G):=\{m_{k}\colon k \in \pi _{e}(G)\}$. In fact ${\rm nse}(G)$ is the set of sizes of elements with the same order in $G$. In this paper, by ${\rm nse}(G)$ and order, we give a new characterization of finite projective special linear groups $L_{2}(p)$ over a field with $p$ elements, where $p$ is prime. We prove the following theorem: If $G$ is a group such that $|G|=|L_{2}(p)|$ and ${\rm nse}(G)$ consists of $1$, $p^{2}-1$, $p(p+\epsilon )/2$ and some numbers divisible by $2p$, where $p$ is a prime greater than $3$ with $p \equiv 1$ modulo $4$, then $G \cong L_{2}(p)$.
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.
A cheap chlorophyll (Chl) a fluorescence imaging system was developed for measuring leaf areas of 30×45 cm. Uniform saturating irradiances were created using CuSO4 filtered radiation from stroboscopes. The system was tested using maize leaves treated with diuron. Comparison was made with a small-area-measuring pulse amplified modulation Chl fluorometer. and P. Lootens, P. Vandecasteele.
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.