An edge of $G$ is singular if it does not lie on any triangle of $G$; otherwise, it is non-singular. A vertex $u$ of a graph $G$ is called locally connected if the induced subgraph $G[N(u)]$ by its neighborhood is connected; otherwise, it is called locally disconnected. In this paper, we prove that if a connected claw-free graph $G$ of order at least three satisfies the following two conditions: (i) for each locally disconnected vertex $v$ of degree at least $3$ in $G,$ there is a nonnegative integer $s$ such that $v$ lies on an induced cycle of length at least $4$ with at most $s$ non-singular edges and with at least $s-5$ locally connected vertices; (ii) for each locally disconnected vertex $v$ of degree $2$ in $G,$ there is a nonnegative integer $s$ such that $v$ lies on an induced cycle $C$ with at most $s$ non-singular edges and with at least $s-3$ locally connected vertices and such that $G[V (C)\cap V_{2} (G)]$ is a path or a cycle, then $G$ has a 2-factor, and it is the best possible in some sense. This result generalizes two known results in Faudree, Faudree and Ryjáček (2008) and in Ryjáček, Xiong and Yoshimoto (2010).
The Ondřejov 2-meter Telescope is used either in the Cassegrain or in the coudé focus; the primary focus is not used. The primary goal is the spectroscopy. Nowadays, the Cassegrain focus is equipped with the fiber-fed echelle spectrograph HEROS owned by the Landessternwarte Heidelberg-Konigstuhl. The coudé focus is equipped with the slit spectrograph. Usually, the slit coudé spectrograph is being used in winter due to the lower sensitivity to the weather condition (seeing).
Let $\tau $ be a type of algebras. A valuation of terms of type $\tau $ is a function $v$ assigning to each term $t$ of type $\tau $ a value $v(t) \geq 0$. For $k \geq 1$, an identity $s \approx t$ of type $\tau $ is said to be $k$-normal (with respect to valuation $v$) if either $s = t$ or both $s$ and $t$ have value $\geq k$. Taking $k = 1$ with respect to the usual depth valuation of terms gives the well-known property of normality of identities. A variety is called $k$-normal (with respect to the valuation $v$) if all its identities are $k$-normal. For any variety $V$, there is a least $k$-normal variety $N_k(V)$ containing $V$, namely the variety determined by the set of all $k$-normal identities of $V$. The concept of $k$-normalization was introduced by K. Denecke and S. L. Wismath in their paper (Algebra Univers., 50, 2003, pp.107-128) and an algebraic characterization of the elements of $N_k(V)$ in terms of the algebras in $V$ was given in (Algebra Univers., 51, 2004, pp. 395--409). In this paper we study the algebras of the variety $N_2(V)$ where $V$ is the type $(2,2)$ variety $L$ of lattices and our valuation is the usual depth valuation of terms. We introduce a construction called the {\it $3$-level inflation} of a lattice, and use the order-theoretic properties of lattices to show that the variety $N_2(L)$ is precisely the class of all $3$-level inflations of lattices. We also produce a finite equational basis for the variety $N_2(L)$.
We present 2.2 micron maps of selected areas of the Galactic Plane, taken with the 1.5 m. Sánchez-Magro telescope on the island of Tenerife. A model of the galactic stellar distribution has been developed and the derived stellar surface densities are compared with the observations. The results are in good agreement with the experimental data and suggest remarkable differences between
the luminosity functions for the disk and the spheroid components. The extinction toward the galactic centre shows an abrupt increase when compared with other galactic directions. We note also that a
better fit is obtained when the 5 Kpc ring is included in the model, but cannot infer from our data the existence of a thick disk.
(Statement of Responsibility) de Haydn, (Ownership) Procvenience: Hudební spolek bohoslovců v ČB, koupil spolek hudebníků v theolog. semináři Č. Budějovicích, and (Version Identification) Fragment (chybí party houslí a violoncella)