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.
The UN General Assembly has declared 2015 the International Year of Soils to raise awareness of the vital importance of soil, which is essential not only for food security and for cultivating plants for feed, fibre, fuel and medicinal products, but also for maintaining biodiversity as it hosts countless organisms. It plays a key role in storing and filtering water, in carbon and other nutrients cycling and performs other irreplaceable ecosystem functions. The Institute of Soil Biology of the CAS Biology Centre carries out biological research into many of those functions of soil in both natural and human–affected environments, including studies of the soil microstructure, soil organism communities and their dynamics and interactions and so on. Researchers at the Institute of Soil Biology focus, among other things, on the contribution of soil fungi to nitrous oxide emissions and on the production of methane. The latter is a potent greenhouse gas and a substantial part of atmospheric methane is produced by anaerobic microorganisms called Archaea found in the soil and in animal digestive tracts, while soil is also a significant methane sink. Research is also being concentrated on the characterization and risk assessment of antibiotic resistance-reservoirs in soil, which is connected with the massive use of antibiotics in the past five decades. Scientists examine ways of preventing the antibiotic resistance spreading in the environment through food chains as well as and on the role played by the soil microflora in those processes, as Doctor Dana Elhottová explains in the corresponding article. and Jana Olivová.