The main goal of this paper is to show an application of Graph Theory to classifying Lie algebras over finite fields. It is rooted in the representation of each Lie algebra by a certain pseudo-graph. As partial results, it is deduced that there exist, up to isomorphism, four, six, fourteen and thirty-four $2$-, $3$-, $4$-, and $5$-dimensional algebras of the studied family, respectively, over the field $\mathbb {Z}/2\mathbb {Z}$. Over $\mathbb {Z}/3\mathbb {Z}$, eight and twenty-two $2$- and $3$-dimensional Lie algebras, respectively, are also found. Finally, some ideas for future research are presented.
Recently, the eminently popular standard quantile regression has been generalized to the multiple-output regression setup by means of directional regression quantiles in two rather interrelated ways. Unfortunately, they lead to complicated optimization problems involving parametric programming, and this may be the main obstacle standing in the way of their wide dissemination. The presented R package modQR is intended to address this issue. It originates as a quite faithful translation of the authors' moQuantile toolbox for Octave and MATLAB, and provides all the necessary computational support for both the directional multiple-output quantile regression methods to the wide statistical public. The article offers a concise summary of the statistical theory behind modQR, overviews the package in brief, points out its departures from moQuantile, comments on its use and performance, and demonstrates its application.
We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.
It is well-known that every MV-algebra is a distributive lattice with respect to the induced order. Replacing this lattice by the so-called directoid (introduced by J. Ježek and R. Quackenbush) we obtain a weaker structure, the so-called skew MV-algebra. The paper is devoted to the axiomatization of skew MV-algebras, their properties and a description of the induced implication algebras.
Dírkonošci (Foraminifera), mořští prvoci s vápenatou schránkou, obývají naši planetu více než půl miliardy let. Zkoumáním způsobu života těch současných se mnohé dozvíme o jejich pravěkých předcích i o dávných mořích, ve kterých žili., Foraminifera - a rich group of mainly marine microorganisms - are widely used for paleoecological reconstructions. Their occurrence provides important data about past ecological conditions of the sites. We reconstructed former conditions in Židlochovice research site (southern Moravia) by comparing fossil communities with the recent ones present on the island of Rab (Adriatic Sea)., and Anna Poštulková.
To build a general model for the propagation of destructive events during disasters, we consider a networked system. The model involves network nodes as single objects and delayed interactions along directed links.
In this work, a disaster is understood as a sequence of dynamic destructive events which cause nonreversible changes, spreading in cascade-like manner. We define a global state of the system and suppose that the Markovian property holds. Hence, we can describe any object‘s first affect using the phase type distribution. This model can be used to improve disaster awareness and anticipated disaster response management. and Obsahuje seznam literatury
This paper is concerned with the determination of the relationship for the calculation of the discharge coefficient at free overflow over a rectangular sharp-edged broad-crested weir without lateral contraction. The determination was made on the basis of new measurement in a range of the relative thickness of the weir from 0.12 to 0.30 and newly in a large range of relative height of the weir extremely from 0.24 to 6.8 which greatly expands the application possibilities of low weirs. In addition, the effects of friction and surface tension on the value of the discharge coefficient were evaluated as well as the effect of the relative thickness of the weir. The new equation for discharge coefficient, expressed using the relative height of the weir, was subjected to verification made by an independent laboratory which confirmed its accuracy.