Abstract:
Our aim was the prediction of karstification. We measured the karstic bedrock and the overlying superficial cover in four areas of Hungary and one area in Romania. One of our tools was the widely used geophysical techniques i.e. VES and multi-electrode method. We also made observations on mountainous, Mediterranean and tropical karsts. In these areas the occurrence of covered karsts, of either syngenetic or postgenetic type, is high. Based on the measured data we determined the conditions under which covered karst formation is possible. For example the conditions that induce syngenetic karstification are: cavities, caves, and shafts within the bedrock, places where the superficial cover is locally thinner, or places where the impermeable beds edge out. An indicator of postgenetic karstification is the presence of lenticular intercalations in the superficial cover (sites of former dolines). Knowing these conditions in any karst area we can readily identify the potential sites where covered karst formation is possible in the near future. If these sites are known, engineering structures can be planned so that potential dangers due to karstification are avoided.

Abstract:
Hemodynamic instability often leads to hypoperfusion, which has a significant impact on outcome in both medical and surgical patients. Measures to detect and treat tissue hypoperfusion early by correcting the imbalance between oxygen delivery and consumption is of particular importance. There are several studies targeting different hemodynamic endpoints in order to investigate the effects of goal-directed therapy on outcome. A so-called multimodal concept putting several variables in context follows simple logic and may provide a broader picture. Furthermore, rather than treating population based “normal” values of certain indices, this concept can be translated into the individualized patient care to reach adequate oxygen supply and tissue oxygenation in order to avoid under, or over resuscitation, which are equally harmful. The purpose of this review is to give an overview of current data providing the basis of this a multimodal, individualized approach of hemodynamic monitoring and treatment.

Abstract:
The mineralogy, geochemistry and magnetic properties of total suspended particulate (TSP) matter in Budapest, Hungary were studied to identify their heavy metal-bearing mineral phases. Amorphous organic matter, magnetite, salts as well as mineral phases characteristic of the surrounding geology are the main components of the TSP. They show significant enrichment in several heavy metals, such as Zn (up to 19 046 mg/kg), Pb (up to 3597 mg/kg), Cu (up to 699 mg/kg) and Mo (up to 53 mg/kg). The most frequent heavy metal-bearing mineral phases are spherular or xenomorphic magnetite particles containing 2-3 wt% Pb and Zn. They often form aggregates and are closely associated with soot and/or clay minerals. The size of these particles is rarely below 30 nm. Cu and Mo could be associated to magnetite too. Clay minerals and mica particles may also contain significant amount of Zn (up to 5wt%). Additionally, ZnO and ZnCO3 particles were found in the sample with highest Zn content and our data suggest the potential association of Pb and carbonates, as well. Magnetite particles are resistant to weathering releasing its toxic components slowly to the environment, while layer silicates (and carbonates) may be the potential source of mobile toxic metals in the TSP.

Abstract:
It is a well-known fact that the Baltic area is traditionally one of the most diverse regions of Europe in terms of ethnic concerns; we can observe in many settlements that four or even five religions have their own churches, cemeteries and at least as many ethnic groups are having their schools etc. Regarding geography literature, no generally accepted method has been applied yet to measure the population’s diversity and spatial segregation; in most cases only the number and ratio of ethnic groups were described. This research paper proposes a different approach: the adaptation of the so-called Simpson’s Diversity Index, based on probability theory and originally used by ecologists to measure biodiversity, to human geography. The study seeks the answers to: where, when, why and how has the Ethnic Diversity and Ethnic Segregation Index changed in Latvia during the first and second independence periods? What kind of spatial patterns are possible to observe on the basis of the transformation? The enormous data is processed by modern GIS software products and projected on thematic maps.

Abstract:
In this article, we describe a recursive method to construct a subset of relevant Slater-determinants for the use in many-body diagonalization schemes that will be employed in our forthcoming papers on the simulation of excited many-body states in discrete electronic nanosystems. The algorithm is intended for the realistic simulation of nanodevices which typically requires the consideration of a large number of single-particle basis states (typ. 256) and the calculation of a sufficient number (typ. a few 1000) of relevant excited many-body states.

Abstract:
In our article we deal with studying the accuracy of DGPS surveys. The test measurements focussed on this purpose with a LEICA GS20 GPS receiver were very useful for us for various reasons. Firstly, we got acquainted with the operation of a hand-held GIS GPS receiver which is considered to be a relatively new one on the market and the usage of the appropriate post-processing software, secondly when analyzing the results we studied the improving accuracy of our test measurements performed with a single receiver using various corrections. Accordingly, ground corrections originated from PENC control station were considered on the one hand, on the other hand EGNOS corrections were applied when we formed an opinion of the problem raised in the title of this study.

Abstract:
Let $G$ be an abelian Polish group, e.g. a separable Banach space. A subset $X \subset G$ is called Haar null (in the sense of Christensen) if there exists a Borel set $B \supset X$ and a Borel probability measure $\mu$ on $G$ such that $\mu(B+g)=0$ for every $g \in G$. The term shy is also commonly used for Haar null, and co-Haar null sets are often called prevalent. Answering an old question of Mycielski we show that if $G$ is not locally compact then there exists a Borel Haar null set that is not contained in any $G_\delta$ Haar null set. We also show that $G_\delta$ can be replaced by any other class of the Borel hierarchy, which implies that the additivity of the $\sigma$-ideal of Haar null sets is $\omega_1$. The definition of a generalised Haar null set is obtained by replacing the Borelness of $B$ in the above definition by universal measurability. We give an example of a generalised Haar null set that is not Haar null, more precisely we construct a coanalytic generalised Haar null set without a Borel Haar null hull. This solves Problem GP from Fremlin's problem list. Actually, all our results readily generalise to all Polish groups that admit a two-sided invariant metric.

Abstract:
In the 1970s M. Laczkovich posed the following problem: Let $\mathcal{B}_1(X)$ denote the set of Baire class $1$ functions defined on a Polish space $X$ equipped with the pointwise ordering. \[\text{Characterize the order types of the linearly ordered subsets of $\mathcal{B}_1(X)$.} \]The main result of the present paper is a complete solution to this problem. We prove that a linear order is isomorphic to a linearly ordered family of Baire class $1$ functions iff it is isomorphic to a subset of the following linear order that we call $([0,1]^{<\omega_1}_{\searrow 0},<_{altlex})$, where $[0,1]^{<\omega_1}_{\searrow 0}$ is the set of strictly decreasing transfinite sequences of reals in $[0, 1]$ with last element $0$, and $<_{altlex}$, the so called \emph{alternating lexicographical ordering}, is defined as follows: if $(x_\alpha)_{\alpha\leq \xi}, (x'_\alpha)_{\alpha\leq \xi'} \in [0,1]^{<\omega_1}_{\searrow 0}$, and $\delta$ is the minimal ordinal where the two sequences differ then we say that \[ (x_\alpha)_{\alpha\leq \xi} <_{altlex} (x'_\alpha)_{\alpha\leq \xi'} \iff (\delta \text{ is even and } x_{\delta}x'_{\delta}). \] Using this characterization we easily reprove all the known results and answer all the known open questions of the topic.

Abstract:
Let $(G,\cdot)$ be a Polish group. We say that a set $X \subset G$ is Haar null if there exists a universally measurable set $U \supset X$ and a Borel probability measure $\mu$ such that for every $g, h \in G$ we have $\mu(gUh)=0$. We call a set $X$ naively Haar null if there exists a Borel probability measure $\mu$ such that for every $g, h \in G$ we have $\mu(gXh)=0$. Generalizing a result of Elekes and Stepr\=ans, which answers the first part of Problem FC from Fremlin's list, we prove that in every abelian Polish group there exists a naively Haar null set that is not Haar null.

Abstract:
We present the plane-sweep incremental algorithm, a hybrid approach for computing Delaunay tessellations of large point sets whose size exceeds the computer's main memory. This approach unites the simplicity of the incremental algorithms with the comparatively low memory requirements of plane-sweep approaches. The procedure is to first sort the point set along the first principal component and then to sequentially insert the points into the tessellation, essentially simulating a sweeping plane. The part of the tessellation that has been passed by the sweeping plane can be evicted from memory and written to disk, limiting the memory requirement of the program to the "thickness" of the data set along its first principal component. We implemented the algorithm and used it to compute the Delaunay tessellation and Voronoi partition of the Sloan Digital Sky Survey magnitude space consisting of 287 million points.