The article deals with estimating deformation between the African and the Eurasian Plate in the Eastern Mediterranean on the basis of GPS coordinate time series. Two sources of velocities were used for processing. The first was the freely available site velocities from the European Permanent Network (EPN). The second was the Egyptian GPS permanent network velocities. Their values were determined by the following technique. Firstly, the Egyptian site coordinates were computed from GPS daily observations, using the fiducial EPN stations. The daily site coordinates at a given time interval result in coordinate time series, which were analysed and used on velocity estimation of the Egyptian stations. Then the apparatus of the mechanics of continuum was applied to all resultant velocities. The regions of possible mutual interactions between the Eurasian and the African Plate in the Eastern Mediterranean were detected. The basic idea of this contribution is the common processing of GPS daily measurements from the Egyptian permanent network together with the EPN data. The available Egyptian GPS data cover almost the last three years, which represents a sufficient time interval for velocity estimation. Introducing the Egyptian permanent GPS measurements into processing enables a better estimate of deformations in the Eastern Mediterranean., Antonín Zeman, Khalil Hassan, Jan Holešovský, Abdel Monem S. Mohamed, Zbyněk Novotný, Mahmoud M. Salah, Jan Kostelecký and Radwan M. Ali., and Obsahuje bibliografii
Brown coal open pit mining in the basin under Krušné Hory Mts. came to contact with slopes of the mountains, and a problem of the stability in high and steep slopes in the crystalline rock became an important question. The question concerns Jezeří Castle built on the top of one of the hills in a most endangered section where even a supporting pillar in the sediments under the slope toe was left to support the slope. As a result, an extensive monitoring program regarding deformations was initiated in the region. The program involved several methods and some important results are discussed. The results that are displayed concern mainly measurements done in geophysical tiltmeter stations in two underground galleries driven into the two steep slope sections showing most dangerous situation, as well as extensometers located in the same locations. Long-term monitoring revealed a tectonic deformation process of a natural origin that is registered as slow and systematic tilts. Besides, it revealed several periods of anomalies that are of basic importance. During a long period of observation from 1982 till 2005 three important deformation anomalies were registered: the event of 1994, the event of 2002, and the event of 2003/2004. The first and the third event have been classified as of a large regional character that affected a wide mountainous area and could be interpreted as a tectonic impulse originating within the mountainous structure of the so called "Dome of Hora Svaté Kateřiny". The second event has been considered different, strictly connected with extreme precipitation of August 2002. The anomaly was evidenced even deep in the crystalline, so that it could not be seen as of a superficial character only. The movement which was registered at that time was oriented right into the pillar supporting the slope., It is concluded that it was a short manifestation of instability in the critical profile "Jezeří - pillar", which stresses the important stabilisation function of the supporting pillar without which the profile will be probably destabilised., Blahoslav Košťák, Bohumil Chán and Jan Rybář., and Obsahuje bibliografii
This paper is devoted to the study of matrix elements of irreducible representations of the enveloping deformed Heisenberg algebra with reflection, motivated by recurrence relations satisfied by hypergeometric functions. It is shown that the matrix elements of a suitable operator given as a product of exponential functions are expressed in terms of d-orthogonal polynomials, which are reduced to the orthogonal Meixner polynomials when d = 1. The underlying algebraic framework allowed a systematic derivation of the recurrence relations, difference equation, lowering and rising operators and generating functions which these polynomials satisfy., Fethi Bouzeffour, Hanen Ben Mansour, Ali Zaghouani., and Obsahuje bibliografii
The modern trend in high power laser applications such as welding, cutting and surface hardening lies in the use of solid-state lasers. The output beam of these lasers is characterized by a Gaussian intensity distribution. However, the laser beams with different intensity distributions, e.g. top-hat, are preferable in various applications. In this paper we present a new type of deformable mirror suitable for the corresponding laser beam shaping. The deformation of the mirror is achieved by an underlying array of actuators and a pressurized coolant that also provides the necessary cooling. We describe the results of the surface shape measurement using a 3D scanner for different settings of actuators. Further, we show the achieved intensity distributions measured by a beam profiler for a low power laser beam reflected from the mirror. and V poslední době nastává rozmach používání pevnolátkových laserů ve výkonových aplikacích, jako jsou laserové svařování, řezání a povrchové kalení. Výstupní svazek těchto laserů má gaussovské rozložení intenzity svazku. Pro výše uvedené aplikace by však v mnoha případech bylo žádoucí rozložení s konstantní intenzitou svazku v jeho průřezu, tzv. top-hat. Článek popisuje nový typ deformovatelného zrcadla vhodný pro transformaci rozložení intenzity ve svazku. Deformace zrcadla je vyvolána maticí tahových elementů připojených na zadní stranu tenkého zrcadla, které působí proti tlakové síle chladicí vody. Byl zhotoven funkční vzorek deformovatelného zrcadla. Bylo provedeno měření jeho tvaru povrchu pro tři nastavení tahových elementů pomocí 3D skeneru. Dále byla ověřena schopnost požadované transformace svazku užitím nízkovýkonového laseru s gaussovským rozložením a měřením odraženého svazku profilometrem intenzity.
In order to further understand a complex 3-D dynamical system proposed by Qi et al, showing four-wing chaotic attractors with very complicated topological structures over a large range of parameters, we study degenerate Hopf bifurcations in the system. It exhibits the result of a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.
This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent domain which characterizes the nondegenerated elastic material regions. We choose a notion of weak solutions which consists of weak formulations of the Cahn-Hilliard system and the momentum balance equation, a variational inequality for the damage evolution and an energy inequality. For the introduced degenerating system, we prove global-in-time existence of weak solutions. The main results are sketched from our recent paper [WIAS preprint no. 1759 (2012)].
Probability logic studies the properties resulting from the probabilistic interpretation of logical argument forms. Typical examples are probabilistic Modus Ponens and Modus Tollens. Argument forms with two premises usually lead from precise probabilities of the premises to imprecise or interval probabilities of the conclusion. In the contribution, we study generalized inference forms having three or more premises. Recently, Gilio has shown that these generalized forms "degrade'' -- more premises lead to more imprecise conclusions, i. e., to wider intervals. We distinguish different forms of degradation. We analyse Predictive Inference, Modus Ponens, Bayes' Theorem, and Modus Tollens. Special attention is devoted to the case where the conditioning events have zero probabilities. Finally, we discuss the relation of degradation to monotonicity.
Let $r\ge 3$, $n\ge r$ and $\pi =(d_1,d_2,\ldots ,d_n)$ be a non-increasing sequence of nonnegative integers. If $\pi $ has a realization $G$ with vertex set $V(G)=\{v_1,v_2,\ldots ,v_n\}$ such that $d_G(v_i)=d_i$ for $i=1,2,\ldots , n$ and $v_1v_2\cdots v_rv_1$ is a cycle of length $r$ in $G$, then $\pi $ is said to be potentially $C_r''$-graphic. In this paper, we give a characterization for $\pi $ to be potentially $C_r''$-graphic.
A graph $G$ is degree-continuous if the degrees of every two adjacent vertices of $G$ differ by at most 1. A finite nonempty set $S$ of integers is convex if $k \in S$ for every integer $k$ with $\min (S) \le k \le \max (S)$. It is shown that for all integers $r > 0$ and $s \ge 0$ and a convex set $S$ with $\min (S) = r$ and $\max (S) = r+s$, there exists a connected degree-continuous graph $G$ with the degree set $S$ and diameter $2s+2$. The minimum order of a degree-continuous graph with a prescribed degree set is studied. Furthermore, it is shown that for every graph $G$ and convex set $S$ of positive integers containing the integer 2, there exists a connected degree-continuous graph $H$ with the degree set $S$ and containing $G$ as an induced subgraph if and only if $\max (S)\ge \Delta (G)$ and $G$ contains no $r-$regular component where $r = \max (S)$.