V astronomické a fyzikální komunitě panuje všeobecné přesvědčení, že dodatečně relativistické stáčení perihelia dráhy Merkuru 43" za století je již dávno a mnohokrát prověřená hodnota, na které není třeba nic měnit. Že je dána rozdílem pozorovaného stáčení perihelia Merkuru a počítaného stáčení pomocí Newtonovy mechaniky. V tomto případě se ale odečítají dvě skoro stejně velká čísla, která jsou navíc zatížena mnoha chybami. Výsledný rozdíl 43" za století je tak nejistý a nemusí odpovídat skutečnosti., The perihelion shift of Mercury's orbit is thought to be one of the fundamental tests of the validity of the general theory of relativity. In the current (astro)physical community, it is generally accepted that the additional relativistic perihelion shift of Mercury is the difference between its observed perihelion shift and the one predicted by Newtonian mechanics, and that this difference equals 43" per century. However, as it results from the subtraction of two quite inexact numbers of almost equal magnitude, it may be subject to cancelation errors. As such, the above accepted value is highly uncertain and may not correspond to reality., Michal Křížek., and Obsahuje seznam literatury
The notion of ‘undisturbed motion‘ in this paper expresses the natural elastic oscillations of a robot manipulation system (MS) insulated from external effects. The natural frequencies and the normal functions of a two-link robot with a manipulation system of ‘stiff units with variable geometry‘ are determined. The differential equations of the natural oscillations of systems are worked out and their common solution is determined. and Obsahuje seznam literatury
Axioms are given for positive comparative probabilities and plausibilities defined either on Boolean algebras or on arbitrary sets of events. These axioms allow to characterize binary relations representable by either standard or nonstandard measures (i. e. taking values either on the real field or on a hyperreal field). We also study relations between conditional events induced by preferences on conditional acts.
In this article the history and current status of the standard model of electroweak interactions is briefly described. Starting with quantum electrodynamics and the phenomenological V - A theory of weak interactions, we proceed to the key theoretical concepts of the Yang-Mills field and the Higgs mechanism. The idea of the electroweak unification and the birth of the standard model is then discussed in more detail, including the peculiarities of the quark sector, anomalies and CP violation. Some open problems that could lead us to new physics beyond the standard model are mentioned in the concluding section. Future prospects of particle physics using high energy colliders are also briefly discussed., Jiří Hořejší., and Obsahuje bibliografii
We define nice partitions of the multicomplex associated with a Stanley ideal. As the main result we show that if the monomial ideal $I$ is a CM Stanley ideal, then $I^p$ is a Stanley ideal as well, where $I^p$ is the polarization of $I$.
Let $G$ be a multigraph. The star number ${\mathrm s}(G)$ of $G$ is the minimum number of stars needed to decompose the edges of $G$. The star arboricity ${\mathrm sa}(G)$ of $G$ is the minimum number of star forests needed to decompose the edges of $G$. As usual $\lambda K_n$ denote the $\lambda $-fold complete graph on $n$ vertices (i.e., the multigraph on $n$ vertices such that there are $\lambda $ edges between every pair of vertices). In this paper, we prove that for $n \ge 2$ \[ \begin{aligned} {\mathrm s}(\lambda K_n)&= \left\rbrace \begin{array}{ll}\frac{1}{2}\lambda n&\text{if}\ \lambda \ \text{is even}, \frac{1}{2}(\lambda +1)n-1&\text{if}\ \lambda \ \text{is odd,} \end{array}\right. {\vspace{2.0pt}} {\mathrm sa}(\lambda K_n)&= \left\rbrace \begin{array}{ll}\lceil \frac{1}{2}\lambda n \rceil &\text{if}\ \lambda \ \text{is odd},\ n = 2, 3 \ \text{or}\ \lambda \ \text{is even}, \lceil \frac{1}{2}\lambda n \rceil +1 &\text{if}\ \lambda \ \text{is odd},\ n\ge 4. \end{array}\right. \end{aligned} \qquad \mathrm{(1,2)}\].
The problem of finding an input-output representation of a nonlinear state space system, usually referred to as the state elimination, plays an important role in certain control problems. Though, it has been shown that such a representation, at least locally, always exists for both the systems with and without delays, it might be a neutral input-output differential equation in the former case, even when one starts with a retarded system. In this paper the state elimination is therefore extended further to nonlinear neutral state-space systems, and it is shown that also in such a case an input-output representation, at least locally, always exists. In general, it represents a neutral system again. Computational aspects related to the state elimination problem are discussed as well.
Riečan [12] and Chovanec [1] investigated states in $MV$-algebras. Earlier, Riečan [11] had dealt with analogous ideas in $D$-posets. In the monograph of Riečan and Neubrunn [13] (Chapter 9) the notion of state is applied in the theory of probability on $MV$-algebras. We remark that a different definition of a state in an $MV$-algebra has been applied by Mundici [9], [10] (namely, the condition (iii) from Definition 1.1 above was not included in his definition of a state; in other words, only finite additivity was assumed). Below we work with the definition from [13]; but, in order to avoid terminological problems we use the term “state-homomorphism” (instead of “state”). The author is indebted to the referee for his suggestion concerning terminology. Let $\mathcal A$ be an $MV$-algebra which is defined on a set $A$ with $\mathop {\mathrm card}A>1$. In the present paper we show that there exists a one-to-one correspondence between the system of all state-homomorphisms on $\mathcal A$ and the system of all $\sigma $-closed maximal ideals of $\mathcal A$. For $MV$-algebras we apply the notation and the definitions as in Gluschankof [3]. The relations between $MV$-algebras and abelian lattice ordered groups (cf. Mundici [8]) are substantially used in the present paper.