The paper presents a simple method to check a positiveness of symmetric multivariate polynomials on the unit multi-circle. The method is based on the sampling polynomials using the fast Fourier transform. The algorithm is described and its possible applications are proposed. One of the aims of the paper is to show that presented algorithm is significantly faster than commonly used method based on the semi-definite programming expression.
This paper discusses an experiment in cognitive psychology called the Linda problem. Firstly, some natural conditions for the correctness of the interpretation of psychological experiments (such as the Linda problem) are formulated. The article is essentially a critique of the interpretation of the results of the Linda problem experiment provided by Kahneman and Tversky as well as – indirectly – their concept of heuristics. It is shown that the interpretation provided by Kahneman and Tversky does not meet the aforementioned conditions for correctness. The main argument is justified utilizing such rules of rationality as conditional probability and Grice’s conversational maxims. It is also pointed out that this argument can be reformulated in terms of the intuitive system of reasoning., Tento příspěvek pojednává o experimentu v kognitivní psychologii nazývaném problém Lindy. Za prvé jsou formulovány některé přírodní podmínky pro správnost interpretace psychologických experimentů (jako je problém Lindy). Článek je v podstatě kritikou interpretace výsledků problému Linda, který poskytli Kahneman a Tversky, stejně jako - nepřímo - jejich pojetí heuristiky. Ukazuje se, že výklad poskytnutý Kahnemanem a Tversky nesplňuje výše uvedené podmínky správnosti. Hlavní argument je odůvodněn použitím takových pravidel racionality jako podmíněné pravděpodobnosti a Griceho konverzačních maxim. Rovněž je zdůrazněno, že tento argument lze přeformulovat z hlediska intuitivního systému uvažování., and Adam Olszewski
The perturbed Laplacian matrix of a graph G is defined as DL = D−A, where D is any diagonal matrix and A is a weighted adjacency matrix of G. We develop a Fiedler-like theory for this matrix, leading to results that are of the same type as those obtained with the algebraic connectivity of a graph. We show a monotonicity theorem for the harmonic eigenfunction corresponding to the second smallest eigenvalue of the perturbed Laplacian matrix over the points of articulation of a graph. Furthermore, we use the notion of Perron component for the perturbed Laplacian matrix of a graph and show how its second smallest eigenvalue can be characterized using this definition., Israel Rocha, Vilmar Trevisan., and Obsahuje seznam literatury
Dieser Artikel erforscht die Quellen, analysiert die Sprache, erötert den historischen Kontext und die Umstände der Entstehung der ruthenischen Übersetzung des Liedes der Lieder aus dem tschechischen. Die Handschrift, die ein Bestandteil einer handschriftlichen Sammlung aus den 15.-16. Jahrhunderten ist, liegt heute in dem Staatlichen Historischen Museum in Moskau unter der Nr. 558 in der Abteilung der Handschriften aus der Bibliothek des Heiligen Synods. Die linguistische und textologische Analyse der Übersetzung, wie auch der handschriftlichen Sammlung im ganzen, legt die Hypothese nahe, daß die Entstehung der ruthenischen Übersetzung des Liedes der Lieder mit der Missionsaktivität der Mönchen - Glagoljaši bei der orthodoxen Bevölkerung südwestlichen Rußlands (Ruthenia) verbunden war. Diese waren von Wladyslaw Jagiello aus dem Emmaus-Kloster in Prag eingeladen worden, um hier die slavische Liturgie "nach dem Gesetz des römischen Hofes" einzuführen.
Matrix polynomials play an important role in the theory of matrix differential equations. We develop a fixed point method to compute solutions of matrix polynomials equations, where the matricial elements of the matrix polynomial are considered separately as complex polynomials. Numerical examples illustrate the method presented.
For a $C^1$-function $f$ on the unit ball $\mathbb B \subset \mathbb C ^n$ we define the Bloch norm by $\|f\|_\mathfrak B=\sup \|\tilde df\|,$ where $\tilde df$ is the invariant derivative of $f,$ and then show that $$ \|f\|_\mathfrak B= \sup _{z,w\in {\mathbb B} \atop z\neq w} (1-|z|^2)^{1/2}(1-|w|^2)^{1/2}\frac {|f(z)-f(w)|}{|w-P_wz-s_wQ_wz|}.$$.
We study a generalization of the classical Henstock-Kurzweil integral, known as the strong $\rho $-integral, introduced by Jarník and Kurzweil. Let $(\mathcal S_{\rho } (E), \Vert \cdot \Vert )$ be the space of all strongly $\rho $-integrable functions on a multidimensional compact interval $E$, equipped with the Alexiewicz norm $\Vert \cdot \Vert $. We show that each element in the dual space of $(\mathcal S_{\rho } (E), \Vert \cdot \Vert )$ can be represented as a strong $\rho $-integral. Consequently, we prove that $fg$ is strongly $\rho $-integrable on $E$ for each strongly $\rho $-integrable function $f$ if and only if $g$ is almost everywhere equal to a function of bounded variation (in the sense of Hardy-Krause) on $E$.
An infinite series which arises in certain applications of the Lagrange-Bürmann formula to exponential functions is investigated. Several very exact estimates for the Laplace transform and higher moments of this function are developed.
The paper presents an application of fuzzy logic modeling techniques for design and development of a classification system for car driver's vigilance level detection. Especially, the micro-sleeps detection is of our primary interest. Detection is based on a pattern analysis of EEG signal spectrograms, which are acquired by monitoring the driver during a driving process. The system is based on the concept of radial implicative fuzzy system, which can be treated as a logical system accommodating acquired knowledge in a structured form.
Data mining nowadays belongs to the most prominent Information
technologies, experiencing a boom of interest from users and software producers. Traditionally, extracting knowledge from data has been a domain of statisticians, and the largest variety of rnethods encountered in commercial data mining systems are actually methods for statistical data analysis tasks. One of the most important ones among them is testing hypotheses about the probability distribution underlying the data. Basically, it consists in checking the null hypothesis that the probability distribution, a priori cissumed to belong to a broad set of distributions, actually belongs to one of its narrow subsets, which must be precisely delimited in advance. However, in a situation in which the data mining is performed, there are seldom enough clues for such a precise delimitation. That is why the generalizations of statistical hypotheses testing to vague hypotheses háve been investigated for more than a decade, so far following the most straightforward way - to replace the set defining the null hypothesis by a fuzzy set. In this páper, a principally different generalization is proposed, based on the observational-logic approach to data mining, and in particular to hypotheses testing. Its key idea is to view statistical testing of a fuzzy hypothesis cis an application of an appropriate generalized quantifier of a fuzzy predicate calculus to predicates describing the data. The theoretical principles of the approach are elaborated for both crisp and fuzzy significance levels, and illustrated on the quantifier lower critical implication, well known from the data mining system Guha. Finally, the implementation of the approach is briefly sketched.