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.
This paper deals with the application of a fluidized layer of granular material (FLGM) for the direct separation of destabilized impurities during drinking water treatment. Further, it investigates the effect of operation parameters (fluidized layer grain size, technological arrangement, velocity gradient, retention time, dosage of destabilisation reagent and temperature) on the aggregation and separation efficiency of the layer. The tests were carried out in a pilot plant scale. Aluminium sulphate was used as the destabilisation reagent. The highest separation efficiencies were achieved, when the particles entered the fluidized layer immediately after the dosing of the destabilisation reagent, when they had the lowest degree of aggregation. The separation efficiency (ϕ) also increased with increasing velocity gradient and the maximal value was reached at the velocity gradient of about 250 s-1. The most efficient separation of aluminium was achieved at 5 °C, but the effect of temperature on the efficiency of organic matter separation (ϕTOC) was not very significant. The maximal efficiency of separation on the layer grains reached the values ϕAl = 0.81 at the optimal dosage DAl = 1.55 mg L-1 and ϕTOC = 0.31 at the optimal dosage DAl = 2.36 mg L-1. The indisputable advantage of using FLGM for the separation of impurities is that they are intercepted on the layer grains in a form of solid, water-free shell (or coat) with the density of 2450 kg m-3, and there is no need to deal with the sludge dewatering. and Příspěvek se zabývá využitím fluidní vrstvy zrnitého materiálu (FLGM) pro přímou separaci destabilizovaných nečistot při úpravě vody a vlivem provozních parametrů (velikost zrn náplně, technologické uspořádání, gradient rychlosti, doba zdržení, dávka destabilizačního činidla, teplota) na agregační a separační účinnost vrstvy. Testy byly prováděny na poloprovozním modelu fluidní vrstvy. Jako destabilizační činidlo byl použit síran hlinitý. Nejvyšší separační účinnosti byly dosahovány, pokud částice nečistot vstupovaly do fluidní vrstvy bezprostředně po nadávkování destabilizačního činidla, kdy byl jejich stupeň agregace nejnižší. Separační účinnost (ϕ) se také zvyšovala s narůstající hodnotou gradientu rychlosti ve fluidní vrstvě a maximální hodnoty dosáhla při gradientu kolem 250 s-1. Hliník byl nejúčinněji separován při nízké teplotě (5 °C), nicméně na účinnost separace organických látek (ϕTOC) teplota příliš velký vliv neměla. Maximální účinnost separace na zrnech fluidní vrstvy dosáhla hodnot ϕAl = 0,81 při optimální dávce DAl = 1,55 mg L-1 a ϕTOC = 0,31 při optimální dávce DAl = 2,36 mg L-1. Nespornou výhodou využití fluidní vrstvy jako separačního prvku je skutečnost, že nečistoty jsou na zrnech FLGM zachycovány ve formě pevné skořápky (hustota 2450 kg m-3), která neobsahuje kapalnou vodu, a kal tudíž nemusí být odvodňován.
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.
In elementary robotics, it is very well known that the rotation of an object by the angles respectively Ψ (x), Θ (y), Φ (z) wrt** a fixed coordinate system (RPY) results in the same angular position for the object as the position achieved by the rotation of that object by the angles respectively Φ (z), Θ (y), Ψ (x) wrt a moving (with the object) coordinate system (euler angles). The proofs given up to now for such consequences are not general and for any such problem usually involve the calculation of the transformation matrix for both cases and observing the equivalence of the two matrices [1, 2, 3]. In this paper a fundamental and at the same time general proof is given for such results. It is shown that this equivalence in reverse order can be extended to the general class of transformations which keep the local relations constant (i.e., each transformation should keep the local relations constant). For example, rotation, translation and scaling are 3 types of transformations which can be located in this general class.
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.