Let $G$ be a $k$-connected graph with $k \ge 2$. A hinge is a subset of $k$ vertices whose deletion from $G$ yields a disconnected graph. We consider the algebraic connectivity and Fiedler vectors of such graphs, paying special attention to the signs of the entries in Fiedler vectors corresponding to vertices in a hinge, and to vertices in the connected components at a hinge. The results extend those in Fiedler's papers Algebraic connectivity of graphs (1973), A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory (1975), and Kirkland and Fallat's paper Perron Components and Algebraic Connectivity for Weighted Graphs (1998).
This paper deals with integrability issues of the Euler-Lagrange equations associated to a variational problem, where the energy function depends on acceleration and drag. Although the motivation came from applications to path planning of underwater robot manipulators, the approach is rather theoretical and the main difficulties result from the fact that the power needed to push an object through a fluid increases as the cube of its speed.
We consider a decision-making problem to evaluate absolute ratings of alternatives that are compared in pairs according to two criteria, subject to box constraints on the ratings. The problem is formulated as the log-Chebyshev approximation of two pairwise comparison matrices by a common consistent matrix (a symmetrically reciprocal matrix of unit rank), to minimize the approximation errors for both matrices simultaneously. We rearrange the approximation problem as a constrained bi-objective optimization problem of finding a vector that determines the approximating consistent matrix, and then represent the problem in terms of tropical algebra. We apply methods and results of tropical optimization to derive an analytical solution of the constrained problem. The solution consists in introducing two new variables that describe the values of the objective functions and allow reducing the problem to the solution of a system of parameterized inequalities constructed for the unknown vector, where the new variables play the role of parameters. We exploit the existence condition for solutions of the system to derive those values of the parameters that belong to the Pareto front inherent to the problem. Then, we solve the system for the unknown vector and take all solutions that correspond to the Pareto front, as a complete solution of the bi-objective problem. We apply the result obtained to the bi-criteria decision problem under consideration and present illustrative examples.
A DC-space (or space of dense constancies) is a Tychonoff space $X$ such that for each $f\in C(X)$ there is a family of open sets $\lbrace U_i\: i\in I\rbrace $, the union of which is dense in $X$, such that $f$, restricted to each $U_i$, is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean $f$-algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions are dense), and it is shown that all metrizable spaces have this property.
Growth factors are powerful molecules that regulate cellular growth, proliferation, healing, and cellular differentiation. A delivery matrix that incorporates growth factors with high loading efficiencies, controls their release, and maintains bioactivity would be a powerful tool for regenerative medicine. Alginate has several unique properties that make it an excellent platform for the delivery of proteins. Mild gelling conditions can minimize the risk of protein denaturation; moreover, alginate can serve as protection from degradation until protein release. Various modifications have been proposed to tune alginate binding and release proteins, simultaneously adjusting alginate degradability, mechanical stiffness, swelling, gelation properties and cell affinity. The primary objective of this article is to review the literature related to recent advances in the application of alginate matrices in protein delivery in regenerative medicine. A special emphasis is put on the relevance of delivery of growth factors and chemokine., E. Wawrzyńska, D. Kubies., and Obsahuje bibliografii
Fractal image coding is a new and modern technique for lossy image compression. This paper contains a general description of fractal image compression techniques and describes basic algorithms used for encoding and decoding of images. Some examples are presented. For our experiments we use the famous static gray-scale image of LENNA. Some problems of color image coding are also shortly mentioned. and Fraktálové kódování obrazů patří mezi nové účinné techniky ztrátové komprese obrazů. Článek obsahuje obecný popis technik a základní algoritmy fraktálovho kódování a dekódování (šedých) obrazů. Jsou uvedeny některé příklady. Experimenty byly realizovány na proslulém statickém šedém obrazu LENNA, který dnes již představuje určitý standard pro testování většiny procedur zpracování obrazu. Krátce jsou zmíněny i některé základní problémy kódování barevných obrazů.
The article describes automation of 2-dimensional surface analysis in the aparature for laser spectroscopy (LIBS). Such analysis give us 2D map of presented chemical elements. The main part is dedicated to algorithm choosing suitable for evaluation of the image sharpness. Digital camera and ablation laser share the same focusing optics, so knowing the exact image sharpness it is possible to set sample object to focal plane. There are theoretically described and experimentaly tested different kinds of methods how to obtain a relative sharpness number: gradient based method and methods working in frequency domain. Digital noise phenomenon is also discussed. As an output a selection of suitable method has been made with respect to its speed, accuracy and durability against digital noise. and Článek popisuje řešení automatizace dvourozměrné povrchové analýzy v zařízení pro laserovou spektroskopii (LIBS), jejímž výsledkem je 2D mapa přítomnosti chemických prvků. Hlavní část je věnována výběru algoritmu pro opětovné nastavení mapovaného vzorku do ohniskové roviny objektivu, který zároveň slouží k fokusaci laserového svazku. Děje se tak pomocí analýzy ostrosti snímku vzorku. Teoreticky jsou rozebrány a experimentálně otestovány různé metody vyhodno cení ostrosti snímku, a to metoda gradientní a metody pracující s frekvenčním spektrem obrazu. Článek se zabývá také problematikou filtrace digitálního šumu. Výstupem je volba vhodného algoritmu s ohledem na rychlost, přesnost a odolnost vůči digitálnímu šumu.
This article examines the thoughts of Ali Abd al-Raziq, an important Egyptian scholar and author of a book called Islam and the Bases of Rule (al-Islam wa Usul al-Hukm), published in 1925. In this work, Abd al-Raziq presented fundamental arguments in support of the separation of religion and politics, which were fully supported by a very original analysis of Islam's holy text, the Quran, as well as by the historical situation of the Muslim community at the time of the Prophet Muhammad. Although the publication of this book caused a great scandal in Egypt, with its author being forced to withdraw from Egyptian public life for quite a long period of time, the arguments contained in the book represent an important contribution to the debates about the desirable degree of linkage between Islam and politics in the Muslim world., Jan Kondrys., and Obsahuje bibliografii