An application of Mittag-Leffler lemma in the category of quotients of Fréchet spaces. We use Mittag-Leffler Lemma to prove that for a nonempty interval ]a, b[⊂ R, the restriction mapping H∞(]a, b[+iR) → C∞ (]a, b[) is surjective and we give a corollary.
Mild hyperhomocysteinemia has been established as a new independent risk factor for atherosclerosis and thrombosis. The metabolic syndrome of insulin resistance is associated with a high risk of coronary heart disease. Our objective was to determine if any relationship exists between the metabolic syndrome of insulin resistance in non-diabetic subjects and total serum homocysteine levels. Sixty-six healthy volunteers (33 males and 33 females) were selected from the population of Pilsen. Insulin resistance was measured by the Insulin Suppression Test using Octreotide. Steady-state plasma glucose concentrations at the end of the test period provided a quantitative measure of insulin resistance. Serum homocysteine level was estimated by high-pressure liquid chromatography. Serum folate and vitamin B12 were estimated using commercial kits on an Abbott IMx analyzer. All other laboratory tests were performed by standard methods in a routine biochemical laboratory. Subjects with the highest tertile of steady-state plasma glucose showed a significantly higher body mass index, blood pressure, fasting plasma triglyceride levels, plasminogen activator inhibitor-1 and lower HDL-cholesterol, i.e. an insulin resistance pattern. These subjects had significantly lower serum homocysteine levels compared with non-insulin resistant subjects. The negative association of insulin resistance and serum homocysteine was unexpected. The contribution of plasma folate levels to serum homocysteine levels and serum creatinine was significantly negative and positive, respectively., H. Rosolová, J. Šimon, O. Mayer Jr., J. Racek, T. Dierzé, D. W. Jacobsen., and Obsahuje bibliografii
A graph is nonsingular if its adjacency matrix $A(G)$ is nonsingular. The inverse of a nonsingular graph $G$ is a graph whose adjacency matrix is similar to $A(G)^{-1}$ via a particular type of similarity. Let $\mathcal{H}$ denote the class of connected bipartite graphs with unique perfect matchings. Tifenbach and Kirkland (2009) characterized the unicyclic graphs in $\mathcal{H}$ which possess unicyclic inverses. We present a characterization of unicyclic graphs in $\mathcal{H}$ which possess bicyclic inverses., Swarup Kumar Panda., and Obsahuje bibliografii
Terminology for microtriches, the surface features both unique to and ubiquitous among cestodes, is standardised based on discussions that occurred at the International Workshops on Cestode Systematics in Storrs, Connecticut, USA in 2002, in České Budějovice, Czech Republic in 2005 and in Smolenice, Slovakia in 2008. The following terms were endorsed for the components of individual microtriches: The distal, electron-dense portion is the cap, the proximal more electron-lucent region is the base. These two elements are separated from one another by the baseplate. The base is composed of, among other elements, microfilaments. The cap is composed of cap tubules. The electron-lucent central portion of the base is referred to as the core. The core may be surrounded by an electron-dense tunic. The entire microthrix is bounded by a plasma membrane, the external layer of which is referred to as the glycocalyx. Two distinct sizes of microtriches are recognised: those <= 200 nm in basal width, termed filitriches, and those >200 nm in basal width, termed spinitriches. Filitriches are considered to occur in three lengths: papilliform (<= 2 times as long as wide), acicular (2-6 times as long as wide), and capilliform (>6 times as long as wide). In instances in which filitriches appear to be doubled at their base, the modifier duplicated is used. Spinitriches are much more variable in form. At present a total of 25 spinithrix shapes are recognised. These consist of 13 in which the width greatly exceeds the thickness (i.e., bifid, bifurcate, cordate, gladiate, hamulate, lanceolate, lineate, lingulate, palmate, pectinate, spathulate, trifid, and trifurcate), and 12 in which width and thickness are approximately equal (i.e., chelate, clavate, columnar, coniform, costate, cyrillionate, hastate, rostrate, scolopate, stellate, trullate, and uncinate). Spiniform microtriches can bear marginal (serrate) and/or dorsoventral (gongylate) elaborations; they can also bear apical features (aristate). The latter two modifiers should be used only if the features are present. The terminology to describe the overall form of a spinithrix should be used in the following order: tip, margins, shape. Each type of microthrix variation is defined and illustrated with one or more scanning electron micrographs. An indication of the taxa in which each of the microthrix forms is found is also provided.
This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see \cite{Coirier1} and \cite{Coirier2}). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient in normal direction. Moreover, the proofs of L2(Ω) - a priori estimates for our discrete solution are given. Finally we present our computational results.
This paper is devoted to studying the effects of a vanishing structural damping on the controllability properties of the one dimensional linear beam equation. The vanishing term depends on a small parameter $\varepsilon \in (0,1)$. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls $v_{\varepsilon }$ as $\varepsilon $ goes to zero. It is shown that for any time $T$ sufficiently large but independent of $\varepsilon $ and for each initial data in a suitable space there exists a uniformly bounded family of controls $(v_\varepsilon )_\varepsilon $ in $L^2(0, T)$ acting on the extremity $x = \pi $. Any weak limit of this family is a control for the beam equation. This analysis is based on Fourier expansion and explicit construction and evaluation of biorthogonal sequences. This method allows us to measure the magnitude of the control needed for each eigenfrequency and to show their uniform boundedness when the structural damping tends to zero.