Non-surgical management of aortic valve disease has been given considerable attention. Several recent publications have already reported its use in clinical practice. The main issue is to get an understanding of the pathophysiological processes and, most importantly, extensive experimental activity. In addition to testing various animal models, technical and material aspects are also being intensively investigated. It is not clear yet whether the durability and applicability of this promising development will be comparable with the standard of current cardiac surgery. Nonetheless, even the use of some models as a temporary approach helping to improve the circulatory status, not allowing safe surgery, is certainly justified. At any rate, a new stage of research and clinical application has been set off. However, experimental background continues to be simply indispensable. The paper is a short review of the issue., J. Šochman, J. H. Peregrin., and Obsahuje bibliografii a bibliografické odkazy
This paper gives the local existence of mild solutions to the Cauchy problem for the complex Ginzburg-Landau type equation ∂u ∂t − (λ + iα)∆u + (κ + iβ)|u| q−1 u − γu = 0 in R N × (0, ∞) with L p -initial data u0 in the subcritical case (1 6 q < 1 + 2p/N), where u is a complex-valued unknown function, α, β, γ, κ ∈ R, λ > 0, p > 1, i = √ −1 and N ∈ N. The proof is based on the L p -L q estimates of the linear semigroup {exp(t(λ + iα)∆)} and usual fixed-point argument.
Global solvability and asymptotics of semilinear parabolic Cauchy problems in $\mathbb R^n$ are considered. Following the approach of A. Mielke [15] these problems are investigated in weighted Sobolev spaces. The paper provides also a theory of second order elliptic operators in such spaces considered over $\mathbb R^n$, $n\in \mathbb N$. In particular, the generation of analytic semigroups and the embeddings for the domains of fractional powers of elliptic operators are discussed.
Let $[ a,b] $ be an interval in $\mathbb R$ and let $F$ be a real valued function defined at the endpoints of $[a,b]$ and with a certain number of discontinuities within $[ a,b] $. Assuming $F$ to be differentiable on a set $[ a,b] \backslash E$ to the derivative $f$, where $E$ is a subset of $[ a,b] $ at whose points $F$ can take values $\pm \infty $ or not be defined at all, we adopt the convention that $F$ and $f$ are equal to $0$ at all points of $E$ and show that $\mathcal {KH}\hbox {\rm -vt}\int _a^bf=F( b) -F( a) $, where $\mathcal {KH}\hbox {\rm -vt}$ denotes the total value of the {\it Kurzweil-Henstock} integral. The paper ends with a few examples that illustrate the theory.
Commuting is an important property in any two-step information merging procedure where the results should not depend on the order in which the single steps are performed. In the case of bisymmetric aggregation operators with the neutral elements, Saminger, Mesiar and Dubois, already reduced characterization of commuting n-ary operators to resolving the unary distributive functional equations. And then the full characterizations of these equations are obtained under the assumption that the unary function is non-decreasing and distributive over special aggregation operators, for examples, continuous t-norms, continuous t-conorms and two classes of uninorms. Along this way of thinking, in this paper, we will investigate and fully characterize the following unary distributive functional equation f(U(x,y))=U(f(x),f(y)), where f:[0,1]→[0,1] is an unknown function but unnecessarily non-decreasing, a uninorm U∈Umin has a continuously underlying t-norm TU and a continuously underlying t-conorm SU. Our investigation shows that the key point is a transformation from this functional equation to the several known ones. Moreover, this equation has also non-monotone solutions completely different with already obtained ones. Finally, our results extend the previous ones about the Cauchy-like equation f(A(x,y))=B(f(x),f(y)), where A and B are some continuous t-norm or t-conorm.
The development of the cauda equina syndrome in the dog and the involvement of spinal nitric oxide synthase immunoreactivity (NOS-IR) and catalytic nitric oxide synthase (cNOS) activity were studied in a pain model caused by multiple cauda equina constrictions. Increased NOS-IR was found two days post-constriction in neurons of the deep dorsal horn and in large, mostly bipolar neurons located in the internal basal nucleus of Cajal seen along the medial border of the dorsal horn. Concomitantly, NOS-IR was detected in small neurons close to the medioventral border of the ventral horn. High NOS-IR appeared in a dense sacral vascular body close to the Lissauer tract in S1-S3 segments. Somatic and fiber-like NOS-IR appeared at five days post-constriction in the Lissauer tract and in the lateral and medial collateral pathways arising from the Lissauer tract. Both pathways were accompanied by a dense punctate NOS immunopositive staining. Simultaneously, the internal basal nucleus of Cajal and neuropil of this nucleus exhibited high NOS-IR. A significant decrease in the number of small NOS immunoreactive somata was noted in laminae I-II of L6-S2 segments at five days post-constriction while, at the same time, the number of NOS immunoreactive neurons located in laminae VIII and IX was significantly increased. Moreover, high immunopositivity in the sacral vascular body persisted along with a highly expressed NOS-IR staining of vessels supplying the dorsal sacral gray commissure and dorsal horn in S1-S3 segments. cNOS activity, based on a radioassay of compartmentalized gray and white matter regions of lower lumbar segments and non-compartmentalized gray and white matter of S1-S3 segments, proved to be highly variable for both post-constriction periods., J. Maršala, J. Kafka, N. Lukáčová, D. Čížková, M. Maršala, N. Katsube., and Obsahuje bibliografii