Let T be an infinite locally finite tree. We say that T has exactly one end, if in T any two one-way infinite paths have a common rest (infinite subpath). The paper describes the structure of such trees and tries to formalize it by algebraic means, namely by means of acyclic monounary algebras or tree semilattices. In these algebraic structures the homomorpisms and direct products are considered and investigated with the aim of showing, whether they give algebras with the required properties. At the end some further assertions on the structure of such trees are stated, without the algebraic formalization.
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.
The consequences of epileptic seizures related to postictal inhibition in early postictal period include postictal analgesia. We studied this phenomenon over 96 h following flurothyl-induced seizures in adult male Wistar rats. Nociception of control (no seizure) and seizured groups were tested using the plantar and von Frey hair tests. We determined latency of forepaw and hind paw reactions using plantar tests and the number of von Frey hairs reactions. Shortly after seizures, longer plantar test latencies were seen relative to the control group. Before the seizures the plantar test reaction times were significantly shorter in forepaws than in hind paws. The effect disappeared post-seizure and surprisingly, it also disappeared at the corresponding time in controls; it reappeared after 48 h in the seizure group and after 24 h in controls. Differences in the von Frey hairs test occurred at 5 and 60 min post-seizure, however, these differences could not be explained by limb anatomy; although, different thermal and mechanical nociception mechanisms could be significant. The unexpected reactions in controls could be related to brief social and physical interactions between the two groups. and J. Mareš, R. Rokyta.
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
Mnohočetný myelom (MM) a solitární plazmocytom (SP) jsou nejčastější primární nádory páteře. Léčba MM a SP páteře je komplexní proces, který zahrnuje léčbu kauzální s cílem potlačit nádorový klon a dále léčbu podpůrnou, jejíž součástí je i chirurgická terapie. Operace přispívají k lepší kvalitě života a nabývají na významu a smysluplnosti zejm. díky zlepšené prognóze onemocnění. Navrhli jsme algoritmus operační léčby MM a SP a ten jsme dále prospektivně ověřovali a jeho vyhodnocení bylo cílem této studie. Pacienti byli operováni v průběhu 10 let, minimální doba sledování byl jeden rok. Soubor tvořilo 32 pacientů (20 mužů a 12 žen) s průměrným věkem 61 let. Operováno bylo celkem 61 obratlů. Důvodem k operaci byly projevy útlaku míchy a progredující neurologický deficit (hodnoceno Frankelovou škálou) nebo na konzervativní léčbu nereagující axiální bolest (hodnoceno VAS; Visual Analogue Scale) páteře. Provedena byla některá z těchto operací: vertebroplastika (VP), laminektomie, transpedikulární fixace, somatektomie a jejich kombinace, nebo okcipito‑cervikální fixace. Pooperační VAS a Frankelova škála byly vyhodnoceny za jeden rok, skiagramy a MR jsme provedli a zhodnotili každý jeden rok. U žádného pacienta nenastala lokální recidiva tumoru ani selhání stabilizace na operovaném úseku v celém sledovaném období. Průměrný předoperační VAS byl 6,8 a jeden rok po operaci se průměrný VAS snížil na 1,1. Všechny operační výkony vedly nejen ke kontrole bolesti, ale také k prevenci nebo zlepšení neurologického postižení po celou dobu sledování. Hodnotili jsme náš postup – algoritmus operací, míru radikality a jejich načasování jako optimální pro MM i SP., Multiple myeloma (MM) and solitary plasmacytoma (SP) are the most frequent primary tumors of the spine. Management of the spinal MM and SP is a complex process involving causal treatment to suppress the tumor clone, as well as supportive therapy, including surgery and radiotherapy. Surgery should be considered because of its favourable effect on disease prognosis. We proposed a surgical treatment algorithm in patients with spinal MM and SP and the aim of this article is to present prospective evaluation of this algorithm. Patients undergoing surgical treatment during the past 10 years were included in this study, with the minimum follow-up of one year. A total of 32 patients (20 males and 12 females) with the mean age of 61 years were included. Surgery of 61 vertebrae was performed. The procedures were indicated for progressing neurological deficit (Frankel score) and for axial spinal pain (VAS classification). We performed the following procedures: vertebroplasty, laminectomy, transpedicular fixation, somatectomy, and their combination, or occipito-cervical fixation. Frankel score and VAS was assessed one year after the surgery and X-ray and spinal MRI was performed every year. No local relapses of the tumor or stabilization failure were detected. The mean preoperative VAS was 6.8 and improved to 1.1 one year after the surgery. During the follow up period, we observed positive effect of surgery on pain control and on prevention or improvement of neurological dysfunction. The authors concluded that all surgical procedures, the extent of resection and timing were adequate in all subjects. Key words: multiple myeloma – solitary plasmacytoma –vertebroplasty – transpedicular fixation – somatectomy The authors declare they have no potential conflicts of interest concerning drugs, products, or services used in the study. The Editorial Board declares that the manuscript met the ICMJE “uniform requirements” for biomedical papers., and L. Hrabálek, T. Wanek, J. Minařík, J. Bačovský, V. Ščudla, M. Vaverka