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2922. Algebraic approach to locally finite trees with one end
- Creator:
- Zelinka, Bohdan
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- locally finite tree, one-way infinite path, acyclic monounary algebra, and tree semilattice
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
2923. Algebraic conditions for $t$-tough graphs
- Creator:
- Liu, Bolian and Chen, Siyuan
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- $t$-tough graph, Laplacian matrix, adjacent matrix, and eigenvalues
- Language:
- English
- Description:
- We give some algebraic conditions for $t$-tough graphs in terms of the Laplacian eigenvalues and adjacency eigenvalues of graphs.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
2924. Algebraic connectivity of $k$-connected graphs
- Creator:
- Kirkland, Steve, Rocha, Israel, and Trevisan, Vilmar
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- algebraic connectivity and Fiedler vector
- Language:
- English
- Description:
- 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).
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
2925. Algebraic duality of constant algebras
- Creator:
- Chajda, Ivan, Halaš, Radomír, and Pinus, Alexander G.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- math and constant algebras
- Language:
- English
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
2926. Algebraic integrability for minimum energy curves
- Creator:
- Yudin, Ivan and Silva Leite, Fátima
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Darboux polynomials, drag power, Euler-Lagrange equations, grading, integrability, and vector fields
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
2927. Algebraic solution to box-constrained bi-criteria problem of rating alternatives through pairwise comparisons
- Creator:
- Krivulin, Nikolai
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- idempotent semifield, tropical optimization, constrained bi-criteria decision problem, Pareto-optimal solution, box constraints, and pairwise comparisons
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public
2928. Algebras and spaces of dense constancies
- Creator:
- Bella, Angelo, Martinez, Jorge, and Woodward, Scott D.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- space and algebra of dense constancy and $c$-spectrum
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
2929. Algesthesia after epileptic seizure
- Creator:
- Jan Mareš and Richard Rokyta
- Format:
- Type:
- article, články, model:article, and TEXT
- Subject:
- Patologie. Klinická medicína, patologie, epileptické záchvaty, analgezie, krysa obecná, pathology, epileptic seizures, analgesia, Rattus rattus, nociception, flurothyl, postictal analgesia, 14, and 616
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public
2930. Alginate matrices for protein delivery: a short review
- Creator:
- Wawrzyńska, E and Dana Kubies
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- algináty, růstové faktory, alginates, growth factors, biomaterials, protein release, growth factor release, 14, and 612
- Language:
- English
- Description:
- 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
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public