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61.
We show that an arbitrary infinite graph G can be compactified by its ends plus its critical vertex sets, where a finite set X of vertices of an infinite graph is critical if its deletion leaves some infinitely many components each with neighbourhood precisely equal to X. We further provide a concrete separation system whose ?0‐tangles are precisely the ends plus critical vertex sets. Our tangle compactification is a quotient of Diestel's (denoted by ), and both use tangles to compactify a graph in much the same way as the ends of a locally finite and connected graph compactify it in its Freudenthal compactification. Finally, generalising both Diestel's construction of and our construction of , we show that G can be compactified by every inverse limit of compactifications of the sets of components obtained by deleting a finite set of vertices. Diestel's is the finest such compactification, and our is the coarsest one. Both coincide if and only if all tangles are ends. This answers two questions of Diestel. 相似文献
62.
Douglas R. Woodall 《Journal of Graph Theory》2019,92(4):488-490
In the article “The average degree of an edge-chromatic critical graph II” by Douglas R. Woodall (J. Graph Theory 56 (2007), 194-218), it was claimed that the average degree of an edge-chromatic critical graph with maximum degree is at least if , at least if , and at least if . Unfortunately there were mistakes in the proof of the last two of these results, which are now proved only if and , respectively. 相似文献
63.
In this paper we study a Hamiltonian function on the cotangent bundle of the space of Riemannian metrics on a 3-manifold M and prove the orbits of the constrained Hamiltonian dynamical system correspond to -manifolds foliated by hypersurfaces diffeomorphic to . 相似文献
64.
Justin Z. Schroeder 《组合设计杂志》2019,27(1):42-52
We provide two new constructions for pairs of mutually orthogonal symmetric hamiltonian double Latin squares. The first is a tripling construction, and the second is derived from known constructions of hamilton cycle decompositions of when is prime. 相似文献
65.
Heavy metal ions are harmful to aquatic life and humans owing to their high toxicity and non‐biodegradability, so their removal from wastewater is an important task. Therefore, this work focuses on designing suitable, simple and economical nanosensors to detect and remove these metal ions with high selectivity and sensitivity. Based on this idea, different types of mesoporous materials such as hexagonal SBA‐15, cubic SBA‐16 and spherical MCM‐41, their chloro‐functionalized derivatives, as well as 4‐(4‐nitro‐phenylazo)‐naphthalen‐1‐ol (NPAN) azo dye have been synthesized, with the aim of designing some optical nanosensors for metal ions sensing applications. The mentioned azo dye has been anchored into the chloro‐functionalized mesoporous materials. The designed nanosensors were characterized using scanning and transmission electron microscopy as well as Fourier transform infrared and UV–visible spectral analysis, nitrogen adsorption–desorption isotherms, low‐angle X‐ray diffraction and thermogravimetric analyses. Their optical sensing to various toxic metal ions such as Cd (II), Hg (II), Mn (II), Fe (II), Zn (II) and Pb (II) at different values of pH (1.1, 4.9, 7 and 12) was investigated. The optimization of experimental conditions, including the effect of pH and metal ion concentration, was examined. The experimental results showed that the solution pH had a major impact on metal ion detection. The optical nanosensors respond well to the tested metal ions, as reflected by the enhancement in both absorption and emission spectra upon adding different concentrations of the metal salts and were fully reversible on adding ethylene diamine tetra acetic acid or citric acid to the formed complexes. High values of the binding constants for the designed nanosensors were observed at pHs 7 and 12, confirming the strong chelation of different metals to the nanosensor at these pHs. Also, high binding constants and sensitivity were observed for NPAN‐MCM‐41 as a nanosensor to detect the different metal ions. From the obtained results, we succeeded in transforming the harmful azo dye into an environmentally friendly form via designing of the optical nanosensors used to detect toxic metal ions in wastewater with high sensitivity. 相似文献
66.
Kreweras conjectured that every perfect matching of a hypercube for can be extended to a hamiltonian cycle of . Fink confirmed the conjecture to be true. It is more general to ask whether every perfect matching of for can be extended to two or more hamiltonian cycles of . In this paper, we prove that every perfect matching of for can be extended to at least different hamiltonian cycles of . 相似文献
67.
We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation. 相似文献
68.
Medical treatment and vaccination decisions are often sequential and uncertain. Markov decision process is an appropriate means to model and handle such stochastic dynamic decisions. This paper studies the near‐optimality of a stochastic SIRS epidemic model that incorporates vaccination and saturated treatment with regime switching. The stochastic model takes white noises and color noise into account. We first prove some priori estimates of the susceptible, infected, and recovered populations. Moreover, we establish some sufficient and necessary conditions of the near‐optimality by Pontryagin stochastic maximum principle. Our results show that the two kinds of environmental noises have great impacts on the infectious diseases. Finally, we illustrate our conclusions through numerical simulations. 相似文献
69.
Let m ≤ n ≤ k. An m × n × k 0‐1 array is a Latin box if it contains exactly m n ones, and has at most one 1 in each line. As a special case, Latin boxes in which m = n = k are equivalent to Latin squares. Let be the distribution on m × n × k 0‐1 arrays where each entry is 1 with probability p, independently of the other entries. The threshold question for Latin squares asks when contains a Latin square with high probability. More generally, when does support a Latin box with high probability? Let ε > 0. We give an asymptotically tight answer to this question in the special cases where n = k and , and where n = m and . In both cases, the threshold probability is . This implies threshold results for Latin rectangles and proper edge‐colorings of Kn,n. 相似文献