Range-preserving AE(0)-spaces

[EN] All spaces here are Tychonoff spaces. The class AE(0) consists of those spaces which are absolute extensors for compact zero-dimensional spaces. We define and study here the subclass AE(0)rp, consisting of those spaces for which extensions of continuous functions can be chosen to have the same range. We prove these results. If each point of T 2 AE(0) is a G-point of T , then T 2 AE(0)rp. These are equivalent: (a) T 2 AE(0)rp; (b) every compact subspace of T is metrizable; (c) every compact subspace of T is dyadic; and (d) every subspace of T is AE(0). Thus in particular, every metrizable space is an AE(0)rp-space.Comfort, W.; Hager, A. (2013). Range-preserving AE(0)-spaces. Applied General Topology. 14(1):33-40. doi:10.4995/agt.2013.1614.SWORD3340141A. B laszczyk, Compactness, in: Encyclopedia of General Topology (K. Hart, J. Nagata, and J. Vaughan, eds.), pp. 169–173. Elsevier, Amsterdam, 2004.B. Efimov, Dyadic bicompacta, Soviet Math. Doklady 4 (1963), 496–500, Russian original in: Doklady Akad. Nauk SSSR 149 (1963), 1011-1014.R. Engelking, Cartesian products and dyadic spaces, Fund. Math. 57 (1965), 287–304.Ryszard Engelking, General Topology, Heldermann Verlag, Berlin, 1989.R. Haydon, On a problem of Pelczynski: Milutin spaces, Dugunjdi spaces, and AE(0 − dim), Studia Math. 52 (1974), 23–31.Hoffmann, B. (1979). A surjective characterization of Dugundji spaces. Proceedings of the American Mathematical Society, 76(1), 151-151. doi:10.1090/s0002-9939-1979-0534408-xIsbell, J. (1964). Uniform Spaces. Mathematical Surveys and Monographs. doi:10.1090/surv/012W. Sierpinski, Sur les projections des ensembles complémentaire aux ensembles (a), Fund. Math. 11 (1928), 117–122

Embedding in a Finite 2-Generator Semigroup

We augment the body of existing results on embedding finite semigroups of a certain type into 2-generator finite semigroups of the same type. The approach adopted applies to finite semigroups the idempotents of which form a band and also to finite orthodox semigroups

Large Alphabets and Incompressibility

We briefly survey some concepts related to empirical entropy -- normal numbers, de Bruijn sequences and Markov processes -- and investigate how well it approximates Kolmogorov complexity. Our results suggest $\ell$th-order empirical entropy stops being a reasonable complexity metric for almost all strings of length $m$ over alphabets of size $n$ about when $n^\ell$ surpasses $m$

Sequences of iterates of random-valued vector functions and continuous solutions of related equations

Given a probability space (Ω, A, P), a separable metric space X, and a random-valued vector function f : X × Ω → X, we obtain some theorems on the existence and on the uniqueness of continuous solutions φ : X → R of the equation φ(x) = ∫Ω φ(f(x,ω)) P(dω)

Comportamento biogeoquímico do ferro no complexo estuarino de Paranaguá

Orientador: Prof. Dr. Marco Tadeu GrassiTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Química. Defesa : Curitiba, 30/01/2020Inclui referênciasResumo: Neste trabalho foram estabelecidas bases analíticas para a análise de especiação do ferro no Complexo Estuarino de Paranaguá (CEP). Na implantação dos protocolos de especiação para ferro, a principal ferramenta analítica empregada foi a técnica de voltametria adsortiva de redissolução catódica aliada à competição por ligantes empregando 2,3-dihidroxinaftaleno (DHN) como ligante sintético para o Fe. As condições experimentais foram otimizadas em um tempo de deposição de 90 s, realizada em um potencial de -0,1 V, concentração de ligante (DHN) de 40,0 µmol L-1 e modo de varredura por corrente contínua. Essas condições otimizadas e procedimentos que minimizam a contaminação dos reagentes, vidrarias e equipamentos utilizados nos procedimento, resultaram em valores de limite de detecção de 40,0 pmol L-1 e limite de quantificação de 135,0 pmol L-1 e faixa de trabalho linear de 135 pmol L-1 a 95,5 nmol L-1, com contribuição de ferro nos reagentes de 577 pmol L-1 de Fe(III) para 500 µL de adição na mistura de BrO3 - /POPSO e de 138 pmol L-1 de Fe(III) para adições de 40 µL de DHN. Além disso, foi investigada a distribuição espacial e sazonal de ferro dissolvido total e suas frações lábeis e complexadas; e de ligantes orgânicos nas águas do CEP. As campanhas de amostragem realizadas no inverno de 2014 e verão de 2015 em dezoito estações de amostragem permitiram entender melhor a interação entre Fe e fatores que interferem no CEP e as relações entre a concentração de espécies de Fe e diversos parâmetros físico-químicos como oxigênio dissolvido, pH, salinidade entre outros. As concentrações médias das diferentes frações de ferro dissolvido (FeD) e de sítios complexantes (Li) nas águas superficiais coletadas no verão foram maiores que no inverno. A concentração média de FeD durante o verão foi de 64,6 ± 33,9 nmol L-1, e no inverno foi de 44,6 ± 28,6 nmol L-1. A média da fração lábil (Fe’) foi de 3,20 ± 3,00 nmol L-1 durante a coleta de inverno e de 14,8 ± 10,7 nmol L-1 durante o verão. As concentrações médias de Li e os valores médios do logaritmo das constantes de estabilidade (log KFe-L) foram de 103 ± 67,4 nmol L-1 e 12,0 ± 0,35 nmol L-1 para o inverno e de 135 ± 78,2 nmol L-1 e 11,6 ± 0,50 nmol L-1 para o verão respectivamente, indicando a presença de ligantes estáveis no estuário. Com relação à variação espacial os maiores valores das frações de ferro foram observados nos locais onde há o aporte de esgotos e locais onde ocorrem o aporte dos rios Cachoeira e Nhundiaquara, enquanto os locais mais próximos ao oceano apresentaram os menores valores de FeD, Fe’ e Li.Abstract: Paranaguá Estuarine Complex (PEC). In the implementation of iron speciation protocols, the main analytical tool employed was the technique of cathodic adsorptive stripping voltammetry combined with ligand competition using 2,3- dihydroxynaphthalene (DHN) as a synthetic ligand for Fe. Experimental conditions were optimized with a deposition time of 90 s, performed at a potential of -0.1 V, ligand concentration (DHN) of 40.0 µmol L-1, and continuous current scan mode. These optimized conditions and procedures minimizing contamination of reagents, glassware, and equipment used in the procedure resulted in detection limits of 40.0 pmol L-1 and quantification limits of 135.0 pmol L-1, with a linear working range from 135 pmol L-1 to 95.5 nmol L-1. Iron contributions in the reagents were observed at 577 pmol L-1 of Fe(III) for 500 µL addition in the BrO3 -/POPSO mixture and 138 pmol L-1 of Fe(III) for 40 µL additions of DHN. Additionally, spatial and seasonal distribution of total dissolved iron and its labile and complexed fractions, as well as organic ligands in PEC waters, were investigated. Sampling campaigns conducted in the winter of 2014 and summer of 2015 at eighteen sampling stations provided a better understanding of the interaction between Fe and factors influencing PEC and the relationships between Fe species concentration and various physicochemical parameters such as dissolved oxygen, pH, salinity, among others. Mean concentrations of different fractions of dissolved iron (FeD) and complexing sites (Li) in surface waters collected in summer were higher than in winter. The average concentration of FeD during summer was 64.6 ± 33.9 nmol L-1, and in winter it was 44.6 ± 28.6 nmol L-1. The mean labile fraction (Fe') was 3.20 ± 3.00 nmol L-1 during winter collection and 14.8 ± 10.7 nmol L-1 during summer. Mean concentrations of Li and mean values of the logarithm of stability constants (log KFe-L) were 103 ± 67.4 nmol L-1 and 12.0 ± 0.35 nmol L-1 for winter, and 135 ± 78.2 nmol L-1 and 11.6 ± 0.50 nmol L-1 for summer, respectively, indicating the presence of stable ligands in the estuary. Concerning spatial variation, higher iron fraction values were observed at sites receiving sewage inputs and locations where the Cachoeira and Nhundiaquara rivers discharge, while sites closer to the ocean showed lower values of FeD, Fe', and Li

An attempt to determine the impact of the implementation of autonomous vehicles on a larger scale on the planning of city transport systems

Purpose: This paper aims to explore the potential impact of autonomous vehicles (AVs) on urban planning, sustainable urban development, and tourism. Methodology: The paper is a conceptual study that reviews and synthesizes existing literature on AVs, urban planning, and tourism. It also uses case studies to illustrate the potential effects of AVs. Results: The widespread adoption of AVs is likely to have significant implications for urban planning, including changes in land use, infrastructure design, and transportation patterns. AVs may also contribute to sustainable urban development by reducing traffic congestion and air pollution. In the tourism sector, AVs could lead to spatial changes, new social inequalities, and changes in the overnight visitor economy. Theoretical contribution: The paper contributes to the understanding of the complex interplay between AVs, urban planning, and tourism. It highlights the need for urban planners and tourism stakeholders to consider the potential impact of AVs in their decision-making processes. Practical implications: The paper provides practical insights for urban planners, tourism stakeholders, and policymakers on how to prepare for and adapt to the widespread use of AVs. It also emphasizes the importance of considering the potential benefits and challenges of AVs in the context of specific cities and tourism destinations

Determining mean first-passage time on a class of treelike regular fractals

Relatively general techniques for computing mean first-passage time (MFPT) of random walks on networks with a specific property are very useful, since a universal method for calculating MFPT on general graphs is not available because of their complexity and diversity. In this paper, we present techniques for explicitly determining the partial mean first-passage time (PMFPT), i.e., the average of MFPTs to a given target averaged over all possible starting positions, and the entire mean first-passage time (EMFPT), which is the average of MFPTs over all pairs of nodes on regular treelike fractals. We describe the processes with a family of regular fractals with treelike structure. The proposed fractals include the $T$ fractal and the Peano basin fractal as their special cases. We provide a formula for MFPT between two directly connected nodes in general trees on the basis of which we derive an exact expression for PMFPT to the central node in the fractals. Moreover, we give a technique for calculating EMFPT, which is based on the relationship between characteristic polynomials of the fractals at different generations and avoids the computation of eigenvalues of the characteristic polynomials. Making use of the proposed methods, we obtain analytically the closed-form solutions to PMFPT and EMFPT on the fractals and show how they scale with the number of nodes. In addition, to exhibit the generality of our methods, we also apply them to the Vicsek fractals and the iterative scale-free fractal tree and recover the results previously obtained.Comment: Definitive version published in Physical Review

Derivation of the Rules of Quantum Mechanics from Information-Theoretic Axioms

Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing properties of probability distributions for the outcome of measurements. Axioms I,II,III are common to quantum mechanics and hidden variable theories. Axiom IV recognizes a phenomenon, first noted by Turing and von Neumann, in which the increase in entropy resulting from a measurement is reduced by a suitable intermediate measurement. This is shown to be impossible for local hidden variable theories. Axiom IV, together with the first three, almost suffice to deduce the conventional rules but allow some exotic, alternatives such as real or quaternionic quantum mechanics. Axiom V recognizes a property of the distribution of outcomes of random measurements on qubits which holds only in the complex Hilbert space model. It is then shown that the five axioms also imply the conventional rules for all dimensions.Comment: 20 pages, 6 figure

Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation

Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski networks, which are induced by the famous Sierpinski fractals and constructed in a simple iterative way. We derive analytical expressions for degree distribution, strength distribution, clustering coefficient, and strength-degree correlation, which agree well with the characterizations of various real-life networks. Moreover, we show that the introduced Sierpinski networks are maximal planar graphs.Comment: 6 pages, 5 figures, accepted by EP