The Strong Property (B) for $$L_p$$ Spaces

Given a purely non-atomic, finite measure space $$(\Omega ,\Sigma ,\nu )$$ ( Ω , Σ , ν ) , it is proved that for every closed, infinite-dimensional subspace V of $$L_p(\nu )$$ L p ( ν ) ($$1\le p<\infty $$ 1 ≤ p < ∞ ) there exists a decomposition $$L_p(\nu )=X_1\oplus X_2$$ L p ( ν ) = X 1 ⊕ X 2 , such that both subspaces $$X_1$$ X 1 and $$X_2$$ X 2 are isomorphic to $$L_p(\nu )$$ L p ( ν ) and both $$V\cap X_1$$ V ∩ X 1 and $$V\cap X_2$$ V ∩ X 2 are infinite-dimensional. Some consequences concerning dense, non-closed range operators on $$L_1$$ L 1 are derived.

Variational Principles for Maximization Problems with Lower-semicontinuous Goal Functions

Let X be a completely regular topological space and f a real-valued bounded from above lower semicontinuous function in it. Let C(X) be the space of all bounded continuous real-valued functions in X endowed with the usual sup-norm. We show that the following two properties are equivalent: X is α-favourable (in the sense of the Banach-Mazur game); The set of functions h in C(X) for which f + h attains its supremum in X contains a dense and Gδ-subset of the space C(X). In particular, property (b) has place if X is a compact space or, more generally, if X is homeomorphic to a dense Gδ subset of a compact space.We show also the equivalence of the following stronger properties: X contains some dense completely metrizable subset; the set of functions h in C(X) for which f + h has strong maximum in X contains a dense and Gδ-subset of the space C(X). If X is a complete metric space and f is bounded, then the set of functions h from C(X) for which f + h has both strong maximum and strong minimum in X contains a dense Gδ-subset of C(X).

DIREITO REAL DE HABITAÇÃO: CONFLITO ENTRE O DIREITO REAL DE HABITAÇÃO E O DIREITO À HERANÇA, E A POSSÍVEL MITIGAÇÃO NO CASO CONCRETO POR MEIO DO JUÍZO DE PONDERAÇÃO

The real property law is a legal institution of civil law, introduced in the Civil Code of 1916 by Status of Women Married - Law nº 4.121 / 1962, which required numerous requirements for its grant and maintenance, namely, (a) were married under the regime of community property; (b) during his lifetime; (c) and remained widow; (d) subject to the inheritance share, the property should be for the family residence and, finally, (e) were the only asset of this nature to inventory. With the advent of the Civil Code of 2002, however, it was extended to all property regime, removed the final term and with the Domestic Partnership Act, It was no longer needed that it was the only good of that nature to inventory. It was questioned the extent of its application in this case and the need for consideration to not fade the right to inheritance. Analyzed the rights involved, Right to inheritance, Property Rights, Right to living and the Real Property Law. It was concluded that the interpreter of the Law must, before the case, carry out the judgment of balancing the conflicting fundamental Rights so that there is maximum preservation of conflicting values, and hence the greatest achievement of constitutional values.

INFLUENCE OF NATIVE VEGETATION ON PEQUIÁ FRUIT (Caryocar villosum [Aubl.] Pers) PRODUCTION AND TRAITS

This study aims to determine the influence of native vegetation on production and traits of fruit from pequiá (Caryocar villosum [Aubl.] Pers), in the city of Nova Xavantina, Mato Grosso, Brazil. Fruits were collected from pequiá trees from two sites over a three-year period (2016, 2017, and 2018). The first site (Property A) was located near a fragment of natural vegetation, and the second site (Property B) was located in an anthropized area, far from any fragments of vegetation. The fruit samples (N = 40) were taken to the laboratory and, using a digital scale and calipers, each fruit’s weight, the weight of the outer shell, the equatorial diameter of the fruit, the longitudinal diameter of the fruit, the equatorial diameter of the seed, the longitudinal diameter of the seed, the thickness of the outer shell, and the number of seeds per fruit were measured or counted. The pequiá seeds were separated into batches of ten to evaluate the weight with pulp, their weight without pulp, the weight of the pulp, and the pulp yield as variables. Student’s t-test was used to compare the fruit traits between the two sites. Analysis of variance was also applied to the data. Property A was found to have larger and heavier fruits and a higher pulp weight in each batch. The climate may have been the main factor that influenced pequiá production from one year to the next during the study period. A lack of vegetation is one of the causes of distancing and reductions in pollinators, which, in turn, directly influence production and traits of pequiá fruits. Keywords: ecosystem services; pollination; climate. INFLUÊNCIA DA VEGETAÇÃO NATIVA NA PRODUÇÃO E BIOMETRIA DE FRUTOS DE PEQUIÁ (Caryocar villosum [Aubl.] Pers) O objetivo deste trabalho foi verificar a influência da vegetação nativa na produção e biometria de frutos de pequiás (Caryocar villosum [Aubl.] Pers) em Nova Xavantina, Mato Grosso, Brasil. Para a realização deste estudo foram feitas coletas de frutos de pequiá em duas áreas durante três anos (2016, 2017 e 2018). Sendo a primeira área localizada próximo de um fragmento de vegetação natural (Propriedade A) e a segunda área está situada em área antropizada e distante de qualquer fragmento de vegetação (Propriedade B). Em cada propriedade foram coletados 40 frutos maduros de pequiá. Os frutos foram levados para laboratório e com o auxílio de uma balança digital e paquímetro avaliaram-se os seguintes parâmetros: peso do fruto, peso da casca, diâmetro equatorial do fruto, diâmetro longitudinal do fruto, diâmetro equatorial do caroço, diâmetro longitudinal do caroço, espessura da casca e número de caroços por fruto. Os caroços de pequiá foram separados em lotes de dez unidades para avaliar as variáveis de peso com polpa, peso sem polpa, peso da polpa e rendimento da polpa. Para a comparação das variáveis biométricas entre as propriedades foi utilizado o teste t de Student, já para o fator ano os dados foram submetidos à análise de variância. A propriedade A apresentou frutos maiores, mais pesados e com maior peso de polpa por lotes. O clima foi possivelmente o principal fator que influenciou na produção dos pequiás entre os anos analisados. A ausência de vegetação é um dos motivos que causa distanciamento e redução dos polinizadores, influenciando diretamente na produção e biometria dos frutos de pequiás. Palavras-chave: serviço ecossistêmico; polinização; clima.

A quantitative Lovász criterion for Property B

A well-known observation of Lovász is that if a hypergraph is not 2-colourable, then at least one pair of its edges intersect at a single vertex. In this short paper we consider the quantitative version of Lovász’s criterion. That is, we ask how many pairs of edges intersecting at a single vertex should belong to a non-2-colourable n-uniform hypergraph. Our main result is an exact answer to this question, which further characterizes all the extremal hypergraphs. The proof combines Bollobás’s two families theorem with Pluhar’s randomized colouring algorithm.

The Effects of Property Tax Abatements on School District Property Tax Bases and Rates

The authors analyze the effects of property tax abatement on the property tax base and rates of school districts within a municipality offering the abatement using data from Franklin County, Ohio, one of the most populous counties in the United States. An increase in a school district’s Community Reinvestment Area abatement intensity correlates with (a) a decrease in the mill rate for real property, (b) a decrease in effective residential and nonresidential property tax rates, and (c) an increase in total market value of property. While these effects are small, they indicate that a municipality’s decision to abate has generated enough growth in property values, either through improvements to physical property or positive capitalization for existing property values, to offset the negative effects of an abatement. The reason for this may be that the restrictions and oversight used in this abatement program are greater than in most other places.

Leptospirosis in donkeys (Equus asinus) destined for slaughter and export

Brazil is the eighth largest exporter of equidae meat in the world. Most donkey meat is obtained from discarded animals, raising concerns about their health status, particularly regarding zoonotic infections such as leptospirosis. Thus, this study aimed to determine the frequency of anti-Leptospira sp. antibodies in Northeastern donkeys at two properties specializing in producing donkeys for slaughter and export to the Chinese market, in the municipalities of Parnamirim (A) and Araripina (B), both located in the mesoregion of the Sertão of Pernambuco, Northeastern Brazil. The serum of 349 donkeys was collected, including 147 males and 202 females, aged 3 to 12 years. All animals were subjected to the Microscopic Agglutination Test (MAT) using a cut-off point of 1:50. A total of 19.8% seropositive animals were obtained. The Icterohaemorrhagiae serogroup was the most found in this study (40.6%), followed by Australis (27.5%), Autumnalis (8.7%), Sejroe (8.7%), Pomona (8.7%), Celledoni (2.9%), and Tarassovi (2.9%). A higher overall rate of seropositivity was found in donkeys from property B (2.2.4%) in the municipality of Araripina. In the association analysis, it was observed that animals less than 9 years of age were more likely to be seropositive, this may be due to the acquisition of resistance to Leptospira sp. as age advances. A significant number of donkeys seropositive for Leptospira sp. was found, thus, breeding these animals for slaughter and export requires implementing prophylactic measures.

Neutral Difference System and its Nonoscillatory Solutions

The paper deals with a system of four nonlinear difference equations where the first equation is of a neutral type. We study nonoscillatory solutions of the system and we present sufficient conditions for the system to have weak property B.