A generalized Hausdorff dimension for functions and sets

Let E be a compact subset of the n-dimensional unit cube, 1_n, and let C be a collection of convex bodies, all of positive n-dimensional Lebesgue measure, such that C contains bodies with arbitrarily small measure. The dimension of E with respect to the covering class C is defined to be the number

d_C(E) = sup(β:H_{β, C}(E) > 0),

where H_{β, C} is the outer measure

inf(Ʃm(C_i)^β:UC_i Ↄ E, C_i ϵ C) .

Only the one and two-dimensional cases are studied. Moreover, the covering classes considered are those consisting of intervals and rectangles, parallel to the coordinate axes, and those closed under translations. A covering class is identified with a set of points in the left-open portion, 1’_n, of 1_n, whose closure intersects 1_n - 1’_n. For n = 2, the outer measure H_{β, C} is adopted in place of the usual:

Inf(Ʃ(diam. (C_i))^β: UC_i Ↄ E, C_i ϵ C),

for the purpose of studying the influence of the shape of the covering sets on the dimension d_C(E).

If E is a closed set in 1₁, let M(E) be the class of all non-decreasing functions μ(x), supported on E with μ(x) = 0, x ≤ 0 and μ(x) = 1, x ≥ 1. Define for each μ ϵ M(E),

d_C(μ) = lim/c → inf/0 log ∆μ(c)/log c , (c ϵ C)

where ∆μ(c) = v/x (μ(x+c) – μ(x)). It is shown that

d_C(E) = sup (d_C(μ):μ ϵ M(E)).

This notion of dimension is extended to a certain class Ӻ of sub-additive functions, and the problem of studying the behavior of d_C(E) as a function of the covering class C is reduced to the study of d_C(f) where f ϵ Ӻ. Specifically, the set of points in 1₁,

(*) {d_B(F), d_C(f)): f ϵ Ӻ}

is characterized by a comparison of the relative positions of the points of B and C. A region of the form (*) is always closed and doubly-starred with respect to the points (0, 0) and (1, 1). Conversely, given any closed region in 1₂, doubly-starred with respect to (0, 0) and (1, 1), there are covering classes B and C such that (*) is exactly that region. All of the results are shown to apply to the dimension of closed sets E. Similar results can be obtained when a finite number of covering classes are considered.

In two dimensions, the notion of dimension is extended to the class M, of functions f(x, y), non-decreasing in x and y, supported on 1₂ with f(x, y) = 0 for x · y = 0 and f(1, 1) = 1, by the formula

d_C(f) = lim/s · t → inf/0 log ∆f(s, t)/log s · t , (s, t) ϵ C

where

∆f(s, t) = V/x, y (f(x+s, y+t) – f(x+s, y) – f(x, y+t) + f(x, t)).

A characterization of the equivalence d_C1(f) = d_C2(f) for all f ϵ M, is given by comparison of the gaps in the sets of products s · t and quotients s/t, (s, t) ϵ C_i (I = 1, 2).

Should EFL Teachers Present Vocabulary in Semantically Related Sets?

[EN] Teaching vocabulary in semantically related sets is common practice among EFL teachers. The present study tests the effectiveness of this method by comparing it to the alternative technique: presenting vocabulary in an unrelated way. In the study two intact classes of Spanish learners of English in high-school were presented with a set of unrelated and related words and were then asked to complete a post-test to measure the impact of both techniques on learning. The results indicate that, while both techniques successfully help the learners to acquire new words, presenting words in unrelated sets seems to be more effective.

Discurso e ensino: o curso de Letras e a formação docente

Esta tese tem por objetivo discutir a política científico-educacional do curso de Letras, por meio da análise do projeto político-pedagógico (PPP) que norteia a formação do acadêmico e do futuro professor de Língua Portuguesa. A compreensão de que toda esfera da atividade humana elabora os seus gêneros mais ou menos estáveis, segundo os quais os sujeitos se relacionam e interagem socialmente (BAKHTIN, 1997) é significativa, pois permite afirmar que o PPP é um documento norteador de uma política científico-educacional, podendo se manifestar nas práticas discursivas próprias da vida universitária de um curso. No PPP se delineiam, entre outros princípios, concepções filosófico-educacionais e abordagens teóricas e metodológicas que fundamentam o discurso científico-educacional e os saberes instituídos do curso de Letras. Em virtude disso, procurou-se traçar um percurso histórico das referências locais e globais, a partir de concepções sobre ser, tempo, acontecimento e alteridade, advindas do saber literário (BARTHES, 1992 e BAKHTIN, 2010) e da trajetória universitária em foco, articuladas à conjuntura que vem marcando o movimento por mudanças nas ciências e na educação. Investigou-se, em seguida, o PPP do curso de Letras, analisando esse gênero do discurso acadêmico-universitário, consoante a forma e tipo de interação em relação com a situação concreta de enunciação e com o horizonte histórico e social mais amplo (BAKHTIN/VOLOCHINOV, 1992), em que se configuram novos sentidos que convergem e/ou confrontam com discursos e saberes historicamente instituídos do curso. Refletiu-se, pois, se a introdução de novas disciplinas em estudos da linguagem resulta de uma transição consensual de uma Linguística do enunciado para uma Linguística da enunciação ou marca uma crise de paradigma(s) no âmbito da Linguística. Procedeu-se, por fim, a uma análise dos discursos dos acadêmicos de Letras da UFPA-Marabá, a fim de compreender os sentidos que constroem sobre o curso, sobre o projeto político-pedagógico, a imagem que constroem da instituição, de si mesmos, como acadêmicos e futuros professores de Língua Portuguesa. Objetivou-se, com isso, confrontar a política científico-educacional proposta pelo PPP com o discurso desses sujeitos, a fim de compreender seus posicionamentos diante da formação que permeia o projeto, bem como sua avaliação a respeito do discurso de integração curricular. Procurou-se, por fim, focalizar outras referências de cursos de Letras, com o objetivo de cotejar os posicionamentos de diferentes PPP em relação ao perfil que pretendem construir de professor de Língua Portuguesa, consoante o quadro curricular proposto em estudos da linguagem. Toma-se como córpus os PPPs dos Cursos de Letras do Câmpus Universitário de Marabá e de Belém, da Universidade Federal do Pará e, da Universidade Federal de Goiás (Câmpus de Catalão e Câmpus de Goiânia), para então compará-los com depoimentos escritos dos acadêmicos de Letras da UFPA-Marabá

Initiatives for the improvement of continuous management training

[EN] Purpose. This work aims to present, from the company viewpoint, a structured account of management proposals and practices directed toward improving the intensity and effectiveness of continuous management training (CMT). Design/methodology/approach. The article takes as its main theoretical referents the Theory of Human Capital, the Resource-Based Vision and the contributions made via the new institutional economy with regard to the problems of information asymmetry between companies, employees and training providers and completes the proposals that derive from this theoretical approach. To do this, experience-based contributions are collected from a selection of company training and HR managers from twelve Basque companies characterised by their strong investment in management training. The methodology used was qualitative and obtained by different qualitative techniques: Focus Groups, Nominal Groups and the Delphi Method, which make up the so-called Hybrid Delphi. Findings and implications. The proposals are aimed at the main agents in training activity: training providers, associations and public agents engaged in management training and, particularly, companies themselves. The initiatives seek above all to increase training market transparency, to improve mutual commitments between companies and managers, and to link training and development with culture and strategic management, so that firms make optimal investment in management training. Originality/value. The methodology used is original, and the contributions are consistent with the theory, have a proven practical utility, and are presented in a hierarchy, which facilitates decision making.

Integrated treatment of first episode psychosis with online training (e-learning): study protocol for a randomised controlled trial

Background: The integrated treatment of first episode psychosis has been shown to improve functionality and negative symptoms in previous studies. In this paper, we describe a study of integrated treatment (individual psychoeducation complementary to pharmacotherapy) versus treatment as usual, comparing results at baseline with those at 6-month re-assessment (at the end of the study) for these patients, and online training of professionals to provide this complementary treatment, with the following objectives: 1) to compare the efficacy of individual psychoeducation as add-on treatment versus treatment as usual in improving psychotic and mood symptoms; 2) to compare adherence to medication, functioning, insight, social response, quality of life, and brain-derived neurotrophic factor, between both groups; and 3) to analyse the efficacy of online training of psychotherapists. Methods/design: This is a single-blind randomised clinical trial including patients with first episode psychosis from hospitals across Spain, randomly assigned to either a control group with pharmacotherapy and regular sessions with their psychiatrist (treatment as usual) or an intervention group with integrated care including treatment as usual plus a psychoeducational intervention (14 sessions). Training for professionals involved at each participating centre was provided by the coordinating centre (University Hospital of Alava) through video conferences. Patients are evaluated with an extensive battery of tests assessing clinical and sociodemographic characteristics (Positive and Negative Syndrome Scale, State-Trait Anxiety Inventory, Liebowitz Social Anxiety Scale, Hamilton Rating Scale for Depression, Scale to Assess Unawareness of Mental Disorders, Strauss and Carpenter Prognostic Scale, Global Assessment of Functioning Scale, Morisky Green Adherence Scale, Functioning Assessment Short Test, World Health Organization Quality of Life instrument WHOQOL-BREF (an abbreviated version of the WHOQOL-100), and EuroQoL questionnaire), and brain-derived neurotrophic factor levels are measured in peripheral blood at baseline and at 6 months. The statistical analysis, including bivariate analysis, linear and logistic regression models, will be performed using SPSS. Discussion: This is an innovative study that includes the assessment of an integrated intervention for patients with first episode psychosis provided by professionals who are trained online, potentially making it possible to offer the intervention to more patients.

Efeito agudo dos exercícios resistidos sobre a reatividade vascular e adipocitocinas de mulheres com sobrepeso e obesidade

Introdução O exercício resistido (ER) agudo parece resultar em importantes efeitos sobre a liberação de substâncias vasoativas e sobre o controle endotélio-dependente do tônus vascular. Objetivos O objetivo do presente estudo foi avaliar os efeitos agudos de um ER isolado sobre a pressão arterial (PA), frequência cardíaca (FC), fluxo sanguíneo do antebraço (FSA), condutância vascular (CV), respostas endotelial e inflamatória de mulheres jovens com sobrepeso/obesidade (Sp/Ob). Materiais e Métodos As voluntárias foram separadas em grupos: controle (n = 16) e Sp/Ob (n = 16). Ambos os grupos realizaram cinco séries de 10 repetições com 70% de uma repetição máxima (1-RM) no exercício de flexão unilateral do cotovelo. A PA, FC e o FSA (medido por pletismografia por oclusão venosa), foram avaliados em repouso e durante uma hora após o ER em ambos os grupos. Adipocitocinas e endotelina-1 (ET-1) foram avaliadas em repouso nos dois grupos e após o ER apenas no grupo Sp/Ob. Resultados O grupo Sp/Ob apresentou massa corporal e IMC significativamente maiores que o controle (p<0,05). Surpreendentemente, o grupo Sp/Ob apresentou relação cintura-quadril significativamente menor (p<0,05). As diferenças entre grupos nas PAs diastólica e média observadas antes do ER (repouso) foram também observadas imediatamente e 20 minutos após a sessão de ER (p<0,05). Ambos os grupos apresentaram reduções significativas na PA diastólica imediatamente após a sessão de ER (p<0,01). A PA média apresentou redução significativa imediatamente após a sessão de ER apenas no grupo controle (p<0,05). O grupo Sp/Ob apresentou valores de FSA significativamente maiores que o controle em repouso (p<0,05), em 20 (p<0,01) e em 40 (p<0,01) minutos após o ER. A CV não apresentou diferença em repouso, porém em 20 e 40 minutos após o ER, o grupo Sp/Ob apresentou valores significativamente maiores (p<0,01). Em repouso e imediatamente após a sessão de ER, não foram observadas diferenças entre o grupo controle e o grupo Sp/Ob na vasodilatação endotélio-dependente. Deve-se ressaltar que em 30 minutos após a realização do ER, o grupo Sp/Ob apresentou maior vasodilatação endotélio-dependente que o controle (p<0,05). Surpreendentemente, a vasodilatação endotélio-independente em repouso era menor no grupo controle quando comparado ao grupo Sp/Ob (p<0,05). Entretanto, não foi observada diferença significativa entre os grupos 50 minutos após a sessão de ER. Como esperado, o grupo Sp/Ob apresentou valores significativamente menores de adiponectina (p<0,01) e significativamente maiores de IL-6 e leptina que o grupo controle (p<0,001). Foram observadas reduções significativas nos valores de IL-6 (p<0,05) e leptina (p<0,01), enquanto a ET-1 (p<0,05) apresentou aumento significativo. Conclusões Em conclusão, a realização do ER resultou em melhora aguda do FSA, da CV e da vasodilatação endotélio-dependente concomitantemente com mudanças no perfil inflamatório e ET-1 de mulheres saudáveis com Sp/Ob.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

Mindfulness training for reducing anger, anxiety, and depression in fibromyalgia patients

Fibromyalgia is a disabling syndrome. Results obtained with different therapies are very limited to date.The goal of this study was to verify whether the application of a mindfulnessbased training program was effective in modifying anger, anxiety, and depression levels in a group of women diagnosed with fibromyalgia. This study is an experimental trial that employed a waiting list control group. Measures were taken at three different times: pretest, posttest, and follow-up. The statistical analyses revealed a significant reduction of anger (trait) levels, internal expression of anger, state anxiety, and depression in the experimental group as compared to the control group, as well as a significant increase in internal control of anger. It can be concluded that the mindfulness-based treatment was effective after 7 weeks. These results were maintained 3 months after the end of the intervention.