Self-similar solutions to the mean curvature flow in R3\mathbb{R}^{3}

In this paper we make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces of revolution and ruled surfaces in $\mathbb{R}^{3}$. We prove that self-similar solutions of the MCF by non-cylindrival surfaces and conical surfaces in $\mathbb{R}^{3}$ are trivial. Moreover, we characterize the self-similar solutions of the MCF by surfaces of revolutions under a homothetic helicoidal motion in $\mathbb{R}^{3}$ in terms of the curvature of the generating curve. Finally, we characterize the self-similar solutions for the MCF by cylindrical surfaces under a homothetic helicoidal motion in $\mathbb{R}^3$. Explicit families of exact solutions for the MCF by cylindrical surfaces in $\mathbb{R}^{3}$ are also given

PEIRCE, FREGE, RUSSELL E O SURGIMENTO DA PREDICAÇÃO LÓGICA CONTEMPORÂNEA

Apresentamos neste artigo explicitações histórico-conceituais sobre o surgimento da predicação lógica contemporânea. Quando se trata de predicação, remete-se de imediato à obra de Aristóteles, mas, com as transformações trazidas pela Lógica Contemporânea, o estudo da predicação deixa o plano do estudo lógico-gramatical para o estudo do plano da análise lógicomatemática. Veremos, nesse sentido, a importância dos trabalhos de Peirce, Frege e Russell para o surgimento da predicação lógica contemporânea. Embora Peirce tenha sido o precursor da introdução do conceito de função proposicional na História da Lógica, ganha destaque, contemporaneamente, o modelo de interpretação da predicação inicialmente proposto por Frege

Spectral smooth tests for goodness-of-fit

Goodness-of-fit tests are crucial tools for assessing the validity of statistical models. In this paper, we introduce a novel approach, the Spectral Smooth Test (SST), that generalizes Neyman's smooth test to high-dimensional data settings. While conventional goodness-of-fit tests for univariate data are well-established, extending them to high dimensions, such as images, trajectories, and SNPs, poses significant challenges. Our proposed SST leverages spectral bases, which adapt naturally to the geometry of feature spaces, to model multivariate distributions. Unlike traditional orthogonal bases, these spectral bases are tailored to the data distribution, enabling more effective function modeling. The SST framework offers a principled way to estimate the underlying model, thereby providing actionable insights even when the null hypothesis is rejected. We present experimental results demonstrating the robustness of SST across various tuning parameter choices and compare its performance against other goodness-of-fit tests. Furthermore, we apply SST to the MNIST dataset as a real-world example, showcasing its effectiveness in high-dimensional scenarios

How to construct remainder sets for paraconsistent revisions: preliminary report

Revision operation is the consistent expansion of a theory by a new belief-representing sentence. We consider that in a paraconsistent setting this desideratum can be accomplished in at least three distinct ways: the output of a revision op eration should be either non-trivial or non-contradictory (in general or relative to the new belief). In this paper those dis tinctions will be explored in the constructive level by showing how the remainder sets could be refined, capturing the key concepts of paraconsistency in a dynamical scenario. These are preliminaries results of a wider project on Paraconsistent Belief Change conduced by the authors.info:eu-repo/semantics/publishedVersio

Interpreting data of a repeated sprint test

Alterations in performance are often quantified through physical tests. However, although frequently used there are a few discussions about the reliability and interpretation of their results. The purpose of this study was to verify the reliability of a new method to access the repeated sprint ability denominated Labex-Test (LT) as well as analyzing the effect of 10 weeks of systematized training in soccer players\u27 performance. LT consists of an uncertain number of sprints of 30m until a fall of performance of 10% is observed in relation to its initial speed. All the sprints are intercalated with 20 seconds of active recovery and monitored by a set of photocells placed at each 6 m. The variables analyzed through LT were initial speed (mean speed of the first 30m sprint), initial acceleration (first 6m) and the number of sprints. Twelve soccer players aged 17.2±0.4 years participated of this study. Two sets of 3 tests were accomplished, with intervals of 48 hours, one before and the other at the end of the 10 weeks of training. LT detected increase of the initial speed and of the initial acceleration in 79% and 64% of the tests, respectively. On the other hand, there was a reduction of the sprints number in 79% of the tests. The same variables presented average and standard deviation of 7.30±0.22 m/sec; 8.96±0.85 m/sec and 4.98±1.61 sprints before and 7.60±0.30 m/sec; 9.87±0.90 m/sec and 4.10±1.11 sprints after the training period. LT has shown to be sensitive for the three studied variables