Search results for " MATHEMATICAL"
showing 10 items of 686 documents
Gradient Estimate for Solutions to Poisson Equations in Metric Measure Spaces
2011
Let $(X,d)$ be a complete, pathwise connected metric measure space with locally Ahlfors $Q$-regular measure $\mu$, where $Q>1$. Suppose that $(X,d,\mu)$ supports a (local) $(1,2)$-Poincar\'e inequality and a suitable curvature lower bound. For the Poisson equation $\Delta u=f$ on $(X,d,\mu)$, Moser-Trudinger and Sobolev inequalities are established for the gradient of $u$. The local H\"older continuity with optimal exponent of solutions is obtained.
Early mathematical skill profiles of prematurely and full-term born children
2017
Abstract Preterm birth is associated with low mathematical skills in children. This study on five-year-old Finnish children investigated whether mathematical skill profiles would differ between prematurely and full-term born children and how such profiles and other cognitive skills would be related. Mathematical skills included digit knowledge, spontaneous focusing on numerosity, arithmetic, counting and geometric skills. The investigated cognitive skills were phonological processing, working memory, instruction comprehension, speeded naming, inhibition and visuomotor skills. The participants were 119 preterm children with birth weight
Linear stability analysis of gas-fluidized beds for the prediction of incipient bubbling conditions
2010
Abstract This work focuses on the development of a novel linear stability criterion for the state of homogeneous fluidization regime, based on a new mathematical model for gas-fluidized beds. The model is developed starting from the well-known particle bed model. A mono-dimensional momentum balance is derived leading to a set of equations which explicitly include voidage-gradient dependent terms (elastic force) for both solid and fluid phases. A fully predictive criterion for the stability of homogeneous fluidization state is here proposed, based on the well-known Wallis’ linear stability analysis. The criterion requires the choice of an appropriate averaging distance, which in the present …
Atypical transistor-based chaotic oscillators: Design, realization, and diversity
2017
In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predom…
On Independent Component Analysis with Stochastic Volatility Models
2017
Consider a multivariate time series where each component series is assumed to be a linear mixture of latent mutually independent stationary time series. Classical independent component analysis (ICA) tools, such as fastICA, are often used to extract latent series, but they don't utilize any information on temporal dependence. Also financial time series often have periods of low and high volatility. In such settings second order source separation methods, such as SOBI, fail. We review here some classical methods used for time series with stochastic volatility, and suggest modifications of them by proposing a family of vSOBI estimators. These estimators use different nonlinearity functions to…
The Raising Factor, That Great Unknown. A Guided Activity for Undergraduate Students
2020
In the first years of their economics degree programs, students will face many problems successfully dealing with a range of subjects with quantitative content. Specifically, in the field of statistics, difficulties to reach some basic academic achievements have been observed. Hence, a continuing challenge for statistics teachers is how to make this subject more appealing for students through the design and implementation of new teaching methodologies. The latter tend to follow two main approaches. On the one hand, it is useful for the learning process to propose practical activities that can connect theoretical concepts with real applications in the economic context. On the other hand, we …
Bayesian joint ordinal and survival modeling for breast cancer risk assessment
2016
We propose a joint model to analyze the structure and intensity of the association between longitudinal measurements of an ordinal marker and time to a relevant event. The longitudinal process is defined in terms of a proportional-odds cumulative logit model. Time-to-event is modeled through a left-truncated proportionalhazards model, which incorporates information of the longitudinal marker as well as baseline covariates. Both longitudinal and survival processes are connected by means of a common vector of random effects. General inferences are discussed under the Bayesian approach and include the posterior distribution of the probabilities associated to each longitudinal category and the …
Wardowski conditions to the coincidence problem
2015
In this article we first discuss the existence and uniqueness of a solution for the coincidence problem: Find p ∈ X such that Tp = Sp, where X is a nonempty set, Y is a complete metric space, and T, S:X → Y are two mappings satisfying a Wardowski type condition of contractivity. Later on, we will state the convergence of the Picard-Juncgk iteration process to the above coincidence problem as well as a rate of convergence for this iteration scheme. Finally, we shall apply our results to study the existence and uniqueness of a solution as well as the convergence of the Picard-Juncgk iteration process toward the solution of a second order differential equation. Ministerio de Economía y Competi…
Lévy–Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups
2018
We study the first and second cohomology groups of the $^*$-algebras of the universal unitary and orthogonal quantum groups $U_F^+$ and $O_F^+$. This provides valuable information for constructing and classifying L\'evy processes on these quantum groups, as pointed out by Sch\"urmann. In the case when all eigenvalues of $F^*F$ are distinct, we show that these $^*$-algebras have the properties (GC), (NC), and (LK) introduced by Sch\"urmann and studied recently by Franz, Gerhold and Thom. In the degenerate case $F=I_d$, we show that they do not have any of these properties. We also compute the second cohomology group of $U_d^+$ with trivial coefficients -- $H^2(U_d^+,{}_\epsilon\Bbb{C}_\epsil…
Juggler's exclusion process
2012
Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.