Existence, uniqueness and numerical solution of a fractional PDE with integral conditions

This paper is devoted to the solution of one-dimensional Fractional Partial Differential Equation (FPDE) with nonlocal integral conditions. These FPDEs have been of considerable interest in the recent literature because fractional-order derivatives and integrals enable the description of the memory and hereditary properties of different substances. Existence and uniqueness of the solution of this FPDE are demonstrated. As for the numerical approach, a Galerkin method based on least squares is considered. The numerical examples illustrate the fast convergence of this technique and show the efficiency of the proposed method

Efficient high-order finite difference methods for nonlinear Klein–Gordon equations. I: Variants of the phi-four model and the form-I of the nonlinear Klein–Gordon equation

In this paper, the problem of solving some nonlinear Klein–Gordon equations (KGEs) is considered. Here, we derive different fourth- and sixth-order explicit and implicit algorithms to solve the phi-four equation and the form-I of the nonlinear Klein–Gordon equation. Stability and consistency of the proposed schemes are studied under certain conditions. Numerical results are presented and then compared with others obtained from some methods already existing in the scientific literature to explain the efficiency of the new algorithms. It is also shown that similar schemes can be proposed to solve many classes of nonlinear KGEs

Polynomial-based mean weighted residuals methods for elliptic problems with nonlocal boundary conditions in the rectangle

In this paper, polynomial-based mean weighted residuals methods for the solution of elliptic problems with nonlocal boundary conditions, in rectangular domains, are numerically studied. When these methods are employed, the nonclassical boundary conditions involve the solution of large systems of linear equations or least squares problems, hence some numerical techniques for these solvers are compared to show the importance of using efficient algorithms for this purpose. Different kinds of nodes are used to demonstrate how they can be employed to solve different numerical problems when large derivatives of the solution appear. We will also study how using extra precision and/or oversampling can often reduce the computational effort.These methods can also be combined with others (as, for example, finite difference or spline methods) to solve linear and nonlinear parabolic or hyperbolic partial differential equations. The numerical study of some techniques as those explained above can help to obtain significantly better numerical approximations with a smaller computational effort

Mathematics and Its Applications in Science and Engineering

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The usefulness of the Spanish version of the STOP-Bang questionnaire for screening for moderate or severe sleep apnea syndrome in primary care.

Sleep apnea-hypopnea syndrome (OSA) is a highly prevalent disease and has been related to cardiovascular diseases and occupational and traffic accidents. Currently, it is estimated that there is a significant underdiagnosis of OSA, mainly due to the difficulty accessing the tests for that purpose. To determine the usefulness of the Spanish version of the STOP-Bang questionnaire (SBQ) for screening for moderate or severe OSA in the adult population attending primary care. A descriptive observational multicenter study was conducted. Through an opportunistic search, (patients over 18 years old), were recruited in seven primary care centers. The SBQ was applied to them and home respiratory polygraphy (HRP) was subsequently performed to confirm the diagnosis of OSA. The criterion validity of the SBQ was analyzed, comparing the score obtained by the SBQ with the apnea-hypopnea index (AHI) obtained by RP, establishing the diagnosis of OSA for an AHI>5. The reliability of the questionnaire was evaluated. A total of 255 subjects, 54.1% men, with a mean age of 54.76 ± 10 years, were recruited in the study. The results showed that 61.57% (95% Confidence Interval: 55.57-67.57) of the subjects presented OSA, presenting 22.75% (17.57-57.92) a mild OSA (530) (11.54-20.62). The Kuder and Richardson coefficient was 0.623 (0.335-0.788) and Cohen's Kappa coefficient was 0.871 (0.520-1.00; p 15) the SBQ obtained an ROC curve of 0.769 (0.704-0.833) that with an optimal cutoff of 3, achieved a sensitivity of 84.85% (77.28-92.42) and a specificity of 55.10% (44.74-65.46). The SBQ is very effective for detecting moderate/severe OSA. Its psychometric properties are similar to those obtained in studies on other populations. Because of its ease of use, the SBQ is a very useful tool for primary health care professionals

Analysis of the determinants of sleep quality in a Spanish population: a study protocol for a cross-sectional study

Introduction Sleep problems are a growing public health concern being related, among others, to an increased risk of cardiovascular diseases or worse cognitive functioning. In addition, they can affect aspects related to personal motivation and quality of life. However, very few studies have analysed the possible determinants of sleep quality in the adult population as a whole, establishing patterns based on these determinants.The objectives are to evaluate the determinants of sleep quality in a representative sample of the general adult population between 25 and 65 years old, and to establish patterns of sleep quality based on lifestyles, psychological factors, morbidities, sociodemographic variables, biological markers and other possible determinants.Methods and analysis Descriptive observational cross-sectional study. The study population will include a representative sample of 500 people between 25 and 65 years old from the cities of Salamanca and Ávila (Spain) selected by random sampling stratified by age groups and sex. A 90-minute visit will be performed, during which sleep quality will be assessed. The variables collected will be: morbidity, lifestyles (physical activity, diet, toxic habits), psychological factors (depression, stress, occupational stress and anxiety), socioeconomic and work-related variables, habitability conditions of the habitual residence and rest area, screen time, relaxation techniques and melatonin as a biological marker related to sleep quality.Discussion With the results of this work, improved interventions for behaviour modification could be designed, as well as intervention and education programmes or other research aimed at improving sleep quality.Ethics and dissemination This study has a favourable opinion from the Ethics Committee for Drug Research of the Health Areas of Salamanca and Ávila (CEim Code: PI 2021 07 815). The results of this study will be published in international impact journals of different specialties.Trial registration number NCT05324267