Abstract
In this paper, we investigate the well-posedness of a fully nonlinear elliptic problem. By using the acute angle principle for the weakly continuous operator, we obtained the
W
2,
p
-strong ...solution of the fully nonlinear elliptic problem.
Recently, Zayernouri and Karniadakis in (2013) 78 investigated two classes of fractional Sturm–Liouville eigenvalue problems on compact interval a,b in more detail. They were the first authors who ...not only obtained some explicit forms for the eigensolutions of these problems but also derived some useful spectral properties of the obtained eigensolutions. Until now, to the best of our knowledge, fractional Sturm–Liouville eigenvalue problems on non-compact interval, such as 0,+∞) are not analyzed. So, our aim in this paper is to study these problems in detail. To do so, we study at first fractional Sturm–Liouville operators (FSLOs) of the confluent hypergeometric differential equations of the first kind and then two special cases of FSLOs: FSLOs-1 and FSLOs-2 are considered. After this, we obtain the analytical eigenfunctions for the cases and investigate the spectral properties of eigenfunctions and their corresponding eigenvalues. Also, we derive two fractional types of the associated Laguerre differential equations. Due to the non-polynomial nature of the eigenfunctions obtained from the two fractional associated Laguerre differential equations, they are defined as generalized associated Laguerre functions of the first and second kinds, GALFs-1 and GALFs-2. Furthermore, we prove that these fractional Sturm–Liouville operators are self-adjoint and the obtained eigenvalues are all real, the corresponding eigenfunctions are orthogonal with respect to the weight function associated to FSLOs-1 and FSLOs-2 and form two sets of non-polynomial bases. At the end, two new quadrature rules and L2-orthogonal projections with respect to and based on GALFs-1 and GALFs-2 are introduced. The upper bounds of the truncation errors of these new orthogonal projections according to some prescribed norm are proved and then verified numerically with some test examples. Finally, some fractional differential equations are provided and analyzed numerically.
When adolescents live with a parent with mental illness, they often partly take over the parental role. Little is known about the consequences of this so‐called parentification on the adolescents' ...internalizing and externalizing problems. This survey study examined this effect cross‐sectionally and longitudinally in a sample of 118 adolescents living with a parent suffering from mental health problems. In addition, the study examined a possible indirect effect via perceived stress. Path analyses were used to examine the direct associations between parentification and problem behavior as well as the indirect relations via perceived stress. The results showed that parentification was associated with both internalizing and externalizing problems cross‐sectionally, but it predicted only internalizing problems 1 year later. An indirect effect of parentification on adolescent internalizing and externalizing problems via perceived stress was found, albeit only cross‐sectionally. These findings imply that parentification can be stressful for adolescents who live with a parent with mental health problems, and that a greater awareness of parentification is needed to prevent adolescents from developing internalizing problems.
Cuando los adolescentes viven con un padre que padece una enfermedad mental, generalmente asumen parcialmente el rol parental. Se sabe muy poco acerca de las consecuencias que tiene esta supuesta parentificación en los problemas internalizantes y externalizantes de los adolescentes. Este estudio de investigación analizó este efecto transversalmente y longitudinalmente en una muestra de 118 adolescentes que vivían con un padre que padecía problemas de salud mental. Además, el estudio examinó un posible efecto indirecto a través del estrés percibido. Se utilizaron análisis de ruta para examinar las asociaciones directas entre la parentificación y el comportamiento problemático así como las relaciones indirectas a través del estrés percibido. Los resultados demostraron que la parentificación estuvo asociada tanto con problemas internalizantes como externalizantes a nivel transversal, pero que predijo solamente problemas internalizantes un año después. Se descubrió un efecto indirecto de la parentificación en los problemas internalizantes y externalizantes de los adolescentes a través del estrés percibido, pero solo transversalmente. Estos hallazgos implican que la parentificación puede ser estresante para los adolescentes que viven con un padre que sufre de problemas de salud mental, y que es necesario un mayor conocimiento de la parentificación para evitar que los adolescentes desarrollen problemas internalizantes.
当青少年和一个有精神疾病的家长生活在一起时,他们经常部分的扮演家长的角色。关于所谓的家长化对于青少年内化和外化问题的后果我们知之甚少。该调查横向和纵向考察了118位与有精神疾病的家长生活在一起的青少年中这一影响。此外,该研究考察了感知到的压力可能带来的一个间接影响。我们使用通道分析考察了家长化和问题行为的直接联系以及感知到的压力带来的其间接关系。结果表明家长化和内在外及外在化问题有横向联系,然而其对内在化问题的预期出现在一年后。我们还发现了感知到的压力在家长化对青少年内在化和外在化问题的一个间接影响,尽管这一影响只是横向的。这些发现暗示家长化对于和有精神疾病的家长生活在一起的青少年造成压力,我们需提高对家长化问题的认识来防止青少年出现内在化问题。
Maternal mental health problems during pregnancy and the postnatal period are a major public health issue. Despite evidence that symptoms of both depression and anxiety are common during pregnancy ...and the postpartum, the impact of maternal anxiety on the child has received relatively less attention than the impact of maternal depression. Furthermore, the evidence base for the direct impact of maternal anxiety during pregnancy and the postpartum on children’s emotional outcomes lacks cohesion. The aim of this systematic review is to summarise the empirical evidence regarding the impact of maternal prenatal and postnatal anxiety on children’s emotional outcomes. Overall, both maternal prenatal and postnatal anxiety have a small adverse effect on child emotional outcomes. However, the evidence appears stronger for the negative impact of prenatal anxiety. Several methodological weaknesses make conclusions problematic and replication of findings is required to improve the identification of at-risk parents and children with appropriate opportunities for intervention and prevention.
Neurological conditions and mental health problems are common in children in low- and middle-income countries, but the risk factors and downstream impact of these problems on children with ...neurological conditions are not reported.
To determine the association of neurological conditions with behavioural and emotional problems in children, the prevalence and risk factors of behavioural and emotional problems, and long-term impact of these conditions.
Data on multiple neurological conditions and mental health problems were available for 1,616 children (aged 6-9 years) from Kilifi, Kenya. Neurological conditions were diagnosed using standardised tools and clinical examination. Behavioural and emotional problems assessed using Child Behaviour Questionnaire for Parents. Long-term outcomes were obtained from census data of the Kilifi Health and Demographic Surveillance System. Logistic and linear regression were used to measure associations.
Mental health problems were higher in those with any neurological condition compared to those without (24% vs. 12%, p < 0.001). Cognitive (odds ratio (OR) = 2.39; 95% CI: 1.59-3.59), motor (OR = 3.17; 95% CI: 1.72-5.82), hearing (OR = 2.07; 95% CI:1.12-3.83) impairments, and epilepsy (OR = 4.18; 95% CI: 2.69-6.48), were associated with mental health problems. Prevalence of any mental health problem was 15%, with externalizing problems more common than internalizing problems (21% vs. 17%, p = 0.004). Longitudinal follow-up indicated that the disorders affected an individual's future schooling (e.g. OR = 1.25; 95% CI: 0.14-1.46 following cognitive impairments), occupation (OR = 2.44; 95% CI: 1.09-5.44 following mental health problems), and access to household assets (OR = 2.78; 95% CI: 0.99-7.85 following epilepsy).
Neurological conditions in school-aged children in Kilifi are associated with mental health problems, and both disorders have long-term consequences. Preventive and therapeutic measures for these conditions are needed to improve outcomes of these children.
In this paper, we investigate the application of the fading regularization method with the method of fundamental solutions (MFS) to the ill-posed Cauchy-Stokes problem. For both smooth and piecewise ...smooth two-dimensional geometries, we present a numerical reconstruction of the missing velocity and normal stress tensor on an inaccessible part of the boundary based on knowledge of over-prescribed noisy data acquired on the remaining accessible boundary part. Three numerical examples demonstrate the proposed numerical algorithm’s accuracy, convergence, stability, and efficiency, as well as its ability to deblur the data.
One of the most crucial aspects of image segmentation is multilevel thresholding. However, multilevel thresholding becomes increasingly more computationally complex as the number of thresholds grows. ...In order to address this defect, this paper proposes a new multilevel thresholding approach based on the Evolutionary Arithmetic Optimization Algorithm (AOA). The arithmetic operators in science were the inspiration for AOA. DAOA is the proposed approach, which employs the Differential Evolution technique to enhance the AOA local research. The proposed algorithm is applied to the multilevel thresholding problem, using Kapur’s measure between class variance functions. The suggested DAOA is used to evaluate images, using eight standard test images from two different groups: nature and CT COVID-19 images. Peak signal-to-noise ratio (PSNR) and structural similarity index test (SSIM) are standard evaluation measures used to determine the accuracy of segmented images. The proposed DAOA method’s efficiency is evaluated and compared to other multilevel thresholding methods. The findings are presented with a number of different threshold values (i.e., 2, 3, 4, 5, and 6). According to the experimental results, the proposed DAOA process is better and produces higher-quality solutions than other comparative approaches. Moreover, it achieved better-segmented images, PSNR, and SSIM values. In addition, the proposed DAOA is ranked the first method in all test cases.
Hyper-heuristics aim at interchanging different solvers while solving a problem. The idea is to determine the best approach for solving a problem at its current state. This way, every time we make a ...move it gets us closer to a solution. The problem changes; so does its state. As a consequence, for the next move, a different solver may be invoked. Hyper-heuristics have been around for almost 20 years. However, combinatorial optimization problems date from way back. Thus, it is paramount to determine whether the efforts revolving around hyper-heuristic research have been targeted at the problems of the highest interest for the combinatorial optimization community. In this work, we tackle such an endeavor. We begin by determining the most relevant combinatorial optimization problems, and then we analyze them in the context of hyper-heuristics. The idea is to verify whether they remain as relevant when considering exclusively works related to hyper-heuristics. We find that some of the most relevant problem domains have also been popular for hyper-heuristics research. Alas, others have not and few efforts have been directed towards solving them. We identify the following problem domains, which may help in furthering the impact of hyper-heuristics: Shortest Path, Set Cover, Longest Path, and Minimum Spanning Tree. We believe that focusing research on ways for solving them may lead to an increase in the relevance and impact that hyper-heuristics have on combinatorial optimization problems.
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