Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line

This paper investigates the solvability of the second-order boundary value problems with the one-dimensional $p$-Laplacian at resonance on a half-line $$\left\{\begin{array}{llll} (c(t)\phi_{p}(x'(t)))'=f(t,x(t),x'(t)),~~~~0<t<\infty,\\ x(0)=\sum\limits_{i=1}^{n}\mu_ix(\xi_{i}), ~~\lim\limits_{t\rightarrow +\infty}c(t)\phi_{p}(x'(t))=0 \end{array}\right.$$ and $$\left\{\begin{array}{llll} (c(t)\phi_{p}(x'(t)))'+g(t)h(t,x(t),x'(t))=0,~~~~0<t<\infty,\\ x(0)=\int_{0}^{\infty}g(s)x(s)ds,~~\lim\limits_{t\rightarrow +\infty}c(t)\phi_{p}(x'(t))=0 \end{array}\right.$$ with multi-point and integral boundary conditions, respectively, where $\phi_{p}(s)=|s|^{p-2}s$, $p>1$. The arguments are based upon an extension of Mawhin's continuation theorem due to Ge. And examples are given to illustrate our results

Positive solutions of singular four-point boundary value problem with pp-Laplacian

In this paper, we deal with the following singular four-point boundary value problem with $p$-Laplacian $$\left\{\begin{aligned} &(\phi_{p}(u'(t)))'+q(t)f(t,u(t))=0,\ t\in(0,1),\\ &u(0)-\alpha u'(\xi)=0,\ u(1)+\beta u'(\eta)=0, \end{aligned}\right.$$ where $f(t,u)$ may be singular at $u=0$ and $q(t)$ may be singular at $t=0$ or $1$. By imposing some suitable conditions on the nonlinear term $f$, existence results of at least two positive solutions are obtained. The proof is based upon theory of Leray-Schauder degree and Krasnosel'skii's fixed point theorem

On-line recognition of abnormal patterns in bivariate autocorrelated process using random forest

It is not uncommon that two or more related process quality characteristics are needed to be monitored simultaneously in production process for most of time. Meanwhile, the observations obtained online are often serially autocorrelated due to high sampling frequency and process dynamics. This goes against the statistical I.I.D assumption in using the multivariate control charts, which may lead to the performance of multivariate control charts collapse soon. Meanwhile, the process control method based on pattern recognition as a non-statistical approach is not confined by this limitation, and further provide more useful information for quality practitioners to locate the assignable causes led to process abnormalities. This study proposed a pattern recognition model using Random Forest (RF) as pattern model to detect and identify the abnormalities in bivariate autocorrelated process. The simulation experiment results demonstrate that the model is superior on recognition accuracy (RA) (97.96%) to back propagation neural networks (BPNN) (95.69%), probability neural networks (PNN) (94.31%), and support vector machine (SVM) (97.16%). When experimenting with simulated dynamic process data flow, the model also achieved better average running length (ARL) and standard deviation of ARL (SRL) than those of the four comparative approaches in most cases of mean shift magnitude. Therefore, we get the conclusion that the RF model is a promising approach for detecting abnormalities in the bivariate autocorrelated process. Although bivariate autocorrelated process is focused in this study, the proposed model can be extended to multivariate autocorrelated process control

The Genus Adonis as an Important Cardiac Folk Medicine: A Review of the Ethnobotany, Phytochemistry and Pharmacology

The genus Adonis L. (Ranunculaceae), native to Europe and Asia, comprises 32 annual or perennial herbaceous species. Due to their cardiac-enhancing effects, Adonis spp. have long been used in European and Chinese folk medicine. These plants have been widely investigated since the late 19th century, when the cardiovascular activity of Adonis vernalis L. was noted in Europe. The present paper provides a review of the phytochemistry, biological activities and toxicology in order to highlight the future prospects of the genus. More than 120 chemical compounds have been isolated, with the most important components being cardiac glycosides as well as flavones, carotenoids, coumarins and other structural types. Plants of the genus, especially A. vernalis L. and A. amurensis Regel &amp; Radde, their extracts and their active constituents possess broad pharmacological properties, including cardiovascular, antiangiogenic, antibacterial, antioxidant, anti-inflammatory and acaricidal activities, and exhibit both diuretic effects and effects on the central nervous system. However, most plants within the 32 species have not been comprehensively studied, and further clinical evaluation of their cardiovascular activity and toxicity should be conducted after addressing the problem of the rapidly decreasing resources. This review provides new insight into the genus and lays a solid foundation for further development of Adonis

Segawa syndrome caused by TH gene mutation and its mechanism

Dopa-responsive dystonia (DRD), also known as Segawa syndrome, is a rare neurotransmitter disease. The decrease in dopamine caused by tyrosine hydroxylase (TH) gene mutation may lead to dystonia, tremor and severe encephalopathy in children. Although the disease caused by recessive genetic mutation of the tyrosine hydroxylase (TH) gene is rare, we found that the clinical manifestations of seven children with tyrosine hydroxylase gene mutations are similar to dopa-responsive dystonia. To explore the clinical manifestations and possible pathogenesis of the disease, we analyzed the clinical data of seven patients. Next-generation sequencing showed that the TH gene mutation in three children was a reported homozygous mutation (c.698G&gt;A). At the same time, two new mutations of the TH gene were found in other children: c.316_317insCGT, and c.832G&gt;A (p.Ala278Thr). We collected venous blood from four patients with Segawa syndrome and their parents for real-time quantitative polymerase chain reaction analysis of TH gene expression. We predicted the structure and function of proteins on the missense mutation iterative thread assembly refinement (I-TASSER) server and studied the conservation of protein mutation sites. Combined with molecular biology experiments and related literature analysis, the qPCR results of two patients showed that the expression of the TH gene was lower than that in 10 normal controls, and the expression of the TH gene of one mother was lower than the average expression level. We speculated that mutation in the TH gene may clinically manifest by affecting the production of dopamine and catecholamine downstream, which enriches the gene pool of Segawa syndrome. At the same time, the application of levodopa is helpful to the study, diagnosis and treatment of Segawa syndrome

Associations of Educational Attainment, Occupation, Social Class and Major Depressive Disorder among Han Chinese Women

Background The prevalence of major depressive disorder (MDD) is higher in those with low levels of educational attainment, the unemployed and those with low social status. However the extent to which these factors cause MDD is unclear. Most of the available data comes from studies in developed countries, and these findings may not extrapolate to developing countries. Examining the relationship between MDD and socio economic status in China is likely to add to the debate because of the radical economic and social changes occurring in China over the last 30 years. Principal findings We report results from 3,639 Chinese women with recurrent MDD and 3,800 controls. Highly significant odds ratios (ORs) were observed between MDD and full time employment (OR = 0.36, 95% CI = 0.25–0.46, logP = 78), social status (OR = 0.83, 95% CI = 0.77–0.87, logP = 13.3) and education attainment (OR = 0.90, 95% CI = 0.86–0.90, logP = 6.8). We found a monotonic relationship between increasing age and increasing levels of educational attainment. Those with only primary school education have significantly more episodes of MDD (mean 6.5, P-value = 0.009) and have a clinically more severe disorder, while those with higher educational attainment are likely to manifest more comorbid anxiety disorders. Conclusions In China lower socioeconomic position is associated with increased rates of MDD, as it is elsewhere in the world. Significantly more episodes of MDD occur among those with lower educational attainment (rather than longer episodes of disease), consistent with the hypothesis that the lower socioeconomic position increases the likelihood of developing MDD. The phenomenology of MDD varies according to the degree of educational attainment: higher educational attainment not only appears to protect against MDD but alters its presentation, to a more anxious phenotype