An induction theorem and nonlinear regularity models

A general nonlinear regularity model for a set-valued mapping $F:X\times R_+\rightrightarrows Y$, where $X$ and $Y$ are metric spaces, is considered using special iteration procedures, going back to Banach, Schauder, Lusternik and Graves. Namely, we revise the induction theorem from Khanh, J. Math. Anal. Appl., 118 (1986) and employ it to obtain basic estimates for studying regularity/openness properties. We also show that it can serve as a substitution of the Ekeland variational principle when establishing other regularity criteria. Then, we apply the induction theorem and the mentioned estimates to establish criteria for both global and local versions of regularity/openness properties for our model and demonstrate how the definitions and criteria translate into the conventional setting of a set-valued mapping $F:X\rightrightarrows Y$.Comment: 28 page

Associations of Underlying Health Conditions With Anxiety and Depression Among Outpatients: Modification Effects of Suspected COVID-19 Symptoms, Health-Related and Preventive Behaviors

Objectives: We explored the association of underlying health conditions (UHC) with depression and anxiety, and examined the modification effects of suspected COVID-19 symptoms (S-COVID-19-S), health-related behaviors (HB), and preventive behaviors (PB).Methods: A cross-sectional study was conducted on 8,291 outpatients aged 18–85 years, in 18 hospitals and health centers across Vietnam from 14th February to May 31, 2020. We collected the data regarding participant's characteristics, UHC, HB, PB, depression, and anxiety.Results: People with UHC had higher odds of depression (OR = 2.11; p < 0.001) and anxiety (OR = 2.86; p < 0.001) than those without UHC. The odds of depression and anxiety were significantly higher for those with UHC and S-COVID-19-S (p < 0.001); and were significantly lower for those had UHC and interacted with “unchanged/more” physical activity (p < 0.001), or “unchanged/more” drinking (p < 0.001 for only anxiety), or “unchanged/healthier” eating (p < 0.001), and high PB score (p < 0.001), as compared to those without UHC and without S-COVID-19-S, “never/stopped/less” physical activity, drinking, “less healthy” eating, and low PB score, respectively.Conclusion: S-COVID-19-S worsen psychological health in patients with UHC. Physical activity, drinking, healthier eating, and high PB score were protective factors

Validation and utilization of an internally controlled multiplex Real-time RT-PCR assay for simultaneous detection of enteroviruses and enterovirus A71 associated with hand foot and mouth disease

BACKGROUND: Hand foot and mouth disease (HFMD) is a disease of public health importance across the Asia-Pacific region. The disease is caused by enteroviruses (EVs), in particular enterovirus A71 (EV-A71). In EV-A71-associated HFMD, the infection is sometimes associated with severe manifestations including neurological involvement and fatal outcome. The availability of a robust diagnostic assay to distinguish EV-A71 from other EVs is important for patient management and outbreak response. METHODS: We developed and validated an internally controlled one-step single-tube real-time RT-PCR in terms of sensitivity, linearity, precision, and specificity for simultaneous detection of EVs and EV-A71. Subsequently, the assay was then applied on throat and rectal swabs sampled from 434 HFMD patients. RESULTS: The assay was evaluated using both plasmid DNA and viral RNA and has shown to be reproducible with a maximum assay variation of 4.41 % and sensitive with a limit of detection less than 10 copies of target template per reaction, while cross-reactivity with other EV serotypes was not observed. When compared against a published VP1 nested RT-PCR using 112 diagnostic throat and rectal swabs from 112 children with a clinical diagnosis of HFMD during 2014, the multiplex assay had a higher sensitivity and 100 % concordance with sequencing results which showed EVs in 77/112 (68.8 %) and EV-A71 in 7/112 (6.3 %). When applied to clinical diagnostics for 322 children, the assay detected EVs in throat swabs of 257/322 (79.8 %) of which EV-A71 was detected in 36/322 (11.2 %) children. The detection rate increased to 93.5 % (301/322) and 13.4 % (43/322) for EVs and EV-A71, respectively, when rectal swabs from 65 throat-negative children were further analyzed. CONCLUSION: We have successfully developed and validated a sensitive internally controlled multiplex assay for rapid detection of EVs and EV-A71, which is useful for clinical management and outbreak control of HFMD. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12985-015-0316-2) contains supplementary material, which is available to authorized users

A projection-type algorithm for pseudo-monotone non-Lipschitzian multivalued variational inequalities

We propose a projection-type algorithm for variational inequalities involving multifunction. The algorithm requires two projections on the constraint set only in a part of iterations (one third of the subcases). For the other iterations, only one projection is used. A global convergence is proved under the weak assumption that the multifunction of the problem is pseudomonotone at a solution, closed, lower hemicontinuous, and bounded on each bounded subset (it is not necessarily continuous). Some numerical test problems are implemented by using MATLAB with encouraging effectiveness

Rapid Fabrication of Pineapple Leaf Fibers from Discarded Leaves by Using Electrolysis of Brine

Instead of contributing to global warming by the traditional method—burning crop wastes—in this study, discarded pineapple leaves were rapidly turned into multifunctional fibers: pineapple leaf fibers (PALF). In addition, the presence of pure hydrogen during treatment can be a competitive advantage. PALF were extracted by a conventional technique, then immersed into sodium hydroxide 6% before it was treated with an electrolysis system of sodium chloride 3%. The crystallinity index increased 57.4% of treated PALF, and was collected from XRD. Meanwhile, the removal of hemicellulose and lignin in the fiber formation was presented at the absorbance peak of around 1730 cm−1 by FTIR spectrums. Simultaneously, the purity of hydrogen reached 99% and was confirmed by GC analysis. The obtained PALF and hydrogen can be used for further consideration, aiming for a circular economy