A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.&nbsp

Solvability and asymptotic properties for an elliptic geophysical fluid flows model in a planar exterior domain

In this paper, we study the solvability and asymptotic properties of a recently derived gyre model of nonlinear elliptic Schrödinger equation arising from the geophysical fluid flows. The existence theorems and the asymptotic properties for radial positive solutions are established due to space theory and analytical techniques, some special cases and specific examples are also given to describe the applicability of model in gyres of geophysical fluid flows

Gut Bacterial Communities of Lymantria xylina and Their Associations with Host Development and Diet

The gut microbiota of insects has a wide range of effects on host nutrition, physiology, and behavior. The structure of gut microbiota may also be shaped by their environment, causing them to adjust to their hosts; thus, the objective of this study was to examine variations in the morphological traits and gut microbiota of Lymantria xylina in response to natural and artificial diets using high-throughput sequencing. Regarding morphology, the head widths for larvae fed on a sterilized artificial diet were smaller than for larvae fed on a non-sterilized host-plant diet in the early instars. The gut microbiota diversity of L. xylina fed on different diets varied significantly, but did not change during different development periods. This seemed to indicate that vertical inheritance occurred in L. xylina mutualistic symbionts. Acinetobacter and Enterococcus were dominant in/on eggs. In the first instar larvae, Acinetobacter accounted for 33.52% of the sterilized artificial diet treatment, while Enterococcus (67.88%) was the predominant bacteria for the non-sterilized host-plant diet treatment. Gut microbe structures were adapted to both diets through vertical inheritance and self-regulation. This study clarified the impacts of microbial symbiosis on L. xylina and might provide new possibilities for improving the control of these bacteria

Two CYP82D Enzymes Function as Flavone Hydroxylases in the Biosynthesis of Root-Specific 4′-Deoxyflavones in Scutellaria baicalensis

Baicalein, wogonin, and their glycosides are major bioactive compounds found in the medicinal plant Scutellaria baicalensis Georgi. These flavones can induce apoptosis in a variety of cancer cell lines but have no effect on normal cells. Furthermore, they have many additional benefits for human health, such as anti-oxidant, antiviral, and liver-protective properties. Here, we report the isolation and characterization of two CYP450 enzymes, SbCYP82D1.1 and SbCYP82D2, which function as the flavone 6-hydroxylase (F6H) and flavone 8-hydroxylase (F8H), respectively, in S. baicalensis. SbCYP82D1.1 has broad substrate specificity for flavones such as chrysin and apigenin and is responsible for biosynthesis of baicalein and scutellarein in roots and aerial parts of S. baicalensis, respectively. When the expression of SbCYP82D1.1 is knocked down, baicalin and baicalein levels are reduced significantly while chrysin glycosides accumulate in hairy roots. SbCYP82D2 is an F8H with high substrate specificity, accepting only chrysin as its substrate to produce norwogonin, although minor 6-hydroxylation activity can also be detected. Phylogenetic analysis suggested that SbCYP82D2 might have evolved from SbCYP82D1.1 via gene duplication followed by neofunctionalization, whereby the ancestral F6H activity is partially retained in the derived SbCYP82D2. We report the characterization of two CYP450 enzymes, which 6- and 8-hydroxylate chrysin to form the 4′-deoxyflavone bioactives in roots of Scutellaria baicalensis. Like the main 4′-deoxyflavone enzymes, these decorating enzymes have evolved their functionalities by convergence with the more ubiquitous 4′-hydroxyflavone pathway enzymes. Key words: Scutellaria baicalensis; Huangqin; baicalein; wogonin; flavone 6-hydroxylase; flavone 8-hydroxylas

Comparison among Reconstruction Algorithms for Quantitative Analysis of 11

Objective. Kinetic modeling of dynamic 11C-acetate PET imaging provides quantitative information for myocardium assessment. The quality and quantitation of PET images are known to be dependent on PET reconstruction methods. This study aims to investigate the impacts of reconstruction algorithms on the quantitative analysis of dynamic 11C-acetate cardiac PET imaging. Methods. Suspected alcoholic cardiomyopathy patients (N=24) underwent 11C-acetate dynamic PET imaging after low dose CT scan. PET images were reconstructed using four algorithms: filtered backprojection (FBP), ordered subsets expectation maximization (OSEM), OSEM with time-of-flight (TOF), and OSEM with both time-of-flight and point-spread-function (TPSF). Standardized uptake values (SUVs) at different time points were compared among images reconstructed using the four algorithms. Time-activity curves (TACs) in myocardium and blood pools of ventricles were generated from the dynamic image series. Kinetic parameters K1 and k2 were derived using a 1-tissue-compartment model for kinetic modeling of cardiac flow from 11C-acetate PET images. Results. Significant image quality improvement was found in the images reconstructed using iterative OSEM-type algorithms (OSME, TOF, and TPSF) compared with FBP. However, no statistical differences in SUVs were observed among the four reconstruction methods at the selected time points. Kinetic parameters K1 and k2 also exhibited no statistical difference among the four reconstruction algorithms in terms of mean value and standard deviation. However, for the correlation analysis, OSEM reconstruction presented relatively higher residual in correlation with FBP reconstruction compared with TOF and TPSF reconstruction, and TOF and TPSF reconstruction were highly correlated with each other. Conclusion. All the tested reconstruction algorithms performed similarly for quantitative analysis of 11C-acetate cardiac PET imaging. TOF and TPSF yielded highly consistent kinetic parameter results with superior image quality compared with FBP. OSEM was relatively less reliable. Both TOF and TPSF were recommended for cardiac 11C-acetate kinetic analysis

Fine-Tuning Stomatal Movement Through Small Signaling Peptides

As sessile organisms, plants are continuously exposed to a wide range of environmental stress. In addition to their crucial roles in plant growth and development, small signaling peptides are also implicated in sensing environmental stimuli. Notably, recent studies in plants have revealed that small signaling peptides are actively involved in controlling stomatal aperture to defend against biotic and abiotic stress. This review illustrates our growing knowledge of small signaling peptides in the modulation of stomatal aperture and highlights future challenges to decipher peptide signaling pathways in guard cells

Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives

In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional differential equations with Riemann–Stieltjes integral boundary conditions involving fractional derivatives are considered under some appropriate conditions, and the nonlinearity is allowed to be singular in regard to not only time variable but also space variable and it includes fractional derivatives. The existence of positive solutions for boundary conditions involving fractional derivatives is established. Finally, an example is given to demonstrate the validity of our main results

Existence and uniqueness of solutions for systems of fractional differential equations with Riemann–Stieltjes integral boundary condition

In this article, we first establish an existence and uniqueness result for a class of systems of nonlinear operator equations under more general conditions by means of the cone theory and monotone iterative technique. Furthermore, the iterative sequence of the solution and the error estimation of the system are given. Then we use this new result to study the existence and uniqueness of the solution for boundary value problems of systems of fractional differential equations with a Riemann–Stieltjes integral boundary condition in real Banach spaces. The results obtained in this paper are more general than many previous results and complement them

Kinetics of the neutralising antibody response in patients with hand, foot, and mouth disease caused by EV-A71: A longitudinal cohort study in Zhengzhou during 2017-2019

BACKGROUND: Hand, foot, and mouth disease (HFMD) caused by enterovirus A71 (EV-A71) poses a serious threat to children's health. Kinetics of the neutralising antibody (NAb) response in EV-A71 infected HFMD patients remains unclear. The ideal sampling time of paired serum samples for serological diagnosis of EV-A71 infection is not well defined. METHODS: HFMD inpatients admitted to Henan Children's Hospital between February 15, 2017 and February 15, 2018 were enrolled. Serial serum samples collected during hospitalisation and up to 1.5 years after discharge were tested for NAb against EV-A71. Random intercept modelling with B-spline was conducted to characterize the kinetics of the EV-A71 NAb response over time after illness onset. FINDINGS: A total of 524 serum samples from 264 EV-A71 RNA positive HFMD inpatients were collected. NAb titres of EV-A71 infected patients were estimated to increase from 40 (95% CI: 9-180) at the day of onset to the peak of 2417 (95% CI: 1859-3143) at day 13, then remained above 1240 until 26 months. For serological diagnosis of EV-A71 infection, if at least a 4-fold rise in titre was used as the criteria, the acute phase serum should be collected at 0-4 days, the corresponding convalescent serum should be collected 14.9 days (95% CI: 9.1-23.8) after illness onset. INTERPRETATION: EV-A71 infection induced a strong and persistent humoral immune response in HFMD patients. The findings provide a scientific support for determining the collection time of paired serum samples for serological diagnosis of EV-A71 infected HFMD patients. FUNDING: National Science Fund for Distinguished Young Scholar

Iterative positive solutions for singular nonlinear fractional differential equation with integral boundary conditions

In this article, we study the existence of iterative positive solutions for a class of singular nonlinear fractional differential equations with Riemann-Stieltjes integral boundary conditions, where the nonlinear term may be singular both for time and space variables. By using the properties of the Green function and the fixed point theorem of mixed monotone operators in cones we obtain some results on the existence and uniqueness of positive solutions. We also construct successively some sequences for approximating the unique solution. Our results include the multipoint boundary problems and integral boundary problems as special cases, and we also extend and improve many known results including singular and non-singular cases