Existence of nontrivial solutions for critical biharmonic equations with logarithmic term

In this paper, we consider the existence of nontrivial solutions to the following critical biharmonic problem with a logarithmic term \begin{equation*} \begin{cases} \Delta^2 u=\mu \Delta u+\lambda u+|u|^{2^{**}-2}u+\tau u\log u^2, \ \ x\in\Omega, u|_{\partial \Omega }=\frac{\partial u}{\partial n}|_{\partial\Omega}=0, \end{cases} \end{equation*} where $\mu,\lambda,\tau \in \mathbb{R}$, $|\mu|+|\tau|\ne 0$, $\Delta ^2=\Delta \Delta$ denotes the iterated N-dimensional Laplacian, $\Omega \subset \mathbb{R}^{N}$ is a bounded domain with smooth boundary $\partial \Omega$, $2^{**}=\frac{2N}{N-4}(N\ge5)$ is the critical Sobolev exponent for the embedding $H_{0}^{2}(\Omega)\hookrightarrow L^{2^{**}}(\Omega)$ and $H_0^2 (\Omega )$ is the closure of $C_0^ \infty (\Omega )$ under the norm $|| u ||:=(\int_{\Omega}|\Delta u|^2)^\frac{1}{2}$. The uncertainty of the sign of $s\log s^2$ in $(0,+\infty)$ has some interest in itself. To know which of the three terms $\mu \Delta u$, $\lambda u$ and $\tau u \log u^2$ has a greater influence on the existence of nontrivial weak solutions, we prove the existence of nontrivial weak solutions to the above problem for $N\ge5$ under some assumptions of $\lambda, \mu$ and $\tau$

Quantitative combination of natural anti-oxidants prevents metabolic syndrome by reducing oxidative stress

AbstractInsulin resistance and abdominal obesity are present in the majority of people with the metabolic syndrome. Antioxidant therapy might be a useful strategy for type 2 diabetes and other insulin-resistant states. The combination of vitamin C (Vc) and vitamin E has synthetic scavenging effect on free radicals and inhibition effect on lipid peroxidation. However, there are few studies about how to define the best combination of more than three anti-oxidants as it is difficult or impossible to test the anti-oxidant effect of the combination of every concentration of each ingredient experimentally. Here we present a math model, which is based on the classical Hill equation to determine the best combination, called Fixed Dose Combination (FDC), of several natural anti-oxidants, including Vc, green tea polyphenols (GTP) and grape seed extract proanthocyanidin (GSEP). Then we investigated the effects of FDC on oxidative stress, blood glucose and serum lipid levels in cultured 3T3-L1 adipocytes, high fat diet (HFD)-fed rats which serve as obesity model, and KK-ay mice as diabetic model. The level of serum malondialdehyde (MDA) in the treated rats was studied and Hematoxylin-Eosin (HE) staining or Oil red slices of liver and adipose tissue in the rats were examined as well. FDC shows excellent antioxidant and anti-glycation activity by attenuating lipid peroxidation. FDC determined in this investigation can become a potential solution to reduce obesity, to improve insulin sensitivity and be beneficial for the treatment of fat and diabetic patients. It is the first time to use the math model to determine the best ratio of three anti-oxidants, which can save much more time and chemical materials than traditional experimental method. This quantitative method represents a potentially new and useful strategy to screen all possible combinations of many natural anti-oxidants, therefore may help develop novel therapeutics with the potential to ameliorate the worldwide metabolic abnormalities

Characterizing corn-straw-degrading actinomycetes and evaluating application efficiency in straw-returning experiments

Corn straw is an abundant lignocellulose resource and by-product of agricultural production. With the continuous increase in agricultural development, the output of corn straw is also increasing significantly. However, the inappropriate disposal of straw results in wasting of resources, and also causes a serious ecological crisis. Screening microorganisms with the capacity to degrade straw and understanding their mechanism of action is an efficient approach to solve such problems. For this purpose, our research group isolated three actinomycete strains with efficient lignocellulose degradation ability from soil in the cold region of China: Streptomyces sp. G1T, Streptomyces sp. G2T and Streptomyces sp. G3T. Their microbial properties and taxonomic status were assessed to improve our understanding of these strains. The three strains showed typical characteristics of the genus Streptomyces, and likely represent three different species. Genome functional annotation indicated that most of their genes were related to functions like carbohydrate transport and metabolism. In addition, a similar phenomenon also appeared in the COG and CAZyme analyses, with a large number of genes encoding carbohydrate-related hydrolases, such as cellulase, glycosidase and endoglucanase, which could effectively destroy the structure of lignocellulose in corn straw. This unambiguously demonstrated the potential of the three microorganisms to hydrolyze macromolecular polysaccharides at the molecular level. In addition, in the straw-returning test, the decomposing consortium composed of the three Streptomyces isolates (G123) effectively destroyed the recalcitrant bonds between the various components of straw, and significantly reduced the content of active components in corn straw. Furthermore, microbial diversity analysis indicated that the relative abundance of Proteobacteria, reportedly associated with soil antibiotic resistance and antibiotic degradation, was significantly improved with straw returning at both tested time points. The microbial diversity of each treatment was also dramatically changed by supplementing with G123. Taken together, G123 has important biological potential and should be further studied, which will provide new insights and strategies for appropriate treatment of corn straw

Comparative efficacy of platelet-rich plasma applied in myringoplasty: A systematic review and meta-analysis.

BackgroundTympanic membrane (TM) perforation is quite common in the clinical setting. Chronic TM perforations require surgical treatments such as myringoplasty. Currently, platelet-rich plasma (PRP) is a novel, effective substance that is increasingly utilized for TM perforation repair. This study aims to evaluate the effectiveness of PRP in the application of TM perforation repair.MethodsA systematic search was conducted to screen the Medline, Embase, Cochrane, Scopus and Web of Science databases up to July 2020. Studies were identified in accordance with the selection criteria by two coauthors independently. Data regarding the healing and hearing outcomes were pooled and analyzed via Review Manager version 5.3 and STATA version 12.0 software. Odds ratio (OR) was utilized to compare the closure rate. Furthermore, the results of hearing improvements and incidence of complications were also compared to evaluate the effectiveness of PRP.ResultsA total of eight studies with 455 participants were eligible according to the selection criteria. Compared to conventional surgery, the OR of closure was 2.70 (95% CI: 1.27 to 5.76, P = 0.01, I2 = 0%) in randomized controlled trial (RCT) subgroup and 6.18 (95% CI: 2.22 to 17.25, P = 0.0005, I2 = 0) in non-RCT subgroup. The overall OR of closure was 3.69 (95% CI: 2.02 to 6.74, PConclusionThe application of PRP during the TM surgeries can enhance the closure rate, provide similar hearing improvements and decrease the incidence of postoperative complications. Given these advantages, PRP can be considered an effective treatment for TM regeneration

Potential Value of Wood Tar as a Natural Fungicide against Valsa mali

The Valsa canker caused by Valsa mali seriously harmed the production of East Asian apples and caused very significant economic losses. Considering the chemical residues and the improvement of people’s awareness of environmental protection, there is a need for screening new green pesticides for the control of Valsa canker. Therefore, we conducted systematic evaluations on the antifungal activity of wood tar. In this research, the effective concentration (EC50) of six strains of V. mali to wood tar was determined, and the EC50 ranged from 69.54 to 92.81 μg/mL. After treatment with wood tar, the hyphae of V. mali broke, swelled, and deformed; the permeability of the cell membrane increased; and the activity of pectinase reduced. Moreover, the expression levels of five genes related to pectinase also decreased significantly. In addition, the activities of phenylalanine ammonia lyase (PAL) and peroxidase (POD) of apple leaves treated with wood tar also increased. On detached apple branches, wood tar also showed therapeutic and protective activities. In the 2016–2019 field experiments, wood tar also showed good efficacy against Valsa canker and promoted the formation of callus. (In the experiments from 2016 to 2019, it can be seen that the control effect of 50% wood tar and 100% wood tar in the field is above 75% and promoted the formation of callus.) This study is the first to report the bidirectional efficacy of wood tar against Valsa mali and for trunk wound healing. The above results evidenced that wood tar has great potential to be developed as a natural alternative to commercial fungicides for the management of apple Valsa canker

Control-Oriented Modeling for Nonlinear MIMO Turbofan Engine Based on Equilibrium Manifold Expansion Model

This paper investigates the control-oriented modeling for turbofan engines. The nonlinear equilibrium manifold expansion (EME) model of the multiple input multiple output (MIMO) turbofan engine is established, which can simulate the variation of high-pressure rotor speed, low-pressure rotor speed and pressure ratio of compressor with fuel flow and throat area of the nozzle. Firstly, the definitions and properties of the equilibrium manifold method are presented. Secondly, the steady-state and dynamic two-step identification method of the MIMO EME model is given, and the effects of scheduling variables and input noise on model accuracy are discussed. By selecting specific path, a small amount of dynamic data is used to identify a complete EME model. Thirdly, modeling and simulation at dynamic off-design conditions show that the EME model has model accuracy close to the nonlinear component-level (NCL) model, but the model structure is simpler and the calculation is faster than that. Finally, the linearization results are obtained based on the properties of the EME model, and the stability of the model is proved through the analysis of the eigenvalues, which all have negative real parts. The EME model constructed in this paper can meet the requirements of real-time simulation and control system design

Synchronous construction of Fe1-xS-embedded and interconnected carbon matrices for high-performance lithium-ion batteries anode

Iron sulfide has stood out from various anode materials on account of its high capacity, low price and environment friendliness. In practice, however, the critical obstacles of iron sulfide limit its practical application, including poor intrinsic conductivity, volume expansion and polysulfide dissolution during charge and discharge. Herein, the carbon-coated Fe1-xS composite with unique interconnected carbon matrices (Fe1-xS@C NW) was successfully synthesized via a facile one-step in situ thermal condensation method, which is intended to improve the conductivity of iron sulfide anode. In this composite, Fe1-xS is surrounded by unique interconnected carbon matrices to facilitate lithium ion diffusion and electron transport. Compared with Fe1-xS@C and Fe1-xS anode, the as-synthesized Fe1-xS@C NW anode exhibits high-rate performance (with a reversible capacity of 446 mAh g(- 1) even at 4 A g(- 1)) and low Rct value (58.2 ohm). The combination of unique interconnected carbon matrices and Fe1-xS may be responsible for the superior rate performance and low Rct of Fe1-xS@C NW anode

Current situation and needs analysis of medical staff first aid ability in China: a cross-sectional study

Abstract Objectives We aim to understand the current situation of the first aid ability and training needs of Chinese medical personnel to provide a scientific basis for formulating the contents and methods of emergency medical rescue training and thereby improve the first aid level of Chinese medical personnel. Methods A cross-sectional survey was conducted between June 2022 and February 2023 using a two-stage cluster sampling method with a structured questionnaire sent to medical workers in 12 provinces in China. 14,527 questionnaires were included in this study. Data were collected on demographic characteristics, first aid knowledge and skills, and training needs. Variance analysis was used to compare the difference between the first aid ability and training needs of medical staff in different hospitals, and multiple linear regression analysis was carried out to evaluate first aid ability and training needs. Result The study included 6041 patients (41.6%) in tertiary hospitals, 5838 patients (40.2%) in secondary hospitals, and 2648 patients (18.2%) in primary hospitals. There were significant differences in the first aid ability and training needs of medical staff in hospitals of different levels (p < 0.001). The score of first aid knowledge and skills in tertiary hospitals was the highest (209.7 ± 45.0), and the score of training needs in primary hospitals was the highest (240.6 ± 44.0). There was a significant correlation between first aid ability and training needs score (p < 0.001). Multiple linear regression analysis shows that geographic region, age, work tenure, gender, job title, department, professional title, monthly income, and hospital level are the influencing factors of training demand. Conclusion Medical staff in primary hospitals generally have low first aid knowledge and skills and a strong willingness to train. Therefore, it is imperative to strengthen the training of first aid ability and research training strategies. The level of the hospital is closely related to the level of first aid, so it is necessary to recognize the commonalities and differences in medical staff’s demand for first aid knowledge and skills and carry out targeted education and training