具有延迟参数的Sturm-Liouville算子的谱特征及其反问题

具有延迟参数的Sturm-Liouville算子的逆谱问题是Sturm-Liouville理论的一个重要分支.延迟参数的Sturm-Liouville微分方程可用于对声波信号的传输以及液压冲击或其他波过程的模拟.本文主要研究有限区间上具有延迟变量的二阶Sturm-Liouville算子的特征值及其逆谱问题,利用势函数的Fourier展开式的方法得出了相应的逆谱问题的唯一性定理,即在某些假设条件下由边值问题的两组谱可以唯一确定延迟变量τ和势函数q(x).最后本文给出势函数的重构算法.

A generalized Liouville's formula

A generalized Liouville’s formula is established for linear matrix differential equations involving left and right multiplications.Its special cases are used to determine the localness of characteristics of symmetries and solutions to Riemann-Hilbert problems in soltion theory.

三维稳态向列型液晶方程各向异性的Liouville定理

该文研究了三维稳态向列型液晶方程的Liouville定理,证明了如果∇d∈L^(2)(R^(3))∩Lq(R^(3)),u∈L6(R^(3))∩L^(q)(R^(3)),以及ui满足各向异性的可积条件u_(i)∈L_(xi)^(q/q−2) L_(x)_(i)^(s)(R×R^(2)),∀i=1,2,3,其中2<q<∞,1≤s≤∞且2/q+1/s≥1/2,则u=0,∇d=0.

三维稳态Q-tensor液晶流系统各向异性的Liouville型定理

考虑速度分量的各向异性进行能量估计,得到三维稳态Q-tensor液晶流系统的Liouville型定理,即若u∈L^(q)(R^(3))∩˙H^(1)(R^(3)),u_(i)∈L xi q/q−2 L s xei(R×R^(2))(i=1,2,3),且Q∈H^(2)(R^(3)),其中2/q+1/s≥1/2,1≤s≤∞,2<q<∞,则该稳态系统只有平凡解.这个结论推广了已有的结果.

Asymptotic Formulas of the Solutions and the Trace Formulas for the Polynomial Pencil of the Sturm-Liouville Operators

This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas for the eigenvalues of a simple boundary problem generated in a finite interval by the considered Sturm-Liouville equation.

Fanlian Huazhuo Formula alleviates high-fat diet-induced nonalcoholic fatty liver disease by modulating autophagy and lipid synthesis signaling pathway

BACKGROUND Fanlian Huazhuo Formula(FLHZF)has the functions of invigorating spleen and resolving phlegm,clearing heat and purging turbidity.It has been identified to have therapeutic effects on type 2 diabetes mellitus(T2DM)in clinical application.Non-alcoholic fatty liver disease(NAFLD)is frequently diagnosed in patients with T2DM.However,the therapeutic potential of FLHZF on NAFLD and the underlying mechanisms need further investigation.AIM To elucidate the effects of FLHZF on NAFLD and explore the underlying hepatoprotective mechanisms in vivo and in vitro.METHODS HepG2 cells were treated with free fatty acid for 24 hours to induce lipid accumulation cell model.Subsequently,experiments were conducted with the different concentrations of freeze-dried powder of FLHZF for 24 hours.C57BL/6 mice were fed a high-fat diet for 8-week to establish a mouse model of NAFLD,and then treated with the different concentrations of FLHZF for 10 weeks.RESULTS FLHZF had therapeutic potential against lipid accumulation and abnormal changes in biochemical indicators in vivo and in vitro.Further experiments verified that FLHZF alleviated abnormal lipid metabolism might by reducing oxidative stress,regulating the AMPKα/SREBP-1C signaling pathway,activating autophagy,and inhibiting hepatocyte apoptosis.CONCLUSION FLHZF alleviates abnormal lipid metabolism in NAFLD models by regulating reactive oxygen species,autophagy,apoptosis,and lipid synthesis signaling pathways,indicating its potential for clinical application in NAFLD.

一类不连续不定Sturm-Liouville算子的自共轭性

该文研究了一类首项系数与权函数均多次变号且带有转移条件的Sturm-Liouville算子的自共轭性。建立新的完备不定度规空间K,将所研究的Sturm-Liouville问题转化为对新算子A的研究,证明了算子A的自共轭性。

含有Hénon项的非线性椭圆系统稳定解的Liouville定理

本文主要研究含有Hénon项的k-耦合椭圆系统-Δu_(i)=Σ_(j-1)^(k)β_(ij)|χ|^(α)|u_(i)|^(q-1)ui|uj|^(q+1),x∈R^(N)其中k是一个固定的正整数,i=1,2,…,k,q≥1,N≥3,B=(β_(ij))_(i,j=1)^(k)为实对称矩阵.首先使用Pohozaev恒等式构造单调公式,并发现其等价关系.当矩阵B严格余正时,联合使用Pohozaev恒等式、单调公式和爆缩序列方法证明了(无论是正的还是变号的)稳定解的Liouville定理.

R_(+)^(N)上不同阶椭圆方程组的Liouville型定理

本文研究带Navier边值的不同阶椭圆方程组的Liouville型问题.主要结论的证明采用了伸缩变换,双边引理和积分形式的移动平面方法.

Stability Analysis of a Class of Nonlinear Fractional Differential Systems With Riemann-Liouville Derivative

Dear Editor,This letter investigates the stability of n-dimensional nonlinear fractional differential systems with Riemann-Liouville derivative.By using the Mittag-Leffler function,Laplace transform and the Gronwall-Bellman lemma,one sufficient condition is attained for the asymptotical stability of a class of nonlinear fractional differential systems whose order lies in(0,2).According to this theory,if the nonlinear term satisfies some conditions,then the stability condition for nonlinear fractional differential systems is the same as the ones for corresponding linear systems.Two examples are provided to illustrate the applications of our result.

A Cauchy integral formula for(p,q)-monogenic functions withα-weight

Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-monogenic functions withα-weight are given.

Trace formula of the integro-differential operator on a quantum graph

In this paper we study the eigenvalue problem for integro-differential operators on a lasso graph.The trace formula of the operator is established by applying the residual technique in complex analysis.

Improved nuclear mass formula with an additional term from the Fermi gas model

Nuclear mass is a fundamental property of nuclear physics and a necessary input in nuclear astrophysics.Owing to the complexity of atomic nuclei and nonperturbative strong interactions,conventional physical models cannot completely describe nuclear binding energies.In this study,the mass formula was improved by considering an additional term from the Fermi gas model.All nuclear masses in the Atomic Mass Evaluation Database were reproduced with a root-mean-square deviation(RMSD)of -1.86 MeV(1.92 MeV).The new mass formula exhibits good performance in the neutron-rich nuclear region.The RMSD decreases to 0.393 MeV when the ratio of the neutron number to the proton number is≥1.6.

Analytical Solution and Simplified Formula for Added Mass of Horizontal and Vertical Motions of Truncated Cylinders Under Earthquake Action

This paper investigates the hydrodynamic characteristics of floating truncated cylinders undergoing horizontal and vertical motions due to earthquake excitations in the finite water depth.The governing equation of the hydrodynamic pressure acting on the cylinder is derived based on the radiation theory with the inviscid and incompressible assumptions.The governing equation is solved by using the method of separating variables and analytical solutions are obtained by assigning reasonable boundary conditions.The analytical result is validated by a numerical model using the exact artificial boundary simulation of the infinite water.The main variation and distribution characteristics of the hydrodynamic pressure acting on the side and bottom of the cylinder are analyzed for different combinations of wide-height and immersion ratios.The added mass coefficient of the cylinder is calculated by integrating the hydrodynamic pressure and simplified formulas are proposed for engineering applications.The calculation results show that the simplified formulas are in good agreement with the analytical solutions.

Examining the Use of Scott’s Formula and Link Expiration Time Metric for Vehicular Clustering

Implementing machine learning algorithms in the non-conducive environment of the vehicular network requires some adaptations due to the high computational complexity of these algorithms.K-clustering algorithms are simplistic,with fast performance and relative accuracy.However,their implementation depends on the initial selection of clusters number(K),the initial clusters’centers,and the clustering metric.This paper investigated using Scott’s histogram formula to estimate the K number and the Link Expiration Time(LET)as a clustering metric.Realistic traffic flows were considered for three maps,namely Highway,Traffic Light junction,and Roundabout junction,to study the effect of road layout on estimating the K number.A fast version of the PAM algorithm was used for clustering with a modification to reduce time complexity.The Affinity propagation algorithm sets the baseline for the estimated K number,and the Medoid Silhouette method is used to quantify the clustering.OMNET++,Veins,and SUMO were used to simulate the traffic,while the related algorithms were implemented in Python.The Scott’s formula estimation of the K number only matched the baseline when the road layout was simple.Moreover,the clustering algorithm required one iteration on average to converge when used with LET.

Modified Sadowski formula-based model for the slope shape amplification effect under multistage slope blasting vibration

Blasting operations,which are crucial to open-pit mine production due to their simplicity and efficiency,require precise control through accurate vibration velocity calculations.The conventional Sadowski formula mainly focuses on blast center distance but neglects the amplification effect of blasting vibration waves by terraced terrain,from which the calculated blasting vibration velocities are smaller than the actual values,affecting the safety of the project.To address this issue,our model introduces the influences of slope and time into Sadowski formula to measure safety through blast vibration displacement.In the northern section of the open-pit quartz mine in Jinchang City,Gansu Province,China,the data of a continuous blasting slope project are referred to.Our findings reveal a noticeable vibration amplification effect during blasting when a multi-stage slope platform undergoes a sudden cross-sectional change near the upper overhanging surface.The amplification vibration coefficient increases with height,while vibration waves within rocks decrease from bottom to top.Conversely,platforms without distinct crosssectional changes exhibit no pronounced amplification during blasting.In addition,the vibration intensity decreases with distance as the rock height difference change propagates.The results obtained by the proposed blast vibration displacement equation incorporating slope shape influence closely agree with real-world scenarios.According to Pearson correlation coefficient(PPMCC)analysis,the average accuracy rate of our model is 88.84%,which exceeds the conventional Sadowski formula(46.92%).

Jianpi Qinghua Formula Alleviates Diabetic Myocardial Injury Through Inhibiting JunB/c-Fos Expression

Objective Diabetic cardiomyopathy(DCM)represents a substantial risk factor for heart failure and increased mortality in individuals afflicted with diabetes mellitus(DM).DCM typically manifests as myocardial fibrosis,myocardial hypertrophy,and impaired left ventricular diastolic function.While the clinical utility of the Jianpi Qinghua(JPQH)formula has been established in treating diabetes and insulin resistance,its potential efficacy in alleviating diabetic cardiomyopathy remains uncertain.This study aims to investigate the impact and underlying molecular mechanisms of the JPQH formula(JPQHF)in ameliorating myocardial injury in nonobese diabetic rats,specifically focusing on apoptosis and inflammation.Methods Wistar rats were assigned as the normal control group(CON),while Goto-Kakizaki(GK)rats were randomly divided into three groups:DM,DM treated with the JPQHF,and DM treated with metformin(MET).Following a 4-week treatment regimen,various biochemical markers related to glucose metabolism,cardiac function,cardiac morphology,and myocardial ultrastructure in GK rats were assessed.RNA sequencing was utilized to analyze differential gene expression and identify potential therapeutic targets.In vitro experiments involved high glucose to induce apoptosis and inflammation in H9c2 cells.Cell viability was evaluated using CCK-8 assay,apoptosis was monitored via flow cytometry,and the production of inflammatory cytokines was measured using quantitative real-time PCR(qPCR)and ELISA.Protein expression levels were determined by Western blotting analysis.The investigation also incorporated the use of MAPK inhibitors to further elucidate the mechanism at both the transcriptional and protein levels.Results The JPQHF group exhibited significant reductions in interventricular septal thickness at end-systole(IVSs)and left ventricular internal diameter at end-systole and end-diastole(LVIDs and LVIDd).JPQHF effectively suppressed high glucose-induced activation of IL-1βand caspase 3 in cardiomyocytes.Furthermore,JPQHF downregulated the expression of myocardial JunB/c-Fos,which was upregulated in both diabetic rats and high glucose-treated H9c2 cells.Conclusion The JPQH formula holds promise in mitigating diabetic myocardial apoptosis and inflammation in cardiomyocytes by inhibiting JunB/c-Fos expression through suppressing the MAPK(p38 and ERK1/2)pathway.

Antidepressant effects of Peiyuan Jieyu formula in a mouse model of chronic stress in conjunction with lipopolysaccharide-induced depression

Objective:To explore the mechanism of the Peiyuan Jieyu formula in treating depression by assessing its impact on a lipopolysaccharide-induced(LPS-induced)depression mouse model.Methods:We created a mouse model of depression by exposing mice that had previously received chronic stress to intraperitoneal LPS injections.The mice were divided into the following groups:control,model,fluoxetine,Tiansi Yin,Sini powder,and low-,medium-,and high-dose Peiyuan Jieyu formula groups.Forced swim and tail suspension tests were used to assess the efficacy of the depression(despair)model,and weight gain rates were also measured.Furthermore,serum levels of various depression and inflammation-associated molecules,including tumor necrosis factor-a(TNF-a),interferon-γ(IFN-γ),tryptophan,5-hydroxytryptamine,kynurenine(KYN),and kynurenic acid(KA)were assessed.Furthermore,the expression levels of ionic calcium-binding adaptor molecule-1(IBA-1)and indoleamine 2,3-dioxygenase(IDO)mRNA in hippocampal microglia were measured.Results:The model group displayed greater despair-associated immobility,which was shortened in response to various doses of Peiyuan Jieyu formula.Furthermore,formula administration significantly reduced serum TNF-a levels and hippocampal IDO mRNA expression.The high formula dose also reduced IFN-γand IBA-1 levels,the latter was also decreased in response to the medium formula dose.However,the low formula dose reduced serum KYN level and KYN/tryptophan(TRP)and KYN/KA ratios.Conclusion:The Peiyuan Jieyu formula holds immense potential in treating depression in a mouse model,potentially inhibiting inflammation and improving TRP-KYN metabolic disorders.

Gastrointestinal tolerability of organic infant formula compared to traditional infant formula: A systematic review

BACKGROUND Infants'nutrition significantly influences their growth,development,and overall well-being.With the increasing demand for organic infant formula driven by the perception of health benefits and growing awareness of natural feeding options,it is crucial to conduct a comparative analysis of the gastrointestinal tolerability between organic and traditional infant formulas.AIM To provide a concise and precise analysis of the gastrointestinal tolerability of organic infant formula compared to traditional infant formula.Due to limited direct comparisons,the review synthesizes available literature on each formula type,presenting insights into their potential effects on infants'digestive health.METHODS An extensive literature search was conducted,compiling studies on organic and traditional infant formulas,their compositions,and reported effects on gastrointestinal tolerability.We searched academic databases such as PubMed and Google Scholar and specialized nutrition,paediatrics,and infant health journals using relevant keywords till October 1,2023.RESULTS Although specific comparative studies are scarce and formula heterogeneity is a significant limitation,this systematic review provides an in-depth understanding of organic infant formulas'composition and potential benefits.While scientific evidence directly comparing gastrointestinal tolerability is limited,organic formulas strive to use carefully selected organic ingredients to imitate breast milk composition.Potential benefits include improved lipid profiles,higher methionine content,and decreased antibiotic-resistant bacteria levels.Understanding the gastrointestinal tolerability of organic and traditional infant formulas is crucial for parents and healthcare providers to make informed decisions.CONCLUSION Despite limitations in direct comparisons,this systematic review provides insights into the composition and potential benefits of organic infant formulas.It emphasizes the need for further research to elucidate their gastrointestinal effects comprehensively.

Evaluation of the famous classic formula Sanhua decoction based on network pharmacology and multi-component quantitative analysis

Background:Sanhua decoction has significant effects in the treatment of stroke.The study of the Sanhua decoction material benchmark was carried out to analyze the value transfer relationship between the Chinese herbal pieces and the substance benchmark.Methods:Network pharmacology was employed to investigate the potential active components and molecular mechanisms of Sanhua decoction in the treatment of stroke.15 batches of Sanhua decoction lyophilized powder were prepared using traditional formulas and subjected to high-performance liquid chromatography analysis to generate fingerprints of the Sanhua decoction substance benchmarks.Then,a multi-component quantitative analysis method was established,allowing for the simultaneous determination of ten components,to study the transfer of quantity values between pieces and substance benchmarks.Results:60 active ingredients were screened from Sanhua decoction by network pharmacology,of which gallic acid,magnolol honokiol,physcion,and aloe-emodin may have a greater effect than other active components.63 key targets and 134 pathways were predicted as the potential mechanism of Sanhua decoction in treating stroke.The fingerprint similarity of the Sanhua decoction substance benchmarks was found to be good among the 15 batches,confirming the 19 common peaks.The content of the 10 components was basically consistent.The components’transfer rates were within 30%of their respective means.Conclusions:This study provided a comprehensive and reliable strategy for the quality evaluation of Sanhua decoction substance benchmarks and held significant importance in improving its application value.