Generalized Cline's Formula and Jacobson's Lemma in a Ring

We present a new generalized version of Cline's formula and Jacobson's lemma for g-Drazin inverses in a ring.These generalized results extend many known results,e.g.,Chen and Abdolyousefi[Generalized Jacobson's lemma in a Banach algebra,Comm.Algebra 49(2021)3263-3272],and Yan and Zeng[The generalized inverses of the products of two elements in a ring,Turkish J.Math.44(2020)1744-1756].

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.

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.

Effect of Luhong formula on the cardiac rehabilitation of patients with chronic heart failure

BACKGROUND Current treatments for chronic heart failure(CHF)are therapeutically ineffective.The optimization of treatments for this disease needs to be explored and analyzed.AIM To analyze the effect of using Luhong Formula in the cardiac rehabilitation of patients with CHF and its influence on cardiopulmonary function(CPF)and prognosis.METHODS In total,160 patients with CHF admitted between June 2022 and June 2023 were selected,including 75 receiving perindopril(control group)and 85 receiving Luhong Formula(research group).We conducted comparative analyses on the curative effects of traditional Chinese medicine(TCM)syndromes and cardiac function,CPF[oxygen consumption at the anaerobic threshold(VO2 AT)and at peak exercise(peak VO2)],echocardiographic indexes[left atrial volume index(LAVI),left ventricular muscle mass index(LVMI),left ventricular ejection fraction(LVEF)],and prognosis[major adverse cardiovascular events(MACEs)at 6 months follow-up].RESULTS The research group showed markedly higher curative effects of TCM syndromes and cardiac function than the control group.In addition,post-treatment VO2 AT,peak VO2,LVMI and LVEF in the research group were significantly higher,whereas LAVI was significantly lower,than those of the control group.Furthermore,fewer patients in the research group developed MACEs at the 6-month follow-up.CONCLUSION Luhong Formula is more therapeutically effective than perindopril for the cardiac rehabilitation of patients with CHF,specifically in enhancing CPF and prognosis.

Optimal traditional Chinese medicine formulas in treating ulcerative colitis:Choose one or take it all?

Ulcerative colitis(UC)is a chronic inflammatory bowel disease that presents significant treatment challenges due to its complexity,especially in terms of the various side effects that traditional medications may bring during the chronic course of the disease.Traditional Chinese medicine(TCM)has emerged as a promising complementary therapy for UC.Based on the latest research,our editorial explored the current issues and potential essential research directions for TCM in treating UC.We anticipate that future high-quality research will pave the way for the optimization of TCM formulas for UC and their broader global application.

Unraveling the mechanism of action of Shangxia Liangji formula for treating insomnia:a metabolomics and network pharmacology approach

Background:Insomnia is a prevalent clinical condition and Shangxia Liangji formula(SXLJF)is a well-established method of treatment.Nevertheless,the specific mechanism of action of SXLJF remains unclear.Methods:The mouse model of insomnia was established by intraperitoneal injection of para-chlorophenylalanine.Forty-two mice were randomly divided into a negative control group,model group,SXLJF group(18.72 g/kg/day),and positive control group(diazepam,2 mg/kg)and treated with the corresponding drugs for 7 consecutive days.The open field test and pentobarbital-induced sleeping test were conducted.LC-MS-based untargeted metabolomics and network pharmacology were applied to explore the potential targets of SXLJF for treating insomnia.Finally,key targets were validated using RT-qPCR.Results:Behavioral tests demonstrated that SXLJF reduced the total distance,average velocity,central distance,and sleep latency,and prolonged sleep duration.Metabolomics and network pharmacology revealed potential targets,signaling pathways,metabolic pathways,and metabolites associated with the anti-insomnia effects of SXLJF.Specifically,tyrosine hydroxylase(TH)and tyrosine metabolism emerged as crucial metabolic pathways and targets,respectively.RT-qPCR results supported the role of TH in the mechanism of SXLJF in treating insomnia.Conclusion:In conclusion,TH and tyrosine metabolism may represent significant targets and pathways for SXLJF in treating insomnia.

Goat milk-based infant formula regulates intestinal barrier function and promotes the production of short-chain fatty acids

Infant formula(IF)based on cow milk and goat milk is a substitute food for infants who are underfed with human milk.In our previous study,we reported the composition and physicochemical stability of IF based on milk from cows and goats and a combination of both milks.Here,we investigated the effects of these 3 IFs on intestinal immunity and short-chain fatty acid production(SCFAs)using human microbiota-associated(HMA)mice and selected human milk as a positive control.The results showed that goat milk-based IF is associated with a functional immune advantage,due to the rise in the levels of immune-related cytokines interleukin(IL)-2 and IL-10,decreased levels of intestinal permeability markers D-lactic acid and endotoxin,and increased mRNA levels of intestinal tight junction proteins occludin and claudin.In addition,the intestine of mice fed with goat milk-based IF contained 12.06μmol/g acetate,2.42μmol/g propionate,and 1.72μmol/g butyrate,which reached 69%,79%,and 60%of the levels in human milk,respectively.Our results indicate that goat milk-based IF improves intestinal immune function and promotes the production of intestinal SCFAs.

Study of the Lift Force Induced by An Interceptor on A High-Speed Mono-Hull:The Affecting Factors and Estimation Formula

To find a better way to estimate the lift force induced by an interceptor on a high-speed mono-hull ship,a series of high-speed mono-hull ship models are designed and investigated under different conditions.Different lift forces are obtained by numerical calculations and validated by a model test in a towing tank.The factors that influence the force are the interceptor height,velocity,draft,and deadrise angle.The relationship between each factor and the induced lift force is investigated and obtained.We found that the induced lift mainly depends on the interceptor height and advancing velocity,and is proportional to the square of the interceptor height and velocity.The results also showed that the effects of the draft and deadrise angle are relatively less important,and the relationship between the induced lift and these two factors is generally linear.Based on the results,a formula including the combined effect of all factors used to estimate the lift force induced by the interceptor is developed based on systematic analysis.The proposed formula could be used to estimate the lift force induced by interceptors,especially under high-speed condition.

Screening of Substrate Formulas for Culture of Auricularia auricula Mycelia with Byproducts

[Objectives]This study was conducted to explore the source of substitutive substrate raw materials for cultivation of edible fungi,reduce the cutting and use of woody materials,and realize harmless treatment and resource utilization of byproducts from Chinese medicine production and bamboo processing.[Methods]Traditional Chinese medicine residue and bamboo shavings were used to partially replace hardwood sawdust in the conventional formula,and the growth of Auricularia auricula mycelia in large test tubes under different substrate formulas was studied.[Results]The results showed that the mycelia of A.auricula could grow normally on substrates with byproducts,and the mycelia grew differently with different formulas,and the performance of different strains of the same species was also different.Compared with the conventional formula,the suitable substitution amount of bamboo shavings for A.auricula strains was 10%-30%,and the substitution amount of Chinese medicine residue was 5%-15%.[Conclusions]This study provides reference for the efficient utilization of byproducts and the expansion of raw material sources for production of edible fungi.

Effect of high-protein peptide-based formula compared with isocaloric isonitrogenous polymeric formula in critically ill surgical patient

BACKGROUND Malnutrition is common in critically ill patients,and it is associated with an increased risk of complications.Early enteral nutrition with adequate caloric and protein intake is critical nevertheless it is difficult to achieve.Peptide-based formulas have been shown to be beneficial in patients with feeding intolerance.However,there are limited studies showing the efficacy and safety of high-protein peptide-based formula in critically ill surgical patients.AIM To determine the effects of a high-protein peptide formulation on gastrointestinal tolerance,nutritional status,biochemical changes,and adverse events in patients in the surgery intensive care unit(SICU)compared to an isocaloric isonitrogenous standard polymeric formulation.METHODS This study was a multi-center double-blind,randomized controlled trial.We enrolled adult patients in the surgical intensive care unit,age≥15 years and expected to receive enteral feeding for at least 5-14 d post-operation.They were randomly assigned to receive either the high-protein peptide-based formula or the isocaloric isonitrogenous standard formula for 14 d.Gastric residual volume(GRV),nutritional status,body composition and biochemical parameters were assessed at baseline and on days 3,5,7,9,11,and 14.RESULTS A total of 19 patients were enrolled,9 patients in the peptide-based formula group and 10 patients in the standard formula group.During the study period,there were no differences of the average GRV,body weight,body composition,nutritional status and biochemical parameters in the patients receiving peptide-based formula,compared to the standard regimen.However,participants in the standard formula lost their body weight,body mass index(BMI)and skeletal muscle mass significantly.While body weight,BMI and muscle mass were maintained in the peptide-based formula,from baseline to day 14.Moreover,the participants in the peptide-based formula tended to reach their caloric target faster than the standard formula.CONCLUSION The study emphasizes the importance of early nutritional support in the SICU and showed the efficacy and safety of a high-protein,peptide-based formula in meeting caloric and protein intake targets while maintaining body weight and muscle mass.

Validation of Molecular Detection Methods for Gluten Allergens in Infant Formula

[Objectives]To verify the specificity,sensitivity,precision and negative-positive deviation of the foodproof gluten component de-tection kit for the detection of gluten allergens in milk powder matrix,and to establish a real-time fluorescent PCR legal method for the detec-tion of gluten allergens in milk powder.[Methods]The specificity,sensitivity,precision and negative-positive deviation of the detection method of foodproof gluten component detection kit(PCR-probe method)were verified by artificially adding different concentrations of wheat bran and extracting sample DNA by kit method,and applied to sample detection.[Results] The specific detection results of two kinds of milk powder with wheat bran and buckwheat added showed that the foodproof gluten component detection kit(PCR-probe method)had good speci-ficity for wheat gluten.The results of artificially added wheat bran positive samples showed that the false positive rate and false negative rate of the kit in the milk powder matrix were O,and the sensitivity and precision were high.[Conclusions]The kit is simple to operate and has high accuracy,which is suitable for the detection of gluten allergen components in milk powder.