Insight Into the Separation-of-Variable Methods for the Closed-Form Solutions of Free Vibration of Rectangular Thin Plates

The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.

Rock fracture mechanism of buffer blasting with cushion layer at the borehole bottom

This study primarily investigates the rock fracture mechanism of bottom cushion layer blasting and explores the effects of the bottom cushion layer on rock fragmentation.It involves analyses of the evolution patterns of blasting stress,characteristics of crack distribution,and rock fracture features in the specimens.First,blasting model experiments were carried out using the dynamic caustics principle to investigate the influence of bottom cushion layers and initiation methods on the integrity of the bottom rock mass.The experimental results indicate that the combined use of bottom cushion layers and inverse initiation effectively protects the integrity of the bottom rock mass.Subsequently,the process of stress wave propagation and dynamic crack propagation in rocks was simulated using the continuum-discontinuum element method(CDEM)and the Landau explosion source model,with varying thicknesses of bottom cushion layers.The numerical simulation results indicate that with increasing cushion thickness,the absorption of energy generated by the explosion becomes more pronounced,resulting in fewer cracks in the bottom rock mass.This illustrates the positive role of the cushion layer in protecting the integrity of the bottom rock mass.

Retrospective comparative study of different surgical methods for gastric ulcer perforation:Efficacy and postoperative complications

BACKGROUND Gastric ulcer perforation is a critical condition that can lead to significant morbidity and mortality if not promptly addressed.It is often the result of chronic peptic ulcer disease,which is characterized by a breach in the gastric wall due to ulceration.Surgical intervention is essential for managing this life-threatening complication.However,the optimal surgical technique remains debatable among clinicians.Various methods have been employed,including simple closure,omental patch repair,and partial gastrectomy,each with distinct advantages and disadvantages.Understanding the comparative efficacy and postoperative outcomes of these techniques is crucial for improving patient care and surgical decision-making.This study addresses the need for a comprehensive analysis in this area.AIM To compare the efficacy and postoperative complications of different surgical methods for the treatment of gastric ulcer perforation.METHODS A retrospective analysis was conducted on 120 patients who underwent surgery for gastric ulcer perforation between September 2020 and June 2023.The patients were divided into three groups based on the surgical method:Simple closure,omental patch repair,and partial gastrectomy.The primary outcomes were the operative success rate and incidence of postoperative complications.Secondary outcomes included the length of hospital stay,recovery time,and long-term quality of life.RESULTS The operative success rates for simple closure,omental patch repair,and partial gastrectomy were 92.5%,95%,and 97.5%,respectively.Postoperative complications occurred in 20%,15%,and 17.5%of patients in each group,respectively.The partial gastrectomy group showed a significantly longer operative time(P<0.001)but the lowest rate of ulcer recurrence(2.5%,P<0.05).The omental patch repair group demonstrated the shortest hospital stay(mean 7.2 days,P<0.05)and fastest recovery time.CONCLUSION While all three surgical methods showed high success rates,omental patch repair demonstrated the best overall outcomes,with a balance of high efficacy,low complication rates,and shorter recovery time.However,the choice of the surgical method should be tailored to individual patient factors and the surgeon’s expertise.

Effects of different processing methods on the quality of Polygonatum cyrtonema Hua

Background:In this study,we explored the effects of different processing methods on the quality of Polygonatum cyrtonema Hua(PC),and the role of Huangjiu in the processing procedure.Methods:The sensory characteristics of the crude product,steamed product,and wine-processed product of PC were described.The colorimeter was used to analyze the chromatic values of three different processed products on PC.At the same time,the contents of the water extract and alcohol extract were measured separately.The content of three different processing Polygonatum Polysaccharide(PCP)was determined using 0.2%anthrone-sulfuric acid.The correlation difference between the chromatic values and chemical composition of different PC products was analyzed using various analytical methods.Results:The surface colors gradually deepened,the sweetness increased,the viscosity strengthened,and the tongue-numbing sensation disappeared after PC processing.The contents of extract and L^(*) gradually decreased from the crude to the steamed to the wine-processed product,consistent with the pattern of surface color alteration.While,E^(*)ab gradually increased.The content of PCP was crude product>wine-processed product>steamed product.The results of multivariate statistical analysis showed that the samples processed for crude,steamed,and wine-processed product were clustered into three classes.The correlation analysis showed that L^(*)and E^(*)ab were highly significant positively correlated with the content of PCP,and a*was significantly negatively correlated with the content of PCP.Conclusion:The results showed that the wine-processed product had the best quality.The internal quality of the PC was correlated with its characteristics and chromatic value.In this study,we investigated the internal and external quality of three different products of PC in order to provide a reference for further research on the impact of different processing methods on PC quality,the standardization of PC processing,and the role of Huangjiu in the processing of PC.

Two-Stream Approximation to the Radiative Transfer Equation:A New Improvement and Comparative Accuracy with Existing Methods

Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.

Effects of Different Grinding Methods on the Quality of Soybean Bean Milk

[Objectives] This study was conducted to improve the nutritional value of soybean milk, enrich the variety and taste of soybean milk, and find healthy food that is more conducive to people s nutritional needs. [Methods] Whole soybean milk was prepared by grinding with a grinding wheel at a low concentration (low-concentration grinding) and a stainless steel mill at a high concentration (high-concentration grinding). The sensory, physical and chemical characteristics and anti-nutritional factors of whole soybean milk produced by different grinding methods were studied. [Results] Compared with low-concentration grinding, the protein content in soybean milk prepared by high-concentration grinding increased by 24%, and the dietary fiber content increased by 74.7%. Before and after high-pressure homogenization, the particle size D(4, 3) of soybean milk prepared by low-concentration grinding was 212.1 and 93.59 μm, respectively, and the particle size D(4, 3) of soybean milk prepared by high-concentration grinding was 134.0 and 64.64 μm, respectively. The trypsin inhibitor activity and phytic acid content of soybean milk prepared by high-concentration grinding were significantly lower than those of soybean milk prepared by low-concentration grinding. [Conclusions] This study improves the diet structure of the broad masses of people, strengthens people s physique, and provides a new idea for the implementation and development of China s "Soybean Action Programme".

Scientific connotation of “treating different diseases with the same method” from the perspective of metabolic-immune dysregulation in inflammation-mediated carcinogenesis of digestive organs

Inflammation-mediated carcinogenesis develops in the context of chronic inflammation and is a significant cause of cancer within the digestive system.In the chronic inflammation microenvironment,the metabolic activity of tissue cells undergoes extensive changes,which interfere with the normal function of immune cells.Dysregulation of cell metabolism and immune function has been identified as a key factor contributing to inflammation-mediated carcinogenesis within the major digestive organs,such as the stomach,liver,and colorectum.This metabolic-immune imbalance also corresponds to traditional Chinese medicine(TCM)theories of“yin-yang disharmony”and“disharmony between Ying-nutrients and Wei-defense.”The metabolic-immune imbalance has also been regarded as the key factor supporting“treatment of different diseases with the same method”,in which the same approach is adopted in the treatment of different conditions.In the TCM treatment process,it is necessary to first identify TCM patterns and then apply the corresponding TCM to correct the dysregulated metabolic and immune function,thereby blocking the progression from inflammation to malignancy.Our study findings deepen the TCM understanding of metabolic-immune dysregulation and the relationship between metabolic-immune dysregulation,pattern identification,and treatment method.They also provide new insights for the treatment of inflammation-mediated carcinogenesis in major digestive organs and help us further explore the scientific connotation of the TCM strategy of“treating different diseases with the same method”.

Temperature and solar radiation utilization of rice for yield formation with different mechanized planting methods in the lower reaches of the Yangtze River,China

Several studies have demonstrated the effect of planting methods on rice yield, but information on the climate resources is limited. This study aims to reveal the effects of planting methods on climate resources associated with rice yield in a rice-wheat rotation system in the lower reaches of the Yangtze River, China. Field experiments were conducted in 2014 and 2015 with two japonica, two indica hybrid, and two japonica-indica hybrid varieties grown under three mechanized planting methods： carpet seedling of mechanical transplanting（CT）, mechanical direct seeding（DS）, and pot-hole seedling of mechanical transplanting（PT）. The rice yield and total dry matter under PT were greater than those under CT and DS methods. Besides, the entire growth duration and daily production showed significant positive relations with rice yield. Compared with CT and DS, the effective accumulated temperature and cumulative solar radiation of rice under PT were higher in phenological phases. In addition, the dry matter/effective accumulated temperature and solar energy utilization of rice under CT and DS were higher during vegetative phase and lower during reproductive and grain filling phases in contrast to PT. The mean daily temperature and mean daily solar radiation in the entire growth duration showed significant positive correlation with rice yield, total dry matter, and harvest index. This study demonstrated that when the mean daily temperature is 〈25.1°C in vegetative phase and 〉20.1°C in grain filling phase, rice yield could be increased by selecting mechanized planting methods. Most varieties under PT method exhibited high yield and climate resources use efficiency compared with CT and DS. In conclusion, the PT method could be a better cultivation measure for high rice yield, accompanied with high temperature and solar radiation use efficiency in a rice-wheat rotation system in the lower reaches of the Yangtze River, China.

Evaluation and Intervention Methods for Patients with Prediabetes of Different Phenotypes

Prediabetes is a heterogeneous condition,encompassing various pathological phenotypes such as hyperinsulinemia,tissue-specific insulin resistance(IR),systemic IR,andβ-cell dysfunction.A significant proportion of individuals with prediabetes remain undiagnosed.Furthermore,although lifestyle interventions have demonstrated efficacy in improving prediabetic conditions,some individuals with prediabetes progress to type 2 diabetes mellitus.This study aims to summarize effective evaluation methods for identifying distinct pathological phenotypes of prediabetes and targeted lifestyle intervention strategies to mitigate the progression from prediabetes to diabetes.

Analysis of Perioperative Respiratory Care Methods and their Application Value in Children with Congenital Heart Disease

Objective:To analyze the perioperative respiratory care methods and application value in children with congenital heart disease.Methods:60 children with congenital heart disease(treated from January 2021 to October 2023)were screened and divided into two groups randomly.Each group consisted of 30 cases.The perioperative routine was used in the control group.The observation group underwent the perioperative routine along with better respiratory care.Oxygenation indicators,surgical complications,and family satisfaction levels of the groups were compared.Results:There was no significant difference in the oxygenation index between the two groups of children at admission(P>0.05).At discharge,the oxygenation indicators in the observation group were better than those of the control group,and the incidence of surgical complications was lower than that of the control group.The total satisfaction of family members in the observation group was higher than that of the control group(P<0.05).Conclusion:During the perioperative period for children with congenital heart disease,the implementation of respiratory care,which mainly involves symptomatic care,catheter care,sputum suction care,etc.,can actively improve the oxygenation indicators,reduce surgical complications,and promote faster and better recovery,of children with congenital heart disease.

Nonlinear constrained optimization using the flexible tolerance method hybridized with different unconstrained methods

This paper proposes the use of the flexible tolerance method(FTM) modified with scaling of variables and hybridized with different unconstrained optimization methods to solve real constrained optimization problems.The benchmark problems used to analyze the performance of the methods were taken from G-Suite functions.The original method(FTM) and other four proposed methods:(i) FTM with scaling of variables(FTMS),(ii) FTMS hybridized with BFGS(FTMS-BFGS),(iii) FTMS hybridized with modified Powell's method(FTMS-Powell)and(iv) FTMS hybridized with PSO(FTMS-PSO), were implemented. The success rates of the methods were 80%,100%, 75%, 95% and 85%, for FTM, FTMS, FTMS-BFGS, FTMS-Powell and FTMS-PSO, respectively. Numerical experiments including real constrained problems indicated that FTMS gave the best performance, followed by FTMSPowell and FTMS-PSO. Despite the inferior performance compared to FTMS and FTMS-Powell, the FTMS-PSO method presented some advantages since good different initial points could be obtained, which allow exploring different routes through the solution space and to escape from local optima. The proposed methods proved to be an effective way of improving the performance of the original FTM.

Reconstruction of the Medial Patellofemoral Ligament Using Hamstring Tendon Graft With Different Methods:a Biomechanical Study

Objective To measure the tensile strength of the normal medial patellofemoral ligament(MPFL),and evaluate the biomechanics of different fixation methods of the hamstring tendon graft on the patella.Methods Eight fresh cadaver knees were prepared by isolating the patella,leaving only the MPFL as its attachment to the medial condyle of femur.The MPFL was reconstructed by three different methods:four-suture fixation,anchors-single suture fixation,and anchors-double suture fixation.The tensile strength and the elongation of the normal MPFL and the tendon grafts were measured.Results The tensile strength of the four-suture fixation group(234.86±49.02 N)was stronger than that of the normal MPFL(146.91±25.30 N,P=0.0014)and the anchors-single suture group(159.17±49.07N,P=0.0077),while weaker than that of the anchors-double suture group(314.74±78.46 N,P=0.0052)Conclusions With regard to the tensile strength,the four-suture fixation method is reliable for clinical use.Compared with the anchor-suture method,the four-suture fixation method which has no specific implants is more economical,convenient and efficient.

Influence on the Quality of Apocynum Venetum with Different Degumming Methods

The biochemical degumming and chemical degumming were employed to process apocynum venetum, and indices values for the residual gum content, fineness, strength of single fiber, average length, moisture regain and whiteness of degummed apocynum venetum fibers are evaluated with fuzzy mathematical method. The results obtained from this investigation show that the general index value of degummed apocynum venetum fibers with biochemical degumming （K1= 0.626 09） is prior to that with chemical degumming（K2=0.421 64）.

Conversion of producer gas using NiO/SBA-15 obtained with different synthesis methods

In this study,NiO/SBA-15 was prepared by both direct and post synthesis methods.TEM images revealed that NiO particles aggregated in NiO/SBA-15 obtained with post synthesis method,regardless of NiO loading.However,NiO particles were monodispersed in NiO/SBA-15 with a NiO loading of less than 15 wt%by using the direct synthesis method.In this case,NiO particles aggregated when NiO loading was over 20 wt%.TPR analysis verified that with direct synthesis method the location boundary of NiO particles on outer and pore surface could be observed clearly,whereas that could not observed in the case of post synthesis method.This indicates that the type of synthesis method displays significant effect on the location of NiO particles dispersed into the SBA-15.Producer gas conversion was carried out using NiO/SBA-15 as catalysts,which were synthesized with different synthesis methods.The gas conversion including methanation occurred at low temperature(i.e.,300-400℃)and the reverse water gas shift(RWGS)reaction at hightemperature(i.e.,400-900℃).High temperatures facilitated CO conversion to CO with CO selectivity close to 100%,regardless of the synthesis method of the used catalyst.At low temperatures the dispersion type of NiO particles affectedthe CO,conversion reaction,i.e.,monodispersed Ni0 particles gave a CO selectivity of close to 100%,similar to thatobtained at high temperature.The aggregated NiO particles resuled in a CO selectivity of less than 100%owing to CH,formation,regardless of synthesis method of catalyst.Therefore,NiO/SBA-15 obtained with direct synthesis methodfavored RWGS reaction because of high CO selectivity.NiOSBA-15 obtained with post synthesis method is suited formethanation because of high CH selectivity,and the conversion of CO,to CHa through methanation increased withincreasing NiO loading.

Density Limits with Different Fuelling Methods in the HL-2A Tokamak

Density limits with different fuelling methods have been compared in HL-2A, i.e. direct gas puffing and supersonic molecular beam injection （SMBI） from outer midplane, and divertor gas fuelling. The maximum densities for low current discharges are 3.4×10^19 m-3, 4.3×10^19 m-3 and 4.7×10^19 m-3 for the 3 kinds of fuelling methods. The corresponding density ratios to Green- wald density limit are 0.9, 1.1, 1.2, respectively. The behavior of density limit disruption is analyzed as well.

Synthesis and optical properties research of gold nanoparticles with different morphologies

This paper presents an approach to synthesis of gold nanoparticles with different morphologies and investigation of the relationship between morphologies and their optical properties.Spherical gold nanoparticles with different sizes are synthesized via reduction method.Using seed-mediated solution growth method,gold nanoparticles with shuttle,star and stick shapes can be obtained.The sizes and morphologies of the gold nanoparticles are characterized by transmission electron microscopy （TEM）.The characterization results illustrate the growth process of the gold nanoparticles with different morphologies.Absorption spectroscopy and Raman spectroscopy measurements are performed to demonstrate the relationship between the morphologies and optical properties.The results of Raman characterization show that the gold nanoparticles with different morphologies can be used to probe molecules with different concentrations.

The θ－Methods in Numerical Solution of Systems of Differential Equations with Two Delay Terms

This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.

The Experimental Research on the Classroom Teaching Mode of Appropriate Combination of Traditional Methods with the Multimedia Overhead Projector

Based on the constructivism, using the College English（new edition） CD-ROMs for classroom teaching as main media, this paper explores the feasibility of the classroom teaching mode of appropriate combination of traditional methods with the multimedia overhead projector. The new teaching mode proves to be successful in that it has greatly improved the students＇ ability to use English in an all-round way and has obvious advantages over the only traditional method.

A comparison study on structure-function relationship of polysaccharides obtained from sea buckthorn berries using different methods:antioxidant and bile acid-binding capacity

In this study,the structural characters,antioxidant activities and bile acid-binding ability of sea buckthorn polysaccharides(HRPs)obtained by the commonly used hot water(HRP-W),pressurized hot water(HRP-H),ultrasonic(HRP-U),acid(HRP-C)and alkali(HRP-A)assisted extraction methods were investigated.The results demonstrated that extraction methods had significant effects on extraction yield,monosaccharide composition,molecular weight,particle size,triple-helical structure,and surface morphology of HRPs except for the major linkage bands.Thermogravimetric analysis showed that HRP-U with filamentous reticular microstructure exhibited better thermal stability.The HRP-A with the lowest molecular weight and highest arabinose content possessed the best antioxidant activities.Moreover,the rheological analysis indicated that HRPs with higher galacturonic acid content and molecular weight showed higher viscosity and stronger crosslinking network(HRP-C,HRP-W and HRP-U),which exhibited stronger bile acid binding capacity.The present findings provide scientific evidence in the preparation technology of sea buckthorn polysaccharides with good antioxidant and bile acid binding capacity which are related to the structure affected by the extraction methods.

Synthesis methods and powder quality of titanium monocarbide

Titanium monocarbide(TiC),which is the most stable titanium-based carbide,has attracted considerable interest in the fields of energy,catalysis,and structural materials due to its excellent properties.Synthesis of high-quality TiC powders with low cost and high efficiency is crucial for industrial applications;however major challenges face its realization.Herein,the methods for synthesizing TiC powders based on a reaction system are reviewed.This analysis is focused on the underlying mechanisms by which synthesis methods affect the quality of powders.Notably,strategies for improving the synthesis of highquality powders are analyzed from the perspective of enhancing heat and mass transfer processes.Furthermore,the critical issues,challenges,and development trends of the synthesis technology and application of high-quality TiC powder are discussed.