Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.

Difference between Responses of Potato Plant Height to Corrected FAO-56-recommended Crop Coefficient and Measured Crop Coefficient

This study was conducted to establish a simple convenient method for calculating crop coefficient, and provide a certain basis for the research of the empirical formula for calculating crop coefficient with plant height which could be measured conveniently with regional differences, especially for the establishment of accurate irrigation schedule of potato in Yunnan. By the field experiment on potato under the condition of drip irrigation, it was found that the models of plant height with corrected FAO-56-recommended K and measured K were a quartic polynomial and a cubic polynomial, respectively, and the polynomial of potato plant height with measured crop coefficient was simpler with higher degree of fitting; and the differences between the period with the highest change rate of potato plant height and the periods with the greatest FAO-56-recommended K and measured K exhibited a differences of 3 d. In conclusion： In the future study of simple or empirical formula calculation of crop coefficient, plant height should be considered as a main dependent variable in that the calculation result would be closer to the measured crop coefficient with the problem of regional difference existing in the FAO method solved and the formula might be simpler; and the irrigation time of potato should be 3 d earlier than the irrigation time determined according to the corrected FAO-56-recommended crop coefficient, especially in the key water requirement stages of potato.

Beyond statistical significance:Embracing minimal clinically important difference for better patient care

The minimal clinically important difference(MCID)represents a pivotal metric in bridging the gap between statistical significance and clinical relevance,addressing the direct impact of medical interventions from the patient's perspective.This comprehensive review analyzes the evolution,applications,and challenges of MCID across medical specialties,emphasizing its necessity in ensuring that clinical outcomes not only demonstrate statistical significance but also offer genuine clinical utility that aligns with patient expectations and needs.We discuss the evolution of MCID since its inception in the 1980s,its current applications across various medical specialties,and the methodologies used in its calculation,highlighting both anchor-based and distribution-based approaches.Furthermore,the paper delves into the challenges associated with the application of MCID,such as methodological variability and the interpretation difficulties that arise in clinical settings.Recommendations for the future include standardizing MCID calculation methods,enhancing patient involvement in setting MCID thresholds,and extending research to incorporate diverse global perspectives.These steps are critical to refining the role of MCID in patient-centered healthcare,addressing existing gaps in methodology and interpretation,and ensuring that medical interventions lead to significant,patient-perceived improvements.

Oscillation of Neutral Differential_difference Equations with Positive and Negative Periodic Coefficients

Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.

Role of disturbance coefficient in monitoring and treatment of cerebral edema in patients with cerebral hemorrhage

BACKGROUND At present,the conventional methods for diagnosing cerebral edema in clinical practice are computed tomography(CT)and magnetic resonance imaging(MRI),which can evaluate the location and degree of peripheral cerebral edema,but cannot realize quantification.When patients have symptoms of diffuse cerebral edema or high cranial pressure,CT or MRI often suggests that cerebral edema is lagging and cannot be dynamically monitored in real time.Intracranial pressure monitoring is the gold standard,but it is an invasive operation with high cost and complications.For clinical purposes,the ideal cerebral edema monitoring should be non-invasive,real-time,bedside,and continuous dynamic monitoring.The dis-turbance coefficient(DC)was used in this study to dynamically monitor the occu-rrence,development,and evolution of cerebral edema in patients with cerebral hemorrhage in real time,and review head CT or MRI to evaluate the development of the disease and guide further treatment,so as to improve the prognosis of patients with cerebral hemorrhage.AIM To offer a promising new approach for non-invasive adjuvant therapy in cerebral edema treatment.METHODS A total of 160 patients with hypertensive cerebral hemorrhage admitted to the Department of Neurosurgery,Second Affiliated Hospital of Xi’an Medical University from September 2018 to September 2019 were recruited.The patients were randomly divided into a control group(n=80)and an experimental group(n=80).Patients in the control group received conventional empirical treatment,while those in the experimental group were treated with mannitol dehydration under the guidance of DC.Subsequently,we compared the two groups with regards to the total dosage of mannitol,the total course of treatment,the incidence of complications,and prognosis.RESULTS The mean daily consumption of mannitol,the total course of treatment,and the mean hospitalization days were 362.7±117.7 mL,14.8±5.2 days,and 29.4±7.9 in the control group and 283.1±93.6 mL,11.8±4.2 days,and 23.9±8.3 in the experimental group(P<0.05).In the control group,there were 20 patients with pulmonary infection(25%),30 with electrolyte disturbance(37.5%),20 with renal impairment(25%),and 16 with stress ulcer(20%).In the experimental group,pulmonary infection occurred in 18 patients(22.5%),electrolyte disturbance in 6(7.5%),renal impairment in 2(2.5%),and stress ulcers in 15(18.8%)(P<0.05).According to the Glasgow coma scale score 6 months after discharge,the prognosis of the control group was good in 20 patients(25%),fair in 26(32.5%),and poor in 34(42.5%);the prognosis of the experimental group was good in 32(40%),fair in 36(45%),and poor in 12(15%)(P<0.05).CONCLUSION Using DC for non-invasive dynamic monitoring of cerebral edema demonstrates considerable clinical potential.It reduces mannitol dosage,treatment duration,complication rates,and hospital stays,ultimately lowering hospital-ization costs.Additionally,it improves overall patient prognosis,offering a promising new approach for non-invasive adjuvant therapy in cerebral edema treatment.

Role of variation coefficient of stone density in determining success of shock wave lithotripsy in urinary calculi

BACKGROUND Various stone factors can affect the net results of shock wave lithotripsy(SWL).Recently a new factor called variation coefficient of stone density(VCSD)is being considered to have an impact on stone free rates.AIM To assess the role of VCSD in determining success of SWL in urinary calculi.METHODS Charts review was utilized for collection of data variables.The patients were subjected to SWL,using an electromagnetic lithotripter.Mean stone density(MSD),stone heterogeneity index(SHI),and VCSD were calculated by generating regions of interest on computed tomography(CT)images.Role of these factors were determined by applying the relevant statistical tests for continuous and categorical variables and a P value of<0.05 was gauged to be statistically significant.RESULTS There were a total of 407 patients included in the analysis.The mean age of the subjects in this study was 38.89±14.61 years.In total,165 out of the 407 patients could not achieve stone free status.The successful group had a significantly lower stone volume as compared to the unsuccessful group(P<0.0001).Skin to stone distance was not dissimilar among the two groups(P=0.47).MSD was significantly lower in the successful group(P<0.0001).SHI and VCSD were both significantly higher in the successful group(P<0.0001).CONCLUSION VCSD,a useful CT based parameter,can be utilized to gauge stone fragility and hence the prediction of SWL outcomes.

THE FEKETE-SZEG?INEQUALITY AND SUCCESSIVE COEFFICIENTS DIFFERENCE FOR A SUBCLASS OF CLOSE-TO-STARLIKE MAPPINGS IN COMPLEX BANACH SPACES

Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.

GLOBAL ATTRACTIVITY OF NEUTRAL DIFFERENCE EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS

A neutral difference equation with positive and negative coefficientsΔ(x n-c nx n-k )+p nx n-l -q nx n-r =0, n=0,1,2,...,is considered and a sufficient condition for the global attractivity of the zero solution of this equation is obtained, which improves and extends the all known results in the literature.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

EXISTENCE OF POSITIVE SOLUTIONS FOR NEUTRAL DIFFERENCE EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS

In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature.

Numerical Analysis of Upwind Difference Schemes for Two-Dimensional First-Order Hyperbolic Equations with Variable Coefficients

In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.

RECENT DEVELOPMENTS IN THE OSCILLATION OF NEUTRAL DELAY DIFFERENCE EQUATIONS WITH SUMMABLE COEFFICIENTS

This paper surveys some new results on the oscillation of all solutions of the linear nentral delaydifference equation of the form △(yn - pnyn-k) + qnyn-l = 0, n = 0,1, 2…where { pn } and { qn } are twe real numbers sequences with qn≥0, and k and l are positive integers. These re-sults do not require the usual assumptionAlso, some interesting open problems on this topic am given.

THE TEMPERATURE STRESS OF RC CONCRETE COMPONENT INDUCED BY LINEAR EXPENSION COEFFICIENT DIFFERENCE

The temperature stress of reinforced concrete component caused by different linear expension coefficient has been discussed in this paper from the point of view of composite materials, The temperature dress can reach about 22 to 45 percent of the tension strength for the concrete with low grade and high ratio of reinforcement which should be considered seriously.

MIKUSINSKI＇S OPERATORS SOLUTION OF THREE－ORDER LINEAR DIFFERENCE EQUATION WITH VARIABLE COEFFICIENTS

This paper proceeds the papers [3] [4], we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators serieswith variable coefficients in the operational field of Mikusinski, it is devoted to thesolution of the general three-order linear difference equation with variable,coefficients,and it is also devoted to the better solution .formula for the some special three-orderlinear difference equations with variable coefficients, in addition, we try to provide theidea and method for realizing solution of the more than three-order linear differenceequation with variable coefficients.

DIFFERENCE SCHEMES BASING ON COEFFICIENT APPROXIMATION

In respect of variable coefficient differential equations, the equations of coefficient function approximation were more accurate than the coefficient to be frozen as a constant in every discrete subinterval. Usually, the difference schemes constructed based on Taylor expansion approximation of the solution do not suit the solution with sharp function. Introducing into local bases to be combined with coefficient function approximation, the difference can well depict more complex physical phenomena, for example, boundary layer as well as high oscillatory,with sharp behavior. The numerical test shows the method is more effective than the traditional one.

Growth of Solutions of Some Linear Difference Equations with Meromorphic Coefficients

In this paper, we investigate the properties of solutions of some linear difference equations with meromorphic coefficients, and obtain some estimates on growth and value distribution of these meromorphic solutions.

DIFFERENCE SCHEME FOR AN INITIAL-BOUNDARY VALUE PROBLEM FOR LINEAR COEFFICIENT-VARIED PARABOLIC DIFFERENTIAL EQUATION WITH A NONSMOOTH BOUNDARY LAYER FUNCTION

In this paper, using nonuniform mesh and exponentially fitted difference method, a uniformly convergent difference scheme for an initial-boundary value problem of linear parabolic differential equation with the nonsmooth boundary layer function with respect to small parameter e is given, and error estimate and numerical result are also given.

High Order Compact Difference Scheme and Multigrid Method for 2D Elliptic Problems with Variable Coefficients and Interior/Boundary Layers on Nonuniform Grids

In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.

Textural differences based on apparent diffusion coefficient maps for discriminating pT3 subclasses of rectal adenocarcinoma

BACKGROUND The accuracy of discriminating pT3a from pT3b-c rectal cancer using highresolution magnetic resonance imaging(MRI)remains unsatisfactory,although texture analysis(TA)could improve such discrimination.AIM To investigate the value of TA on apparent diffusion coefficient(ADC)maps in differentiating pT3a rectal adenocarcinomas from pT3b-c tumors.METHODS This was a case-control study of 59 patients with pT3 rectal adenocarcinoma,who underwent diffusion-weighted imaging(DWI)between October 2016 and December 2018.The inclusion criteria were:(1)Proven pT3 rectal adenocarcinoma;(2)Primary MRI including high-resolution T2-weighted image(T2WI)and DWI;and(3)Availability of pathological reports for surgical specimens.The exclusion criteria were:(1)Poor image quality;(2)Preoperative chemoradiation therapy;and(3)A different pathological type.First-order(ADC values,skewness,kurtosis,and uniformity)and second-order(energy,entropy,inertia,and correlation)texture features were derived from whole-lesion ADC maps.Receiver operating characteristic curves were used to determine the diagnostic value for pT3b-c tumors.RESULTS The final study population consisted of 59 patients(34 men and 25 women),with a median age of 66 years(range,41-85 years).Thirty patients had pT3a,24 had pT3b,and five had pT3c.Among the ADC first-order textural differences between pT3a and pT3b-c rectal adenocarcinomas,only skewness was significantly lower in the pT3a tumors than in pT3b-c tumors.Among the ADC second-order textural differences,energy and entropy were significantly different between pT3a and pT3b-c rectal adenocarcinomas.For differentiating pT3a rectal adenocarcinomas from pT3b-c tumors,the areas under the curves(AUCs)of skewness,energy,and entropy were 0.686,0.657,and 0.747,respectively.Logistic regression analysis of all three features yielded a greater AUC(0.775)in differentiating pT3a rectal adenocarcinomas from pT3b-c tumors(69.0%sensitivity and 83.3%specificity).CONCLUSION TA features derived from ADC maps might potentially differentiate pT3a rectal adenocarcinomas from pT3b-c tumors.

SOLUTIONS OF THE GENERALn－TH ORDER VARIABLE COEFFICIENTS LINEAR DIFFERENCE EQUATION

In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s sequence convergence.After turning ageneral variable coefficient linear difference equation of order n into a set of operatorequations.we can obtain the solutions of the general n-th order variable coefficientlinear difference equation.