Impact of effective stress on permeability for carbonate fractured-vuggy rocks

To gain insight into the flow mechanisms and stress sensitivity for fractured-vuggy reservoirs,several core models with different structural characteristics were designed and fabricated to investigate the impact of effective stress on permeability for carbonate fractured-vuggy rocks(CFVR).It shows that the permeability performance curves under different pore and confining pressures(i.e.altered stress conditions)for the fractured core models and the vuggy core models have similar change patterns.The ranges of permeability variation are significantly wider at high pore pressures,indicating that permeability reduction is the most significant during the early stage of development for fractured-vuggy reservoirs.Since each obtained effective stress coefficient for permeability(ESCP)varies with the changes in confining pressure and pore pressure,the effective stresses for permeability of four representative CFVR show obvious nonlinear characteristics,and the variation ranges of ESCP are all between 0 and 1.Meanwhile,a comprehensive ESCP mathematical model considering triple media,including matrix pores,fractures,and dissolved vugs,was proposed.It is proved theoretically that the ESCP of CFVR generally varies between 0 and 1.Additionally,the regression results showed that the power model ranked highest among the four empirical models mainly applied in stress sensitivity characterization,followed by the logarithmic model,exponential model,and binomial model.The concept of“permeability decline rate”was introduced to better evaluate the stress sensitivity performance for CFVR,in which the one-fracture rock is the strongest,followed by the fracture-vug rock and two-horizontalfracture rock;the through-hole rock is the weakest.In general,this study provides a theoretical basis to guide the design of development and adjustment programs for carbonate fractured-vuggy reservoirs.

Machine learning-based comparison of factors influencing estimated glomerular filtration rate in Chinese women with or without nonalcoholic fatty liver

BACKGROUND The prevalence of non-alcoholic fatty liver(NAFLD)has increased recently.Subjects with NAFLD are known to have higher chance for renal function impairment.Many past studies used traditional multiple linear regression(MLR)to identify risk factors for decreased estimated glomerular filtration rate(eGFR).However,medical research is increasingly relying on emerging machine learning(Mach-L)methods.The present study enrolled healthy women to identify factors affecting eGFR in subjects with and without NAFLD(NAFLD+,NAFLD-)and to rank their importance.AIM To uses three different Mach-L methods to identify key impact factors for eGFR in healthy women with and without NAFLD.METHODS A total of 65535 healthy female study participants were enrolled from the Taiwan MJ cohort,accounting for 32 independent variables including demographic,biochemistry and lifestyle parameters(independent variables),while eGFR was used as the dependent variable.Aside from MLR,three Mach-L methods were applied,including stochastic gradient boosting,eXtreme gradient boosting and elastic net.Errors of estimation were used to define method accuracy,where smaller degree of error indicated better model performance.RESULTS Income,albumin,eGFR,High density lipoprotein-Cholesterol,phosphorus,forced expiratory volume in one second(FEV1),and sleep time were all lower in the NAFLD+group,while other factors were all significantly higher except for smoking area.Mach-L had lower estimation errors,thus outperforming MLR.In Model 1,age,uric acid(UA),FEV1,plasma calcium level(Ca),plasma albumin level(Alb)and T-bilirubin were the most important factors in the NAFLD+group,as opposed to age,UA,FEV1,Alb,lactic dehydrogenase(LDH)and Ca for the NAFLD-group.Given the importance percentage was much higher than the 2nd important factor,we built Model 2 by removing age.CONCLUSION The eGFR were lower in the NAFLD+group compared to the NAFLD-group,with age being was the most important impact factor in both groups of healthy Chinese women,followed by LDH,UA,FEV1 and Alb.However,for the NAFLD-group,TSH and SBP were the 5th and 6th most important factors,as opposed to Ca and BF in the NAFLD+group.

Understanding the Relationship Between Shrinking Cities and Land Prices:Spatial Pattern,Effectiveness,and Policy Implications

Urban shrinkage has emerged as a widespread phenomenon globally and has a significant impact on land,particularly in terms of land use and price.This study focuses on 2851 county-level cities in China in 2005–2018(excluding Hong Kong,Macao,Taiwan,and‘no data’areas in Qinhai-Tibet Plateau)as the fundamental units of analysis.By employing nighttime light(NTL)data to identify shrinking cities,the propensity score matching(PSM)model was used to quantitatively examine the impact of shrinking cities on land prices,and evaluate the magnitude of this influence.The findings demonstrate the following:1)there were 613 shrinking cities in China,with moderate shrinkage being the most prevalent and severe shrinkage being the least.2)Regional disparities are evident in the spatial distribution of shrinking cities,especially in areas with diverse terrain.3)The spatial pattern of land price exhibits a significant correlated to the economic and administrative levels.4)Shrinking cities significantly negatively impact on the overall land price(ATT=–0.1241,P<0.05).However,the extent of the effect varies significantly among different spatial regions.This study contributes novel insights into the investigation of land prices and shrinking cities,ultimately serving as a foundation for government efforts to promote the sustainable development of urban areas.

Thrust estimate method of an on-orbit Hall thruster using Hall drift current

In order to realize the thrust estimation of the Hall thruster during its flight mission,this study establishes an estimation method based on measurement of the Hall drift current.In this method,the Hall drift current is calculated from an inverse magnetostatic problem,which is formulated according to its induced magnetic flux density detected by sensors,and then the thrust is estimated by multiplying the Hall drift current with the characteristic magnetic flux density of the thruster itself.In addition,a three-wire torsion pendulum micro-thrust measurement system is utilized to verify the estimate values obtained from the proposed method.The errors were found to be less than 8%when the discharge voltage ranged from 250 V to 350 V and the anode flow rate ranged from 30 sccm to 50 sccm,indicating the possibility that the proposed thrust estimate method could be practically applied.Moreover,the measurement accuracy of the magnetic flux density is suggested to be lower than 0.015 mT and improvement on the inverse problem solution is required in the future.

Leading directions and effective distance of larch offspring dispersal at the upper treeline in the Northern and Polar Urals, Russia

Climate has changed sufficiently over the last 150 years and forced out upper treeline advance at the most studied sites around the world.The rate of advance has been extremely variable–from tens to hundreds meters in altitude.This is because the degree at which tree frontal populations respond to climate change depends on the complex interaction of biological and physical factors.The resulting stand pattern is the consequence of the interaction between dispersal and survival functions.A few publications have addressed the question of how this pattern is generated.In order to understand how the spatial structure of tree stands was formed at the upper limit of their distribution in the Ural Mountains,we assessed the distance and direction of dispersal of offspring from maternal individuals.We found that in frontal Larix sibirica Ledeb.populations,‘effective’dispersal of offspring ranges from 3 to 758 m(with a median of 20–33 m in open forest and 219 m in single-tree tundra in the Polar Urals and 107 m in open forest in the Northern Urals).We revealed that most of the offspring effectively dispersed not only in the direction of the prevailing winds,but also in the opposite direction up the slope,and the distance can reach 500–760 m.The data obtained can be used to develop an individual-based model which is capable of simulating in detail the dynamics of tree stands at the upper limit of their growth and reliably predicting the future position and pattern of treeline ecotone as growth conditions continue to improve in the face of observed climate change.

Improving the utility of locally differentially private protocols for longitudinal and multidimensional frequency estimates

This paper investigates the problem of collecting multidimensional data throughout time(i.e.,longitudinal studies)for the fundamental task of frequency estimation under Local Differential Privacy(LDP)guarantees.Contrary to frequency estimation of a single attribute,the multidimensional aspect demands particular attention to the privacy budget.Besides,when collecting user statistics longitudinally,privacy progressively degrades.Indeed,the“multiple”settings in combination(i.e.,many attributes and several collections throughout time)impose several challenges,for which this paper proposes the first solution for frequency estimates under LDP.To tackle these issues,we extend the analysis of three state-of-the-art LDP protocols(Generalized Randomized Response–GRR,Optimized Unary Encoding–OUE,and Symmetric Unary Encoding–SUE)for both longitudinal and multidimensional data collections.While the known literature uses OUE and SUE for two rounds of sanitization(a.k.a.memoization),i.e.,L-OUE and L-SUE,respectively,we analytically and experimentally show that starting with OUE and then with SUE provides higher data utility(i.e.,L-OSUE).Also,for attributes with small domain sizes,we propose Longitudinal GRR(L-GRR),which provides higher utility than the other protocols based on unary encoding.Last,we also propose a new solution named Adaptive LDP for LOngitudinal and Multidimensional FREquency Estimates(ALLOMFREE),which randomly samples a single attribute to be sent with the whole privacy budget and adaptively selects the optimal protocol,i.e.,either L-GRR or L-OSUE.As shown in the results,ALLOMFREE consistently and considerably outperforms the state-of-the-art L-SUE and L-OUE protocols in the quality of the frequency estimates.

Genetic and Agronomic Parameter Estimates of Growth, Yield and Related Traits of Maize (Zea mays L.) under Different Rates of Nitrogen Fertilization

This study evaluated the genetic and agronomic parameter estimates of maize under different nitrogen rates. The trial was established at the Njala Agricultural Research Centre experimental site during 2021 and 2022 in a split block design with three maize varieties (IWCD2, 2009EVDT, and DMR-ESR-Yellow) and seven nitrogen (0, 30, 60, 90, 120, 150 and 180 kg∙N∙ha−1) rates. Findings showed that cob diameter and anthesis silking time (ASI) had intermediate heritability, ASI had high genetic advance, ASI and grain yield had high genotypic coefficient of variation (GCV), while traits with high phenotypic coefficient of variation (PCV) were plant height, ASI, grain yield, number of kernel per cob, number of kernel rows, ear length, and ear height. The PCV values were higher than GCV, indicating the influence of the environment in the studied traits. Nitrogen rates and variety significantly (p < 0.05) influenced grain yield production. Mean grain yields and economic parameter estimates increased with increasing nitrogen rates, with the 30 and 180 kg∙N∙ha−1 plots exhibiting the lowest and highest grain yields of 1238 kg∙ha−1 and 2098 kg∙ha−1, respectively. Variety and nitrogen effects on partial factor productivity (PFPN), agronomic efficiency (AEN), net returns (NR), value cost ratio (VCR) and marginal return (MR) indicated that these parameters were significantly affected (p < 0.05) by these factors. The highest PFPN (41.3 kg grain kg−1∙N) and AEN (29.4 kg grain kg−1∙N) were obtained in the 30 kg∙N∙ha−1 plots, while the highest VCR (2.8) and MR (SLL 1.8 SLL−1 spent on N) were obtained in the 180 kg∙N∙ha−1. The significant influence of variety and nitrogen on traits suggests that increasing yields and maximizing profits require use of appropriate nitrogen fertilization and improved farming practices that could be exploited for increased productivity of maize.

Review on Hydroxyurea Usage in Young Children with Sickle Cell Disease: Examining Hemoglobin Induction, Potential Benefits, Responses, Safety, and Effectiveness

Sickle cell disease (SCD) is a prevalent condition, particularly in the countries of sub-Saharan Africa, where the presence of specific genes associated with Malaria contributes to its high prevalence. Patients with sickle cell disease frequently experience painful episodes necessitating hospitalization, and their hemoglobin levels are typically lower than those of the general population. There are different treatment options available to manage complications, such as transfusing blood, hydroxyurea, and strong anti-pains. However, with all these treatments, patients still commonly experience pain crises and suffer from organ damage. Hydroxyurea, the sole approved medication for sickle cell anemia in developed and developing countries, is widely used in children despite being primarily indicated for adults. Multiple studies have demonstrated the efficacy of hydroxyurea in inducing HbF production in young children with SCD. Elevated HbF levels have been associated with improved clinical outcomes, including a reduction in vaso-occlusive crises, acute chest syndrome, and the need for blood transfusions. Furthermore, increased HbF levels have been shown to ameliorate disease-related organ damage, such as pulmonary hypertension and sickle cell retinopathy. The response to hydroxyurea treatment in young children with SCD is variable. Some patients achieve substantial increases in HbF levels and experience significant clinical benefits, while others may have a more modest response. Factors influencing the response include baseline HbF levels, genetic modifiers, treatment adherence, and dose optimization. Safety is a crucial consideration when using hydroxyurea in young children. Studies have shown that hydroxyurea is generally well-tolerated, with the most common adverse effects being myelosuppression, gastrointestinal symptoms, and dermatological manifestations. However,long-term effects and potential risks, such as renal dysfunction and reproductive impacts, require further investigation. The effectiveness of hydroxyurea in young children with SCD has been demonstrated in various clinical trials and observational studies. These studies have shown a significant reduction in disease-related complications and improved quality of life. However, optimal dosing, treatment duration, and long-term outcomes are still areas of ongoing research. This review focuses on recent studies investigating the benefits, effectiveness, responses, and safety of hydroxyurea in pediatric individuals diagnosed with sickle cell disease.

A Formulation of the Porous Medium Equation with Time-Dependent Porosity: A Priori Estimates and Regularity Results

We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0.

Method for rapid warning and activity concentration estimates in online waterγ-spectrometry systems

Onlineγ-spectrometry systems for inland waters,most of which extract samples in situ and in real time,are able to produce reliable activity concentration measurements for waterborne radionuclides only when they are distributed relatively uniformly and enter into a steady-state diffusion regime in the measurement chamber.To protect residents’health and ensure the safety of the living environment,better timeliness is required for this measurement method.To address this issue,this study established a mathematical model of the online waterγ-spectrometry system so that rapid warning and activity estimates can be obtained for water under non-steady-state(NSS)conditions.In addition,the detection efficiency of the detector for radionuclides during the NSS diffusion process was determined by applying the computational fluid dynamics technique in conjunction with Monte Carlo simulations.On this basis,a method was developed that allowed the online waterγ-spectrometry system to provide rapid warning and activity concentration estimates for radionuclides in water.Subsequent analysis of the NSS-mode measurements of^(40)K radioactive solutions with different activity concentrations determined the optimum warning threshold and measurement time for producing accurate activity concentration estimates for radionuclides.The experimental results show that the proposed NSS measurement method is able to give warning and yield accurate activity concentration estimates for radionuclides 55.42 and 69.42 min after the entry of a 10 Bq/L^(40)K radioactive solution into the measurement chamber,respectively.These times are much shorter than the 90 min required by the conventional measurement method.Furthermore,the NSS measurement method allows the measurement system to give rapid(within approximately 15 min)warning when the activity concentrations of some radionuclides reach their respective limits stipulated in the Guidelines for Drinking-water Quality of the WHO,suggesting that this method considerably enhances the warning capacity of in situ online waterγ-spectrometry systems.

Evaluation of the effectiveness of preventive nursing measures for pressure injuries in patients in the neurology intensive care unit

BACKGROUND Patients in neurology intensive care units(ICU)are prone to pressure injuries(PU)due to factors such as severe illness,long-term bed rest,and physiological dysfunction.PU not only causes pain and complications to patients,but also increases medical burden,prolongs hospitalization time,and affects the recovery process.AIM To evaluate and optimize the effectiveness of pressure injury prevention nursing measures in neurology ICU patients.METHODS A retrospective study was conducted,and 60 patients who were admitted to the ICU of the Department of Neurology were selected and divided into an observation group and a control group according to the order of admission,with 30 people in each group.The observation group implemented pressure injury prevention and nursing measures,while the control group adopted routine care.RESULTS Comparison between observation and control groups following pressure injury prevention nursing intervention revealed significantly lower incidence rates in the observation group compared to the control group at 48 h(8.3%vs 26.7%),7 d(16.7%vs 43.3%),and 14 d(20.0%vs 50.0%).This suggests a substantial reduction in pressure injury incidence in the observation group,with the gap widening over time.Additionally,patients in the observation group exhibited quicker recovery,with a shorter average time to get out of bed(48 h vs 72 h)and a shorter average length of stay(12 d vs 15 d)compared to the control group.Furthermore,post-intervention,patients in the observation group reported significantly improved quality of life scores,including higher scores in body satisfaction,feeling and function,and comfort(both psychological and physiological),indicating enhanced overall well-being and comfort following the implementation of pressure injury prevention nursing measures.CONCLUSION Implementing pressure injury preventive care measures for neurology ICU patients will have better results.

Using Extreme Value Theory Approaches to Estimate High Quantiles for Stroke Data

This paper aims to explore the application of Extreme Value Theory (EVT) in estimating the conditional extreme quantile for time-to-event outcomes by examining the functional relationship between ambulatory blood pressure trajectories and clinical outcomes in stroke patients. The study utilizes EVT to analyze the functional connection between ambulatory blood pressure trajectories and clinical outcomes in a sample of 297 stroke patients. The 24-hour ambulatory blood pressure measurement curves for every 15 minutes are considered, acknowledging a censored rate of 40%. The findings reveal that the sample mean excess function exhibits a positive gradient above a specific threshold, confirming the heavy-tailed distribution of data in stroke patients with a positive extreme value index. Consequently, the estimated conditional extreme quantile indicates that stroke patients with higher blood pressure measurements face an elevated risk of recurrent stroke occurrence at an early stage. This research contributes to the understanding of the relationship between ambulatory blood pressure and recurrent stroke, providing valuable insights for clinical considerations and potential interventions in stroke management.

Source localization in signed networks with effective distance

While progress has been made in information source localization,it has overlooked the prevalent friend and adversarial relationships in social networks.This paper addresses this gap by focusing on source localization in signed network models.Leveraging the topological characteristics of signed networks and transforming the propagation probability into effective distance,we propose an optimization method for observer selection.Additionally,by using the reverse propagation algorithm we present a method for information source localization in signed networks.Extensive experimental results demonstrate that a higher proportion of positive edges within signed networks contributes to more favorable source localization,and the higher the ratio of propagation rates between positive and negative edges,the more accurate the source localization becomes.Interestingly,this aligns with our observation that,in reality,the number of friends tends to be greater than the number of adversaries,and the likelihood of information propagation among friends is often higher than among adversaries.In addition,the source located at the periphery of the network is not easy to identify.Furthermore,our proposed observer selection method based on effective distance achieves higher operational efficiency and exhibits higher accuracy in information source localization,compared with three strategies for observer selection based on the classical full-order neighbor coverage.

THE GRADIENT ESTIMATE OF SUBELLIPTIC HARMONIC MAPS WITH A POTENTIAL

In this paper,we investigate subelliptic harmonic maps with a potential from noncompact complete sub-Riemannian manifolds corresponding to totally geodesic Riemannian foliations.Under some suitable conditions,we give the gradient estimates of these maps and establish a Liouville type result.

Effects of Initial Defects on Effective Elastic Modulus of Concrete with Mesostructure

An exquisite mesostructure model was presented to predict the effective elastic modulus of concrete,in which concrete is realized as a four-phase composite material consisting of coarse aggregates,mortar matrix,interfacial transition zone(ITZ),and initial defects.With the three-dimensional(3D)finite element(FE)simulation,the highly heterogeneous composite elastic behavior of concrete was modeled,and the predicted results were compared with theoretical estimations for validation.Monte Carlo(MC)simulations were performed with the proposed mesostructure model to investigate the various factors of initial defects influencing the elastic modulus of concrete,such as the shape and concentration(pore volume fraction or crack density)of microspores and microcracks.It is found that the effective elastic modulus of concrete decreases with the increase of initial defects concentration,while the distribution and shape characteristics also exert certain influences due to the stress concentration caused by irregular inclusion shape.

Electronic structure and effective mass of pristine and Cl-doped CsPbBr_(3)

Organic–inorganic lead halide perovskites(LHPs) have attracted great interest owing to their outstanding optoelectronic properties.Typically,the underlying electronic structure would determinate the physical properties of materials.But as for now,limited studies have been done to reveal the underlying electronic structure of this material system,comparing to the huge amount of investigations on the material synthesis.The effective mass of the valance band is one of the most important physical parameters which plays a dominant role in charge transport and photovoltaic phenomena.In pristine CsPbBr_(3),the Fr?hlich polarons associated with the Pb–Br stretching modes are proposed to be responsible for the effective mass renormalization.In this regard,it would be very interesting to explore the electronic structure in doped LHPs.Here,we report high-resolution angle-resolved photoemission spectroscopy(ARPES) studies on both pristine and Cl-doped CsPbBr_(3).The experimental band dispersions are extracted from ARPES spectra along both ■ and ■ high symmetry directions.DFT calculations are performed and directly compared with the ARPES data.Our results have revealed the band structure of Cl-doped CsPbBr_(3) for the first time,which have also unveiled the effective mass renormalization in the Cl-doped CsPbBr_(3) compound.Doping dependent measurements indicate that the chlorine doping could moderately tune the renormalization strength.These results will help understand the physical properties of LHPs as a function of doping.

Models to Simulate Effective Coverage of Fire Station Based on Real-Time Travel Times

In recent years,frequent fire disasters have led to enormous damage in China.Effective firefighting rescues can minimize the losses caused by fires.During the rescue processes,the travel time of fire trucks can be severely affected by traffic conditions,changing the effective coverage of fire stations.However,it is still challenging to determine the effective coverage of fire stations considering dynamic traffic conditions.This paper addresses this issue by combining the traveling time calculationmodelwith the effective coverage simulationmodel.In addition,it proposes a new index of total effective coverage area(TECA)based on the time-weighted average of the effective coverage area(ECA)to evaluate the urban fire services.It also selects China as the case study to validate the feasibility of the models,a fire station(FS-JX)in Changsha.FS-JX station and its surrounding 9,117 fire risk points are selected as the fire service supply and demand points,respectively.A total of 196 simulation scenarios throughout a consecutiveweek are analyzed.Eventually,1,933,815 sets of valid sample data are obtained.The results showed that the TECA of FS-JX is 3.27 km^(2),which is far below the standard requirement of 7.00 km^(2) due to the traffic conditions.The visualization results showed that three rivers around FS-JX interrupt the continuity of its effective coverage.The proposed method can provide data support to optimize the locations of fire stations by accurately and dynamically determining the effective coverage of fire stations.

Effectively modulating spatial vortex four-wave mixing in a diamond atomic system

Due to the spatial characteristics of orbital angular momentum,vortex fields can be applied in the fields of quantum storage and quantum information.We study the realization of spatially modulated vortex fields based on four-wave mixing in a four-level atomic system with a diamond structure.The intensity and spiral phase of the vortex field are effectively transferred to the generated four-wave mixing field.By changing the detuning of the probe field,the phase and intensity of the generated vertex four-wave mixing field can be changed.When the probe field takes a large detuning value,the spatial distribution of the intensity and phase of the vertex four-wave mixing field can be effectively tuned by adjusting the Rabi frequency or detuning value of the coupled field.At the same time,we also provide a detailed explanation based on the dispersion relationship,and the results agree well with our simulation results.

Prevention and Control Strategies of Nosocomial Infection and Effectiveness Evaluation in a Tertiary Teaching Hospital during the Epidemic of COVID-19

Objective: To evaluate the role of prevention and control strategies for nosocomial infection in a tertiary teaching hospital during the sudden outbreak of Corona Virus Disease 2019 (COVID-19). Methods: The hospital initiated an emergency plan involving multi-departmental defense and control. It adopted a series of nosocomial infection prevention and control measures, including strengthening pre-examination and triage, optimizing the consultation process, improving the hospital’s architectural composition, implementing graded risk management, enhancing personal protection, and implementing staff training and supervision. Descriptive research was used to evaluate the short-term effects of these in-hospital prevention and control strategies. The analysis compared changes in related evaluation indicators between January 24, 2020 and February 12, 2020 (Chinese Lunar New Year’s Eve 2020 to lunar January 19) and the corresponding lunar period of the previous year. Results: Compared to the same period last year, the outpatient fever rate increased by 1.85-fold (P P Conclusion: The nosocomial infection prevention and control strategies implemented during this specific period improved the detection and control abilities for the COVID-19 source of infection and enhanced the compliance with measures. This likely contributed significantly to avoiding the occurrence of nosocomial infection.

The UNIFORM C^(0)ESTIMATE AND WEIGHTED ESTIMATE OF GENERALIZED CHRISTOFFEL-MINKOWSKI PROBLEMS

In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the weighted gradient estimate and uniform C^(0)estimate for the positive convex even solutions,which is a generalization of Guan-Xia[1]and Guan[2].