In this paper,we introduce the notion of G_(C)-X-injective modules,where X denotes a class of left S-modules and C represents a faithfully semidualizing bimodule.Under the condition that X satisfies certain hypotheses...In this paper,we introduce the notion of G_(C)-X-injective modules,where X denotes a class of left S-modules and C represents a faithfully semidualizing bimodule.Under the condition that X satisfies certain hypotheses,some properties and some equivalent characterizations of G_(C)-X-injective modules are investigated,and we also show that the triple(■,cores■,■)is a weak co-AB-context.As an application,two complete cotorsion pairs and a new model structure in Mod S are given.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
Weak measurement offers a powerful framework for probing nonclassical features of quantum mechanics,with anomalous weak values serving as operational signatures of contextuality.While the anomalous weak value verifica...Weak measurement offers a powerful framework for probing nonclassical features of quantum mechanics,with anomalous weak values serving as operational signatures of contextuality.While the anomalous weak value verification of quantum contextuality has been predominantly investigated in the single-photon regime and analyzed under approximation condition of infinitesimally small perturbation strength.This study releases the approximation condition and takes into account the impact of perturbation strength on the rigor of the verification.And the investigation on the verification of contextuality is extended to the multi-photon scenarios for observing the influence of the correlation between photons on the verification.Without the limitation of infinitesimally small probability of disturbance,anomalous weak values are identified as necessary for contextuality to emerge,thereby refining the criterion proposed by Pusey[Phys.Rev.Lett.113200401(2014)].In the multi-photon scenarios,the emergence of contextuality also depends strongly on both the photon number and the photon-number distribution state.In particular,contextuality is found to be maximized when the single-photon component dominates and the second-order correlation is lower.These results highlight the critical role of photon statistics in experimental tests of contextuality via anomalous weak values.展开更多
Objective:To investigate the impact of targeted nursing interventions based on frailty prediction models on peri-hospitalization clinical outcomes in middle-aged and elderly patients with upper gastrointestinal bleedi...Objective:To investigate the impact of targeted nursing interventions based on frailty prediction models on peri-hospitalization clinical outcomes in middle-aged and elderly patients with upper gastrointestinal bleeding(UGIB).Methods:A prospective cohort study was conducted,and 126 middle-aged and elderly patients with UGIB admitted from August 2024 to August 2025 were selected as the study subjects.The patients were divided into the intervention group(63 cases)and the control group(63 cases)based on whether they received nursing intervention based on frailty prediction models.The control group received routine care,while the intervention group,on the basis of routine care,used the FRAIL scale combined with laboratory indicators(albumin,hemoglobin,etc.)to establish a predictive model to evaluate patients within 24 hours of admission,and implemented multi-dimensional targeted nursing intervention for pre-frailty or frailty patients screened out.The incidence of frailty,rebleeding rate,average length of stay,hospitalization cost,and nursing satisfaction during hospitalization were compared between the two groups.Results:The incidence of frailty during hospitalization in the intervention group was 11.1%(7 cases/63 cases),significantly lower than 31.7%(20 cases/63 cases)in the control group,and the difference was statistically significant(p<0.05).The rebleeding rate of 4.8%vs 12.7%,the average length of stay of(7.2±1.5)days vs(9.1±2.2)days,and the average hospitalization cost of(23,000±6,000)yuan vs(28,000±7,000)yuan in the intervention group were all lower than those in the control group(all p<0.05).The nursing satisfaction score of the intervention group(93.5±4.2)points was higher than that of the control group(86.3±5.8)points(p<0.05).Conclusion:The frailty prediction model applied to the peri-hospitalization care of middle-aged and elderly patients with UGIB can effectively identify frailty risk.Through early targeted intervention,the incidence of frailty and rebleeding rate can be reduced,the length of hospital stay can be shortened,medical expenses can be reduced,and nursing satisfaction can be improved,which has clinical promotion value.展开更多
Weakly Supervised Semantic Segmentation(WSSS),which relies only on image-level labels,has attracted significant attention for its cost-effectiveness and scalability.Existing methods mainly enhance inter-class distinct...Weakly Supervised Semantic Segmentation(WSSS),which relies only on image-level labels,has attracted significant attention for its cost-effectiveness and scalability.Existing methods mainly enhance inter-class distinctions and employ data augmentation to mitigate semantic ambiguity and reduce spurious activations.However,they often neglect the complex contextual dependencies among image patches,resulting in incomplete local representations and limited segmentation accuracy.To address these issues,we propose the Context Patch Fusion with Class Token Enhancement(CPF-CTE)framework,which exploits contextual relations among patches to enrich feature repre-sentations and improve segmentation.At its core,the Contextual-Fusion Bidirectional Long Short-Term Memory(CF-BiLSTM)module captures spatial dependencies between patches and enables bidirectional information flow,yield-ing a more comprehensive understanding of spatial correlations.This strengthens feature learning and segmentation robustness.Moreover,we introduce learnable class tokens that dynamically encode and refine class-specific semantics,enhancing discriminative capability.By effectively integrating spatial and semantic cues,CPF-CTE produces richer and more accurate representations of image content.Extensive experiments on PASCAL VOC 2012 and MS COCO 2014 validate that CPF-CTE consistently surpasses prior WSSS methods.展开更多
Phosphatase and tensin homolog deleted on chromosome 10(PTEN)messenger RNA(mRNA)delivery has fueled a great hope for tumor immunotherapy via augmenting the immune sensitivity in many human cancers.However,therapeutic ...Phosphatase and tensin homolog deleted on chromosome 10(PTEN)messenger RNA(mRNA)delivery has fueled a great hope for tumor immunotherapy via augmenting the immune sensitivity in many human cancers.However,therapeutic efficacy and clinical translation are limited by inadequate mRNA expression,insufficient immune stimulation and stringent storage requirements.Herein,inspired by the intrinsic properties of metal ions and exosomes,we developed a biomimetic delivery system(Mn-NP@PM)with superior stability for precise colorectal cancer immunotherapy.This platform employs adjuvant-metal-ion chelation for PTEN mRNA loading and PD-L1 antibodies(αPD-L1)-modified monocyte-macrophage membrane coating for mRNA protection and tumor targeting.Mn^(2+) was specifically selected due to its capacity for reversible mRNA binding through weak non-electrostatic interactions,facilitating efficient release,while simultaneously activating the stimulator of interferon genes(STING)pathway.Importantly,Mn-NP@PM exhibited membrane fusion for immediate cytosolic mRNA delivery,bypassing endo-lysosomal escape,optimizing transportation efficiency.Clinical-data-driven analyses further demonstrated that Mn-NP@PM-mediated PTEN restoration significantly increased T-cell infiltration and strengthened antitumor immunity in humanized patient derived xenograft(PDX)models.Collectively,this biomimetic,metal-ion-chelating,membrane-coated mRNA delivery system represents a versatile and clinically translatable strategy for personalized cancer immunotherapy.展开更多
This paper addresses weak target detection problem for bistatic radar via a pseudo-spectrum(PS)based track-before-detect(TBD).Generally,PS-TBD estimates target position and velocity by means of pseudo-spectrum constru...This paper addresses weak target detection problem for bistatic radar via a pseudo-spectrum(PS)based track-before-detect(TBD).Generally,PS-TBD estimates target position and velocity by means of pseudo-spectrum construction in the discrete measurement space and accurate energy accumulation in mixed coordinates.However,the grids within the polar sensing region of the receivers in the bistatic radar are not aligned.Traditional PS-TBD can not directly process these measurements.In this paper,a PS-TBD method for bistatic radar is proposed to overcome this problem.Each cell in the measurement space of the receivers is mapped to the aligned Cartesian coordinates and predicted to the integration frame according to the assumed filter velocity.A PS is formulated centered on the predicted Cartesian position.Then the samples of the pseudo-spectra are accumulated to the nearest cell around the predicted Cartesian position.The procedure of the energy integration is derived in detail.Simulation results validate the efficacy of the proposed method in terms of detection accuracy and parameter estimation.展开更多
Autonomous navigation is a key technology for unmanned motion platforms to perform their tasks smoothly.The current approaches for daytime polarization navigation have been extensively researched.However,the polarizat...Autonomous navigation is a key technology for unmanned motion platforms to perform their tasks smoothly.The current approaches for daytime polarization navigation have been extensively researched.However,the polarization light intensity is the fundamental information within the polarization image,and the light intensity at night is 6-8 orders of magnitude lower than that during the day,which increase the noise and the loss of local polarization information due to occlusion,resulting in a significant decrease in the polarization orientation accuracy.Aimed at the problem,a bio-inspired model is introduced to denoise and enhance weak nighttime polarization patterns.Further,to address the issue of outlier interference in the occluded environment during practical application,a fast-fitting method of the solar meridian based on the anti-symmetric distribution of the polarization angle adjusted by Proportional and Differential(PD)control is proposed.The experimental results show that the method proposed in this paper achieves a dynamic orientation error Root Mean Square Error(RMSE)of 0.7°in the weak polarization mode at night and in the presence of local occlusion.The proposed method has strong robustness under weak polarization occlusion at night,and the orientation accuracy is improved by 97%and 80%in comparison to the least squares method,which provides a new method for polarization navigation at night.This effectively improves the robustness and environmental applicability of the bionic polarization compass for nighttime applications.展开更多
The photoacoustic imaging of lipid is intrinsically constrained by the feeble nature of endogenous lipid signals,posing a persistent sensitivity challenge that demands innovative solutions.Although adopting high-effic...The photoacoustic imaging of lipid is intrinsically constrained by the feeble nature of endogenous lipid signals,posing a persistent sensitivity challenge that demands innovative solutions.Although adopting high-efficiency excitation and detection elements may improve the imaging sensitivity to a certain extent,the application of the elements is inevitably subject to various limitations in practical applications,particularly during in vivo imaging and endoscopic imaging.In this study,we propose a multi-combinatorial approach to enhance the sensitivity of lipid photoacoustic imaging.The approach involves wavelet transform processing of one-dimensional A-line signals,gradient-based denoising of two-dimensional B-scan images,and finally,threedimensional spatial weighted averaging of the data processed by the previous two steps.This method not only significantly improves the signal-to-noise ratio(SNR)in distinguished feature regions of the image by around 10 dB,but also efficiently extracts weak signals with no distinct features in the original image.After processing with this method,the images acquired under single scanning were compared with those obtained under multiple scanning.The results showed highly consistent image features,with the structural similarity index increasing from 0.2 to 0.8,confirming the accuracy and reliability of the multi-combinatorial approach.展开更多
The weak and broken roof,explosive control and other problems seriously restrict the promotion of non coal pillar self-forming roadway technology.In order to solve such problems,a new method of non coal pillar self-fo...The weak and broken roof,explosive control and other problems seriously restrict the promotion of non coal pillar self-forming roadway technology.In order to solve such problems,a new method of non coal pillar self-forming roadway through non-blasting roof cutting and pressure relief was proposed in this study.A systematic research system of"theoretical analysis-physical experiment-engineering verification"was constructed with the 9103 working face of Longmenta Coal Mine as the research object.Firstly,the theoretical analysis was conducted to reveal the roof cutting mechanics mechanism of rock mass weakened by dense drilling,establish the design criteria for key drilling parameters,and obtain the key design parameters of dense drilling in the test working face.Secondly,the physical model test was conducted to make clear that the dense drilling method can directionally cut off the goaf roof along the set position,reducing the stress and deformation of the roadway surrounding rock.Finally,the field engineering tests were conducted,and monitoring results showed that the pressure relief effect of the dense drilling method was comparable to that of the directional blasting method,achieving non coal pillar self-forming roadway mining under non blasting conditions.展开更多
Weakly supervised semantic segmentation(WSSS)is a tricky task,which only provides category information for segmentation prediction.Thus,the key stage of WSSS is to generate the pseudo labels.For convolutional neural n...Weakly supervised semantic segmentation(WSSS)is a tricky task,which only provides category information for segmentation prediction.Thus,the key stage of WSSS is to generate the pseudo labels.For convolutional neural network(CNN)based methods,in which class activation mapping(CAM)is proposed to obtain the pseudo labels,and only concentrates on the most discriminative parts.Recently,transformer-based methods utilize attention map from the multi-headed self-attention(MHSA)module to predict pseudo labels,which usually contain obvious background noise and incoherent object area.To solve the above problems,we use the Conformer as our backbone,which is a parallel network based on convolutional neural network(CNN)and Transformer.The two branches generate pseudo labels and refine them independently,and can effectively combine the advantages of CNN and Transformer.However,the parallel structure is not close enough in the information communication.Thus,parallel structure can result in poor details about pseudo labels,and the background noise still exists.To alleviate this problem,we propose enhancing convolution CAM(ECCAM)model,which have three improved modules based on enhancing convolution,including deeper stem(DStem),convolutional feed-forward network(CFFN)and feature coupling unit with convolution(FCUConv).The ECCAM could make Conformer have tighter interaction between CNN and Transformer branches.After experimental verification,the improved modules we propose can help the network perceive more local information from images,making the final segmentation results more refined.Compared with similar architecture,our modules greatly improve the semantic segmentation performance and achieve70.2%mean intersection over union(mIoU)on the PASCAL VOC 2012 dataset.展开更多
Cascading failures pose a serious threat to the survivability of underwater unmanned swarm networks(UUSNs),significantly limiting their service ability in collaborative missions such as military reconnaissance and env...Cascading failures pose a serious threat to the survivability of underwater unmanned swarm networks(UUSNs),significantly limiting their service ability in collaborative missions such as military reconnaissance and environmental monitoring.Existing failure models primarily focus on power grids and traffic systems,and don't address the unique challenges of weak-communication UUSNs.In UUSNs,cascading failure present a complex and dynamic process driven by the coupling of unstable acoustic channels,passive node drift,adversarial attacks,and network heterogeneity.To address these challenges,a directed weighted graph model of UUSNs is first developed,in which node positions are updated according to ocean-current-driven drift and link weights reflect the probability of successful acoustic transmission.Building on this UUSNs graph model,a cascading failure model is proposed that integrates a normal-failure-recovery state-cycle mechanism,multiple attack strategies,and routingbased load redistribution.Finally,under a five-level connectivity UUSNs scheme,simulations are conducted to analyze how dynamic topology,network load,node recovery delay,and attack modes jointly affect network survivability.The main findings are:(1)moderate node drift can improve survivability by activating weak links;(2)based-energy routing(BER)outperform based-depth routing(BDR)in harsh conditions;(3)node self-recovery time is critical to network survivability;(4)traditional degree-based critical node metrics are inadequate for weak-communication UUSNs.These results provide a theoretical foundation for designing robust survivability mechanisms in weak-communication UUSNs.展开更多
This study proposes a class of augmented subspace schemes for the weak Galerkin(WG)finite element method used to solve eigenvalue problems.The augmented subspace is built with the conforming linear finite element spac...This study proposes a class of augmented subspace schemes for the weak Galerkin(WG)finite element method used to solve eigenvalue problems.The augmented subspace is built with the conforming linear finite element space defined on the coarse mesh and the eigen-function approximations in the WG finite element space defined on the fine mesh.Based on this augmented subspace,solving the eigenvalue problem in the fine WG finite element space can be reduced to the solution of the linear boundary value problem in the same WG finite element space and a low dimensional eigenvalue problem in the augmented sub-space.The proposed augmented subspace techniques have the second order convergence rate with respect to the coarse mesh size,as demonstrated by the accompanying error esti-mates.Finally,a few numerical examples are provided to validate the proposed numerical techniques.展开更多
In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitud...In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitudinal strong focusing(GLSF).At present,GLSF is the most promising method for realizing high-power short-wavelength coherent radiation with mild requirements on modulation laser power.Its essence is to exploit the ultrasmall natural vertical emittance of an electron beam in a planar storage ring for efficient microbunching formation,like a partial transverse-longitudinal emittance exchange in the optical laser wavelength range.Based on an in-depth investigation of related beam physics,a solution for a GLSF SSMB storage ring that can deliver 1 kW average-power EUV light is presented.The work in this paper,such as the generalized Courant–Snyder formalism,analysis of theoretical minimum emittances,transverse-longitudinal coupling dynamics,and derivation of the bunching factor and modulation strengths for laser-induced microbunching schemes,is expected to be useful not only for the development of SSMB but also for future accelerator light sources in general that demand increasingly precise electron beam phase space manipulations.展开更多
BACKGROUND: This study aimed to explore the risk factors associated with intensive care unitacquired weakness(ICU-AW) in critically ill patients at risk of malnutrition and to evaluate the efficacy of early enteral nu...BACKGROUND: This study aimed to explore the risk factors associated with intensive care unitacquired weakness(ICU-AW) in critically ill patients at risk of malnutrition and to evaluate the efficacy of early enteral nutrition(EEN) and the role of biomarkers in managing ICU-AW.METHODS: This retrospective, observational cohort study included 180 patients at risk of malnutrition admitted to the emergency intensive care unit of the First Affiliated Hospital of Xiamen University Hospital from January 2022 to December 2023. Patients were divided into ICU-AW group and non-ICU-AW group according to whether they developed ICU-AW, or categorized into EEN and parenteral nutrition(PN) groups according to nutritional support. ICU-AW was diagnosed using the Medical Research Council score. The primary outcome was the occurrence of ICU-AW.RESULTS: The significant factors associated with ICU-AW included age, sex, type of nutritional therapy, mechanical ventilation(MV), body mass index(BMI), blood urea nitrogen(BUN), and creatinine(Cr) levels(P<0.05). The PN group developed ICU-AW earlier than did the EEN group, with a significant difference observed(log-rank P<0.001). Among biomarkers for ICU-AW, the mean prealbumin(PAB)/C-reactive protein(CRP) ratio had the highest diagnostic accuracy(area under the curve [AUC] 0.928, 95% confidence interval [95% CI] 0.892–0.946), surpassing the mean Cr/BUN ratio(AUC 0.740, 95% CI 0.663–0.819) and mean transferrin levels(AUC 0.653, 95% CI 0.574–0.733).CONCLUSION: Independent risk factors for ICU-AW include female sex, advanced age, PN, MV, lower BMI, and elevated BUN and Cr levels. EEN may potentially delay ICU-AW onset, and the PAB/CRP ratio may be an effective diagnostic marker for this condition.展开更多
The potential of 2-amino-1-propanol(AP)as a novel depressant in selectively floating ilmenite from titanaugite under weakly acidic conditions was investigated.Micro-flotation results show that AP significantly reduces...The potential of 2-amino-1-propanol(AP)as a novel depressant in selectively floating ilmenite from titanaugite under weakly acidic conditions was investigated.Micro-flotation results show that AP significantly reduces the recovery of titanaugite while having no evident impact on ilmenite flotation.Subsequent bench-scale flotation tests further confirm a remarkable improvement in separation efficiency upon the introduction of AP.Contact angle and adsorption tests reveal a stronger affinity of AP towards the titanaugite surface in comparison to ilmenite.Zeta potential measurements and X-ray photoelectron spectroscopy(XPS)analyses exhibit favorable adsorption characteristics of AP on titanaugite,resulting from a synergy of electrostatic attraction and chemical interaction.In contrast,electrostatic repulsion hinders any significant interaction between AP and the ilmenite surface.These findings highlight the potential of AP as a highly efficient depressant for ilmenite flotation,paving the way for reduced reliance on sulfuric acid in the industry.展开更多
The phase-locked loop(PLL)plays an essential role for synchronizing renewable power generation to the grid.However,as per the grid-code compliance for reactive current support,the PLL output frequency fluctuates signi...The phase-locked loop(PLL)plays an essential role for synchronizing renewable power generation to the grid.However,as per the grid-code compliance for reactive current support,the PLL output frequency fluctuates significantly and exceeds the limitation,which seriously threaten the safe supply of electricity.In this paper,the underlying theoretical mechanism and dominant force behind the maximum PLL frequency deviation are revealed.Accordingly,two feasible approaches are proposed to enhance the PLL frequency stability with validations in experimental results.展开更多
Natural cemented calcareous sand and limestone are highly complex and not well understood in terms of the me-chanical behavior due to the difficulty of obtaining undisturbed samples from far sea.This paper proposes an...Natural cemented calcareous sand and limestone are highly complex and not well understood in terms of the me-chanical behavior due to the difficulty of obtaining undisturbed samples from far sea.This paper proposes an artificial method in a laboratory setting using microbial-induced carbonate precipitation(MICP)to simulate the natural process of cementation of limestone.The artificially cemented sand has a high degree of similarity with the natural weakly limestone in three aspects:(1)the mineral composition of the cemented material is also granular calcite and acicular aragonite;(2)the microstructure in interconnected open pore network can be gradually closed and contracted with cementation.The porosity reaches to approximately 9.2%;(3)both the stress-strain relationship and the unconfined strength closely resemble that of natural weakly limestone.Furthermore,both static and dynamic behaviors of artificial limestone were studied by quasi-static compression tests and Split Hopkinson Pressure Bar(SHPB)tests,finding that the unconfined strength of weakly artifical limestone exponentially increases with increasing strain rate.A rate-dependent bond strength was proposed and implemented in software to reveal the mechanism of strain rate effects.It is found that the loading velocity is too high to keep in sync with the initiation and propagation of cracks under impact loading.This delay-induced viscosity may restrict the movement of the surrounding balls,thus increasing resistance.展开更多
The Rh blood group system,especially the D antigen,is crucial in transfusion medicine and obstetrics.Weak D phenotypes,caused by mutations in the Rhesus D antigen(RhD)blood group(RHD)gene,result in reduced antigen exp...The Rh blood group system,especially the D antigen,is crucial in transfusion medicine and obstetrics.Weak D phenotypes,caused by mutations in the Rhesus D antigen(RhD)blood group(RHD)gene,result in reduced antigen expression,posing challenges in serological testing and clinical management.Variability in detection methods leads to inconsistent results,making accurate classification difficult.Molecular techniques like polymerase chain reaction and DNA sequencing have significantly improved the identification of weak D variants,offering more reliable transfusion strategies and reducing the risk of alloimmunization.However,challenges such as lack of standardized protocols,cost constraints,and population-specific variations remain.In obstetrics,proper management of pregnant women with weak D is essential to prevent hemolytic disease of the fetus and newborn.Non-invasive prenatal testing using cell-free fetal DNA shows promise in predicting RhD incompatibility and minimizing unnecessary Rh immune globulin administration.Future advancements in highthroughput genotyping and discovery of novel RHD alleles could enhance RhD testing accuracy and efficiency.Standardizing RHD genotyping and adopting genotype-based management strategies for Rh immune globulin therapy and red blood cell transfusions will improve patient safety and clinical outcomes.This review examines the molecular basis,challenges,and future prospects in weak D phenotype management.展开更多
本文主要考虑可压欧拉方程组的初边值问题。研究了两类具有高阶精度的熵稳定有限体积格式的收敛性,通过对数值解建立合适的一致性估计,证明随着步长 h → 0,若数值解的密度是远离真空且有界的,则由这两类熵稳定数值格式构造的解可以生...本文主要考虑可压欧拉方程组的初边值问题。研究了两类具有高阶精度的熵稳定有限体积格式的收敛性,通过对数值解建立合适的一致性估计,证明随着步长 h → 0,若数值解的密度是远离真空且有界的,则由这两类熵稳定数值格式构造的解可以生成耗散测度值解。In this paper, we primarily consider the initial boundary value problem for compress-ible Euler equations. We study the convergence of two classes of high-order accurate entropy stable finite volume schemes. By establishing appropriate the priori esti-mates for the numerical solutions, we prove that as the step size h → 0, the solutionsconstructed by these two types of entropy stable numerical schemes can generate dissipative measure-valued solutions, provided that the density of the approximate solutions is bounded away from vacuum and bounded above.展开更多
文摘In this paper,we introduce the notion of G_(C)-X-injective modules,where X denotes a class of left S-modules and C represents a faithfully semidualizing bimodule.Under the condition that X satisfies certain hypotheses,some properties and some equivalent characterizations of G_(C)-X-injective modules are investigated,and we also show that the triple(■,cores■,■)is a weak co-AB-context.As an application,two complete cotorsion pairs and a new model structure in Mod S are given.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金Project supported by the National Natural Science Foun-dation of China(Grant Nos.62371199 and 62071186)the Natural Science Foundation of Guangdong Province,China(Grant No.2024A1515012427)+1 种基金the Quantum Science Strate-gic Initiative Project of Guangdong Province,China(Grant No.GDZX2305001)the Key Laboratory Project of Guangdong Province,China(Grant No.2020B1212060066).
文摘Weak measurement offers a powerful framework for probing nonclassical features of quantum mechanics,with anomalous weak values serving as operational signatures of contextuality.While the anomalous weak value verification of quantum contextuality has been predominantly investigated in the single-photon regime and analyzed under approximation condition of infinitesimally small perturbation strength.This study releases the approximation condition and takes into account the impact of perturbation strength on the rigor of the verification.And the investigation on the verification of contextuality is extended to the multi-photon scenarios for observing the influence of the correlation between photons on the verification.Without the limitation of infinitesimally small probability of disturbance,anomalous weak values are identified as necessary for contextuality to emerge,thereby refining the criterion proposed by Pusey[Phys.Rev.Lett.113200401(2014)].In the multi-photon scenarios,the emergence of contextuality also depends strongly on both the photon number and the photon-number distribution state.In particular,contextuality is found to be maximized when the single-photon component dominates and the second-order correlation is lower.These results highlight the critical role of photon statistics in experimental tests of contextuality via anomalous weak values.
基金Construction and Application of Frailty Trajectory Prediction Model for Middle-aged and Elderly Patients with Upper Gastrointestinal Bleeding,Project Source:Sichuan Vocational College of Nursing(Project No.:2024ZRY25)。
文摘Objective:To investigate the impact of targeted nursing interventions based on frailty prediction models on peri-hospitalization clinical outcomes in middle-aged and elderly patients with upper gastrointestinal bleeding(UGIB).Methods:A prospective cohort study was conducted,and 126 middle-aged and elderly patients with UGIB admitted from August 2024 to August 2025 were selected as the study subjects.The patients were divided into the intervention group(63 cases)and the control group(63 cases)based on whether they received nursing intervention based on frailty prediction models.The control group received routine care,while the intervention group,on the basis of routine care,used the FRAIL scale combined with laboratory indicators(albumin,hemoglobin,etc.)to establish a predictive model to evaluate patients within 24 hours of admission,and implemented multi-dimensional targeted nursing intervention for pre-frailty or frailty patients screened out.The incidence of frailty,rebleeding rate,average length of stay,hospitalization cost,and nursing satisfaction during hospitalization were compared between the two groups.Results:The incidence of frailty during hospitalization in the intervention group was 11.1%(7 cases/63 cases),significantly lower than 31.7%(20 cases/63 cases)in the control group,and the difference was statistically significant(p<0.05).The rebleeding rate of 4.8%vs 12.7%,the average length of stay of(7.2±1.5)days vs(9.1±2.2)days,and the average hospitalization cost of(23,000±6,000)yuan vs(28,000±7,000)yuan in the intervention group were all lower than those in the control group(all p<0.05).The nursing satisfaction score of the intervention group(93.5±4.2)points was higher than that of the control group(86.3±5.8)points(p<0.05).Conclusion:The frailty prediction model applied to the peri-hospitalization care of middle-aged and elderly patients with UGIB can effectively identify frailty risk.Through early targeted intervention,the incidence of frailty and rebleeding rate can be reduced,the length of hospital stay can be shortened,medical expenses can be reduced,and nursing satisfaction can be improved,which has clinical promotion value.
文摘Weakly Supervised Semantic Segmentation(WSSS),which relies only on image-level labels,has attracted significant attention for its cost-effectiveness and scalability.Existing methods mainly enhance inter-class distinctions and employ data augmentation to mitigate semantic ambiguity and reduce spurious activations.However,they often neglect the complex contextual dependencies among image patches,resulting in incomplete local representations and limited segmentation accuracy.To address these issues,we propose the Context Patch Fusion with Class Token Enhancement(CPF-CTE)framework,which exploits contextual relations among patches to enrich feature repre-sentations and improve segmentation.At its core,the Contextual-Fusion Bidirectional Long Short-Term Memory(CF-BiLSTM)module captures spatial dependencies between patches and enables bidirectional information flow,yield-ing a more comprehensive understanding of spatial correlations.This strengthens feature learning and segmentation robustness.Moreover,we introduce learnable class tokens that dynamically encode and refine class-specific semantics,enhancing discriminative capability.By effectively integrating spatial and semantic cues,CPF-CTE produces richer and more accurate representations of image content.Extensive experiments on PASCAL VOC 2012 and MS COCO 2014 validate that CPF-CTE consistently surpasses prior WSSS methods.
基金supported by the Basic Science Center Project of the National Natural Science Foundation of China(22388101)New Cornerstone Science Foundation(NCI202318)+6 种基金the National Natural Science Foundation of China(32171398 and T242200557)the National Key R&D Program of China(2023YFA1610200 and 2022YFA1603701)Beijing Nova Program(20220484060,20230484426,and 20240484661)Beijing Natural Science Foundation(F251001)Chinese Academy of Sciences Project for Young Scientists in Basic Research(YSBR-036)the One Hundred Talents Program of Chinese Academy of Sciences(E3G551R1ZX)Chinese Academy of Medical Sciences(CAMS)and Innovation Fund for Medical Sciences(CIFMS2019-I2M-5-018).
文摘Phosphatase and tensin homolog deleted on chromosome 10(PTEN)messenger RNA(mRNA)delivery has fueled a great hope for tumor immunotherapy via augmenting the immune sensitivity in many human cancers.However,therapeutic efficacy and clinical translation are limited by inadequate mRNA expression,insufficient immune stimulation and stringent storage requirements.Herein,inspired by the intrinsic properties of metal ions and exosomes,we developed a biomimetic delivery system(Mn-NP@PM)with superior stability for precise colorectal cancer immunotherapy.This platform employs adjuvant-metal-ion chelation for PTEN mRNA loading and PD-L1 antibodies(αPD-L1)-modified monocyte-macrophage membrane coating for mRNA protection and tumor targeting.Mn^(2+) was specifically selected due to its capacity for reversible mRNA binding through weak non-electrostatic interactions,facilitating efficient release,while simultaneously activating the stimulator of interferon genes(STING)pathway.Importantly,Mn-NP@PM exhibited membrane fusion for immediate cytosolic mRNA delivery,bypassing endo-lysosomal escape,optimizing transportation efficiency.Clinical-data-driven analyses further demonstrated that Mn-NP@PM-mediated PTEN restoration significantly increased T-cell infiltration and strengthened antitumor immunity in humanized patient derived xenograft(PDX)models.Collectively,this biomimetic,metal-ion-chelating,membrane-coated mRNA delivery system represents a versatile and clinically translatable strategy for personalized cancer immunotherapy.
基金supported by the National Natural Science Foundation of China(62371155)the Heilongjiang Outstanding Youth Science Fund(JQ2022F002)。
文摘This paper addresses weak target detection problem for bistatic radar via a pseudo-spectrum(PS)based track-before-detect(TBD).Generally,PS-TBD estimates target position and velocity by means of pseudo-spectrum construction in the discrete measurement space and accurate energy accumulation in mixed coordinates.However,the grids within the polar sensing region of the receivers in the bistatic radar are not aligned.Traditional PS-TBD can not directly process these measurements.In this paper,a PS-TBD method for bistatic radar is proposed to overcome this problem.Each cell in the measurement space of the receivers is mapped to the aligned Cartesian coordinates and predicted to the integration frame according to the assumed filter velocity.A PS is formulated centered on the predicted Cartesian position.Then the samples of the pseudo-spectra are accumulated to the nearest cell around the predicted Cartesian position.The procedure of the energy integration is derived in detail.Simulation results validate the efficacy of the proposed method in terms of detection accuracy and parameter estimation.
基金co-supported by the Excellent Youth Foundation of Shanxi Province,China(No.202103021222011)the Key Research and Development project of Shanxi Province of China(No.202202020101002)+3 种基金the Fundamental Research Program of Shanxi Province of China(No.202303021211150)the Aviation Science Foundation of China(No.2022Z0220U0002)the Graduate Education Innovation Plan Project of Shanxi Province,China(No.2023KY588)the Shanxi Province Key Laboratory of Quantum Sensing and Precision Measurement,China(No.201905D121001).
文摘Autonomous navigation is a key technology for unmanned motion platforms to perform their tasks smoothly.The current approaches for daytime polarization navigation have been extensively researched.However,the polarization light intensity is the fundamental information within the polarization image,and the light intensity at night is 6-8 orders of magnitude lower than that during the day,which increase the noise and the loss of local polarization information due to occlusion,resulting in a significant decrease in the polarization orientation accuracy.Aimed at the problem,a bio-inspired model is introduced to denoise and enhance weak nighttime polarization patterns.Further,to address the issue of outlier interference in the occluded environment during practical application,a fast-fitting method of the solar meridian based on the anti-symmetric distribution of the polarization angle adjusted by Proportional and Differential(PD)control is proposed.The experimental results show that the method proposed in this paper achieves a dynamic orientation error Root Mean Square Error(RMSE)of 0.7°in the weak polarization mode at night and in the presence of local occlusion.The proposed method has strong robustness under weak polarization occlusion at night,and the orientation accuracy is improved by 97%and 80%in comparison to the least squares method,which provides a new method for polarization navigation at night.This effectively improves the robustness and environmental applicability of the bionic polarization compass for nighttime applications.
基金supported by the National Key Research and Development Program of China(2022YFC2402400)the National Natural Science Foundation of China(82027803,62275062)+7 种基金the Guangdong Provincial Key Laboratory of Biomedical Optical Imaging Technology(2020B121201010)the Shenzhen Science and Technology Innovation Committee under Grant(JCYJ20220818101417039)the Shenzhen Key Laboratory for Molecular lmaging(ZDSY20130401165820357)the Shenzhen Medical Research Fund(D2404002)the Project of Shandong Innovation and Startup Community of High-end Medical Apparatus and Instruments(2023-SGTTXM-002 and 2024-SGTTXM-005)the Shandong Province Technology Innovation Guidance Plan(Central Leading Local Science and Technology Development Fund)(YDZX2023115)the Taishan Scholar Special Funding Project of Shandong Provinceand the Shandong Laboratory of Advanced Biomaterials and Medical Devices in Weihai(ZL202402).
文摘The photoacoustic imaging of lipid is intrinsically constrained by the feeble nature of endogenous lipid signals,posing a persistent sensitivity challenge that demands innovative solutions.Although adopting high-efficiency excitation and detection elements may improve the imaging sensitivity to a certain extent,the application of the elements is inevitably subject to various limitations in practical applications,particularly during in vivo imaging and endoscopic imaging.In this study,we propose a multi-combinatorial approach to enhance the sensitivity of lipid photoacoustic imaging.The approach involves wavelet transform processing of one-dimensional A-line signals,gradient-based denoising of two-dimensional B-scan images,and finally,threedimensional spatial weighted averaging of the data processed by the previous two steps.This method not only significantly improves the signal-to-noise ratio(SNR)in distinguished feature regions of the image by around 10 dB,but also efficiently extracts weak signals with no distinct features in the original image.After processing with this method,the images acquired under single scanning were compared with those obtained under multiple scanning.The results showed highly consistent image features,with the structural similarity index increasing from 0.2 to 0.8,confirming the accuracy and reliability of the multi-combinatorial approach.
基金Project(2024YFC2909500)supported by the National Key Research and Development Program of ChinaProjects(42377148,52204164)supported by the National Natural Science Foundation of ChinaProject(2022XJSB03)supported by the Fundamental Research Funds for the Central Universities,China。
文摘The weak and broken roof,explosive control and other problems seriously restrict the promotion of non coal pillar self-forming roadway technology.In order to solve such problems,a new method of non coal pillar self-forming roadway through non-blasting roof cutting and pressure relief was proposed in this study.A systematic research system of"theoretical analysis-physical experiment-engineering verification"was constructed with the 9103 working face of Longmenta Coal Mine as the research object.Firstly,the theoretical analysis was conducted to reveal the roof cutting mechanics mechanism of rock mass weakened by dense drilling,establish the design criteria for key drilling parameters,and obtain the key design parameters of dense drilling in the test working face.Secondly,the physical model test was conducted to make clear that the dense drilling method can directionally cut off the goaf roof along the set position,reducing the stress and deformation of the roadway surrounding rock.Finally,the field engineering tests were conducted,and monitoring results showed that the pressure relief effect of the dense drilling method was comparable to that of the directional blasting method,achieving non coal pillar self-forming roadway mining under non blasting conditions.
文摘Weakly supervised semantic segmentation(WSSS)is a tricky task,which only provides category information for segmentation prediction.Thus,the key stage of WSSS is to generate the pseudo labels.For convolutional neural network(CNN)based methods,in which class activation mapping(CAM)is proposed to obtain the pseudo labels,and only concentrates on the most discriminative parts.Recently,transformer-based methods utilize attention map from the multi-headed self-attention(MHSA)module to predict pseudo labels,which usually contain obvious background noise and incoherent object area.To solve the above problems,we use the Conformer as our backbone,which is a parallel network based on convolutional neural network(CNN)and Transformer.The two branches generate pseudo labels and refine them independently,and can effectively combine the advantages of CNN and Transformer.However,the parallel structure is not close enough in the information communication.Thus,parallel structure can result in poor details about pseudo labels,and the background noise still exists.To alleviate this problem,we propose enhancing convolution CAM(ECCAM)model,which have three improved modules based on enhancing convolution,including deeper stem(DStem),convolutional feed-forward network(CFFN)and feature coupling unit with convolution(FCUConv).The ECCAM could make Conformer have tighter interaction between CNN and Transformer branches.After experimental verification,the improved modules we propose can help the network perceive more local information from images,making the final segmentation results more refined.Compared with similar architecture,our modules greatly improve the semantic segmentation performance and achieve70.2%mean intersection over union(mIoU)on the PASCAL VOC 2012 dataset.
基金supported in part by the National Natural Science Foundation of China(Key Program)under Grant No.62031021。
文摘Cascading failures pose a serious threat to the survivability of underwater unmanned swarm networks(UUSNs),significantly limiting their service ability in collaborative missions such as military reconnaissance and environmental monitoring.Existing failure models primarily focus on power grids and traffic systems,and don't address the unique challenges of weak-communication UUSNs.In UUSNs,cascading failure present a complex and dynamic process driven by the coupling of unstable acoustic channels,passive node drift,adversarial attacks,and network heterogeneity.To address these challenges,a directed weighted graph model of UUSNs is first developed,in which node positions are updated according to ocean-current-driven drift and link weights reflect the probability of successful acoustic transmission.Building on this UUSNs graph model,a cascading failure model is proposed that integrates a normal-failure-recovery state-cycle mechanism,multiple attack strategies,and routingbased load redistribution.Finally,under a five-level connectivity UUSNs scheme,simulations are conducted to analyze how dynamic topology,network load,node recovery delay,and attack modes jointly affect network survivability.The main findings are:(1)moderate node drift can improve survivability by activating weak links;(2)based-energy routing(BER)outperform based-depth routing(BDR)in harsh conditions;(3)node self-recovery time is critical to network survivability;(4)traditional degree-based critical node metrics are inadequate for weak-communication UUSNs.These results provide a theoretical foundation for designing robust survivability mechanisms in weak-communication UUSNs.
基金partly supported by the Beijing Natural Science Foundation(Grant No.Z200003)by the National Natural Science Foundation of China(Grant Nos.12331015,12301475,12301465)+1 种基金by the National Center for Mathematics and Interdisciplinary Science,Chinese Academy of Sciencesby the Research Foundation for the Beijing University of Technology New Faculty(Grant No.006000514122516).
文摘This study proposes a class of augmented subspace schemes for the weak Galerkin(WG)finite element method used to solve eigenvalue problems.The augmented subspace is built with the conforming linear finite element space defined on the coarse mesh and the eigen-function approximations in the WG finite element space defined on the fine mesh.Based on this augmented subspace,solving the eigenvalue problem in the fine WG finite element space can be reduced to the solution of the linear boundary value problem in the same WG finite element space and a low dimensional eigenvalue problem in the augmented sub-space.The proposed augmented subspace techniques have the second order convergence rate with respect to the coarse mesh size,as demonstrated by the accompanying error esti-mates.Finally,a few numerical examples are provided to validate the proposed numerical techniques.
基金supported by the National Key Research and Development Program of China(No.2022YFA1603401)National Natural Science Foundation of China(Nos.12035010 and 12342501)+1 种基金Beijing Outstanding Young Scientist Program(No.JWZQ20240101006)the Tsinghua University Dushi Program.
文摘In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitudinal strong focusing(GLSF).At present,GLSF is the most promising method for realizing high-power short-wavelength coherent radiation with mild requirements on modulation laser power.Its essence is to exploit the ultrasmall natural vertical emittance of an electron beam in a planar storage ring for efficient microbunching formation,like a partial transverse-longitudinal emittance exchange in the optical laser wavelength range.Based on an in-depth investigation of related beam physics,a solution for a GLSF SSMB storage ring that can deliver 1 kW average-power EUV light is presented.The work in this paper,such as the generalized Courant–Snyder formalism,analysis of theoretical minimum emittances,transverse-longitudinal coupling dynamics,and derivation of the bunching factor and modulation strengths for laser-induced microbunching schemes,is expected to be useful not only for the development of SSMB but also for future accelerator light sources in general that demand increasingly precise electron beam phase space manipulations.
文摘BACKGROUND: This study aimed to explore the risk factors associated with intensive care unitacquired weakness(ICU-AW) in critically ill patients at risk of malnutrition and to evaluate the efficacy of early enteral nutrition(EEN) and the role of biomarkers in managing ICU-AW.METHODS: This retrospective, observational cohort study included 180 patients at risk of malnutrition admitted to the emergency intensive care unit of the First Affiliated Hospital of Xiamen University Hospital from January 2022 to December 2023. Patients were divided into ICU-AW group and non-ICU-AW group according to whether they developed ICU-AW, or categorized into EEN and parenteral nutrition(PN) groups according to nutritional support. ICU-AW was diagnosed using the Medical Research Council score. The primary outcome was the occurrence of ICU-AW.RESULTS: The significant factors associated with ICU-AW included age, sex, type of nutritional therapy, mechanical ventilation(MV), body mass index(BMI), blood urea nitrogen(BUN), and creatinine(Cr) levels(P<0.05). The PN group developed ICU-AW earlier than did the EEN group, with a significant difference observed(log-rank P<0.001). Among biomarkers for ICU-AW, the mean prealbumin(PAB)/C-reactive protein(CRP) ratio had the highest diagnostic accuracy(area under the curve [AUC] 0.928, 95% confidence interval [95% CI] 0.892–0.946), surpassing the mean Cr/BUN ratio(AUC 0.740, 95% CI 0.663–0.819) and mean transferrin levels(AUC 0.653, 95% CI 0.574–0.733).CONCLUSION: Independent risk factors for ICU-AW include female sex, advanced age, PN, MV, lower BMI, and elevated BUN and Cr levels. EEN may potentially delay ICU-AW onset, and the PAB/CRP ratio may be an effective diagnostic marker for this condition.
基金supported by the National Key Research and Development Program of China(No.2019YFC1803501)the National Natural Science Foundation of China(No.52074357)+2 种基金the Natural Science Foundation of Hunan Province,China(No.2022JJ30713)the Vanadium Titanium Union Foundationthe Project of Technology Innovation Center for Comprehensive Utilization of Strategic Mineral Resources,Ministry of Natural Resources,China。
文摘The potential of 2-amino-1-propanol(AP)as a novel depressant in selectively floating ilmenite from titanaugite under weakly acidic conditions was investigated.Micro-flotation results show that AP significantly reduces the recovery of titanaugite while having no evident impact on ilmenite flotation.Subsequent bench-scale flotation tests further confirm a remarkable improvement in separation efficiency upon the introduction of AP.Contact angle and adsorption tests reveal a stronger affinity of AP towards the titanaugite surface in comparison to ilmenite.Zeta potential measurements and X-ray photoelectron spectroscopy(XPS)analyses exhibit favorable adsorption characteristics of AP on titanaugite,resulting from a synergy of electrostatic attraction and chemical interaction.In contrast,electrostatic repulsion hinders any significant interaction between AP and the ilmenite surface.These findings highlight the potential of AP as a highly efficient depressant for ilmenite flotation,paving the way for reduced reliance on sulfuric acid in the industry.
基金supported by the National Natural Science Foundation of China under Grant 52407069the Science and Technology Project of Zhejiang Province under Grant 2024C01254the China Postdoctoral Science Foundation under Grant 2024T170766 and 2024M762824。
文摘The phase-locked loop(PLL)plays an essential role for synchronizing renewable power generation to the grid.However,as per the grid-code compliance for reactive current support,the PLL output frequency fluctuates significantly and exceeds the limitation,which seriously threaten the safe supply of electricity.In this paper,the underlying theoretical mechanism and dominant force behind the maximum PLL frequency deviation are revealed.Accordingly,two feasible approaches are proposed to enhance the PLL frequency stability with validations in experimental results.
基金The authors would like to acknowledge the support of the National Natural Science Foundation of China(No.52279097,No.51779264)Blue and Green Project of Jiangsu Province.
文摘Natural cemented calcareous sand and limestone are highly complex and not well understood in terms of the me-chanical behavior due to the difficulty of obtaining undisturbed samples from far sea.This paper proposes an artificial method in a laboratory setting using microbial-induced carbonate precipitation(MICP)to simulate the natural process of cementation of limestone.The artificially cemented sand has a high degree of similarity with the natural weakly limestone in three aspects:(1)the mineral composition of the cemented material is also granular calcite and acicular aragonite;(2)the microstructure in interconnected open pore network can be gradually closed and contracted with cementation.The porosity reaches to approximately 9.2%;(3)both the stress-strain relationship and the unconfined strength closely resemble that of natural weakly limestone.Furthermore,both static and dynamic behaviors of artificial limestone were studied by quasi-static compression tests and Split Hopkinson Pressure Bar(SHPB)tests,finding that the unconfined strength of weakly artifical limestone exponentially increases with increasing strain rate.A rate-dependent bond strength was proposed and implemented in software to reveal the mechanism of strain rate effects.It is found that the loading velocity is too high to keep in sync with the initiation and propagation of cracks under impact loading.This delay-induced viscosity may restrict the movement of the surrounding balls,thus increasing resistance.
文摘The Rh blood group system,especially the D antigen,is crucial in transfusion medicine and obstetrics.Weak D phenotypes,caused by mutations in the Rhesus D antigen(RhD)blood group(RHD)gene,result in reduced antigen expression,posing challenges in serological testing and clinical management.Variability in detection methods leads to inconsistent results,making accurate classification difficult.Molecular techniques like polymerase chain reaction and DNA sequencing have significantly improved the identification of weak D variants,offering more reliable transfusion strategies and reducing the risk of alloimmunization.However,challenges such as lack of standardized protocols,cost constraints,and population-specific variations remain.In obstetrics,proper management of pregnant women with weak D is essential to prevent hemolytic disease of the fetus and newborn.Non-invasive prenatal testing using cell-free fetal DNA shows promise in predicting RhD incompatibility and minimizing unnecessary Rh immune globulin administration.Future advancements in highthroughput genotyping and discovery of novel RHD alleles could enhance RhD testing accuracy and efficiency.Standardizing RHD genotyping and adopting genotype-based management strategies for Rh immune globulin therapy and red blood cell transfusions will improve patient safety and clinical outcomes.This review examines the molecular basis,challenges,and future prospects in weak D phenotype management.
文摘本文主要考虑可压欧拉方程组的初边值问题。研究了两类具有高阶精度的熵稳定有限体积格式的收敛性,通过对数值解建立合适的一致性估计,证明随着步长 h → 0,若数值解的密度是远离真空且有界的,则由这两类熵稳定数值格式构造的解可以生成耗散测度值解。In this paper, we primarily consider the initial boundary value problem for compress-ible Euler equations. We study the convergence of two classes of high-order accurate entropy stable finite volume schemes. By establishing appropriate the priori esti-mates for the numerical solutions, we prove that as the step size h → 0, the solutionsconstructed by these two types of entropy stable numerical schemes can generate dissipative measure-valued solutions, provided that the density of the approximate solutions is bounded away from vacuum and bounded above.
