AIM:To compare relative peripheral refraction(RPR)in Chinese school children with different refractive errors using multispectral refraction topography(MRT).METHODS:A total of 713 eyes of primary school children[172 e...AIM:To compare relative peripheral refraction(RPR)in Chinese school children with different refractive errors using multispectral refraction topography(MRT).METHODS:A total of 713 eyes of primary school children[172 emmetropia(E),429 low myopia(LM),80 moderate myopia(MM),and 32 low hypermetropia(LH)]aged 10 to 13y were analyzed.RPRs were measured using MRT without mydriasis.MRT results showed RPR at 0-15°(RPR 0-15),15°-30°(RPR 15-30),and 30°-45°(RPR 30-45)annular in the inferior(RPR-I),superior(RPR-S),nasal(RPR-N),and temporal(RPR-T)quadrants.Spherical equivalent(SE)was detected and calculated using an autorefractor.RESULTS:There were significant differences of RPR 15-30 between groups MM[0.02(-0.12;0.18)]and LH[-0.13(-0.36;0.12)](P<0.05),MM and E[-0.06(-0.20;0.10)](P<0.05),and LM[-0.02(-0.15;0.15)]and E(P<0.05).There were also significant differences of RPR 30-45 between groups MM[0.45(0.18;0.74)]and E[0.29(-0.09;0.67)](P<0.05),and LM[0.44(0.14;0.76)]and E(P<0.001).RPR values increased from the hyperopic to medium myopic group in each annular.There were significant differences of RPR-S between groups MM[-0.02(-0.60;0.30)]and E[-0.44(-0.89;-0.04)](P<0.001),and LM[-0.28(-0.71;0.12)]and E(P<0.05).There were also significant differences of RPR-T between groups MM[0.37(0.21;0.78)]and LH[0.14(-0.52;0.50)](P<0.05),LM[0.41(0.06;0.84)]and LH(P<0.05),and LM and E[0.29(-0.10;0.68),P<0.05].A Spearman’s correlation analysis showed a negative correlation between RPR and SE in the 15°-30°(P=0.005),30°-45°(P<0.05)annular(P=0.002),superior(P<0.001),and temporal(P=0.001)quadrants.CONCLUSION:Without pupil dilation,values for RPR 15-30,30-45,RPR-S,and T shows significant differences between myopic eyes and emmetropia,and the differences are negatively correlated with SE.展开更多
Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic waves.However,most of them rely on the resonant structural components,and thus are...Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic waves.However,most of them rely on the resonant structural components,and thus are frequency-dependent and unchangeable.Here,we present a reconfigurable 2D mechanism-based metamaterial which possesses transformable and frequency-independent elastic properties.Based on the proposed mechanism-based metamaterial,interesting functionalities,such as ternarycoded elastic wave polarizer and programmable refraction,are demonstrated.Particularly,unique ternary-coded polarizers,with 1-trit polarization filtering and 2-trit polarization separating of longitudinal and transverse waves,are first achieved.Then,the strong anisotropy of the proposed metamaterial is harnessed to realize positive-negative bi-refraction,only-positive refraction,and only-negative refraction.Finally,the wave functions with detailed microstructures are numerically verified.展开更多
Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE...Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE source using refraction path is proposed.Firstly,the control equation of the refraction path is established according to the sensor coordinates and arrival times.Secondly,considering the influence of time-difference-of-arrival(TDOA)errors,the residual of the governing equation is calculated to estimate the equation weight.Thirdly,the refraction points in different directions are solved using Snell’s law and orthogonal constraints.Finally,the source coordinates are iteratively solved by weighted correction terms.The feasibility and accuracy of the proposed method are verified by pencil-lead breaking experiments.The simulation results show that the new method is almost unaffected by the refraction ratio,and always holds more stable and accurate positioning performance than the traditional method under different ratios and scales of TDOA outliers.展开更多
AIM:To investigate the differences in retinal refraction difference values(RDVs)of adult patients with myopic anisometropia compared with those without myopic anisometropia,and to investigate the relationship between ...AIM:To investigate the differences in retinal refraction difference values(RDVs)of adult patients with myopic anisometropia compared with those without myopic anisometropia,and to investigate the relationship between ocular biometric measurements and relative peripheral refraction.METHODS:This clinical observation study included 130 patients with myopia(-0.25 to-10.00 D)between October 2022 and January 2023 aged between 18 and 40y.The patients were divided into anisometropia(n=63;difference in binocular anisometropia≥1.00 D)and non-anisometropia(n=67;difference in binocular anisometropia<1.00 D)groups accordingly.Ocular biometric measurements were performed by optical biometrics and corneal topography to assess the steep keratometry(Ks),flap keratometry(Kf),axial length(AL),corneal astigmatism(CYL;Ks-Kf),surface regularity index(SRI),surface asymmetry index(SAI),and central corneal thickness(CCT).The RDV was measured at five retinal areas from the fovea to 53 degrees(RDV-0-10,RDV-10-20,RDV-20-30,RDV-30-40,and RDV-40-53),the total RDV(TRDV)of 53 degrees,and four regions,including RDV-superior,RDV-inferior,RDV-temporal,and RDV-nasal.An analysis of Spearman correlation was carried out to examine the correlation between RDV and the spherical equivalent(SE)and ocular biological parameters.RESULTS:Within RDV-20-53,both groups showed relative hyperopic defocus,and the increase in RDV corresponds to the increase in eccentricity.In the myopic anisometropia group,the TRDV,RDV-20-53,RDV-superior,and more myopic eyes had significantly higher RDVtemporal values than less myopic eyes.(P<0.05).In the non-anisometropia group,there was no significant difference in the RDV between the more and less myopic eyes at different eccentricities(P>0.05).There was a negative correlation between SE and TRDV(r=-0.205,P=0.001),RDV-20-53(r=-0.281,-0.183,-0.176,P<0.05),RDV-superior(r=-0.251,P<0.001),and RDV-temporal(r=-0.230,P<0.001),a negative correlation between CYL and RDV-10-30(r=-0.147,-0.180,P<0.05),and a negative correlation between SRI and RDV-0-20(r=-0.190,-0.170,P<0.05).AL had a positive correlation with RDV-20-30(r=0.164,P=0.008)and RDV-temporal(r=0.160,P=0.010).CONCLUSION:More myopic eyes in patients with myopic anisometropia show more peripheral hyperopic defocus.Diopter and corneal morphology may affect peripheral retinal defocus.展开更多
AIM:To investigate the prevalence of visual impairment(VI)and provide an estimation of uncorrected refractive errors in school-aged children,conducted by optometry students as a community service.METHODS:The study was...AIM:To investigate the prevalence of visual impairment(VI)and provide an estimation of uncorrected refractive errors in school-aged children,conducted by optometry students as a community service.METHODS:The study was cross-sectional.Totally 3343 participants were included in the study.The initial examination involved assessing the uncorrected distance visual acuity(UDVA)and visual acuity(VA)while using a+2.00 D lens.The inclusion criteria for a subsequent comprehensive cycloplegic eye examination,performed by an optometrist,were as follows:a UDVA<0.6 decimal(0.20 logMAR)and/or a VA with+2.00 D≥0.8 decimal(0.96 logMAR).RESULTS:The sample had a mean age of 10.92±2.13y(range 4 to 17y),and 51.3%of the children were female(n=1715).The majority of the children(89.7%)fell within the age range of 8 to 14y.Among the ethnic groups,the highest representation was from the Luhya group(60.6%)followed by Luo(20.4%).Mean logMAR UDVA choosing the best eye for each student was 0.29±0.17(range 1.70 to 0.22).Out of the total,246 participants(7.4%)had a full eye examination.The estimated prevalence of myopia(defined as spherical equivalent≤-0.5 D)was found to be 1.45%of the total sample.While around 0.18%of the total sample had hyperopia value exceeding+1.75 D.Refractive astigmatism(cil<-0.75 D)was found in 0.21%(7/3343)of the children.The VI prevalence was 1.26%of the total sample.Among our cases of VI,76.2%could be attributed to uncorrected refractive error.Amblyopia was detected in 0.66%(22/3343)of the screened children.There was no statistically significant correlation observed between age or gender and refractive values.CONCLUSION:The primary cause of VI is determined to be uncorrected refractive errors,with myopia being the most prevalent refractive error observed.These findings underscore the significance of early identification and correction of refractive errors in school-aged children as a means to alleviate the impact of VI.展开更多
We demonstrate a method to realize unidirectional negative refraction in an acoustic parity-time(P T)-symmetric system, which is composed of a pair of metasurfaces sandwiching an air gap. The pair of metasurfaces poss...We demonstrate a method to realize unidirectional negative refraction in an acoustic parity-time(P T)-symmetric system, which is composed of a pair of metasurfaces sandwiching an air gap. The pair of metasurfaces possesses loss and gain modulations. The unidirectional negative refraction, which is strictly limited to the case of incident wave imposing on the loss end of the metasurface, is demonstrated at the exception point(EP) in this P T-symmetric system, while the incidence from the other side leads to strong reflection. Based on rigorous calculations, we explicitly show the underlying mechanism of this model to achieve unidirectional wave scatterings around the EP in the parametric space. In addition, the perfect imaging of a point source in the three-dimensional space, as a signature of negative refraction, is simulated to provide a verification of our work. We envision that this work may sharpen the understanding of P T-symmetric structures and inspire more acoustic functional devices.展开更多
AIM:To compare the subjective refraction data with non-cycloplegic auto-refraction findings in the geriatric population above 60 years of age according to the different crystalline lens conditions.METHODS:This report ...AIM:To compare the subjective refraction data with non-cycloplegic auto-refraction findings in the geriatric population above 60 years of age according to the different crystalline lens conditions.METHODS:This report is a part of the Tehran Geriatric Eye Study(TGES)that was conducted from January 2019 to January 2020 on elderly population 60 years of age and above in Tehran.The samples were selected by multistage stratified random cluster sampling.Of 3791 individual invitees,3310(response rate:87.3%)participated in this study.All study participants underwent non-cycloplegic autorefraction(auto-refractometer/keratometer Nidek ARK-510)and subjective refraction.RESULTS:Regarding the sphere,eyes with mixed cataract had the worst limits of agreement(LoA:-1.24 to 0.87)and the best agreement was related to the pseudophakic eyes(LoA:-0.83 to 0.54).The highest(0.27±0.31 D)and lowest(0.21±0.27 D)differences between the two methods regarding the cylinder power were observed in eyes with cortical cataract and normal eyes,respectively.The worst LoA between the two methods in measuring the cylinder power was related to the eyes with mixed cataract(LoA:-0.44 to 0.96).Regarding the J0(horizontal/vertical components of astigmatism),the mean values of J0 obtained by auto-refraction were tended more toward against the rule direction in all crystalline lens conditions,and the two methods had the greatest difference in cortical cataract cases(0.05±0.17 D).Regarding the J45(oblique components of astigmatism),the lowest(0±0.11 D)and highest(-0.01±0.12 D)differences were observed in normal eyes and eyes with cortical cataract,respectively.CONCLUSION:The auto-refractometer/keratometer Nidek ARK-510 results in the elderly with different phakic and pseudophakic conditions do not correspond well with subjective refraction findings.This discrepancy in spherical findings is more pronounced in individuals with mixed cataract than in other cases.展开更多
We investigate the electromagnetic properties of a four-level dense atomic gas medium with Doppler effect.It is shown that the relative permittivity and relative permeability of the medium can be negative simultaneous...We investigate the electromagnetic properties of a four-level dense atomic gas medium with Doppler effect.It is shown that the relative permittivity and relative permeability of the medium can be negative simultaneously with low absorption in the same detuning interval on account of electromagnetically induced transparency.Furthermore,with the suitable parameters,the nonreciprocal negative refraction can be obtained due to the Doppler effect,and the nonreciprocity frequency band can be regulated by adjusting the temperature,the intensity of the control field and the atomic density in this hot atomic medium.展开更多
Today’s forensic science introduces a new research area for digital image analysis formultimedia security.So,Image authentication issues have been raised due to the wide use of image manipulation software to obtain a...Today’s forensic science introduces a new research area for digital image analysis formultimedia security.So,Image authentication issues have been raised due to the wide use of image manipulation software to obtain an illegitimate benefit or createmisleading publicity by using tempered images.Exiting forgery detectionmethods can classify only one of the most widely used Copy-Move and splicing forgeries.However,an image can contain one or more types of forgeries.This study has proposed a hybridmethod for classifying Copy-Move and splicing images using texture information of images in the spatial domain.Firstly,images are divided into equal blocks to get scale-invariant features.Weber law has been used for getting texture features,and finally,XGBOOST is used to classify both Copy-Move and splicing forgery.The proposed method classified three types of forgeries,i.e.,splicing,Copy-Move,and healthy.Benchmarked(CASIA 2.0,MICCF200)and RCMFD datasets are used for training and testing.On average,the proposed method achieved 97.3% accuracy on benchmarked datasets and 98.3% on RCMFD datasets by applying 10-fold cross-validation,which is far better than existing methods.展开更多
Introduction: Undetected refractive errors constitute a health problem among school children who cannot take advantage of educational opportunities. The authors studied the prevalence of refractive errors in school ch...Introduction: Undetected refractive errors constitute a health problem among school children who cannot take advantage of educational opportunities. The authors studied the prevalence of refractive errors in school children aged 5 to 15 at CHU-IOTA. Patients and Method: This is a prospective, descriptive cross-sectional study carried out in the ophthalmic-pediatrics department of CHU-IOTA, from October to November 2023. Results: We received 340 school children aged 5 to 15, among whom 111 presented ametropia, i.e. a prevalence of 32.65%. The average age was 11.42 ± 2.75 years and a sex ratio of 0.59. The average visual acuity was 4/10 (range 1/10 and 10/10). We found refractive defects: astigmatism 73.87%, hyperopia 23.87% of cases and myopia 2.25%. The decline in distance visual acuity was the most common functional sign. Ocular abnormalities associated with ametropia were dominated by allergic conjunctivitis (26.13%) and papillary excavation (6.31%) in astigmatics;allergic conjunctivitis (9.01%) and papillary excavation (7.20%) in hyperopic patients;turbid vitreous (0.90%), myopic choroidosis (0.45%) and allergic conjunctivitis (0.45%) in myopes. Conclusion: Refractive errors constitute a reality and a major public health problem among school children.展开更多
Transparent photoresists with a high refractive index(RI)and high transmittance in visible wavelengths have promising functionalities in optical fields.This work reports a kind of tunable optical material composed of ...Transparent photoresists with a high refractive index(RI)and high transmittance in visible wavelengths have promising functionalities in optical fields.This work reports a kind of tunable optical material composed of titanium dioxide nanoparticles embedded in acrylic resin with a high RI for ultraviolet(UV)-imprint lithography.The hybrid film exhibits a tunable RI of up to 1.67(589 nm)after being cured by UV light,while maintaining both a high transparency of over 98%in the visible light range and a low haze of less than 0.05%.The precision machining of optical microstructures can be imprinted easily and efficiently using the hybrid resin,which acts as a light guide plate(LGP)to guide the light from the side to the top in order to conserve the energy of the display device.These preliminary studies based on both laboratory and commercial experiments pave the way for exploiting the unparalleled optical properties of nanocomposite resins and promoting their industrial application.展开更多
AIM:To compare the consistency of two autorefractors(Tianle RM-9000 and Topcon KR-800)for school-age myopia children,and to provide a basis for largescale data analysis and comparison.METHODS:The refractive error in 9...AIM:To compare the consistency of two autorefractors(Tianle RM-9000 and Topcon KR-800)for school-age myopia children,and to provide a basis for largescale data analysis and comparison.METHODS:The refractive error in 909 subjects(age 4–18y)were measured using both autorefractors without cycloplegia.The data were analyzed using Fourier decomposition and the correlation coefficients,intraclass correlation coefficients(ICC),and Bland-Altman limits of agreement(LoA)for each parameter were calculated.RESULTS:There was a strong correlation between the spherical equivalent(SE),sphere diopter(DS),and cylinder diopter(DC)readings of the Tianle RM-9000 and those of the Topcon KR-800,with correlation coefficient values of 0.98,0.98 and 0.83 and ICC values of 0.99,0.99 and 0.93,respectively.However,the correlation coefficients and ICC values of J0 and J45 were unreliable(R=-0.004,-0.034;both ICC<0.10).Bland-Altman analysis revealed that SE,DS,and DC measured by the Tianle RM-9000 were significantly biased toward myopia compared with the Topcon KR-800,and the mean differences were-0.072,-0.026,-0.091 D,respectively(all P<0.01).The minimum absolute value of the difference within the 95%LoA for SE,DS,and DC was 0.63 D,0.50 D,0.62 D,respectively;all these values were in the clinically acceptable range.For J0 and J45,the mean differences were close to zero(P=0.43,0.84);however,the 95%LoA were relatively wide(J0 SD:0.53;95%CI:-1.00,1.10;J45 SD:0.52;95%CI:-1.00,1.00).CONCLUSION:The two autorefractors are consistent with each other,as the differences in SE,DS,and DC were within the clinically acceptable range.Readers can compare the data measured by either device in different studies and use the two devices in the same study to generate a dataset that can be analyzed together.However,the J0 and J45 vectors are unreliable and should not be used to assess astigmatism.展开更多
Metal-based surface plasmon resonance(SPR)plays an important role in enhancing the photonic spin Hall effect(SHE)and developing sensitive optical sensors.However,the very large negative permittivities of metals limit ...Metal-based surface plasmon resonance(SPR)plays an important role in enhancing the photonic spin Hall effect(SHE)and developing sensitive optical sensors.However,the very large negative permittivities of metals limit their applications beyond the near-infrared regime.In this work,we theoretically present a new mechanism to enhance the photonic SHE by taking advantage of SiC-supported surface phonon resonance(SPhR)in the mid-infrared regime.The transverse displacement of photonic SHE is very sensitive to the wavelength of incident light and the thickness of SiC layer.Under the optimal parameter setup,the calculated largest transverse displacement of SiC-based SPhR structure reaches up to 163.8 ym,which is much larger than the condition of SPR.Moreover,an NO_(2) gas sensor based on the SPhR-enhanced photonic SHE is theoretically proposed with the superior sensing performance.Both the intensity and angle sensitivity of this sensor can be effectively manipulated by varying the damping rate of SiC.The results may provide a promising paradigm to enhance the photonic SHE in the mid-infrared region and open up new opportunity of highly sensitive refractive index sensors.展开更多
In this article,a series of high refractive indices(1.50-1.53)thiol phenyl polysiloxane(TPS)were synthesized via hydrolytic sol-gel reaction.The Fourier transform infrared spectra(FT-IR)and nuclear magnetic resonance ...In this article,a series of high refractive indices(1.50-1.53)thiol phenyl polysiloxane(TPS)were synthesized via hydrolytic sol-gel reaction.The Fourier transform infrared spectra(FT-IR)and nuclear magnetic resonance spectra(NMR)results showed that TPS conformed to the predicted structures.Natural terpene linalool was exploited as photocrosslinker to fabricate UV-curing linalool-polysiloxane hybrid films(LPH)with TPS via photoinitiated thiol-ene reaction.LPH rapidly cured under UV irradiation at the intensity of 80 mW/cm^(2) in 30 s,exhibiting good UV-curing properties.The optical transmittance of LPH in the wavelength of 300-800 nm was over 90%,exhibiting good optical transparency.The water contact angle and water vapor permeability results showed that the introduction of phenyl groups enhance the hydrophobicity and water vapor barrier properties of LPH.The results indicated the potential of LPHs in the applications of optical functional coatings.展开更多
An unstably stratified flow entering into a stably stratified flow is referred to as penetrative convection,which is crucial to many physical processes and has been thought of as a key factor for extreme weather condi...An unstably stratified flow entering into a stably stratified flow is referred to as penetrative convection,which is crucial to many physical processes and has been thought of as a key factor for extreme weather conditions.Past theoretical,numerical,and experimental studies on penetrative convection are reviewed,along with field studies providing insights into turbulence modeling.The physical factors that initiate penetrative convection,including internal heat sources,nonlinear constitutive relationships,centrifugal forces and other complicated factors are summarized.Cutting-edge methods for understanding transport mechanisms and statistical properties of penetrative turbulence are also documented,e.g.,the variational approach and quasilinear approach,which derive scaling laws embedded in penetrative turbulence.Exploring these scaling laws in penetrative convection can improve our understanding of large-scale geophysical and astrophysical motions.To better the model of penetrative turbulence towards a practical situation,new directions,e.g.,penetrative convection in spheres,and radiation-forced convection,are proposed.展开更多
Introduction: WHO estimated that uncorrected refractive errors are the leading cause of visual impairment and second leading cause of blindness globally. University students are prone to developing refractive errors d...Introduction: WHO estimated that uncorrected refractive errors are the leading cause of visual impairment and second leading cause of blindness globally. University students are prone to developing refractive errors due to their curriculum that requires a lot of near work affecting their performance and quality of life unknowingly. Genetic and environmental factors are thought to play a role in the development of refractive errors. This study addresses the paucity of knowledge about refractive errors among university students in East Africa, providing a foundation for further research. Objectives: To determine the prevalence and factors associated with refractive errors among students in the Faculty of Medicine at Mbarara University of Science and Technology. Methodology: This was a cross-sectional descriptive and analytical study in which 368 undergraduate students selected using random sampling were assessed for refractive errors from March 2021-July 2021. Eligible participants were recruited and their VA assessment done after answering a questionnaire. Students whose VA improved on pin hole had subjective retinoscopy and results were compiled and imported to STATA 14 for analysis. Results: The prevalence of refractive errors was 26.36% with (95% CI) among university students especially myopia. Myopia is most predominant at 60%, followed by 37% Astigmatism and hyperopia of 3% among medical students. Astigmatism consisted of largely myopic astigmatism 72% (26) and 28% (10) compound/mixed astigmatism only. Student positive family history of refractive error was found to have a statistically significant relationship with refractive errors with AOR 1.68 (1.04 - 2.72) (95% CI) and P (0.032). Conclusion: The prevalence of refractive errors among university students, especially myopia, was found to be high and family history was associated with students having refractive errors.展开更多
AIM:To compare relative peripheral refractive errors(RPREs)in Chinese children with and without myopic anisometropia(MAI)and to explore the relationship between RPRE and myopia.METHODS:This observational cross-section...AIM:To compare relative peripheral refractive errors(RPREs)in Chinese children with and without myopic anisometropia(MAI)and to explore the relationship between RPRE and myopia.METHODS:This observational cross-sectional study included 160 children divided into two groups according to the interocular spherical equivalent refraction(SER)difference≥1.0 D in the MAI group(n=80)and<1.0 D in the non-MAI group(n=80).The MAI group was further divided into two subgroups:ΔSER<2.0 D group and ΔSER≥2.0 D group.Basic ocular biometric parameters of axial length(AL),average keratometry(Ave K),cylinder(CYL),surface regularity index(SRI),and surface asymmetry index(SAI)were recorded.In addition,multispectral refraction topography was performed to measure RPRE,and the parameters were recorded as total refraction difference value(TRDV),refraction difference value(RDV)0-10,RDV10-20,RDV20-30,RDV30-40,RDV40-53,RDV-superior(RDV-S),RDV-inferior(RDV-I),RDV-temporal(RDV-T)and RDV-nasal(RDV-N).RESULTS:In the non-MAI group,the interocular differences of all parameters of RPRE were not significant.In the MAI group,the interocular differences of TRDV,RDV10-53,RDV-S,RDV-I,RDV-T,and RDV-N were significant.In subgroup analysis,the interocular differences of TRDV,RDV30-53,RDV-I,and RDV-T were significant in ΔSER<2.0 D group and ΔSER≥2.0 D group,but the interocular differences of RDV10-30,RDV-S and RDV-N were only significant in the ΔSER≥2.0 D group.In correlation analysis,ΔTRDV,ΔRDV 10-53,ΔRDV-S,and ΔRDV-N were negatively correlated with ΔSER but positively correlated with ΔAL.CONCLUSION:The more myopic eyes have larger hyperopic RPRE in Chinese children with MAI in certain retinal range,and partialΔRPRE is closely associated with ΔSER and ΔAL.展开更多
In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results a...In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results apply to all nonlinear scalar conservation laws and to nonlinear hyperbolic systems of two equations.展开更多
In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linea...In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.展开更多
基金Supported by the Shenzhen Science and Technology Program (No.JCYJ20210324142800001).
文摘AIM:To compare relative peripheral refraction(RPR)in Chinese school children with different refractive errors using multispectral refraction topography(MRT).METHODS:A total of 713 eyes of primary school children[172 emmetropia(E),429 low myopia(LM),80 moderate myopia(MM),and 32 low hypermetropia(LH)]aged 10 to 13y were analyzed.RPRs were measured using MRT without mydriasis.MRT results showed RPR at 0-15°(RPR 0-15),15°-30°(RPR 15-30),and 30°-45°(RPR 30-45)annular in the inferior(RPR-I),superior(RPR-S),nasal(RPR-N),and temporal(RPR-T)quadrants.Spherical equivalent(SE)was detected and calculated using an autorefractor.RESULTS:There were significant differences of RPR 15-30 between groups MM[0.02(-0.12;0.18)]and LH[-0.13(-0.36;0.12)](P<0.05),MM and E[-0.06(-0.20;0.10)](P<0.05),and LM[-0.02(-0.15;0.15)]and E(P<0.05).There were also significant differences of RPR 30-45 between groups MM[0.45(0.18;0.74)]and E[0.29(-0.09;0.67)](P<0.05),and LM[0.44(0.14;0.76)]and E(P<0.001).RPR values increased from the hyperopic to medium myopic group in each annular.There were significant differences of RPR-S between groups MM[-0.02(-0.60;0.30)]and E[-0.44(-0.89;-0.04)](P<0.001),and LM[-0.28(-0.71;0.12)]and E(P<0.05).There were also significant differences of RPR-T between groups MM[0.37(0.21;0.78)]and LH[0.14(-0.52;0.50)](P<0.05),LM[0.41(0.06;0.84)]and LH(P<0.05),and LM and E[0.29(-0.10;0.68),P<0.05].A Spearman’s correlation analysis showed a negative correlation between RPR and SE in the 15°-30°(P=0.005),30°-45°(P<0.05)annular(P=0.002),superior(P<0.001),and temporal(P=0.001)quadrants.CONCLUSION:Without pupil dilation,values for RPR 15-30,30-45,RPR-S,and T shows significant differences between myopic eyes and emmetropia,and the differences are negatively correlated with SE.
基金supported by the National Key R&D Program of China(No.2021YFE0110900)the National Natural Science Foundation of China(Nos.U22B2078 and 11991033)。
文摘Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic waves.However,most of them rely on the resonant structural components,and thus are frequency-dependent and unchangeable.Here,we present a reconfigurable 2D mechanism-based metamaterial which possesses transformable and frequency-independent elastic properties.Based on the proposed mechanism-based metamaterial,interesting functionalities,such as ternarycoded elastic wave polarizer and programmable refraction,are demonstrated.Particularly,unique ternary-coded polarizers,with 1-trit polarization filtering and 2-trit polarization separating of longitudinal and transverse waves,are first achieved.Then,the strong anisotropy of the proposed metamaterial is harnessed to realize positive-negative bi-refraction,only-positive refraction,and only-negative refraction.Finally,the wave functions with detailed microstructures are numerically verified.
基金the National Natural Science Foundation of China (Nos.52304123 and 52104077)the Postdoctoral Fellowship Program of CPSF (No.GZB20230914)+1 种基金the China Postdoctoral Science Foundation (No.2023M730412)the National Key Research and Development Program for Young Scientists (No.2021YFC2900400)。
文摘Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE source using refraction path is proposed.Firstly,the control equation of the refraction path is established according to the sensor coordinates and arrival times.Secondly,considering the influence of time-difference-of-arrival(TDOA)errors,the residual of the governing equation is calculated to estimate the equation weight.Thirdly,the refraction points in different directions are solved using Snell’s law and orthogonal constraints.Finally,the source coordinates are iteratively solved by weighted correction terms.The feasibility and accuracy of the proposed method are verified by pencil-lead breaking experiments.The simulation results show that the new method is almost unaffected by the refraction ratio,and always holds more stable and accurate positioning performance than the traditional method under different ratios and scales of TDOA outliers.
文摘AIM:To investigate the differences in retinal refraction difference values(RDVs)of adult patients with myopic anisometropia compared with those without myopic anisometropia,and to investigate the relationship between ocular biometric measurements and relative peripheral refraction.METHODS:This clinical observation study included 130 patients with myopia(-0.25 to-10.00 D)between October 2022 and January 2023 aged between 18 and 40y.The patients were divided into anisometropia(n=63;difference in binocular anisometropia≥1.00 D)and non-anisometropia(n=67;difference in binocular anisometropia<1.00 D)groups accordingly.Ocular biometric measurements were performed by optical biometrics and corneal topography to assess the steep keratometry(Ks),flap keratometry(Kf),axial length(AL),corneal astigmatism(CYL;Ks-Kf),surface regularity index(SRI),surface asymmetry index(SAI),and central corneal thickness(CCT).The RDV was measured at five retinal areas from the fovea to 53 degrees(RDV-0-10,RDV-10-20,RDV-20-30,RDV-30-40,and RDV-40-53),the total RDV(TRDV)of 53 degrees,and four regions,including RDV-superior,RDV-inferior,RDV-temporal,and RDV-nasal.An analysis of Spearman correlation was carried out to examine the correlation between RDV and the spherical equivalent(SE)and ocular biological parameters.RESULTS:Within RDV-20-53,both groups showed relative hyperopic defocus,and the increase in RDV corresponds to the increase in eccentricity.In the myopic anisometropia group,the TRDV,RDV-20-53,RDV-superior,and more myopic eyes had significantly higher RDVtemporal values than less myopic eyes.(P<0.05).In the non-anisometropia group,there was no significant difference in the RDV between the more and less myopic eyes at different eccentricities(P>0.05).There was a negative correlation between SE and TRDV(r=-0.205,P=0.001),RDV-20-53(r=-0.281,-0.183,-0.176,P<0.05),RDV-superior(r=-0.251,P<0.001),and RDV-temporal(r=-0.230,P<0.001),a negative correlation between CYL and RDV-10-30(r=-0.147,-0.180,P<0.05),and a negative correlation between SRI and RDV-0-20(r=-0.190,-0.170,P<0.05).AL had a positive correlation with RDV-20-30(r=0.164,P=0.008)and RDV-temporal(r=0.160,P=0.010).CONCLUSION:More myopic eyes in patients with myopic anisometropia show more peripheral hyperopic defocus.Diopter and corneal morphology may affect peripheral retinal defocus.
文摘AIM:To investigate the prevalence of visual impairment(VI)and provide an estimation of uncorrected refractive errors in school-aged children,conducted by optometry students as a community service.METHODS:The study was cross-sectional.Totally 3343 participants were included in the study.The initial examination involved assessing the uncorrected distance visual acuity(UDVA)and visual acuity(VA)while using a+2.00 D lens.The inclusion criteria for a subsequent comprehensive cycloplegic eye examination,performed by an optometrist,were as follows:a UDVA<0.6 decimal(0.20 logMAR)and/or a VA with+2.00 D≥0.8 decimal(0.96 logMAR).RESULTS:The sample had a mean age of 10.92±2.13y(range 4 to 17y),and 51.3%of the children were female(n=1715).The majority of the children(89.7%)fell within the age range of 8 to 14y.Among the ethnic groups,the highest representation was from the Luhya group(60.6%)followed by Luo(20.4%).Mean logMAR UDVA choosing the best eye for each student was 0.29±0.17(range 1.70 to 0.22).Out of the total,246 participants(7.4%)had a full eye examination.The estimated prevalence of myopia(defined as spherical equivalent≤-0.5 D)was found to be 1.45%of the total sample.While around 0.18%of the total sample had hyperopia value exceeding+1.75 D.Refractive astigmatism(cil<-0.75 D)was found in 0.21%(7/3343)of the children.The VI prevalence was 1.26%of the total sample.Among our cases of VI,76.2%could be attributed to uncorrected refractive error.Amblyopia was detected in 0.66%(22/3343)of the screened children.There was no statistically significant correlation observed between age or gender and refractive values.CONCLUSION:The primary cause of VI is determined to be uncorrected refractive errors,with myopia being the most prevalent refractive error observed.These findings underscore the significance of early identification and correction of refractive errors in school-aged children as a means to alleviate the impact of VI.
基金supported by the National Key R&D Program of China (Grant Nos. 2022YFA1404400 and 2022YFA1404403)the National Natural Science Foundation of China (Grant No. 92263208)+3 种基金the Natural Science Foundation of Jiangsu Province (Grant No. BK20210541)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 21KJB140003)the Fundamental Research Funds for the Central Universitiesthe Open Fund of State Key Laboratory of Acoustics (Grant No. SKLA202313)。
文摘We demonstrate a method to realize unidirectional negative refraction in an acoustic parity-time(P T)-symmetric system, which is composed of a pair of metasurfaces sandwiching an air gap. The pair of metasurfaces possesses loss and gain modulations. The unidirectional negative refraction, which is strictly limited to the case of incident wave imposing on the loss end of the metasurface, is demonstrated at the exception point(EP) in this P T-symmetric system, while the incidence from the other side leads to strong reflection. Based on rigorous calculations, we explicitly show the underlying mechanism of this model to achieve unidirectional wave scatterings around the EP in the parametric space. In addition, the perfect imaging of a point source in the three-dimensional space, as a signature of negative refraction, is simulated to provide a verification of our work. We envision that this work may sharpen the understanding of P T-symmetric structures and inspire more acoustic functional devices.
基金Supported by National Institute for Medical Research Development(NIMAD)affiliated with the Iranian Ministry of Health and Medical Education(No.963660).
文摘AIM:To compare the subjective refraction data with non-cycloplegic auto-refraction findings in the geriatric population above 60 years of age according to the different crystalline lens conditions.METHODS:This report is a part of the Tehran Geriatric Eye Study(TGES)that was conducted from January 2019 to January 2020 on elderly population 60 years of age and above in Tehran.The samples were selected by multistage stratified random cluster sampling.Of 3791 individual invitees,3310(response rate:87.3%)participated in this study.All study participants underwent non-cycloplegic autorefraction(auto-refractometer/keratometer Nidek ARK-510)and subjective refraction.RESULTS:Regarding the sphere,eyes with mixed cataract had the worst limits of agreement(LoA:-1.24 to 0.87)and the best agreement was related to the pseudophakic eyes(LoA:-0.83 to 0.54).The highest(0.27±0.31 D)and lowest(0.21±0.27 D)differences between the two methods regarding the cylinder power were observed in eyes with cortical cataract and normal eyes,respectively.The worst LoA between the two methods in measuring the cylinder power was related to the eyes with mixed cataract(LoA:-0.44 to 0.96).Regarding the J0(horizontal/vertical components of astigmatism),the mean values of J0 obtained by auto-refraction were tended more toward against the rule direction in all crystalline lens conditions,and the two methods had the greatest difference in cortical cataract cases(0.05±0.17 D).Regarding the J45(oblique components of astigmatism),the lowest(0±0.11 D)and highest(-0.01±0.12 D)differences were observed in normal eyes and eyes with cortical cataract,respectively.CONCLUSION:The auto-refractometer/keratometer Nidek ARK-510 results in the elderly with different phakic and pseudophakic conditions do not correspond well with subjective refraction findings.This discrepancy in spherical findings is more pronounced in individuals with mixed cataract than in other cases.
基金Project supported by the National Natural Science Foundation of China(Grant No.61671279)financial support from Xi’an Key Laboratory of Optical Information Manipulation and Augmentation(OMA)。
文摘We investigate the electromagnetic properties of a four-level dense atomic gas medium with Doppler effect.It is shown that the relative permittivity and relative permeability of the medium can be negative simultaneously with low absorption in the same detuning interval on account of electromagnetically induced transparency.Furthermore,with the suitable parameters,the nonreciprocal negative refraction can be obtained due to the Doppler effect,and the nonreciprocity frequency band can be regulated by adjusting the temperature,the intensity of the control field and the atomic density in this hot atomic medium.
基金funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2024R236),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘Today’s forensic science introduces a new research area for digital image analysis formultimedia security.So,Image authentication issues have been raised due to the wide use of image manipulation software to obtain an illegitimate benefit or createmisleading publicity by using tempered images.Exiting forgery detectionmethods can classify only one of the most widely used Copy-Move and splicing forgeries.However,an image can contain one or more types of forgeries.This study has proposed a hybridmethod for classifying Copy-Move and splicing images using texture information of images in the spatial domain.Firstly,images are divided into equal blocks to get scale-invariant features.Weber law has been used for getting texture features,and finally,XGBOOST is used to classify both Copy-Move and splicing forgery.The proposed method classified three types of forgeries,i.e.,splicing,Copy-Move,and healthy.Benchmarked(CASIA 2.0,MICCF200)and RCMFD datasets are used for training and testing.On average,the proposed method achieved 97.3% accuracy on benchmarked datasets and 98.3% on RCMFD datasets by applying 10-fold cross-validation,which is far better than existing methods.
文摘Introduction: Undetected refractive errors constitute a health problem among school children who cannot take advantage of educational opportunities. The authors studied the prevalence of refractive errors in school children aged 5 to 15 at CHU-IOTA. Patients and Method: This is a prospective, descriptive cross-sectional study carried out in the ophthalmic-pediatrics department of CHU-IOTA, from October to November 2023. Results: We received 340 school children aged 5 to 15, among whom 111 presented ametropia, i.e. a prevalence of 32.65%. The average age was 11.42 ± 2.75 years and a sex ratio of 0.59. The average visual acuity was 4/10 (range 1/10 and 10/10). We found refractive defects: astigmatism 73.87%, hyperopia 23.87% of cases and myopia 2.25%. The decline in distance visual acuity was the most common functional sign. Ocular abnormalities associated with ametropia were dominated by allergic conjunctivitis (26.13%) and papillary excavation (6.31%) in astigmatics;allergic conjunctivitis (9.01%) and papillary excavation (7.20%) in hyperopic patients;turbid vitreous (0.90%), myopic choroidosis (0.45%) and allergic conjunctivitis (0.45%) in myopes. Conclusion: Refractive errors constitute a reality and a major public health problem among school children.
基金supported by the National Natural Science Foundation of China(22288102 and 22278027).
文摘Transparent photoresists with a high refractive index(RI)and high transmittance in visible wavelengths have promising functionalities in optical fields.This work reports a kind of tunable optical material composed of titanium dioxide nanoparticles embedded in acrylic resin with a high RI for ultraviolet(UV)-imprint lithography.The hybrid film exhibits a tunable RI of up to 1.67(589 nm)after being cured by UV light,while maintaining both a high transparency of over 98%in the visible light range and a low haze of less than 0.05%.The precision machining of optical microstructures can be imprinted easily and efficiently using the hybrid resin,which acts as a light guide plate(LGP)to guide the light from the side to the top in order to conserve the energy of the display device.These preliminary studies based on both laboratory and commercial experiments pave the way for exploiting the unparalleled optical properties of nanocomposite resins and promoting their industrial application.
基金Supported by the National Natural Science Foundation of China(No.81873683).
文摘AIM:To compare the consistency of two autorefractors(Tianle RM-9000 and Topcon KR-800)for school-age myopia children,and to provide a basis for largescale data analysis and comparison.METHODS:The refractive error in 909 subjects(age 4–18y)were measured using both autorefractors without cycloplegia.The data were analyzed using Fourier decomposition and the correlation coefficients,intraclass correlation coefficients(ICC),and Bland-Altman limits of agreement(LoA)for each parameter were calculated.RESULTS:There was a strong correlation between the spherical equivalent(SE),sphere diopter(DS),and cylinder diopter(DC)readings of the Tianle RM-9000 and those of the Topcon KR-800,with correlation coefficient values of 0.98,0.98 and 0.83 and ICC values of 0.99,0.99 and 0.93,respectively.However,the correlation coefficients and ICC values of J0 and J45 were unreliable(R=-0.004,-0.034;both ICC<0.10).Bland-Altman analysis revealed that SE,DS,and DC measured by the Tianle RM-9000 were significantly biased toward myopia compared with the Topcon KR-800,and the mean differences were-0.072,-0.026,-0.091 D,respectively(all P<0.01).The minimum absolute value of the difference within the 95%LoA for SE,DS,and DC was 0.63 D,0.50 D,0.62 D,respectively;all these values were in the clinically acceptable range.For J0 and J45,the mean differences were close to zero(P=0.43,0.84);however,the 95%LoA were relatively wide(J0 SD:0.53;95%CI:-1.00,1.10;J45 SD:0.52;95%CI:-1.00,1.00).CONCLUSION:The two autorefractors are consistent with each other,as the differences in SE,DS,and DC were within the clinically acceptable range.Readers can compare the data measured by either device in different studies and use the two devices in the same study to generate a dataset that can be analyzed together.However,the J0 and J45 vectors are unreliable and should not be used to assess astigmatism.
基金Project supported by the National Natural Science Foundation of China (Grant No.12175107)the Natural Science Foundation of Nanjing Vocational University of Industry Technology (Grant No.YK22-02-08)+2 种基金the Qing Lan Project of Jiangsu Provincethe Natural Science Foundation of Jiangsu Province of China (Grant No.BK20230347)the Fund from the Research Center of Industrial Perception and Intelligent Manufacturing Equipment Engineering of Jiangsu Province,China (Grant No.ZK21-05-09)。
文摘Metal-based surface plasmon resonance(SPR)plays an important role in enhancing the photonic spin Hall effect(SHE)and developing sensitive optical sensors.However,the very large negative permittivities of metals limit their applications beyond the near-infrared regime.In this work,we theoretically present a new mechanism to enhance the photonic SHE by taking advantage of SiC-supported surface phonon resonance(SPhR)in the mid-infrared regime.The transverse displacement of photonic SHE is very sensitive to the wavelength of incident light and the thickness of SiC layer.Under the optimal parameter setup,the calculated largest transverse displacement of SiC-based SPhR structure reaches up to 163.8 ym,which is much larger than the condition of SPR.Moreover,an NO_(2) gas sensor based on the SPhR-enhanced photonic SHE is theoretically proposed with the superior sensing performance.Both the intensity and angle sensitivity of this sensor can be effectively manipulated by varying the damping rate of SiC.The results may provide a promising paradigm to enhance the photonic SHE in the mid-infrared region and open up new opportunity of highly sensitive refractive index sensors.
基金the financial funding of the Guangdong Province Applied Science and Technology R&D Special Fund Project:Key Technologies for Industrialization of Sulfur-Resistant and High Refractive-Index LED Packaging Silicone Materials(2016B090930010).
文摘In this article,a series of high refractive indices(1.50-1.53)thiol phenyl polysiloxane(TPS)were synthesized via hydrolytic sol-gel reaction.The Fourier transform infrared spectra(FT-IR)and nuclear magnetic resonance spectra(NMR)results showed that TPS conformed to the predicted structures.Natural terpene linalool was exploited as photocrosslinker to fabricate UV-curing linalool-polysiloxane hybrid films(LPH)with TPS via photoinitiated thiol-ene reaction.LPH rapidly cured under UV irradiation at the intensity of 80 mW/cm^(2) in 30 s,exhibiting good UV-curing properties.The optical transmittance of LPH in the wavelength of 300-800 nm was over 90%,exhibiting good optical transparency.The water contact angle and water vapor permeability results showed that the introduction of phenyl groups enhance the hydrophobicity and water vapor barrier properties of LPH.The results indicated the potential of LPHs in the applications of optical functional coatings.
基金supported by the Heilongjiang Touyan Innovative Program Teammade possible through the generous support of the NSFC (Grant No. 52176065)the Fundamental Research Funds for the Central Universities(Grant No. 2022FRFK060022)
文摘An unstably stratified flow entering into a stably stratified flow is referred to as penetrative convection,which is crucial to many physical processes and has been thought of as a key factor for extreme weather conditions.Past theoretical,numerical,and experimental studies on penetrative convection are reviewed,along with field studies providing insights into turbulence modeling.The physical factors that initiate penetrative convection,including internal heat sources,nonlinear constitutive relationships,centrifugal forces and other complicated factors are summarized.Cutting-edge methods for understanding transport mechanisms and statistical properties of penetrative turbulence are also documented,e.g.,the variational approach and quasilinear approach,which derive scaling laws embedded in penetrative turbulence.Exploring these scaling laws in penetrative convection can improve our understanding of large-scale geophysical and astrophysical motions.To better the model of penetrative turbulence towards a practical situation,new directions,e.g.,penetrative convection in spheres,and radiation-forced convection,are proposed.
文摘Introduction: WHO estimated that uncorrected refractive errors are the leading cause of visual impairment and second leading cause of blindness globally. University students are prone to developing refractive errors due to their curriculum that requires a lot of near work affecting their performance and quality of life unknowingly. Genetic and environmental factors are thought to play a role in the development of refractive errors. This study addresses the paucity of knowledge about refractive errors among university students in East Africa, providing a foundation for further research. Objectives: To determine the prevalence and factors associated with refractive errors among students in the Faculty of Medicine at Mbarara University of Science and Technology. Methodology: This was a cross-sectional descriptive and analytical study in which 368 undergraduate students selected using random sampling were assessed for refractive errors from March 2021-July 2021. Eligible participants were recruited and their VA assessment done after answering a questionnaire. Students whose VA improved on pin hole had subjective retinoscopy and results were compiled and imported to STATA 14 for analysis. Results: The prevalence of refractive errors was 26.36% with (95% CI) among university students especially myopia. Myopia is most predominant at 60%, followed by 37% Astigmatism and hyperopia of 3% among medical students. Astigmatism consisted of largely myopic astigmatism 72% (26) and 28% (10) compound/mixed astigmatism only. Student positive family history of refractive error was found to have a statistically significant relationship with refractive errors with AOR 1.68 (1.04 - 2.72) (95% CI) and P (0.032). Conclusion: The prevalence of refractive errors among university students, especially myopia, was found to be high and family history was associated with students having refractive errors.
文摘AIM:To compare relative peripheral refractive errors(RPREs)in Chinese children with and without myopic anisometropia(MAI)and to explore the relationship between RPRE and myopia.METHODS:This observational cross-sectional study included 160 children divided into two groups according to the interocular spherical equivalent refraction(SER)difference≥1.0 D in the MAI group(n=80)and<1.0 D in the non-MAI group(n=80).The MAI group was further divided into two subgroups:ΔSER<2.0 D group and ΔSER≥2.0 D group.Basic ocular biometric parameters of axial length(AL),average keratometry(Ave K),cylinder(CYL),surface regularity index(SRI),and surface asymmetry index(SAI)were recorded.In addition,multispectral refraction topography was performed to measure RPRE,and the parameters were recorded as total refraction difference value(TRDV),refraction difference value(RDV)0-10,RDV10-20,RDV20-30,RDV30-40,RDV40-53,RDV-superior(RDV-S),RDV-inferior(RDV-I),RDV-temporal(RDV-T)and RDV-nasal(RDV-N).RESULTS:In the non-MAI group,the interocular differences of all parameters of RPRE were not significant.In the MAI group,the interocular differences of TRDV,RDV10-53,RDV-S,RDV-I,RDV-T,and RDV-N were significant.In subgroup analysis,the interocular differences of TRDV,RDV30-53,RDV-I,and RDV-T were significant in ΔSER<2.0 D group and ΔSER≥2.0 D group,but the interocular differences of RDV10-30,RDV-S and RDV-N were only significant in the ΔSER≥2.0 D group.In correlation analysis,ΔTRDV,ΔRDV 10-53,ΔRDV-S,and ΔRDV-N were negatively correlated with ΔSER but positively correlated with ΔAL.CONCLUSION:The more myopic eyes have larger hyperopic RPRE in Chinese children with MAI in certain retinal range,and partialΔRPRE is closely associated with ΔSER and ΔAL.
文摘In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results apply to all nonlinear scalar conservation laws and to nonlinear hyperbolic systems of two equations.
基金supported by the NNSF of China(12261065)the NSF of Inner Mongolia(2022MS01005)+1 种基金the Basic Science Research Fund of the Universities Directly under the Inner Mongolia Autonomous Re-gion(JY20220084)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(NMGIRT2317).
文摘In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.