We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartmen...We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.展开更多
Satellite-based products with high spatial and temporal resolution provide useful precipitation information for data-sparse or ungauged large-scale watersheds. In the Lower Lancang-Mekong River Basin, rainfall station...Satellite-based products with high spatial and temporal resolution provide useful precipitation information for data-sparse or ungauged large-scale watersheds. In the Lower Lancang-Mekong River Basin, rainfall stations are sparse and unevenly distributed, and the transboundary characteristic makes the collection of precipitation data more difficult, which has restricted hydrological processes simulation. In this study, daily precipitation data from four datasets(gauge observations, inverse distance weighted(IDW) data, Tropical Rainfall Measuring Mission(TRMM) estimates, and Climate Hazards Group InfraRed Precipitation with Stations(CHIRPS) estimates), were applied to drive the Soil and Water Assessment Tool(SWAT) model, and then their capability for hydrological simulation in the Lower Lancang-Mekong River Basin were examined. TRMM and CHIRPS data showed good performances on precipitation estimation in the Lower Lancang-Mekong River Basin, with the better performance for TRMM product. The Nash-Sutcliffe efficiency(NSE) values of gauge, IDW, TRMM, and CHIRPS simulations during the calibration period were 0.87, 0.86, 0.95, and 0.93 for monthly flow, respectively, and those for daily flow were 0.75, 0.77, 0.86, and 0.84, respectively. TRMM and CHIRPS data were superior to rain gauge and IDW data for driving the hydrological model, and TRMM data produced the best simulation performance. Satellite-based precipitation estimates could be suitable data sources when simulating hydrological processes for large data-poor or ungauged watersheds, especially in international river basins for which precipitation observations are difficult to collect. CHIRPS data provide long precipitation time series from 1981 to near present and thus could be used as an alternative precipitation input for hydrological simulation, especially for the period without TRMM data. For satellite-based precipitation products, the differences in the occurrence frequencies and amounts of precipitation with different intensities would affect simulation results of water balance components, which should be comprehensively considered in water resources estimation and planning.展开更多
In this paper,we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order a on the unit ball E in a complex Banach space X by applying the method ...In this paper,we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order a on the unit ball E in a complex Banach space X by applying the method and technique of complex analysis.Then,as the application of these sharp inequalities,we derive the sharp estimate of third homogeneous expansions for the above mappings defined on the unit polydisk U^n in C^n.展开更多
This work deals with the relationship between the Bayesian and the maximum likelihood estimators in case of dependent observations. In case of Markov chains, we show that the Bayesian estimator of the transition proba...This work deals with the relationship between the Bayesian and the maximum likelihood estimators in case of dependent observations. In case of Markov chains, we show that the Bayesian estimator of the transition probabilities is a linear function of the maximum likelihood estimator (MLE).展开更多
Identifying underground utilities and predicting their depth are fundamental when it comes to civil engineering excavations, for example, to install or repair water, sewer, gas, electric systems and others. The accide...Identifying underground utilities and predicting their depth are fundamental when it comes to civil engineering excavations, for example, to install or repair water, sewer, gas, electric systems and others. The accidental rupture of these systems can lead to unplanned repair costs, delays in completing the service, and risk injury or death of workers. One way to detect underground utilities is using the GPR-Ground Penetrating Radar geophysical method. To estimate depth, the travel time (two-way travel time) information provided by a radargram is used in conjunction with ground wave velocity, which depends on the dielectric constant of materials, where it is usually assumed to be constant for the area under investigation. This procedure provides satisfactory results in most cases. However, wrong depth estimates can result in damage to public utilities, rupturing pipes, cutting lines and so on. These cases occur mainly in areas that have a marked variation of water content and/or soil lithology, thus greater care is required to determine the depth of the targets. The present work demonstrates how the interval velocity of Dix (1955) can be applied in radargram to estimate the depth of underground utilities compared to the conventional technique of constant velocity applied to the same data set. To accomplish this, synthetic and real GPR data were used to verify the applicability of the interval velocity technique and to determine the accuracy of the depth estimates obtained. The studies were carried out at the IAG/USP test site, a controlled environment, where metallic drums are buried in known positions and depths allowing the comparison of real to estimated depths. Numerical studies were also carried out aiming to simulate the real environment with variation of dielectric constant in depth and to validate the results with real data. The results showed that the depths of the targets were estimated more accurately by means of the interval velocity technique in contrast to the constant velocity technique, minimizing the risks of accidents during excavation.展开更多
HIV estimation has become a standard tool for understanding the epidemic. Although the majority of India’s population lives in rural areas, to date, an exploration of the urban and rural HIV epidemic has not been und...HIV estimation has become a standard tool for understanding the epidemic. Although the majority of India’s population lives in rural areas, to date, an exploration of the urban and rural HIV epidemic has not been undertaken. The objective of this study is to develop HIV estimation based on urban and rural adult populations in selected states of India to understand the difference in HIV related indices geographically. Ten states were selected based on HIV prevalence levels-Andhra Pradesh, Tamil Nadu, Karnataka, Maharashtra, Manipur, and Nagaland, Mizoram, Punjab, Odisha and Jharkhand. Spectrum, version 4.53 beta 19, was used. Data files of Indian national estimation, 2010-11 which included population, HIV Sentinel Surveillance, Integrated Bio Behavioral Assessment and program coverage data, were used and alterations made wherever necessary. The urban and rural sub epidemic structures and their subpopulations were separately configured in the Estimation projection package and curve fitting done. Outputs for each state were separately analyzed. Findings show that HIV prevalence is lower in urban than rural areas in Tamil Nadu and Maharashtra;in Karnataka there is no difference in HIV prevalence in the urban and rural populations;and in the remaining seven states urban HIV prevalence is higher as compared to rural HIV prevalence. In the states of Andhra Pradesh, Tamil Nadu, Maharashtra, Odisha and Punjab, the number of people living with HIV, new HIV infections and deaths among people living with HIV is higher in the rural than in the urban population. An early and lower peak in HIV prevalence and incidence in the urban population was seen in Andhra Pradesh, Tamil Nadu, Karnataka and Naga-land, while in Maharashtra the rural peak was earlier and higher. Mizoram shows an earlier and lower peak in the rural population while Manipur shows an earlier and higher urban peak. In Odisha, the epidemic peaked earlier and was lower in the rural than the urban population. HIV prevalence in the urban population in Punjab was still peaking while HIV incidence was earlier and lower in the rural population. In Jharkhand, both urban and rural HIV prevalence and incidence are still increasing. Our findings indicate lower levels of HIV prevalence and incidence in the urban population as compared to the rural populations in Maharashtra and Tamil Nadu. In the remaining eight states, urban prevalence and incidence are higher than their rural counterparts. Future estimations of the HIV epidemic in the country need to adopt a similar approach to inform the design of appropriate state-level strategies for HIV prevention in urban and rural areas.展开更多
By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation i...By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation is considerably more intuitive, and is analytically more tractable.展开更多
Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1]....Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1].Moreover,the application of these results to the well-posedness of some equations are shown in the last section.展开更多
The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence ...The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.展开更多
In this paper we introduce two kinds of parallel Schwarz domain decomposition me thods for general, selfadjoint, second order parabolic equations and study the dependence of their convergence rates on parameters of ti...In this paper we introduce two kinds of parallel Schwarz domain decomposition me thods for general, selfadjoint, second order parabolic equations and study the dependence of their convergence rates on parameters of time-step and space-mesh. We prove that the, approximate solution has convergence independent of iteration times at each time-level. And the L^2 error estimates are given.展开更多
This paper deals with some parabolic equations,where the reaction and the boundary flux are taken of some general forms.We study the explicit blow-up time estimates according to the different coupled relationship,incl...This paper deals with some parabolic equations,where the reaction and the boundary flux are taken of some general forms.We study the explicit blow-up time estimates according to the different coupled relationship,including the lower and upper bounds of blow-up time for every dimension of space domains.As examples,the results could be used to so many completely coupled models.展开更多
Let be a polynomial of degree n having all its zeros in , then for each , , with , Aziz and Ahemad (1996) proved that In this paper, we extend the above inequality to the class of polynomials , having all its zeros in...Let be a polynomial of degree n having all its zeros in , then for each , , with , Aziz and Ahemad (1996) proved that In this paper, we extend the above inequality to the class of polynomials , having all its zeros in , and obtain a generalization as well as refinement of the above result.展开更多
This work deals with the numerical solution of singular perturbation system of ordinary differential equations with boundary layer. For the numerical solution of this problem fitted finite difference scheme on a unifo...This work deals with the numerical solution of singular perturbation system of ordinary differential equations with boundary layer. For the numerical solution of this problem fitted finite difference scheme on a uniform mesh is constructed and analyzed. The uniform error estimates for the approximate solution are obtained.展开更多
In this paper, under weak conditions, we theoretically prove the second-order convergence rate of the Crank-Nicolson scheme for solving a kind of decoupled forward-backward stochastic differential equations.
A nonlinear parabolic system is derived to describe incompressible nuclear waste-disposal contamination in porous media. A sequential implicit tirne-stepping is defined, in which the pressure and Darcy velocity of the...A nonlinear parabolic system is derived to describe incompressible nuclear waste-disposal contamination in porous media. A sequential implicit tirne-stepping is defined, in which the pressure and Darcy velocity of the mixture are approximated simultaneously by a mixed finite element method and the brine, radionuclid and heat are treated by a combination of a Galerkin finite element method and the method of characteristics. Optimal-order convergence in L2 is proved. Time-truncation errors of standard procedures are reduced by time stepping along the characteristics of the hyperbolic part of the brine, radionuclide and heal equalios, temporal and spatial error are lossened by direct compulation of the velocity in the mixed method, as opposed to differentiation of the pressure.展开更多
AIM: To investigate effect of body dimensions obtained from localizer radiograph and transverse abdominal computed tomography(CT) images on Size Specific Dose Estimate. METHODS: This study was approved by Institutiona...AIM: To investigate effect of body dimensions obtained from localizer radiograph and transverse abdominal computed tomography(CT) images on Size Specific Dose Estimate. METHODS: This study was approved by Institutional Review Board and was compliant with Health Insurance Portability and Accountability Act. Fifty patients with abdominal CT examinations(58 ± 13 years, Male: Female 28:22) were included in this study. Anteriorposterior(AP) and lateral(Lat) diameters were measured at 5 cm intervals from the CT exam localizer radiograph(simple X-ray image acquired for planning the CT exam before starting the scan) and transverse CT images. Average of measured AP and Lat diameters, as well as maximum, minimum and mid location AP and Lat were measured on both image sets. In addition, off centering of patients from the gantry iso-center was calculated from the localizers. Conversion factors from American Association of Physicists in Medicine(AAPM) report 204 were obtained for AP, Lat, AP + Lat, and effective diameter(√ AP * Lat) to determine size specificdose estimate(SSDE) from the CT dose index volume(CTDIvol) recorded from the dose reports. Data were analyzed using SPSS v19. RESULTS: Total number of 5376 measurements was done. In some patients entire body circumference was not covered on either projection radiograph or transverse CT images; hence accurate measurement of AP and Lat diameters was not possible in 11%(278/2488) of locations. Forty one patients were off-centered with mean of 1.9 ± 1.8 cm(range: 0.4-7 cm). Conversion factors for attained diameters were not listed on AAPM look-up tables in 3%(80/2488) of measurements. SSDE values were significantly different compared to CTDIvol, ranging from 32% lower to 74% greater than CTDIvol. CONCLUSION: There is underestimation and overestimation of dose comparing SSDE values to CTDIvol. Localizer radiographs are associated with overestimation of patient size and therefore underestimation of SSDE.展开更多
Earthquakes can cause significant damage and loss of life,necessitating immediate assessment of the resulting fatalities.Rapid assessment and timely revision of fatality estimates are crucial for effective emergency d...Earthquakes can cause significant damage and loss of life,necessitating immediate assessment of the resulting fatalities.Rapid assessment and timely revision of fatality estimates are crucial for effective emergency decisionmaking.This study using the February 6,2023,M_(S)8.0 and M_(S)7.9 Kahramanmaras,Türkiye earthquakes as an example to estimate the ultimate number of fatalities.An early Quick Rough Estimate(QRE)based on the number of deaths reported by the Disaster and Emergency Management Presidency of Türkiye(AFAD)is conducted,and it dynamically adjusts these estimates as new data becomes available.The range of estimates of the final number of deaths can be calculated as 31384–56475 based on the"the QRE of the second day multiplied by 2–3" rule,which incorporates the reported final deaths 50500.The Quasi-Linear and Adaptive Estimation(QLAE)method adaptively adjusts the final fatality estimate within two days and predicts subsequent reported deaths.The correct order of magnitude of the final death toll can be estimated as early as 13 hr after the M_(S)8.0 earthquake.In addition,additional earthquakes such as May 12,2008,M_(S)8.1 Wenchuan earthquake(China),September 8,2023,M_(S)7.2 Al Haouz earthquake(Morocco),November 3,2023,M_(S)5.8 Mid-Western Nepal earthquake,December 18,2023,M_(S)6.1 Jishishan earthquake(China),January 1,2024,M_(S)7.2 Noto Peninsula earthquake(Japan)and August 8,2023,Maui,Hawaii,fires are added again to verified the correctness of the model.The fatalities from the Maui fires are found to be approximately equivalent to those resulting from an M_(S)7.4 earthquake.These methods complement existing frameworks such as Quake Loss Assessment for Response and Mitigation(QLARM)and Prompt Assessment of Global.展开更多
In this paper,for the 1-D semilinear wave equation∂_(t)^(2)u-∂_(x)^(2)u+μ/t∂_(t)u=|u|~p with scaling invariant damping,where t≥1,p>1 andμ∈(0,1)∪(1,4/3),we establish the global weighted space-time estimates as ...In this paper,for the 1-D semilinear wave equation∂_(t)^(2)u-∂_(x)^(2)u+μ/t∂_(t)u=|u|~p with scaling invariant damping,where t≥1,p>1 andμ∈(0,1)∪(1,4/3),we establish the global weighted space-time estimates as well as the global existence of small data weak solution u when the nonlinearity power p is larger than some critical power p_(crit)(μ).Our proof is based on a class of new weighted Strichartz estimates with the weight t^(θ)|(1-μ)^(2)t^(2/|1-μ|)-x^(2)|^(γ)(θ>0andγ>0 are appropriate constants)for the solution of linear generalized Tricomi equation∂_(t)^(2)φ-t^(m)∂_(x)^(2)φ=0 with m being any fixed positive number.展开更多
HIV/AIDS is a public health problem especially in sub-Saharan Africa where majority of infections and deaths occur. Despite the large number of studies and efforts made in covering the data gap using mathematical mode...HIV/AIDS is a public health problem especially in sub-Saharan Africa where majority of infections and deaths occur. Despite the large number of studies and efforts made in covering the data gap using mathematical models, little is known on how model estimates are confounded by the transmission variabilities that exist in stages of HIV progression. This work investigates the impact of including stages of HIV transmission in HIV/AIDS models. A deterministic HIV/AIDS model is developed and extended to include stages of HIV progression of infected individuals. Theoretical investigation of the models and numerical analyses indicate that the two models produce different estimates, with the model without stages producing lower estimates than the staged model. These results call for a careful consideration in evaluating the efficiency of HIV/AIDS models that are used to estimate and project the burden of HIV/AIDS disease.展开更多
In this paper, we investigate the coefficient estimates of a class of m-fold bi-univalent function de?ned by subordination. The results presented in this paper improve or generalize the recent works of other authors.
基金The work has been supported by a grant received from the Ministry of Education,Government of India under the Scheme for the Promotion of Academic and Research Collaboration(SPARC)(ID:SPARC/2019/1396).
文摘We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.
基金National Key R&D Program of China(No.2016YFA0601601)National Natural Science Foundation of China(No.41601026,41661099)Science and Technology Planning Project of Yunnan Province,China(No.2017FB073)
文摘Satellite-based products with high spatial and temporal resolution provide useful precipitation information for data-sparse or ungauged large-scale watersheds. In the Lower Lancang-Mekong River Basin, rainfall stations are sparse and unevenly distributed, and the transboundary characteristic makes the collection of precipitation data more difficult, which has restricted hydrological processes simulation. In this study, daily precipitation data from four datasets(gauge observations, inverse distance weighted(IDW) data, Tropical Rainfall Measuring Mission(TRMM) estimates, and Climate Hazards Group InfraRed Precipitation with Stations(CHIRPS) estimates), were applied to drive the Soil and Water Assessment Tool(SWAT) model, and then their capability for hydrological simulation in the Lower Lancang-Mekong River Basin were examined. TRMM and CHIRPS data showed good performances on precipitation estimation in the Lower Lancang-Mekong River Basin, with the better performance for TRMM product. The Nash-Sutcliffe efficiency(NSE) values of gauge, IDW, TRMM, and CHIRPS simulations during the calibration period were 0.87, 0.86, 0.95, and 0.93 for monthly flow, respectively, and those for daily flow were 0.75, 0.77, 0.86, and 0.84, respectively. TRMM and CHIRPS data were superior to rain gauge and IDW data for driving the hydrological model, and TRMM data produced the best simulation performance. Satellite-based precipitation estimates could be suitable data sources when simulating hydrological processes for large data-poor or ungauged watersheds, especially in international river basins for which precipitation observations are difficult to collect. CHIRPS data provide long precipitation time series from 1981 to near present and thus could be used as an alternative precipitation input for hydrological simulation, especially for the period without TRMM data. For satellite-based precipitation products, the differences in the occurrence frequencies and amounts of precipitation with different intensities would affect simulation results of water balance components, which should be comprehensively considered in water resources estimation and planning.
基金supported by Guangdong Natural Science Foundation(2018A030313508)Science and Technology Program of Guangzhou,China(201804010171)
文摘In this paper,we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order a on the unit ball E in a complex Banach space X by applying the method and technique of complex analysis.Then,as the application of these sharp inequalities,we derive the sharp estimate of third homogeneous expansions for the above mappings defined on the unit polydisk U^n in C^n.
文摘This work deals with the relationship between the Bayesian and the maximum likelihood estimators in case of dependent observations. In case of Markov chains, we show that the Bayesian estimator of the transition probabilities is a linear function of the maximum likelihood estimator (MLE).
文摘Identifying underground utilities and predicting their depth are fundamental when it comes to civil engineering excavations, for example, to install or repair water, sewer, gas, electric systems and others. The accidental rupture of these systems can lead to unplanned repair costs, delays in completing the service, and risk injury or death of workers. One way to detect underground utilities is using the GPR-Ground Penetrating Radar geophysical method. To estimate depth, the travel time (two-way travel time) information provided by a radargram is used in conjunction with ground wave velocity, which depends on the dielectric constant of materials, where it is usually assumed to be constant for the area under investigation. This procedure provides satisfactory results in most cases. However, wrong depth estimates can result in damage to public utilities, rupturing pipes, cutting lines and so on. These cases occur mainly in areas that have a marked variation of water content and/or soil lithology, thus greater care is required to determine the depth of the targets. The present work demonstrates how the interval velocity of Dix (1955) can be applied in radargram to estimate the depth of underground utilities compared to the conventional technique of constant velocity applied to the same data set. To accomplish this, synthetic and real GPR data were used to verify the applicability of the interval velocity technique and to determine the accuracy of the depth estimates obtained. The studies were carried out at the IAG/USP test site, a controlled environment, where metallic drums are buried in known positions and depths allowing the comparison of real to estimated depths. Numerical studies were also carried out aiming to simulate the real environment with variation of dielectric constant in depth and to validate the results with real data. The results showed that the depths of the targets were estimated more accurately by means of the interval velocity technique in contrast to the constant velocity technique, minimizing the risks of accidents during excavation.
文摘HIV estimation has become a standard tool for understanding the epidemic. Although the majority of India’s population lives in rural areas, to date, an exploration of the urban and rural HIV epidemic has not been undertaken. The objective of this study is to develop HIV estimation based on urban and rural adult populations in selected states of India to understand the difference in HIV related indices geographically. Ten states were selected based on HIV prevalence levels-Andhra Pradesh, Tamil Nadu, Karnataka, Maharashtra, Manipur, and Nagaland, Mizoram, Punjab, Odisha and Jharkhand. Spectrum, version 4.53 beta 19, was used. Data files of Indian national estimation, 2010-11 which included population, HIV Sentinel Surveillance, Integrated Bio Behavioral Assessment and program coverage data, were used and alterations made wherever necessary. The urban and rural sub epidemic structures and their subpopulations were separately configured in the Estimation projection package and curve fitting done. Outputs for each state were separately analyzed. Findings show that HIV prevalence is lower in urban than rural areas in Tamil Nadu and Maharashtra;in Karnataka there is no difference in HIV prevalence in the urban and rural populations;and in the remaining seven states urban HIV prevalence is higher as compared to rural HIV prevalence. In the states of Andhra Pradesh, Tamil Nadu, Maharashtra, Odisha and Punjab, the number of people living with HIV, new HIV infections and deaths among people living with HIV is higher in the rural than in the urban population. An early and lower peak in HIV prevalence and incidence in the urban population was seen in Andhra Pradesh, Tamil Nadu, Karnataka and Naga-land, while in Maharashtra the rural peak was earlier and higher. Mizoram shows an earlier and lower peak in the rural population while Manipur shows an earlier and higher urban peak. In Odisha, the epidemic peaked earlier and was lower in the rural than the urban population. HIV prevalence in the urban population in Punjab was still peaking while HIV incidence was earlier and lower in the rural population. In Jharkhand, both urban and rural HIV prevalence and incidence are still increasing. Our findings indicate lower levels of HIV prevalence and incidence in the urban population as compared to the rural populations in Maharashtra and Tamil Nadu. In the remaining eight states, urban prevalence and incidence are higher than their rural counterparts. Future estimations of the HIV epidemic in the country need to adopt a similar approach to inform the design of appropriate state-level strategies for HIV prevention in urban and rural areas.
文摘By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation is considerably more intuitive, and is analytically more tractable.
基金supported by the NSFC(12071437)the National Key R&D Program of China(2022YFA1005700).
文摘Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1].Moreover,the application of these results to the well-posedness of some equations are shown in the last section.
基金supported by the National Natural Science Foundation of China(11271141)Chongqing Science&Technology Commission(cstc2018jcyjAX0787)
文摘The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.
基金This work was supported by Natural Science Foundation of China and Shandong Province.
文摘In this paper we introduce two kinds of parallel Schwarz domain decomposition me thods for general, selfadjoint, second order parabolic equations and study the dependence of their convergence rates on parameters of time-step and space-mesh. We prove that the, approximate solution has convergence independent of iteration times at each time-level. And the L^2 error estimates are given.
基金Supported by Shandong Provincial Natural Science Foundation of China。
文摘This paper deals with some parabolic equations,where the reaction and the boundary flux are taken of some general forms.We study the explicit blow-up time estimates according to the different coupled relationship,including the lower and upper bounds of blow-up time for every dimension of space domains.As examples,the results could be used to so many completely coupled models.
文摘Let be a polynomial of degree n having all its zeros in , then for each , , with , Aziz and Ahemad (1996) proved that In this paper, we extend the above inequality to the class of polynomials , having all its zeros in , and obtain a generalization as well as refinement of the above result.
文摘This work deals with the numerical solution of singular perturbation system of ordinary differential equations with boundary layer. For the numerical solution of this problem fitted finite difference scheme on a uniform mesh is constructed and analyzed. The uniform error estimates for the approximate solution are obtained.
文摘In this paper, under weak conditions, we theoretically prove the second-order convergence rate of the Crank-Nicolson scheme for solving a kind of decoupled forward-backward stochastic differential equations.
基金The research was supported by the Natural Science Foundation of China
文摘A nonlinear parabolic system is derived to describe incompressible nuclear waste-disposal contamination in porous media. A sequential implicit tirne-stepping is defined, in which the pressure and Darcy velocity of the mixture are approximated simultaneously by a mixed finite element method and the brine, radionuclid and heat are treated by a combination of a Galerkin finite element method and the method of characteristics. Optimal-order convergence in L2 is proved. Time-truncation errors of standard procedures are reduced by time stepping along the characteristics of the hyperbolic part of the brine, radionuclide and heal equalios, temporal and spatial error are lossened by direct compulation of the velocity in the mixed method, as opposed to differentiation of the pressure.
文摘AIM: To investigate effect of body dimensions obtained from localizer radiograph and transverse abdominal computed tomography(CT) images on Size Specific Dose Estimate. METHODS: This study was approved by Institutional Review Board and was compliant with Health Insurance Portability and Accountability Act. Fifty patients with abdominal CT examinations(58 ± 13 years, Male: Female 28:22) were included in this study. Anteriorposterior(AP) and lateral(Lat) diameters were measured at 5 cm intervals from the CT exam localizer radiograph(simple X-ray image acquired for planning the CT exam before starting the scan) and transverse CT images. Average of measured AP and Lat diameters, as well as maximum, minimum and mid location AP and Lat were measured on both image sets. In addition, off centering of patients from the gantry iso-center was calculated from the localizers. Conversion factors from American Association of Physicists in Medicine(AAPM) report 204 were obtained for AP, Lat, AP + Lat, and effective diameter(√ AP * Lat) to determine size specificdose estimate(SSDE) from the CT dose index volume(CTDIvol) recorded from the dose reports. Data were analyzed using SPSS v19. RESULTS: Total number of 5376 measurements was done. In some patients entire body circumference was not covered on either projection radiograph or transverse CT images; hence accurate measurement of AP and Lat diameters was not possible in 11%(278/2488) of locations. Forty one patients were off-centered with mean of 1.9 ± 1.8 cm(range: 0.4-7 cm). Conversion factors for attained diameters were not listed on AAPM look-up tables in 3%(80/2488) of measurements. SSDE values were significantly different compared to CTDIvol, ranging from 32% lower to 74% greater than CTDIvol. CONCLUSION: There is underestimation and overestimation of dose comparing SSDE values to CTDIvol. Localizer radiographs are associated with overestimation of patient size and therefore underestimation of SSDE.
基金supported by the National Natural Science Foundation of China(NSFC,grant number U2039207).
文摘Earthquakes can cause significant damage and loss of life,necessitating immediate assessment of the resulting fatalities.Rapid assessment and timely revision of fatality estimates are crucial for effective emergency decisionmaking.This study using the February 6,2023,M_(S)8.0 and M_(S)7.9 Kahramanmaras,Türkiye earthquakes as an example to estimate the ultimate number of fatalities.An early Quick Rough Estimate(QRE)based on the number of deaths reported by the Disaster and Emergency Management Presidency of Türkiye(AFAD)is conducted,and it dynamically adjusts these estimates as new data becomes available.The range of estimates of the final number of deaths can be calculated as 31384–56475 based on the"the QRE of the second day multiplied by 2–3" rule,which incorporates the reported final deaths 50500.The Quasi-Linear and Adaptive Estimation(QLAE)method adaptively adjusts the final fatality estimate within two days and predicts subsequent reported deaths.The correct order of magnitude of the final death toll can be estimated as early as 13 hr after the M_(S)8.0 earthquake.In addition,additional earthquakes such as May 12,2008,M_(S)8.1 Wenchuan earthquake(China),September 8,2023,M_(S)7.2 Al Haouz earthquake(Morocco),November 3,2023,M_(S)5.8 Mid-Western Nepal earthquake,December 18,2023,M_(S)6.1 Jishishan earthquake(China),January 1,2024,M_(S)7.2 Noto Peninsula earthquake(Japan)and August 8,2023,Maui,Hawaii,fires are added again to verified the correctness of the model.The fatalities from the Maui fires are found to be approximately equivalent to those resulting from an M_(S)7.4 earthquake.These methods complement existing frameworks such as Quake Loss Assessment for Response and Mitigation(QLARM)and Prompt Assessment of Global.
基金supported by the NSFC(12331007)the National Key Research and Development Program of China(2020YFA0713803)。
文摘In this paper,for the 1-D semilinear wave equation∂_(t)^(2)u-∂_(x)^(2)u+μ/t∂_(t)u=|u|~p with scaling invariant damping,where t≥1,p>1 andμ∈(0,1)∪(1,4/3),we establish the global weighted space-time estimates as well as the global existence of small data weak solution u when the nonlinearity power p is larger than some critical power p_(crit)(μ).Our proof is based on a class of new weighted Strichartz estimates with the weight t^(θ)|(1-μ)^(2)t^(2/|1-μ|)-x^(2)|^(γ)(θ>0andγ>0 are appropriate constants)for the solution of linear generalized Tricomi equation∂_(t)^(2)φ-t^(m)∂_(x)^(2)φ=0 with m being any fixed positive number.
文摘HIV/AIDS is a public health problem especially in sub-Saharan Africa where majority of infections and deaths occur. Despite the large number of studies and efforts made in covering the data gap using mathematical models, little is known on how model estimates are confounded by the transmission variabilities that exist in stages of HIV progression. This work investigates the impact of including stages of HIV transmission in HIV/AIDS models. A deterministic HIV/AIDS model is developed and extended to include stages of HIV progression of infected individuals. Theoretical investigation of the models and numerical analyses indicate that the two models produce different estimates, with the model without stages producing lower estimates than the staged model. These results call for a careful consideration in evaluating the efficiency of HIV/AIDS models that are used to estimate and project the burden of HIV/AIDS disease.
基金The NSF(KJ2018A0839,KJ2018A0833) of Anhui Provincial Department of Education
文摘In this paper, we investigate the coefficient estimates of a class of m-fold bi-univalent function de?ned by subordination. The results presented in this paper improve or generalize the recent works of other authors.
