This article delves Chern's conjecture for hypersurfaces with constant second fundamental form squared length S in the spherical space.At present,determining whether the third gap point of S is 2n remains unsolved...This article delves Chern's conjecture for hypersurfaces with constant second fundamental form squared length S in the spherical space.At present,determining whether the third gap point of S is 2n remains unsolved yet.First,we investigate the height functions and their properties of the position vector and normal vector in natural coordinate vectors,and then prove the existence of a Simons-type integral formula on the hypersurface that simultaneously includes the first,second,and third gap point terms of S.These results can provide new avenues of thought and methods for solving Chern's conjecture.展开更多
Projectile trajectories calculated under non-standard conditions are considered to be perturbed. The tools utilized for the analysis of perturbed trajectories are weighting factor functions(WFFs) which are a special k...Projectile trajectories calculated under non-standard conditions are considered to be perturbed. The tools utilized for the analysis of perturbed trajectories are weighting factor functions(WFFs) which are a special kind of sensitivity functions. WFFs are used for calculation of meteo ballistic elements mB(ballistic wind wB, virtual temperature tB, pressure pB, density rB, speed of sound a) as well. An effect of weapon system parameters can be incorporated into calculations through the reference height of trajectory-RHT.RHT are also calculated from WFFs. Methods based on RHT are far more effective than traditional methods that use weighting factors q.We have found that the existing theory of RHT has several shortcomings due to we created an improved theory of generalized RHT which represent a special sensitivity parameters of dynamical systems. Using this theory will improve methods for designing firing tables, fire control systems algorithms, and meteo message generation algorithms.展开更多
在林业研究中,胸径-树高二元联合分布多由相同边缘分布构造,而林分的胸径与树高的实际分布状况可能有所差异。为降低这种差异带来的影响,依据佳木斯市孟家岗林场的115块长白落叶松人工林数据,选择适用条件低、适应范围广的Copula函数方...在林业研究中,胸径-树高二元联合分布多由相同边缘分布构造,而林分的胸径与树高的实际分布状况可能有所差异。为降低这种差异带来的影响,依据佳木斯市孟家岗林场的115块长白落叶松人工林数据,选择适用条件低、适应范围广的Copula函数方法拟合落叶松胸径-树高二元联合分布模型。首先选择威布尔(Weibull)、广义威布尔(G-Weibull)、逻辑斯蒂(Logistic)、轻量逻辑斯蒂(Logit-Logistic)、伽马(Gamma)、对数正态(Log-Normal)6个分布函数作为备选基础模型,根据K-S(kolmogorov smirnov test)检验与半参数估计结果筛选并构建Copula胸径-树高二元联合分布模型,再通过负对数似然(negative log-likelihood,NLL)、Sn拟合优度统计量和似然比检验(likelihood ratio test,LRT)与二元对数logistic分布函数和二元Weibull分布函数进行比较,最后使用雷诺误差指数(error index of Reynolds,EI)对模型预测能力进行评估。结果表明,基于Copula函数的二元分拟合结果与模型(EI=0.3184)预估能力皆优于二元Weibull分布(EI=0.6381)和二元对数Logistic分布(EI=0.9490),说明此方法构建胸径-树高二元联合Copula分布模型能够很好地描述落叶松人工林胸径树高联合分布,以Copula方法构建树高-胸径联合分布是可行的。展开更多
When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year...When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year observation data to derive 100-year return period design wave height. Therefore, the study of inherent self-similarity in ocean hydrological elements becomes increasingly important to the study of multi-year return period design wave height derivation. In this paper, we introduced multifractal to analyze the statistical characteristics of wave height series data observed from oceanic hydrological station. An improvement is made to address the existing problems of the multifractal detrended fluctuation analysis (MF-DFA) method, where trend function showed a discontinuity between intervals. The improved MFDFA method is based on signal mode decomposition, replacing piecewise polynomial fitting used in the original method. We applied the proposed method to the wave height data collected at Chaolian Island, Shandong, China, from 1963 to 1989 and was able to conclude the wave height sequence presented weak multi-fractality. This result provided strong support to the past research on the derivation of multi-year return period design wave height with observed data. Moreover, the new method proposed in this paper also provides a new perspective to explore the intrinsic characteristic of data.展开更多
A method is presented to extrapolate a time series of wave data to extreme wave heights. The 15-year time series of deepwater wave data collected for 34 min every hour from 1988 to 2002 in the South Pacific Ocean, Aus...A method is presented to extrapolate a time series of wave data to extreme wave heights. The 15-year time series of deepwater wave data collected for 34 min every hour from 1988 to 2002 in the South Pacific Ocean, Australia, is analyzed to generate a set of storm peak wave heights by use of the Peaks-Over-Threshold method. The probability distribution is calculated by grouping the observod storm peak wave heights into a number of wave height classes and assigning a probability to each wave height class. The observed probability distribution is then fitted to eight different probability distribution functions and found to be fitted best by the Weibull distribution （a = 1.17）, nearly best by the FT-Ⅰ, quite well by the exponential, and poorly by the lognormal function based on the criterion of the sum of squares of the errors, SSE （H）. The effect of the threshold wave height on the estimated extreme wave height is also studied and is found insignificant in this study. The 95 % prediction intervals of the best-fit FT-Ⅰ , exponential and Weibull functions are also derived.展开更多
Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh f...Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.展开更多
This paper deals with the issue of preparation of the aiming angles with the use of tabular firing tables and needed determination of the ballistic elements μ_B(ballistic wind w_B,w_(xB),w_(ZB),ballistic(virtual) tem...This paper deals with the issue of preparation of the aiming angles with the use of tabular firing tables and needed determination of the ballistic elements μ_B(ballistic wind w_B,w_(xB),w_(ZB),ballistic(virtual) temperature τ_B.ballistic density p_B) from the standardized met messages.The weighting factors are used for the calculation of ballistic elements μ_B that are incorporated into the trajectory calculations characteristics of weapon and ammunition.Two different methodologies practically used in the praxis are analysed and compared.For the comparison of the two methodologies the reference height of trajectory determined from the weighting factor functions is employed.On the basis of the analyses conducted,the potential for further increase in accuracy of these aiming angles preparation methods is pointed out.展开更多
Residential greening constitutes a significant portion of the urban environment. Trees, as the largest entities in the tree-shrub-herb greening system, are the best choice for residential afforestation. Hence, tree ar...Residential greening constitutes a significant portion of the urban environment. Trees, as the largest entities in the tree-shrub-herb greening system, are the best choice for residential afforestation. Hence, tree arrangement in green space between buildings is significant, for which may exert negative impact on building sunshine. This study takes He Qingyuan residential area in Beijing as a case study to predict the growth in tree height between buildings to meet good sunshine requirements. The procedures were draw as follows: 1) models including building layout and trees were built using computer-aided design (Auto CAD). Afterwards, according to tree crown shape, tree height limits were determined for the same building layout;2) and after that, the growth in tree height was predicted using the nonlinear height-diameter functions to meet the good sunshine requirements. The results allow us to determine which trees to plant between buildings in that the designers can predict the effects of future tree growth on building sunshine.展开更多
Measurements of wave heights with image sequences from a Charged Coupled Device(CCD) camera were made. Sinusoidal, as well as unidirectional and directional, waves were used for the experiments. A transfer function wa...Measurements of wave heights with image sequences from a Charged Coupled Device(CCD) camera were made. Sinusoidal, as well as unidirectional and directional, waves were used for the experiments. A transfer function was obtained by calibration of the magnitudes of the gray values of the images against the results of wave gauge measurements for directional waves. With this transfer function, wave heights for regular waves were deduced. It is shown that the average relative errors are smaller than 16% for both unidirectional and directional waves.展开更多
文摘This article delves Chern's conjecture for hypersurfaces with constant second fundamental form squared length S in the spherical space.At present,determining whether the third gap point of S is 2n remains unsolved yet.First,we investigate the height functions and their properties of the position vector and normal vector in natural coordinate vectors,and then prove the existence of a Simons-type integral formula on the hypersurface that simultaneously includes the first,second,and third gap point terms of S.These results can provide new avenues of thought and methods for solving Chern's conjecture.
基金the Research Project for the Development of the Department of Weapons and Ammunition, Faculty of Military Technology, University of Defence, Brno, DZRO VYZBROJ
文摘Projectile trajectories calculated under non-standard conditions are considered to be perturbed. The tools utilized for the analysis of perturbed trajectories are weighting factor functions(WFFs) which are a special kind of sensitivity functions. WFFs are used for calculation of meteo ballistic elements mB(ballistic wind wB, virtual temperature tB, pressure pB, density rB, speed of sound a) as well. An effect of weapon system parameters can be incorporated into calculations through the reference height of trajectory-RHT.RHT are also calculated from WFFs. Methods based on RHT are far more effective than traditional methods that use weighting factors q.We have found that the existing theory of RHT has several shortcomings due to we created an improved theory of generalized RHT which represent a special sensitivity parameters of dynamical systems. Using this theory will improve methods for designing firing tables, fire control systems algorithms, and meteo message generation algorithms.
文摘在林业研究中,胸径-树高二元联合分布多由相同边缘分布构造,而林分的胸径与树高的实际分布状况可能有所差异。为降低这种差异带来的影响,依据佳木斯市孟家岗林场的115块长白落叶松人工林数据,选择适用条件低、适应范围广的Copula函数方法拟合落叶松胸径-树高二元联合分布模型。首先选择威布尔(Weibull)、广义威布尔(G-Weibull)、逻辑斯蒂(Logistic)、轻量逻辑斯蒂(Logit-Logistic)、伽马(Gamma)、对数正态(Log-Normal)6个分布函数作为备选基础模型,根据K-S(kolmogorov smirnov test)检验与半参数估计结果筛选并构建Copula胸径-树高二元联合分布模型,再通过负对数似然(negative log-likelihood,NLL)、Sn拟合优度统计量和似然比检验(likelihood ratio test,LRT)与二元对数logistic分布函数和二元Weibull分布函数进行比较,最后使用雷诺误差指数(error index of Reynolds,EI)对模型预测能力进行评估。结果表明,基于Copula函数的二元分拟合结果与模型(EI=0.3184)预估能力皆优于二元Weibull分布(EI=0.6381)和二元对数Logistic分布(EI=0.9490),说明此方法构建胸径-树高二元联合Copula分布模型能够很好地描述落叶松人工林胸径树高联合分布,以Copula方法构建树高-胸径联合分布是可行的。
基金Supported by the NSFC-Shandong Joint Fund “Study on the DisasterCausing Mechanism and Disaster Prevention Countermeasures of MultiSource Storm Surges”(No.U1706226)the National Natural Science Foundation of China “Coastal Engineering and Risk Assessment Based on a Four-Layer Nested Multi-Objective Probability Model”(No.51379195)+1 种基金the Natural Science Foundation of Shandong Province “Three-Layer Nested Multi-Objective Probability Prediction and Risk Assessment in Coastal Engineering”(No.ZR2013EEM034)the Program of Promotion Plan for Postgraduates’ Educational Quality “Paying More Attention to the Study on the Cultivation Mode of Mathematical Modeling for Engineering Postgraduates”(No.861801232417)
文摘When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year observation data to derive 100-year return period design wave height. Therefore, the study of inherent self-similarity in ocean hydrological elements becomes increasingly important to the study of multi-year return period design wave height derivation. In this paper, we introduced multifractal to analyze the statistical characteristics of wave height series data observed from oceanic hydrological station. An improvement is made to address the existing problems of the multifractal detrended fluctuation analysis (MF-DFA) method, where trend function showed a discontinuity between intervals. The improved MFDFA method is based on signal mode decomposition, replacing piecewise polynomial fitting used in the original method. We applied the proposed method to the wave height data collected at Chaolian Island, Shandong, China, from 1963 to 1989 and was able to conclude the wave height sequence presented weak multi-fractality. This result provided strong support to the past research on the derivation of multi-year return period design wave height with observed data. Moreover, the new method proposed in this paper also provides a new perspective to explore the intrinsic characteristic of data.
文摘A method is presented to extrapolate a time series of wave data to extreme wave heights. The 15-year time series of deepwater wave data collected for 34 min every hour from 1988 to 2002 in the South Pacific Ocean, Australia, is analyzed to generate a set of storm peak wave heights by use of the Peaks-Over-Threshold method. The probability distribution is calculated by grouping the observod storm peak wave heights into a number of wave height classes and assigning a probability to each wave height class. The observed probability distribution is then fitted to eight different probability distribution functions and found to be fitted best by the Weibull distribution （a = 1.17）, nearly best by the FT-Ⅰ, quite well by the exponential, and poorly by the lognormal function based on the criterion of the sum of squares of the errors, SSE （H）. The effect of the threshold wave height on the estimated extreme wave height is also studied and is found insignificant in this study. The 95 % prediction intervals of the best-fit FT-Ⅰ , exponential and Weibull functions are also derived.
文摘Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.
基金support of financial means from the industrial research project of the Ministry of the Interior of the Czech Republic-project code VG20122015076:"Two survey points range-finding system utilization for perimeter security(screen)"the Research project for the development of the Department of Weapons and Ammunition,Faculty of Military Technology, University of Defence,Brno,PRO K-201
文摘This paper deals with the issue of preparation of the aiming angles with the use of tabular firing tables and needed determination of the ballistic elements μ_B(ballistic wind w_B,w_(xB),w_(ZB),ballistic(virtual) temperature τ_B.ballistic density p_B) from the standardized met messages.The weighting factors are used for the calculation of ballistic elements μ_B that are incorporated into the trajectory calculations characteristics of weapon and ammunition.Two different methodologies practically used in the praxis are analysed and compared.For the comparison of the two methodologies the reference height of trajectory determined from the weighting factor functions is employed.On the basis of the analyses conducted,the potential for further increase in accuracy of these aiming angles preparation methods is pointed out.
文摘Residential greening constitutes a significant portion of the urban environment. Trees, as the largest entities in the tree-shrub-herb greening system, are the best choice for residential afforestation. Hence, tree arrangement in green space between buildings is significant, for which may exert negative impact on building sunshine. This study takes He Qingyuan residential area in Beijing as a case study to predict the growth in tree height between buildings to meet good sunshine requirements. The procedures were draw as follows: 1) models including building layout and trees were built using computer-aided design (Auto CAD). Afterwards, according to tree crown shape, tree height limits were determined for the same building layout;2) and after that, the growth in tree height was predicted using the nonlinear height-diameter functions to meet the good sunshine requirements. The results allow us to determine which trees to plant between buildings in that the designers can predict the effects of future tree growth on building sunshine.
基金This work was financially supported by the Science Council, Taiwan (Project No. NSC 91 2611 E 019 007)
文摘Measurements of wave heights with image sequences from a Charged Coupled Device(CCD) camera were made. Sinusoidal, as well as unidirectional and directional, waves were used for the experiments. A transfer function was obtained by calibration of the magnitudes of the gray values of the images against the results of wave gauge measurements for directional waves. With this transfer function, wave heights for regular waves were deduced. It is shown that the average relative errors are smaller than 16% for both unidirectional and directional waves.
