The degree of numerical linear independence is proposed and discussed. Based on this linear independence theory, a modified limited memory BFGS method is deve loped. Similar to the standard limited memory method, thi...The degree of numerical linear independence is proposed and discussed. Based on this linear independence theory, a modified limited memory BFGS method is deve loped. Similar to the standard limited memory method, this new method determines the new update by applying the updating formula m times to an initial positive diagonal matrix using the m previous pairs of the change in iteration and gradient. Besides the most recent pair of the change, which guarantees the quadratic termination, the choice of the other ( m -1) pairs of the change in the new method is dependent on the degree of numerical linear independence of previous search directions. In addition, the numerical linear independence theory is further discussed and the computation of the degree of linear independence is simplified. Theoretical and numerical results show that this new modified method improves efficiently the standard limited memory method.展开更多
【目的】探究枣树冠层水分的变化对偏振光谱的影响,为后续大面积枣园枣树生理监测提供依据。【方法】基于近红外高光谱成像技术对干湿枣叶不同偏振角度下的图像进行线偏振度(Degree of Linear Polarizationg,Dolp)计算、主成分对比分析...【目的】探究枣树冠层水分的变化对偏振光谱的影响,为后续大面积枣园枣树生理监测提供依据。【方法】基于近红外高光谱成像技术对干湿枣叶不同偏振角度下的图像进行线偏振度(Degree of Linear Polarizationg,Dolp)计算、主成分对比分析。通过对骏枣枣叶的图像处理,可以在图像上和光谱上看出骏枣枣叶水分分布差异。【结果】在对图像进行Dolp计算后可以清楚地看出其光谱差异,新鲜枣叶在波长1450nm附近Dolp图像具有明显的水分特征峰,干燥的枣叶在1450nm处无明显的水分特征峰。【结论】对偏振高光谱图像处理后得到不同颜色标记的不同水分叶片的图像;并在图像上光谱显示其水分特征峰,达到光谱检测差异,图像显示分布的效果为后续定量检测打下基础。展开更多
Based on the study of phase angle and wavelength in pBRDF (Polarized bidirectional reflectance distribution function), roujean model was proposed to describe Orient (Polarization phase angle) quantitatively. The Rouje...Based on the study of phase angle and wavelength in pBRDF (Polarized bidirectional reflectance distribution function), roujean model was proposed to describe Orient (Polarization phase angle) quantitatively. The Roujean model was used to quantitatively describe different fruits intensity components (<i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;">) and polarization phase angle (Orient), and the simulation results were analyzed and compared using statistical analysis and comparison methods to realize the prediction from the regular model to the outdoor fruit tree canopy to the canopy of outdoor fruit tree canopy random distribution. The experimental results showed that: 1) when the phase angle of jujube was 52.19<span style="white-space:nowrap;">°</span>, 66.51<span style="white-space:nowrap;">°</span></span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">and 88.26<span style="white-space:nowrap;">°</span>, the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average errors of </span><i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> parameters described by Roujean model are 0.9982, 0.9963, 0.9912 and 3.80%, 4.17%, 6.40%, respectively;</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">a</span><span style="font-family:Verdana;font-size:12px;">nd the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average error of Orient parameters described by Roujean model are 0.9056,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">0.9223,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">0.9260 and 6.23%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">3.32%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">8.05%, respectively;It can be seen that roujean model can quantitatively describe the Orient parameter of jujube</span><span style="font-family:Verdana;font-size:12px;">;</span><span style="font-family:Verdana;font-size:12px;">2) When the phase angle of apricot was 70.99<span style="white-space:nowrap;">°</span>, 71.28<span style="white-space:nowrap;">°</span> and 67.91<span style="white-space:nowrap;">°</span>, the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average errors of </span><i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> parameters described by Roujean model </span><span style="font-family:Verdana;font-size:12px;">is</span><span style="font-family:Verdana;font-size:12px;"> 0.9862, 0.9823, 0.9792 and 3.40%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">4.82%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">5.19%, respectively;</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">And the R</span><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average error of Orient parameters described by Roujean model are 0.9382, 0.8947, 0.8849 and 7.19%, 9.28%, 9.47%, respectively.</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">Roujean model can also quantitatively describe the Orient parameter of white apricot. In summary, the Roujean model can provide a good quantitative description of </span><i><span style="font-family:Verdana;font-size:12px;">f</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> and a good quantitative description of Orient, which in turn can predict the pBRDF parameter for more fruits with different incidence and detection directions.</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">It can correct the influence of angle factor in the nondestructive testing of outdoor fruits.</span>展开更多
M-Sequences play a big important role,as the other binary orthogonal sequences,for collection the information on the input links and distribution these information on the output links of the communication channels and...M-Sequences play a big important role,as the other binary orthogonal sequences,for collection the information on the input links and distribution these information on the output links of the communication channels and for building new systems with more complexity,larger period,and security,through multiplication these sequences.In our article we try to study the construction of the multiplication sequence{zn}and its linear equivalent,this multiplication sequence is as multiple two sequences,the first sequence{an}is an arbitrary M-sequence and the second sequence{bn}is not completely different but is the reciprocal sequence of the first sequence{an}that is the reciprocal sequence has characteristic polynomial g(x)is reciprocal of f(x),which is the characteristic polynomial of the first sequence{an},also we will study the linear equivalent of the multiplication sequence{zn}and we will see that the length of the linear equivalent of{zn}is equal to((deg f(x))^(2)-deg(f(x)).展开更多
With k_8/k_(16), the ratio of the hydrolytic rate-constants of p-nitrophenyl octanoate (C8) to hexadecanoate (C16), as the indicator of the degree of aggregation, the linear dependence of the deg- ree of aggregation o...With k_8/k_(16), the ratio of the hydrolytic rate-constants of p-nitrophenyl octanoate (C8) to hexadecanoate (C16), as the indicator of the degree of aggregation, the linear dependence of the deg- ree of aggregation on solvent aggregating power (SAgP) has been established in five aquiorgano sol- vents, each within a certain range of volume fraction ( values) of the organic cosolvent. The mea- ning of this linearity has been discussed.展开更多
文摘The degree of numerical linear independence is proposed and discussed. Based on this linear independence theory, a modified limited memory BFGS method is deve loped. Similar to the standard limited memory method, this new method determines the new update by applying the updating formula m times to an initial positive diagonal matrix using the m previous pairs of the change in iteration and gradient. Besides the most recent pair of the change, which guarantees the quadratic termination, the choice of the other ( m -1) pairs of the change in the new method is dependent on the degree of numerical linear independence of previous search directions. In addition, the numerical linear independence theory is further discussed and the computation of the degree of linear independence is simplified. Theoretical and numerical results show that this new modified method improves efficiently the standard limited memory method.
文摘【目的】探究枣树冠层水分的变化对偏振光谱的影响,为后续大面积枣园枣树生理监测提供依据。【方法】基于近红外高光谱成像技术对干湿枣叶不同偏振角度下的图像进行线偏振度(Degree of Linear Polarizationg,Dolp)计算、主成分对比分析。通过对骏枣枣叶的图像处理,可以在图像上和光谱上看出骏枣枣叶水分分布差异。【结果】在对图像进行Dolp计算后可以清楚地看出其光谱差异,新鲜枣叶在波长1450nm附近Dolp图像具有明显的水分特征峰,干燥的枣叶在1450nm处无明显的水分特征峰。【结论】对偏振高光谱图像处理后得到不同颜色标记的不同水分叶片的图像;并在图像上光谱显示其水分特征峰,达到光谱检测差异,图像显示分布的效果为后续定量检测打下基础。
文摘Based on the study of phase angle and wavelength in pBRDF (Polarized bidirectional reflectance distribution function), roujean model was proposed to describe Orient (Polarization phase angle) quantitatively. The Roujean model was used to quantitatively describe different fruits intensity components (<i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;">) and polarization phase angle (Orient), and the simulation results were analyzed and compared using statistical analysis and comparison methods to realize the prediction from the regular model to the outdoor fruit tree canopy to the canopy of outdoor fruit tree canopy random distribution. The experimental results showed that: 1) when the phase angle of jujube was 52.19<span style="white-space:nowrap;">°</span>, 66.51<span style="white-space:nowrap;">°</span></span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">and 88.26<span style="white-space:nowrap;">°</span>, the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average errors of </span><i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> parameters described by Roujean model are 0.9982, 0.9963, 0.9912 and 3.80%, 4.17%, 6.40%, respectively;</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">a</span><span style="font-family:Verdana;font-size:12px;">nd the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average error of Orient parameters described by Roujean model are 0.9056,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">0.9223,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">0.9260 and 6.23%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">3.32%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">8.05%, respectively;It can be seen that roujean model can quantitatively describe the Orient parameter of jujube</span><span style="font-family:Verdana;font-size:12px;">;</span><span style="font-family:Verdana;font-size:12px;">2) When the phase angle of apricot was 70.99<span style="white-space:nowrap;">°</span>, 71.28<span style="white-space:nowrap;">°</span> and 67.91<span style="white-space:nowrap;">°</span>, the </span><i><span style="font-family:Verdana;font-size:12px;">R</span></i><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average errors of </span><i><span style="font-family:Verdana;font-size:12px;">F</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> parameters described by Roujean model </span><span style="font-family:Verdana;font-size:12px;">is</span><span style="font-family:Verdana;font-size:12px;"> 0.9862, 0.9823, 0.9792 and 3.40%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">4.82%,</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">5.19%, respectively;</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">And the R</span><sup><span style="font-family:Verdana;font-size:12px;vertical-align:super;">2</span></sup><span style="font-family:Verdana;font-size:12px;"> and average error of Orient parameters described by Roujean model are 0.9382, 0.8947, 0.8849 and 7.19%, 9.28%, 9.47%, respectively.</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">Roujean model can also quantitatively describe the Orient parameter of white apricot. In summary, the Roujean model can provide a good quantitative description of </span><i><span style="font-family:Verdana;font-size:12px;">f</span></i><sub><span style="font-family:Verdana;font-size:12px;vertical-align:sub;">00</span></sub><span style="font-family:Verdana;font-size:12px;"> and a good quantitative description of Orient, which in turn can predict the pBRDF parameter for more fruits with different incidence and detection directions.</span><span style="font-family:Verdana;font-size:12px;"> </span><span style="font-family:Verdana;font-size:12px;">It can correct the influence of angle factor in the nondestructive testing of outdoor fruits.</span>
文摘M-Sequences play a big important role,as the other binary orthogonal sequences,for collection the information on the input links and distribution these information on the output links of the communication channels and for building new systems with more complexity,larger period,and security,through multiplication these sequences.In our article we try to study the construction of the multiplication sequence{zn}and its linear equivalent,this multiplication sequence is as multiple two sequences,the first sequence{an}is an arbitrary M-sequence and the second sequence{bn}is not completely different but is the reciprocal sequence of the first sequence{an}that is the reciprocal sequence has characteristic polynomial g(x)is reciprocal of f(x),which is the characteristic polynomial of the first sequence{an},also we will study the linear equivalent of the multiplication sequence{zn}and we will see that the length of the linear equivalent of{zn}is equal to((deg f(x))^(2)-deg(f(x)).
基金Project supported by the National Natural Science Foundation of China.
文摘With k_8/k_(16), the ratio of the hydrolytic rate-constants of p-nitrophenyl octanoate (C8) to hexadecanoate (C16), as the indicator of the degree of aggregation, the linear dependence of the deg- ree of aggregation on solvent aggregating power (SAgP) has been established in five aquiorgano sol- vents, each within a certain range of volume fraction ( values) of the organic cosolvent. The mea- ning of this linearity has been discussed.
