There are various applications of the stability theory of the first-order dynamical systems. And the stability of the non-linear control systems can be determined by its linear part. In practice, it is not enough to k...There are various applications of the stability theory of the first-order dynamical systems. And the stability of the non-linear control systems can be determined by its linear part. In practice, it is not enough to know the stability of the dynamical systems. Sometimes we must know the degree of stability of these systems. In this paper, we present some criteria for the degree of stability of the linear constant systems, by using the entries of the coefficient matrix A only.展开更多
A high efficiency, high power factor, and linear constant current LED driver based on adaptive seg- mented linear architecture is presented. When the input voltage varied, the proposed LED driver automatically switche...A high efficiency, high power factor, and linear constant current LED driver based on adaptive seg- mented linear architecture is presented. When the input voltage varied, the proposed LED driver automatically switched over LED strings according to the segmented LED voltage drop, which increased the LED lighting time. The efficiency and power factor are improved, while the system design is simplified by this control scheme. Without the usage of electrolytic capacitor and magnetic components, the proposed driver possesses advantages of smaller size, longer lifetime and lower cost over others. The proposed driver is implemented in 0.8 μm 5 V/40 V HVCMOS process, which occupies an active area of 820× 920μm2. The measured results show that the average value of the internal reference voltage is 500 4- 7 mV, with a standard deviation of only 4.629 mV, thus LED current can be set accurately. Under 220 V root mean square 50 Hz utility voltage and the number ratio of the three LED strings being 47 ： 17 ： 16, the system can realize a high power factor of 0.974 and power conversion efficiency of 93.4%.展开更多
Based on the constant modulus criterion, a new Widely Linear(WL) blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance f...Based on the constant modulus criterion, a new Widely Linear(WL) blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance for complex-valued noncircular signals. The new algorithm takes advantage of the WL filtering theory by taking full use of second-order statistical information of the complex-valued noncircular signals. Therefore, the weight vector contains the complete second-order information of the real and imaginary parts to decrease the residual inter-symbol interference effectively. Theoretical analysis and simulation results show that the proposed scheme can significantly improve the equalization performance for complex-valued noncircular signals compared with traditional blind equalization algorithms.展开更多
According to the appearing of isosbestic point in the absorption spectra of Ho/Y-Tribromoarsenazo (TBA)systems,the complexation reaction is considered to be M+nL=ML_n.A method has been proposed based on it for calcula...According to the appearing of isosbestic point in the absorption spectra of Ho/Y-Tribromoarsenazo (TBA)systems,the complexation reaction is considered to be M+nL=ML_n.A method has been proposed based on it for calculating the mole fraction of free complexing agent in the solutions from spectral data.and two linear regression formula have been introduced to determine the composition,the molar absorptivity,the conditional stability constant of the complex and the concentration of the complexing agent. This method has been used in Ho-TBA and Y-TBA systems.Ho^(3+)and Y^(3+)react with TBA and form 1: 2 complexes in HCl-NaAc buffer solution at pH 3.80.Their molar absorptivities determined are 1.03×10~8 and 1.10×10~8 cm^2·mol^(-1),and the conditional stability constants(logβ_2)are 11.37 and 11.15 respectively.After considering the pH effect in TBA complexing,their stability constants(log β_2^(ahs))are 43.23 and 43.01. respectively.The new method is adaptable to such systems where the accurate concentration of the complexing agent can not be known conveniently.展开更多
The properties of absorption spectra are presented and the linear correlations of Hammett constants with the 0-0 transition energy(E_(o,o))of S_←S_o, and the ratios of oscillator strength(f/f)are used to probe the in...The properties of absorption spectra are presented and the linear correlations of Hammett constants with the 0-0 transition energy(E_(o,o))of S_←S_o, and the ratios of oscillator strength(f/f)are used to probe the interactions betwee π-electron of aromatic maerocycles or metal ion of complexes with the sub- stituents on β-position of benzene ring for porphyrin-like maerocyclic compounds.展开更多
A new method,dual-series linear regression method,has been used to study the complexation equilibrium of praseodymium(Pr^(3+))with tribromoarsenazo(TBA)without knowing the accurate concentra- tion of the complexing ag...A new method,dual-series linear regression method,has been used to study the complexation equilibrium of praseodymium(Pr^(3+))with tribromoarsenazo(TBA)without knowing the accurate concentra- tion of the complexing agent TBA.In 1.2 mol/L HCl solution, Pr^(3+)reacts with TBA and forms 1:3 com- plex,the conditional stability constant(lgβ_3)of the complex determined is 15.47,and its molar absorptivity(ε_3^(630))is 1.48×10~5 L·mol^(-1)·cm^(-1).展开更多
The proposed model considers the products with finite shelf-life which causes a small amount of decay. The market demand is assumed to be level dependent and in a linear form. The model has also considered the constan...The proposed model considers the products with finite shelf-life which causes a small amount of decay. The market demand is assumed to be level dependent and in a linear form. The model has also considered the constant production rate which stops attaining a desired level of inventories and that is the highest level of inventories. Production starts with a buffer stock and without any sort of backlogs. Due to the market demand and product’s decay, the inventory reduces to the level of buffer stock where again the production cycle starts. With a numerical search procedure the proof of the proposed model has been shown. The objective of the model is to obtain the total average optimum inventory cost and optimum ordering cycle.展开更多
Based on a uniform linear array, a new widely linear unscented Kalman filter-based constant modulus algorithm (WL-UKF-CMA) for blind adaptive beamforming is proposed. The new algorithm is designed according to the con...Based on a uniform linear array, a new widely linear unscented Kalman filter-based constant modulus algorithm (WL-UKF-CMA) for blind adaptive beamforming is proposed. The new algorithm is designed according to the constant modulus criterion and takes full advantage of the noncircular property of the signal of interest (SOI), significantly increasing the output signal-to interference-plus-noise ratio (SINR), enhancing the convergence speed and decreasing the steady-state misadjustment. Since it requires no known training data, the proposed algorithm saves a large amount of the available spectrum. Theoretical analysis and simulation results are presented to demonstrate its superiority over the conventional linear least mean square-based CMA (L-LMS-CMA), the conventional linear recursive least square-based CMA (L-RLS-CMA), WL-LMS-CMA, WL-RLS-CMA and L-UKF-CMA.展开更多
This paper considers the Cauchy problem with a kind of non-smooth initial data for general inhomogeneous quasilinear hyperbolic systems with characteristics with constant multiplicity. Under the matching condition, ba...This paper considers the Cauchy problem with a kind of non-smooth initial data for general inhomogeneous quasilinear hyperbolic systems with characteristics with constant multiplicity. Under the matching condition, based on the refined fomulas on the decomposition of waves, we obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution to the Cauchy problem.展开更多
Swept wing is widely used in civil aircraft,whose airfoil is chosen,designed and optimized to increase the cruise speed and decrease the drag coefficient.The parameters of swept wing,such as sweep angle and angle of a...Swept wing is widely used in civil aircraft,whose airfoil is chosen,designed and optimized to increase the cruise speed and decrease the drag coefficient.The parameters of swept wing,such as sweep angle and angle of attack,are determined according to the cruise lift coefficient requirement,and the drag coefficient is expected to be predicted accurately,which involves the instability characteristics and transition position of the flow.The pressure coefficient of the RAE2822 wing with given constant lift coefficient is obtained by solving the three-dimensional Navier-Stokes equation numerically,and then the mean flow is calculated by solving the boundary layer（BL） equation with spectral method.The cross-flow instability characteristic of boundary layer of swept wing in the windward and leeward is analyzed by linear stability theory（LST）,and the transition position is predicted by eNmethod.The drag coefficient is numerically predicted by introducing a laminar/turbulent indicator.A simple approach to calculate the lift coefficient of swept wing is proposed.It is found that there is a quantitative relationship between the angle of attack and sweep angle when the lift coefficient keeps constant;when the angle of attack is small,the flow on the leeward of the wing is stable.when the angle of attack is larger than 3°,the flow becomes unstable quickly;with the increase of sweep angle or angle of attack the disturbance on the windward becomes more unstable,leading to the moving forward of the transition position to the leading edge of the wing;the drag coefficient has two significant jumping growth due to the successive occurrence of transition in the windward and the leeward;the optimal range of sweep angle for civil aircraft is suggested.展开更多
In this present paper, an inventory model with a generalised exponential decreasing demand is considered. A numerical example is used to illustrate the application of the model. Sensitivity analysis of the optimal sol...In this present paper, an inventory model with a generalised exponential decreasing demand is considered. A numerical example is used to illustrate the application of the model. Sensitivity analysis of the optimal solution with respect to various parameters is carried out to see the effect of parameter changes on the solution.展开更多
In this paper,the nonliner response of granular composite medium is studied.The composite medium considered here is composed of nonlinear cylinders with linear concentric shells randomly distributed in linear host.In ...In this paper,the nonliner response of granular composite medium is studied.The composite medium considered here is composed of nonlinear cylinders with linear concentric shells randomly distributed in linear host.In the dilute limit,the effective linear dielectric constant and the high-order nonlinear susceptibilities are presented.展开更多
As a mono-sodium salt form of alendronic acid,alendronate sodium presents multi-level ionization for the dissociation of its four hydroxyl groups.The dissociation constants of alendronate sodium were determined in thi...As a mono-sodium salt form of alendronic acid,alendronate sodium presents multi-level ionization for the dissociation of its four hydroxyl groups.The dissociation constants of alendronate sodium were determined in this work by studying the piecewise linear relationship between volume of titrant and p H value based on acidbase potentiometric titration reaction.The distribution curves of alendronate sodium were drawn according to the determined p Ka values.There were 4 dissociation constants(pKa_1=2.43,pKa_2=7.55,pKa_3=10.80,pKa_4=11.99,respectively) of alendronate sodium,and 12 existing forms,of which 4 could be ignored,existing in different p H environments.展开更多
The paper is concerned with the problem of reduction of the general relativity theory to the Newton gravitation theory for a gravitation field with relatively low intensity. This problem is traditionally solved on the...The paper is concerned with the problem of reduction of the general relativity theory to the Newton gravitation theory for a gravitation field with relatively low intensity. This problem is traditionally solved on the basis of linearized equations of general relativity which, being matched to the Newton theory equations, allow us to link the classical gravitation constant with the constant entering the general relativity equations. Analysis of the linearized general relativity equations shows that it can be done only for empty space in which the energy tensor is zero. In solids, the set of linearized general relativity equations is not consistent and is not reduced to the Newton theory equations. Specific features of the problem are demonstrated with the spherically symmetric static problem of general relativity which has the closed-form solution.展开更多
The reactions LnCl3 (s) + (3/2)Al2Cl6, (g) = LnAl3Cl12 (g) for Ln = La to Lu were studied by quenching experiments in roughly the same temperature and pressure ranges (588-851 K and 0.01-0.22 MPa). Stability constant...The reactions LnCl3 (s) + (3/2)Al2Cl6, (g) = LnAl3Cl12 (g) for Ln = La to Lu were studied by quenching experiments in roughly the same temperature and pressure ranges (588-851 K and 0.01-0.22 MPa). Stability constants Kθ of lanthanide complexes LnAl3Cl12 were calculated from the measurements. The values of Ig Kθ change linearly with the ionpotential (Z+/r) of lanthanide(Ⅲ) from La to Gd and from Tb to Lu, respectively, indicating the Gd break. There exist inclined W effect between Ig Kθ and the total angular momentum L of lanthanide(Ⅲ). And hereby lanthanide elements are divided into four segments, La-Nd, Pm-Gd, Tb-Ho, and Er-Lu. In each segment, the linearity is maintained.展开更多
Variable acceleration linear motion is an important motion model in senior high school. This paper analyzes five common variable acceleration linear motion models in senior high school physics, and summarizes the crit...Variable acceleration linear motion is an important motion model in senior high school. This paper analyzes five common variable acceleration linear motion models in senior high school physics, and summarizes the critical state in the process of object motion, as well as solutions to common problems in the models.展开更多
Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be self- adaptively chosen by bal...Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be self- adaptively chosen by balancing the total variation of the target function. In this paper, we adopt continuous piecewise linear approximation instead of the existing piecewise constants approximation. The results of experiments show that this new method is superior to the old one.展开更多
This paper discusses a procedure that was adopted for the development of a linear regression model for estimating solar radiation in Malawi. By making use of sunshine-hours data recorded at six selected meteorological...This paper discusses a procedure that was adopted for the development of a linear regression model for estimating solar radiation in Malawi. By making use of sunshine-hours data recorded at six selected meteorological stations in the country, namely: Salima, Makoka, Karonga, Bolero, Chileka and Mzimba over the period 1991-1995, a set of Angstrom constants were obtained and averaged in order to develop the linear regression model. This model has potential for generating ground observation data of solar radiation at any given location in the country using sunshine hours as the only required input. The Gunn-Bellan Spherical Pyranometer and the Campbell Stokes Sunshine Recorder were respectively used in the measurement of incident radiation (Ib) in J·cm–2/day (converted to MJ·m–2·day–1) and sunshine hours. An Angstrom model of monthly average Clearness Index with normalized sunshine duration was then developed for each of the six meteorological stations. The resulting linear regression model was applied in estimating monthly average daily solar radiation. Regression analysis between computed and measured radiation data was applied to assess the reliability of the generated Angstrom constants. The results generally show a high degree of agreement between the two variables, with correlation coefficients ranging from 0.63 to 0.90. Angstrom constants obtained at the six meteorological stations were thereafter averaged in order to develop a linear regression model for estimating solar radiation in Malawi. Solar radiation values obtained using this model were noted to be in good agreement with those developed for each of the six meteorological stations.展开更多
In this paper, a mathematical relation was found between interatomic Hooke’s force constant and both the bulk modulus and interatomic distance in solid crystals, considering that the forces which have effect on an at...In this paper, a mathematical relation was found between interatomic Hooke’s force constant and both the bulk modulus and interatomic distance in solid crystals, considering that the forces which have effect on an atom are only those resulted from the neighboring atoms, and the forces are subject to Hooke’s law as the deflections of atoms from their equilibrium positions are very small. This work has been applied on some solid semiconducting crystals of diatomic primitive cell, including crystals of mono-atomic primitive cell automatically, by using linear statistical fitting with computer programming and, then, using mathematical analysis, proceeding from the vibrational dispersion relation of solid linear lattice, these two methods have been used in the process in order to support each other and for the result to be satisfying and reasonable. This is a contribution to the process of using computer programming in physics to facilitate mathematical analyses and obtain the required relations and functions by designing and developing appropriate computer programs in line with the macro and micro natures of materials. The importance of this is in enhancing our understanding of the interatomic actions in cells and of the crystal structure of materials in general and semiconductors in particular, as it is a step of the initial steps to facilitate the process of calculating energies and extracting mathematical relations between correlation energy and temperature as well as between sub-fusion and fusion energies with temperature.展开更多
文摘There are various applications of the stability theory of the first-order dynamical systems. And the stability of the non-linear control systems can be determined by its linear part. In practice, it is not enough to know the stability of the dynamical systems. Sometimes we must know the degree of stability of these systems. In this paper, we present some criteria for the degree of stability of the linear constant systems, by using the entries of the coefficient matrix A only.
基金supported by the National Natural Science Foundation of China(Nos.61234002,61322405,61306044,61376033)
文摘A high efficiency, high power factor, and linear constant current LED driver based on adaptive seg- mented linear architecture is presented. When the input voltage varied, the proposed LED driver automatically switched over LED strings according to the segmented LED voltage drop, which increased the LED lighting time. The efficiency and power factor are improved, while the system design is simplified by this control scheme. Without the usage of electrolytic capacitor and magnetic components, the proposed driver possesses advantages of smaller size, longer lifetime and lower cost over others. The proposed driver is implemented in 0.8 μm 5 V/40 V HVCMOS process, which occupies an active area of 820× 920μm2. The measured results show that the average value of the internal reference voltage is 500 4- 7 mV, with a standard deviation of only 4.629 mV, thus LED current can be set accurately. Under 220 V root mean square 50 Hz utility voltage and the number ratio of the three LED strings being 47 ： 17 ： 16, the system can realize a high power factor of 0.974 and power conversion efficiency of 93.4%.
基金Supported by the National Natural Science Foundation of China(No.61072046)the Basic Scientific and Technological Frontier Project of Henan Province(No.1123004100322)
文摘Based on the constant modulus criterion, a new Widely Linear(WL) blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance for complex-valued noncircular signals. The new algorithm takes advantage of the WL filtering theory by taking full use of second-order statistical information of the complex-valued noncircular signals. Therefore, the weight vector contains the complete second-order information of the real and imaginary parts to decrease the residual inter-symbol interference effectively. Theoretical analysis and simulation results show that the proposed scheme can significantly improve the equalization performance for complex-valued noncircular signals compared with traditional blind equalization algorithms.
文摘According to the appearing of isosbestic point in the absorption spectra of Ho/Y-Tribromoarsenazo (TBA)systems,the complexation reaction is considered to be M+nL=ML_n.A method has been proposed based on it for calculating the mole fraction of free complexing agent in the solutions from spectral data.and two linear regression formula have been introduced to determine the composition,the molar absorptivity,the conditional stability constant of the complex and the concentration of the complexing agent. This method has been used in Ho-TBA and Y-TBA systems.Ho^(3+)and Y^(3+)react with TBA and form 1: 2 complexes in HCl-NaAc buffer solution at pH 3.80.Their molar absorptivities determined are 1.03×10~8 and 1.10×10~8 cm^2·mol^(-1),and the conditional stability constants(logβ_2)are 11.37 and 11.15 respectively.After considering the pH effect in TBA complexing,their stability constants(log β_2^(ahs))are 43.23 and 43.01. respectively.The new method is adaptable to such systems where the accurate concentration of the complexing agent can not be known conveniently.
文摘The properties of absorption spectra are presented and the linear correlations of Hammett constants with the 0-0 transition energy(E_(o,o))of S_←S_o, and the ratios of oscillator strength(f/f)are used to probe the interactions betwee π-electron of aromatic maerocycles or metal ion of complexes with the sub- stituents on β-position of benzene ring for porphyrin-like maerocyclic compounds.
文摘A new method,dual-series linear regression method,has been used to study the complexation equilibrium of praseodymium(Pr^(3+))with tribromoarsenazo(TBA)without knowing the accurate concentra- tion of the complexing agent TBA.In 1.2 mol/L HCl solution, Pr^(3+)reacts with TBA and forms 1:3 com- plex,the conditional stability constant(lgβ_3)of the complex determined is 15.47,and its molar absorptivity(ε_3^(630))is 1.48×10~5 L·mol^(-1)·cm^(-1).
文摘The proposed model considers the products with finite shelf-life which causes a small amount of decay. The market demand is assumed to be level dependent and in a linear form. The model has also considered the constant production rate which stops attaining a desired level of inventories and that is the highest level of inventories. Production starts with a buffer stock and without any sort of backlogs. Due to the market demand and product’s decay, the inventory reduces to the level of buffer stock where again the production cycle starts. With a numerical search procedure the proof of the proposed model has been shown. The objective of the model is to obtain the total average optimum inventory cost and optimum ordering cycle.
基金supported by the National Natural Science Foundation of China(61573113)the Harbin Science and Technology Innovation Talents(Excellent Discipline Leader)Research Fund(2014RFXXJ074)the National Scholarship([2016]3100)
文摘Based on a uniform linear array, a new widely linear unscented Kalman filter-based constant modulus algorithm (WL-UKF-CMA) for blind adaptive beamforming is proposed. The new algorithm is designed according to the constant modulus criterion and takes full advantage of the noncircular property of the signal of interest (SOI), significantly increasing the output signal-to interference-plus-noise ratio (SINR), enhancing the convergence speed and decreasing the steady-state misadjustment. Since it requires no known training data, the proposed algorithm saves a large amount of the available spectrum. Theoretical analysis and simulation results are presented to demonstrate its superiority over the conventional linear least mean square-based CMA (L-LMS-CMA), the conventional linear recursive least square-based CMA (L-RLS-CMA), WL-LMS-CMA, WL-RLS-CMA and L-UKF-CMA.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 11071141 11271192)+4 种基金China Postdoctoral Science Foundation (Grant No. 20100481161)the Postdoctoral Foundation of Jiangsu Province (GrantNo. 1001042C)Qing Lan Project of Jiangsu Provincethe Natural Science Foundation of the Jiangsu Higher Education Committee of China (Grant No. 11KJA110001)the Natural Science Foundation of Jiangsu Provience (Grant No. BK2011777)
文摘This paper considers the Cauchy problem with a kind of non-smooth initial data for general inhomogeneous quasilinear hyperbolic systems with characteristics with constant multiplicity. Under the matching condition, based on the refined fomulas on the decomposition of waves, we obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution to the Cauchy problem.
基金co-supported by the National Natural Science Foundation of China(Nos.11332007,11672351)the Tianjin Natural Science Foundation of China(No.15JCYBJC19500)+1 种基金the Hebei Natural Science Foundation of China(No.A2015105073)an open fund from the State Key Laboratory of Aerodynamics of China(No.SKLA201601)
文摘Swept wing is widely used in civil aircraft,whose airfoil is chosen,designed and optimized to increase the cruise speed and decrease the drag coefficient.The parameters of swept wing,such as sweep angle and angle of attack,are determined according to the cruise lift coefficient requirement,and the drag coefficient is expected to be predicted accurately,which involves the instability characteristics and transition position of the flow.The pressure coefficient of the RAE2822 wing with given constant lift coefficient is obtained by solving the three-dimensional Navier-Stokes equation numerically,and then the mean flow is calculated by solving the boundary layer（BL） equation with spectral method.The cross-flow instability characteristic of boundary layer of swept wing in the windward and leeward is analyzed by linear stability theory（LST）,and the transition position is predicted by eNmethod.The drag coefficient is numerically predicted by introducing a laminar/turbulent indicator.A simple approach to calculate the lift coefficient of swept wing is proposed.It is found that there is a quantitative relationship between the angle of attack and sweep angle when the lift coefficient keeps constant;when the angle of attack is small,the flow on the leeward of the wing is stable.when the angle of attack is larger than 3°,the flow becomes unstable quickly;with the increase of sweep angle or angle of attack the disturbance on the windward becomes more unstable,leading to the moving forward of the transition position to the leading edge of the wing;the drag coefficient has two significant jumping growth due to the successive occurrence of transition in the windward and the leeward;the optimal range of sweep angle for civil aircraft is suggested.
文摘In this present paper, an inventory model with a generalised exponential decreasing demand is considered. A numerical example is used to illustrate the application of the model. Sensitivity analysis of the optimal solution with respect to various parameters is carried out to see the effect of parameter changes on the solution.
文摘In this paper,the nonliner response of granular composite medium is studied.The composite medium considered here is composed of nonlinear cylinders with linear concentric shells randomly distributed in linear host.In the dilute limit,the effective linear dielectric constant and the high-order nonlinear susceptibilities are presented.
基金the support of Key Laboratory of Chinese Medicine Preparation of Solid Dispersion,Gansu Longshenrongfa Pharmaceutical Industry Co.,Ltd.,Gansu Province,China
文摘As a mono-sodium salt form of alendronic acid,alendronate sodium presents multi-level ionization for the dissociation of its four hydroxyl groups.The dissociation constants of alendronate sodium were determined in this work by studying the piecewise linear relationship between volume of titrant and p H value based on acidbase potentiometric titration reaction.The distribution curves of alendronate sodium were drawn according to the determined p Ka values.There were 4 dissociation constants(pKa_1=2.43,pKa_2=7.55,pKa_3=10.80,pKa_4=11.99,respectively) of alendronate sodium,and 12 existing forms,of which 4 could be ignored,existing in different p H environments.
文摘The paper is concerned with the problem of reduction of the general relativity theory to the Newton gravitation theory for a gravitation field with relatively low intensity. This problem is traditionally solved on the basis of linearized equations of general relativity which, being matched to the Newton theory equations, allow us to link the classical gravitation constant with the constant entering the general relativity equations. Analysis of the linearized general relativity equations shows that it can be done only for empty space in which the energy tensor is zero. In solids, the set of linearized general relativity equations is not consistent and is not reduced to the Newton theory equations. Specific features of the problem are demonstrated with the spherically symmetric static problem of general relativity which has the closed-form solution.
文摘The reactions LnCl3 (s) + (3/2)Al2Cl6, (g) = LnAl3Cl12 (g) for Ln = La to Lu were studied by quenching experiments in roughly the same temperature and pressure ranges (588-851 K and 0.01-0.22 MPa). Stability constants Kθ of lanthanide complexes LnAl3Cl12 were calculated from the measurements. The values of Ig Kθ change linearly with the ionpotential (Z+/r) of lanthanide(Ⅲ) from La to Gd and from Tb to Lu, respectively, indicating the Gd break. There exist inclined W effect between Ig Kθ and the total angular momentum L of lanthanide(Ⅲ). And hereby lanthanide elements are divided into four segments, La-Nd, Pm-Gd, Tb-Ho, and Er-Lu. In each segment, the linearity is maintained.
文摘Variable acceleration linear motion is an important motion model in senior high school. This paper analyzes five common variable acceleration linear motion models in senior high school physics, and summarizes the critical state in the process of object motion, as well as solutions to common problems in the models.
文摘Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be self- adaptively chosen by balancing the total variation of the target function. In this paper, we adopt continuous piecewise linear approximation instead of the existing piecewise constants approximation. The results of experiments show that this new method is superior to the old one.
文摘This paper discusses a procedure that was adopted for the development of a linear regression model for estimating solar radiation in Malawi. By making use of sunshine-hours data recorded at six selected meteorological stations in the country, namely: Salima, Makoka, Karonga, Bolero, Chileka and Mzimba over the period 1991-1995, a set of Angstrom constants were obtained and averaged in order to develop the linear regression model. This model has potential for generating ground observation data of solar radiation at any given location in the country using sunshine hours as the only required input. The Gunn-Bellan Spherical Pyranometer and the Campbell Stokes Sunshine Recorder were respectively used in the measurement of incident radiation (Ib) in J·cm–2/day (converted to MJ·m–2·day–1) and sunshine hours. An Angstrom model of monthly average Clearness Index with normalized sunshine duration was then developed for each of the six meteorological stations. The resulting linear regression model was applied in estimating monthly average daily solar radiation. Regression analysis between computed and measured radiation data was applied to assess the reliability of the generated Angstrom constants. The results generally show a high degree of agreement between the two variables, with correlation coefficients ranging from 0.63 to 0.90. Angstrom constants obtained at the six meteorological stations were thereafter averaged in order to develop a linear regression model for estimating solar radiation in Malawi. Solar radiation values obtained using this model were noted to be in good agreement with those developed for each of the six meteorological stations.
文摘In this paper, a mathematical relation was found between interatomic Hooke’s force constant and both the bulk modulus and interatomic distance in solid crystals, considering that the forces which have effect on an atom are only those resulted from the neighboring atoms, and the forces are subject to Hooke’s law as the deflections of atoms from their equilibrium positions are very small. This work has been applied on some solid semiconducting crystals of diatomic primitive cell, including crystals of mono-atomic primitive cell automatically, by using linear statistical fitting with computer programming and, then, using mathematical analysis, proceeding from the vibrational dispersion relation of solid linear lattice, these two methods have been used in the process in order to support each other and for the result to be satisfying and reasonable. This is a contribution to the process of using computer programming in physics to facilitate mathematical analyses and obtain the required relations and functions by designing and developing appropriate computer programs in line with the macro and micro natures of materials. The importance of this is in enhancing our understanding of the interatomic actions in cells and of the crystal structure of materials in general and semiconductors in particular, as it is a step of the initial steps to facilitate the process of calculating energies and extracting mathematical relations between correlation energy and temperature as well as between sub-fusion and fusion energies with temperature.
