Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds t...Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.展开更多
Three kinds of 'films' i.e. cross-linked film, grainy film and transparent film, wereobtained in the process of plasma polymerization of Octamethylcyclotetrasioxane(D4) under dif-ferent conditions. From SEM ph...Three kinds of 'films' i.e. cross-linked film, grainy film and transparent film, wereobtained in the process of plasma polymerization of Octamethylcyclotetrasioxane(D4) under dif-ferent conditions. From SEM photos, we can see that the cross-linked film has a network form.From XPS spectra, we can see that the content of Si-C bond of the cross-linked film is lower thanthat of the transparent film, and this result agrees well with the test results of FTIR spectra. Thisproves that the c1eavage of the Si-C bond and C-H bond are the main cleavage in the formationof cross-linked film, whereas the cleavage of the Si-O is the main cleavage in the formation oftransparent film. In order to enhance the collision of the reactive particles and investigate theinfluence of magnetic field on the plasma polymerization, we introduced the magnetic field, as aresult, we got the grainy film.展开更多
In this paper, the relationships between the region of the two coexisting kinds of macro-defects and the reduction in area, as well as between the region and the relative residual thickness of the billet are studied f...In this paper, the relationships between the region of the two coexisting kinds of macro-defects and the reduction in area, as well as between the region and the relative residual thickness of the billet are studied for the cup-cup axisymmetric combined extrusion, on the basis of the analytical expression obtained by the upper-bound approach. The presented model and conclusions are confirmed by the experimental results in this paper.展开更多
To protect the ecological balance and the environment for our existence, China has organized the projects to Rescue Seven Kinds of Animals, the panda, ibis, Yangtze crocodile, Hainan deer, David’s deer, big nosed ant...To protect the ecological balance and the environment for our existence, China has organized the projects to Rescue Seven Kinds of Animals, the panda, ibis, Yangtze crocodile, Hainan deer, David’s deer, big nosed antelop, and wild horse which are in imminent danger. Panda protection project. From 1992 to the year 2000, 14 panda reserves will be established, covering 4,242 sq km, including 2,479 sq km for the habitation of pandas. The construction and management of the. 13 existing panda reserves will be improved, covering 5,380 sq kin. And 17 new reserve corridors will be set up and 32 stations will be built in展开更多
With the help of the method that combines the first kind of elliptic equation with the function transformation, some kinds of new composite solutions of a kind of coupled Schr?dinger equation are constructed. First, a...With the help of the method that combines the first kind of elliptic equation with the function transformation, some kinds of new composite solutions of a kind of coupled Schr?dinger equation are constructed. First, a kind of function transformation is presented, and then the problem of solving solutions of a kind of coupled Schr?dinger equation can be changed to the problem of solving solutions of the first kind of elliptic equation. Then, with the help of the conclusions of the B?cklund transformation and so on of the first kind of elliptic equation, the new infinite sequence composite solutions of a kind of coupled Schr?dinger equation are constructed. These solutions are consisting of two-soliton solutions and two-period solutions and so on.展开更多
It is reported from NRCCRM (the National Research Center for CRMs) that, China has presently developed 1262 kinds of grade A reference materials and 1739 grade B reference materials, involving the fields of the steel,...It is reported from NRCCRM (the National Research Center for CRMs) that, China has presently developed 1262 kinds of grade A reference materials and 1739 grade B reference materials, involving the fields of the steel, the geology, the petroleum, the nuclear material, the environment, the food and the clinical inspection,and etc. The reference materials play an important role in controlling the production quality, maintaining the market order and promoting the scientific and technological advancement.展开更多
Objective To evaluate and compare 3 kinds of cecocloln urinary reservoir. Methods Perm pouch, indiana pouch or detenial cecocolon reservoir has been performed for 37 patients. The outcome was evaluated by urodynamic a...Objective To evaluate and compare 3 kinds of cecocloln urinary reservoir. Methods Perm pouch, indiana pouch or detenial cecocolon reservoir has been performed for 37 patients. The outcome was evaluated by urodynamic and clinically. Results Good continence has been achieved in all patients with an appendiceal continence mechanism. The capacity and intrareservoir pressure of detenial cecocolon was significantly different from penn or indiana pouch 3 months postoperatively (P【0.01) whereas the difference became in no significant 12 months postoperativelly (P】0. 05). The intrareservoir pressure on contraction was lower with penn pouch. Conclusion The penn or modified indiana pouch is better and more ideal as a urinary reservoir whereas the detenial cecocolon pouch is technically simpler. 6 refs,1 tab.展开更多
Sunshine duration (S) based empirical equations have been employed in this study to estimate the daily global solar radiation on a horizontal surface (G) for six meteorological stations in Burundi. Those equations inc...Sunshine duration (S) based empirical equations have been employed in this study to estimate the daily global solar radiation on a horizontal surface (G) for six meteorological stations in Burundi. Those equations include the Ångström-Prescott linear model and four amongst its derivatives, i.e. logarithmic, exponential, power and quadratic functions. Monthly mean values of daily global solar radiation and sunshine duration data for a period of 20 to 23 years, from the Geographical Institute of Burundi (IGEBU), have been used. For any of the six stations, ten single or double linear regressions have been developed from the above-said five functions, to relate in terms of monthly mean values, the daily clearness index () to each of the next two kinds of relative sunshine duration (RSD): and . In those ratios, G<sub>0</sub>, S<sub>0 </sub>and stand for the extraterrestrial daily solar radiation on a horizontal surface, the day length and the modified day length taking into account the natural site’s horizon, respectively. According to the calculated mean values of the clearness index and the RSD, each station experiences a high number of fairly clear (or partially cloudy) days. Estimated values of the dependent variable (y) in each developed linear regression, have been compared to measured values in terms of the coefficients of correlation (R) and of determination (R<sub>2</sub>), the mean bias error (MBE), the root mean square error (RMSE) and the t-statistics. Mean values of these statistical indicators have been used to rank, according to decreasing performance level, firstly the ten developed equations per station on account of the overall six stations, secondly the six stations on account of the overall ten equations. Nevertheless, the obtained values of those indicators lay in the next ranges for all the developed sixty equations:;;;, with . These results lead to assert that any of the sixty developed linear regressions (and thus equations in terms of and ), fits very adequately measured data, and should be used to estimate monthly average daily global solar radiation with sunshine duration for the relevant station. It is also found that using as RSD, is slightly more advantageous than using for estimating the monthly average daily clearness index, . Moreover, values of statistical indicators of this study match adequately data from other works on the same kinds of empirical equations.展开更多
The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generali...The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .展开更多
To compare and evaluate 3 kinds of treatments of pediatric closed femoral shaft fractures.Methods Seventy-nine patients were divided into 3 groups and treated using hip spica casting after skeletal traction,unilateral...To compare and evaluate 3 kinds of treatments of pediatric closed femoral shaft fractures.Methods Seventy-nine patients were divided into 3 groups and treated using hip spica casting after skeletal traction,unilateral multifunctional fixation and plate fixation.The result were evaluated according to clinical function,time to union,complications,radiology examination and the economic cost.Results Both time to union and economic cost of the external fixation group were shorter than that of the skeletal traction group and plate fixation group.Conclusion The unilateral multi-functional external fixation is an ideal solution to pediatric close femoral shaft fractures.7 refs,3 tabs.展开更多
To investigate the impact of different kinds of nerve injuries of early-stage fracture healing.Methods Three groups of rats were included in the experiment among which group 1 was inflicted with femoral fracture and T...To investigate the impact of different kinds of nerve injuries of early-stage fracture healing.Methods Three groups of rats were included in the experiment among which group 1 was inflicted with femoral fracture and T10 spinal cord transsection (SCI),group 2 was inflicted with femoral and peripheral nerve resection (PNR),and group 3 with simple femoral fracture as control group.Two weeks after operation the femoral bones were collected for X-ray checking and 2 more weeks later X-ray checking was performed again followed by pathomorphologic exams.Results X-ray result showed no massive calluses in the bones in the 2nd week postoperatively,while in the 4th week,callus appeared with larger size in group 3 than that of group 1 and with smaller size than that of group 2.It was the same with the result of pathomorphologic examining.Cortical bone bridges between fracture point and osteiod were also found in group 2 and there were less normal blood vessels and worse bone remodeling than that of group 3.There were relatively immature calluses with more fibroblast-like cells and disordered bone structure in group 2.Group 3 showed normal healing process and callus structure.Conclusion Early-stage bone fracture healing can be influenced significantly by different kinds of nerve injuries.6 refs,6 figs.展开更多
Studies the stability for them manifold of equilibrium state of the autonomous Birkhoffsystem. Uses the Liapunov's direct method and the first approximation method to obtain thestability criterion for the manifold...Studies the stability for them manifold of equilibrium state of the autonomous Birkhoffsystem. Uses the Liapunov's direct method and the first approximation method to obtain thestability criterion for the manifold of equilibrium state of the system. Gives an example toillustrate the application of the result.展开更多
In this paper,we give definition and moduler representation of Kothe root for additive cate gories.Using these results,get inner representation of J-root and fully homomorph class of Jscmisimple additive categories.
Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one ...Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O（1/n｜nn）展开更多
To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are pr...To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.展开更多
文摘Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.
文摘Three kinds of 'films' i.e. cross-linked film, grainy film and transparent film, wereobtained in the process of plasma polymerization of Octamethylcyclotetrasioxane(D4) under dif-ferent conditions. From SEM photos, we can see that the cross-linked film has a network form.From XPS spectra, we can see that the content of Si-C bond of the cross-linked film is lower thanthat of the transparent film, and this result agrees well with the test results of FTIR spectra. Thisproves that the c1eavage of the Si-C bond and C-H bond are the main cleavage in the formationof cross-linked film, whereas the cleavage of the Si-O is the main cleavage in the formation oftransparent film. In order to enhance the collision of the reactive particles and investigate theinfluence of magnetic field on the plasma polymerization, we introduced the magnetic field, as aresult, we got the grainy film.
文摘In this paper, the relationships between the region of the two coexisting kinds of macro-defects and the reduction in area, as well as between the region and the relative residual thickness of the billet are studied for the cup-cup axisymmetric combined extrusion, on the basis of the analytical expression obtained by the upper-bound approach. The presented model and conclusions are confirmed by the experimental results in this paper.
文摘To protect the ecological balance and the environment for our existence, China has organized the projects to Rescue Seven Kinds of Animals, the panda, ibis, Yangtze crocodile, Hainan deer, David’s deer, big nosed antelop, and wild horse which are in imminent danger. Panda protection project. From 1992 to the year 2000, 14 panda reserves will be established, covering 4,242 sq km, including 2,479 sq km for the habitation of pandas. The construction and management of the. 13 existing panda reserves will be improved, covering 5,380 sq kin. And 17 new reserve corridors will be set up and 32 stations will be built in
基金supported by the Natural Natural Science Foundation of China(Grant No.11361040)the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China(Grant No.NJZY12031)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2015MS0128).
文摘With the help of the method that combines the first kind of elliptic equation with the function transformation, some kinds of new composite solutions of a kind of coupled Schr?dinger equation are constructed. First, a kind of function transformation is presented, and then the problem of solving solutions of a kind of coupled Schr?dinger equation can be changed to the problem of solving solutions of the first kind of elliptic equation. Then, with the help of the conclusions of the B?cklund transformation and so on of the first kind of elliptic equation, the new infinite sequence composite solutions of a kind of coupled Schr?dinger equation are constructed. These solutions are consisting of two-soliton solutions and two-period solutions and so on.
文摘It is reported from NRCCRM (the National Research Center for CRMs) that, China has presently developed 1262 kinds of grade A reference materials and 1739 grade B reference materials, involving the fields of the steel, the geology, the petroleum, the nuclear material, the environment, the food and the clinical inspection,and etc. The reference materials play an important role in controlling the production quality, maintaining the market order and promoting the scientific and technological advancement.
文摘Objective To evaluate and compare 3 kinds of cecocloln urinary reservoir. Methods Perm pouch, indiana pouch or detenial cecocolon reservoir has been performed for 37 patients. The outcome was evaluated by urodynamic and clinically. Results Good continence has been achieved in all patients with an appendiceal continence mechanism. The capacity and intrareservoir pressure of detenial cecocolon was significantly different from penn or indiana pouch 3 months postoperatively (P【0.01) whereas the difference became in no significant 12 months postoperativelly (P】0. 05). The intrareservoir pressure on contraction was lower with penn pouch. Conclusion The penn or modified indiana pouch is better and more ideal as a urinary reservoir whereas the detenial cecocolon pouch is technically simpler. 6 refs,1 tab.
文摘Sunshine duration (S) based empirical equations have been employed in this study to estimate the daily global solar radiation on a horizontal surface (G) for six meteorological stations in Burundi. Those equations include the Ångström-Prescott linear model and four amongst its derivatives, i.e. logarithmic, exponential, power and quadratic functions. Monthly mean values of daily global solar radiation and sunshine duration data for a period of 20 to 23 years, from the Geographical Institute of Burundi (IGEBU), have been used. For any of the six stations, ten single or double linear regressions have been developed from the above-said five functions, to relate in terms of monthly mean values, the daily clearness index () to each of the next two kinds of relative sunshine duration (RSD): and . In those ratios, G<sub>0</sub>, S<sub>0 </sub>and stand for the extraterrestrial daily solar radiation on a horizontal surface, the day length and the modified day length taking into account the natural site’s horizon, respectively. According to the calculated mean values of the clearness index and the RSD, each station experiences a high number of fairly clear (or partially cloudy) days. Estimated values of the dependent variable (y) in each developed linear regression, have been compared to measured values in terms of the coefficients of correlation (R) and of determination (R<sub>2</sub>), the mean bias error (MBE), the root mean square error (RMSE) and the t-statistics. Mean values of these statistical indicators have been used to rank, according to decreasing performance level, firstly the ten developed equations per station on account of the overall six stations, secondly the six stations on account of the overall ten equations. Nevertheless, the obtained values of those indicators lay in the next ranges for all the developed sixty equations:;;;, with . These results lead to assert that any of the sixty developed linear regressions (and thus equations in terms of and ), fits very adequately measured data, and should be used to estimate monthly average daily global solar radiation with sunshine duration for the relevant station. It is also found that using as RSD, is slightly more advantageous than using for estimating the monthly average daily clearness index, . Moreover, values of statistical indicators of this study match adequately data from other works on the same kinds of empirical equations.
文摘The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .
文摘To compare and evaluate 3 kinds of treatments of pediatric closed femoral shaft fractures.Methods Seventy-nine patients were divided into 3 groups and treated using hip spica casting after skeletal traction,unilateral multifunctional fixation and plate fixation.The result were evaluated according to clinical function,time to union,complications,radiology examination and the economic cost.Results Both time to union and economic cost of the external fixation group were shorter than that of the skeletal traction group and plate fixation group.Conclusion The unilateral multi-functional external fixation is an ideal solution to pediatric close femoral shaft fractures.7 refs,3 tabs.
文摘To investigate the impact of different kinds of nerve injuries of early-stage fracture healing.Methods Three groups of rats were included in the experiment among which group 1 was inflicted with femoral fracture and T10 spinal cord transsection (SCI),group 2 was inflicted with femoral and peripheral nerve resection (PNR),and group 3 with simple femoral fracture as control group.Two weeks after operation the femoral bones were collected for X-ray checking and 2 more weeks later X-ray checking was performed again followed by pathomorphologic exams.Results X-ray result showed no massive calluses in the bones in the 2nd week postoperatively,while in the 4th week,callus appeared with larger size in group 3 than that of group 1 and with smaller size than that of group 2.It was the same with the result of pathomorphologic examining.Cortical bone bridges between fracture point and osteiod were also found in group 2 and there were less normal blood vessels and worse bone remodeling than that of group 3.There were relatively immature calluses with more fibroblast-like cells and disordered bone structure in group 2.Group 3 showed normal healing process and callus structure.Conclusion Early-stage bone fracture healing can be influenced significantly by different kinds of nerve injuries.6 refs,6 figs.
文摘Studies the stability for them manifold of equilibrium state of the autonomous Birkhoffsystem. Uses the Liapunov's direct method and the first approximation method to obtain thestability criterion for the manifold of equilibrium state of the system. Gives an example toillustrate the application of the result.
文摘In this paper,we give definition and moduler representation of Kothe root for additive cate gories.Using these results,get inner representation of J-root and fully homomorph class of Jscmisimple additive categories.
基金Supported by the National Nature Science Foundation.
文摘Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O（1/n｜nn）
基金supported by the National Natural Science Foundation of China(Grant No.10862003)the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China(Grant No.NJZZ07031)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2010MS0111)
文摘To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.
