We used data from 1960.0,1970.0,1980.0,1990.0,and 2000.0 to study the geomagnetic anomaly field over the Chinese mainland by using the three-dimensional Taylor polynomial（3DTP） and the surface spline（SS） models.To...We used data from 1960.0,1970.0,1980.0,1990.0,and 2000.0 to study the geomagnetic anomaly field over the Chinese mainland by using the three-dimensional Taylor polynomial（3DTP） and the surface spline（SS） models.To obtain the pure anomaly field,the main field and the induced field of the ionospheric and magnetospheric fields were removed from measured data.We also compared the SS model anomalies and the data obtained with Kriging interpolation（KI）.The geomagnetic anomaly distribution over the mainland was analyzed based on the SS and 3DTP models by transferring all points from 1960.0-1990.0 to 2000.0.The results suggest that the total intensity F anomalies estimated based on the SS and KI for each year are basically consistent in distribution and intensity.The anomalous distributions in the X-,Y-,and Z-direction and F are mainly negative.The 3DTP model anomalies suggest that the intensity in the X-direction increases from-100 nT to 0 nT with longitude,whereas the intensity in the Y-direction decreases from 400 nT to 20 nT with longitude and over the eastern mainland is almost negative.The intensity in the Z-direction and F are very similar and in most areas it is about-50 nT and higher in western Tibet.The SS model anomalies overall reflect the actual distribution of the magnetic field anomalies;however,because of the uneven distribution of measurements,it yields several big anomalies.Owing to the added altitude term,the 3DTP model offers higher precision and is consistent with KI.展开更多
In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate con...In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.展开更多
For two given ternary quadratic forms f( x, y, z) and g( x, y, z), let r( f, n) and r( g,n) be the numbers of representations of n represented by f( x, y, z) and g( x, y, z) respectively. In this paper we study the fo...For two given ternary quadratic forms f( x, y, z) and g( x, y, z), let r( f, n) and r( g,n) be the numbers of representations of n represented by f( x, y, z) and g( x, y, z) respectively. In this paper we study the following problem: when will we have r( f, n) = r( g, n) or r( f, n) ≠ r( g, n).Our method is to use elliptic curves and the corresponding new forms.展开更多
In this paper we present a new representation of curve, named parametric curve with an implicit domain(PCID), which is a curve that exists in parametric form defined on an implicit domain. PCID provides a bridge betwe...In this paper we present a new representation of curve, named parametric curve with an implicit domain(PCID), which is a curve that exists in parametric form defined on an implicit domain. PCID provides a bridge between parametric curve and implicit curve because the conversion of parametric form or implicit form to PCID is very convenient and efficient. We propose a framework model for mapping given points to the implicit curve in a homeomorphic manner. The resulting map is continuous and does not overlap. This framework can be used for many applications such as compatible triangulation, image deformation and fisheye views. We also present some examples and experimental results to demonstrate the effectiveness of the framework of our proposed model.展开更多
The S2 flow path design method of the transonic compressor is used to design the one stage fan in order to replace the original designed blade cascade which has two-stage transonic fan rotors.In the modification desig...The S2 flow path design method of the transonic compressor is used to design the one stage fan in order to replace the original designed blade cascade which has two-stage transonic fan rotors.In the modification design,the camber line is parameterized by a quartic polynomial curve and the thickness distribution of the blade profile is controlled by the double-thrice polynomial.Therefore,the inlet flow has been pre-compressed and the location and intensity of the shock wave at supersonic area have been controlled in order to let the new blade profiles have better aerodynamic performance.The computational results show that the new single stage fan rotor increases the efficiency by two percent at the design condition and the total pressure ratio is slightly higher than that of the original design.At the same time,it also meets the mass flow rate and the geometrical size requirements for the modification design.展开更多
基金supported by the National Natural Science Foundation of China(No.41404053)Special Project for MeteoScientific Research in the Public Interest(No.GYHY201306073)+1 种基金Natural Science Foundation of Jiangsu Province(No.BK20140994),Natural Science Foundation of Higher Education Institutions of Jiangsu Province(No.14KJB170012)Training Program of Innovation and Entrepreneurship for Undergraduates of NUIST(No.201510300178)
文摘We used data from 1960.0,1970.0,1980.0,1990.0,and 2000.0 to study the geomagnetic anomaly field over the Chinese mainland by using the three-dimensional Taylor polynomial（3DTP） and the surface spline（SS） models.To obtain the pure anomaly field,the main field and the induced field of the ionospheric and magnetospheric fields were removed from measured data.We also compared the SS model anomalies and the data obtained with Kriging interpolation（KI）.The geomagnetic anomaly distribution over the mainland was analyzed based on the SS and 3DTP models by transferring all points from 1960.0-1990.0 to 2000.0.The results suggest that the total intensity F anomalies estimated based on the SS and KI for each year are basically consistent in distribution and intensity.The anomalous distributions in the X-,Y-,and Z-direction and F are mainly negative.The 3DTP model anomalies suggest that the intensity in the X-direction increases from-100 nT to 0 nT with longitude,whereas the intensity in the Y-direction decreases from 400 nT to 20 nT with longitude and over the eastern mainland is almost negative.The intensity in the Z-direction and F are very similar and in most areas it is about-50 nT and higher in western Tibet.The SS model anomalies overall reflect the actual distribution of the magnetic field anomalies;however,because of the uneven distribution of measurements,it yields several big anomalies.Owing to the added altitude term,the 3DTP model offers higher precision and is consistent with KI.
基金Project supported by the National Basic Research Program (973) of China (No. 2004CB719400)the National Natural Science Founda-tion of China (Nos. 60673031 and 60333010) the National Natural Science Foundation for Innovative Research Groups of China (No. 60021201)
文摘In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.
基金the National Natural Science Foundation of China (Grant No. 19871917).
文摘For two given ternary quadratic forms f( x, y, z) and g( x, y, z), let r( f, n) and r( g,n) be the numbers of representations of n represented by f( x, y, z) and g( x, y, z) respectively. In this paper we study the following problem: when will we have r( f, n) = r( g, n) or r( f, n) ≠ r( g, n).Our method is to use elliptic curves and the corresponding new forms.
基金supported by National Natural Science Foundation of China(Grant Nos.11031007,11171322,61222206 and 11371341)One Hundred Talent Project of the Chinese Academy of Sciencesthe Program for New Century Excellent Talents in University(Grant No.NCET-11-0881)
文摘In this paper we present a new representation of curve, named parametric curve with an implicit domain(PCID), which is a curve that exists in parametric form defined on an implicit domain. PCID provides a bridge between parametric curve and implicit curve because the conversion of parametric form or implicit form to PCID is very convenient and efficient. We propose a framework model for mapping given points to the implicit curve in a homeomorphic manner. The resulting map is continuous and does not overlap. This framework can be used for many applications such as compatible triangulation, image deformation and fisheye views. We also present some examples and experimental results to demonstrate the effectiveness of the framework of our proposed model.
基金support from National Natural Science Foundation of China (Grant No.50706009)
文摘The S2 flow path design method of the transonic compressor is used to design the one stage fan in order to replace the original designed blade cascade which has two-stage transonic fan rotors.In the modification design,the camber line is parameterized by a quartic polynomial curve and the thickness distribution of the blade profile is controlled by the double-thrice polynomial.Therefore,the inlet flow has been pre-compressed and the location and intensity of the shock wave at supersonic area have been controlled in order to let the new blade profiles have better aerodynamic performance.The computational results show that the new single stage fan rotor increases the efficiency by two percent at the design condition and the total pressure ratio is slightly higher than that of the original design.At the same time,it also meets the mass flow rate and the geometrical size requirements for the modification design.
