A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined...A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.展开更多
Radial distribution of vapor local parameters, including local void fraction, interfacial velocity, bubblesize, bubble frequency and interfacial area concentration, are investigated through the measurement in an upwar...Radial distribution of vapor local parameters, including local void fraction, interfacial velocity, bubblesize, bubble frequency and interfacial area concentration, are investigated through the measurement in an upwardboiling tube using dual-sensor optical probe. In addition, a new local parameter -"local bubble number concentra-tion" is developed on the basis of bubble frequency. The analysis shows that this parameter can reflect bubble numberdensity in space, and has clear physical meaning.展开更多
This paper presents a statistical method to calculate local interfacial variable s in horizontal gas-liquid bubbly flows based on the data measured with a double -sensor probe.The geometrical relationship between the ...This paper presents a statistical method to calculate local interfacial variable s in horizontal gas-liquid bubbly flows based on the data measured with a double -sensor probe.The geometrical relationship between the apparent and actual bubbl e velocities and the relationship between the chord intersected by the sensor an d bubble diameter were determined.A probability density function was introduced to consider the effect of both axial and radial movements of bubbles on bubble v elocity and bubble size.展开更多
We present in the work two intriguing results in the entanglement classification of a pure and true tripartite entangled state of 2 × M × N under stochastic local operation and classical communication: (i) t...We present in the work two intriguing results in the entanglement classification of a pure and true tripartite entangled state of 2 × M × N under stochastic local operation and classical communication: (i) the internal symmetric properties of the nonlocal parameters in the continuous entangled class; (ii) the analytic expression for the total numbers of the true and pure entangled class 2 × M × N states. These properties help better understand the nature of the 2 × M × N entangled system.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10171026 and 60473114), the Research Funds forYoung Innovation Group, Education Department of Anhui Prov-ince (No. 2005TD03) and the Natural Science Foundation of An-hui Provincial Education Department (No. 2006KJ252B), China
文摘A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.
基金Supported by the National Science Foundation of China(No.59995460-1) and Nuclear Industry Science Foundation (No.Y7100E51001)
文摘Radial distribution of vapor local parameters, including local void fraction, interfacial velocity, bubblesize, bubble frequency and interfacial area concentration, are investigated through the measurement in an upwardboiling tube using dual-sensor optical probe. In addition, a new local parameter -"local bubble number concentra-tion" is developed on the basis of bubble frequency. The analysis shows that this parameter can reflect bubble numberdensity in space, and has clear physical meaning.
文摘This paper presents a statistical method to calculate local interfacial variable s in horizontal gas-liquid bubbly flows based on the data measured with a double -sensor probe.The geometrical relationship between the apparent and actual bubbl e velocities and the relationship between the chord intersected by the sensor an d bubble diameter were determined.A probability density function was introduced to consider the effect of both axial and radial movements of bubbles on bubble v elocity and bubble size.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10935012, 10928510, 10821063 and 10775179)the Chinese Academy of Sciences Key Projects (Grant Nos. KJCX2-yw-N29 andH92A0200S2)the Scientific Research Fund of Graduate University, the Chinese Academy of Sciences
文摘We present in the work two intriguing results in the entanglement classification of a pure and true tripartite entangled state of 2 × M × N under stochastic local operation and classical communication: (i) the internal symmetric properties of the nonlocal parameters in the continuous entangled class; (ii) the analytic expression for the total numbers of the true and pure entangled class 2 × M × N states. These properties help better understand the nature of the 2 × M × N entangled system.
