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The structure of uniform B-spline curves with parameters

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Progress in Natural Science:Materials International 2008年第3期18卷 303-308页

作者： Juan Cao , Guozhao Wang Institute of Image Processing and Computer Graphic, department of mathematics, zhejiang university, hangzhou 310027, china Institute of Image Processing and Computer Graphic Department of Mathematics Zhejiang University Hangzhou 310027 China

The shape-adjustable curve constructed by uniform B-spline basis function with parameter is an extension of uniform B-spline curve. In this paper, we study the relation between the uniform B-spline basis functions with parameter and the B-spline basis functions. Based on the degree elevation of B-spline, we extend the uniform B-spline basis functions with parameter to ones with multiple parameters. Examples show that the proposed basis functions provide more flexibility for curve design.

关键词： Uniform B-spline Shape parameter Shape-adjustable curve Degree elevation

Analysis on the environmental problems accompanying the high-speed urbanization of small towns in china

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Journal of Environmental Sciences 2002年第1期14卷 120-126页

作者： XU Lei, GE Jian, HUA Ying (department of Architecture, zhejiang university, hangzhou 310027, china department of Architecture Zhejiang University Hangzhou 310027

The environmental problems accompanying the rapid urbanization of many small towns like Keqiao, Shaoxing County of china and their countermeasures are presented. To settle these problems rationally as well as effectively will not only conduce to boost the environmental quality and life quality of cities, but also help to promote the development of regional economy and the realization of sustainable development.

关键词： environmental problems urbanization small towns

The ESTIMATE AND MEASUREMENT OF TRANSVERSE WAVE INTENSITY

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Acta Mechanica Solida Sinica 1997年第3期10卷 235-245页

作者： Ming Ruisen, department of Architecture, zhejiang university, hangzhou 310027, china department of Architecture Zhejiang University Hangzhou 310027 China

Transverse waves are a type of structural waves and should be considered in the analysis of high frequency vibration because the energy carried by transverse waves increases with the increase of frequency and becomes important at high frequencies. This paper studies the estimate theory and measuring technique of the transverse wave intensity in two-dimensional homogeneous structures. In general, the intensity vector is the sum of the effective intensity vector and the intensity variation vector. Each axial intensity component is proportional to two imaginary parts of cross spectral densities and its estimate is complicated. For the special case where transverse waves propagate in one direction, the intensity variation is zero and the estimate of the intensity is simplified. The intensity technique is formed based on the finite difference principle. Transverse wave intensity can be measured using a pair of two-transducer arrays lying in the orthogonal direction for the general case or a two-transducer array lying in the propagating direction for the special case. In order to assess the measurement accuracy of transverse wave intensify, the coupling loss factors from bending to transverse waves in building structures were measured using the intensity technique and compared with the results predicted and measured using the conventional method. It is shown that the agreement between the results measured using the intensity technique and that by the conventional method is good.

关键词： transverse wave intensity estimate theory measurement accuracy

An extension of Bernstein-Bezier surface over the triangular domain

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Progress in Natural Science:Materials International 2007年第3期17卷 352-357页

作者： CAO Juan and WANG Guozhao (Institute of Image Processing and Computer Graphic, department of mathematics, zhejiang university, hangzhou 310027, china) Institute of Image Processing and Computer Graphic Department of Mathematics Zhejiang University Hangzhou 310027 China

In this paper, a set of quasi-Bernstein polynomials of degree n with one parameter is presented, which is an extension of the Bernstein polynomials over the triangular domain. Using the presented polynomials as basis functions, we construct a class of shape adjusting surfaces defined over the triangular domain with a shape parameter, namely, quasi-B-B parametric surfaces. These surfaces share many properties with the B-B parametric surfaces. In particular, when shape parameters equal 1, they degenerate to be the B-B parametric surfaces. By changing the value of the shape parameter, we can get different surfaces under the fixed control net.

关键词： triangular domain shape parameter Bezier surfaces.

A note on certain square functions on product spaces

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Science china mathematics 2006年第1期49卷 98-108页

作者： WANG Meng, CheN Jiecheng2 & FAN Dashan department of mathematics, zhejiang university (at Yuquan campus), hangzhou 310027, china department of mathematics, zhejiang university (at Xixi campus), hangzhou 310028, china department of mathematics, university of Wisconsin-Milwaukee, Milwaukee, WI53201, USA department of mathematics Zhejiang University (at Yuquan campus) Hangzhou China department of mathematics Zhejiang University (at Xixi campus) Hangzhou China department of mathematics University of Wisconsin-Milwaukee Milwaukee USA

We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log+ L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog+ L(Sn-1 × Sm-1) satisfying the cancellation condition.

关键词： square function, Marcinkiewicz integral, product space.

APPLICATION OF NEWTON'S AND CheBYSheV'S METHODS TO PARALLEL FACTORJZATION OF POLYNOMIALS

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Journal of Computational mathematics 2001年第4期19卷 347-356页

作者： Shi-ming Zheng (department of mathematics, Xixi Campus, zhejiang university, hangzhou 310028, china) 浙江大学浙江杭州 310028

In this paper it is shown m two different ways that one of the family of parallel iterations to determine all real quadratic factors of polynomials presented in [12] is Newton's method applied to the special equation (1.7) below. Furthermore, we apply Chebyshev's method to (1.7) and obtain a new parallel iteration for factorization of polynomials. Finally, some properties of the parallel iterations are discussed.

关键词： Newton's method Chebyshev's method Parallel iteration Factorization of polynomial.

A FAMILY OF HIGH-ODER PARALLEL ROOTFINDERS FOR POLYNOMIALS

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Journal of Computational mathematics 2000年第3期18卷 283-288页

作者： Shi-ming Zheng (department of mathematics, Xixi Campus,zhejiang university, hangzhou, 310028, china) 浙江大学浙江杭州 310028

Presents a family of parallel iterations for finding all zeros of a polynomial without evaluation of derivatives. Construction of iterations; Convergence of the iterations; Details on the numerical examples.

关键词： parallel iteration zeros of polynomial order of convergence

The best quadrature based on given hermite information for the Sobolev class KW^r[a,b]

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Science china mathematics 2006年第8期49卷 1146-1152页

作者： WANG Xinghua & YANG Shijun department of mathematics, zhejiang university, hangzhou 310028, china department of mathematics, hangzhou Normal College, hangzhou 310036, china department of mathematics Zhejiang University Hangzhou China department of mathematics Hangzhou Normal College Hangzhou China

As usual, denote by KWr[a,b] the Sobolev class consisting of every function whose (r-1)th derivative is absolutely continuous on the interval [a,b] and rth derivative is bounded by K a.e. In [a,b]. For a function f ∈ KWr[a,b], its values and derivatives up to r-1 order at a set of nodes x are known. These values are said to be the given hermite *** work reports the results on the best quadrature based on the given hermite information for the class KWr[a,b]. Existence and concrete construction issue of the best quadrature are settled down by a perfect spline interpolation. It turns out that the best quadrature depends on a system of algebraic equations satisfied by a set of free nodes of the interpolation perfect spline. From our another new result, it is shown that the system can be converted in a closed form to two single-variable polynomial equations, each being of degree approximately r/2. As a by-product,the best interpolation formula for the class KWr[a,b] is also obtained.

关键词： Sobolev class, hermite information, perfect spline, optimal recovery, best quadrature.

A new method for designing a developable surface utilizing the surface pencil through a given curve

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Progress in Natural Science:Materials International 2008年第1期18卷 105-110页

作者： Hongyan Zhao,Guojin Wang* department of mathematics and State Key Laboratory of CAD&CG,zhejiang university,hangzhou 310027,china department of mathematics and State Key Laboratory of CAD&CG Zhejiang University Hangzhou 310027 China

This paper proposes a new method for designing a developable surface by constructing a surface pencil passing through a given curve, which is quite in accord with the practice in industry design and *** utilizing the Frenet trihedron frame,we derive the necessary and suffcient conditions to construct a developable surface through a given *** the requirements in shoemak- ing and garment-manufacture industries,we also study the special case of specifying the given curve as a *** given geodesic can be classified into three types corresponding to each type of developable *** also present the polynomial representation of the developable *** algorithm is convenient and effcient for applications in engineering.

关键词： CAD/CAM Developable surface Geodesic Frenet frame