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61.
A refinable spline is a compactly supported refinable function that is
piecewise polynomial. Refinable splines, such as the well-known
B-splines, play a key role in computer aided geometric design.
So far all studies on refinable splines have focused on positive
integer dilations and integer translations, and under this setting a rather complete
classification was obtained in [12]. However, refinable splines do
not have to have integer dilations and integer translations. The classification
of refinable splines with noninteger dilations and arbitrary translations
is studied in this paper. We classify completely all refinable splines with
integer translations and arbitrary dilations. Our study involves techniques
from number theory and complex analysis. 相似文献
62.
Chen Weihuan 《东北数学》1998,(1)
in this note we study the maximal surfaces which are congruent with theirconjugate ones in L3, and give a criterion for this kind of surfaces and some examples. 相似文献
63.
Robert Huff 《Geometriae Dedicata》2006,123(1):223-238
In this paper, we consider soap films spanning rectangular prisms with regular n-gon bases. As the number of edges n varies, we show that there are significant changes in the qualitative properties of the spanning soap films as well as a
change in the number of spanning soap films whose existence we can prove: We can find two nontrivial soap films for n = 3, 4, 5 but only one for n ≥ 6. We also prove some results concerning the interval of aspect ratios through which the soap films exist: The interval
is finite if n = 3, 4, 5 and infinite if n ≥ 6. Furthermore, for n > 6, we have that the spanning soap film converges to a soap film spanning the vertical lines through the vertices of a
regular n-gon as the aspect ratio goes to infinity. We can also make sense of the case n = ∞. Here, we discover some interesting singly and triply periodic soap films spanning singly and doubly periodic sets of
vertical lines or spanning singly periodic sets of vertical line segments connected by pairs of parallel, horizontal lines.
Finally, for n = 3, 4, 5, 6, we can derive parameterizations for the spanning soap films, and these parameterizations are explicit up to
knowing the aspect ratio.
相似文献
64.
65.
66.
On three differential equations associated with Chebyshev polynomials of degrees 3, 4 and 6 下载免费PDF全文
Li Chien Shen 《数学学报(英文版)》2017,33(1):21-36
We shall study the differential equation y'~2= T_n(y)-(1-2μ~2);where μ~2 is a constant, T_n(x) are the Chebyshev polynomials with n = 3, 4, 6.The solutions of the differential equations will be expressed explicitly in terms of the Weierstrass elliptic function which can be used to construct theories of elliptic functions based on _2F_1(1/4, 3/4; 1; z),_2F_1(1/3, 2/3; 1; z), _2F_1(1/6, 5/6; 1; z) and provide a unified approach to a set of identities of Ramanujan involving these hypergeometric functions. 相似文献
67.
68.
In this article, we introduce and study the smooth Gauss–Weierstrass singular integral operators on the line of very general kind. We establish their convergence to the unit operator with rates. The estimates are mostly sharp and they are pointwise or uniform. The established inequalities involve the higher order modulus of smoothness. To prove optimality we use mainly the geometric moment theory method. 相似文献
69.
Let C be a projective Gorenstein curve over an algebraically closed field of characteristic 0. A generalized linear system on C is a pair (?, ε) consisting of a torsion-free, rank-1 sheaf ? on C, and a map of vector spaces ε: V → Γ(C, ?). If the system is nondegenerate on every irreducible component of C, we associate to it a 0-cycle W, its Weierstrass cycle. Then we show that for each one-parameter family of curves C t degenerating to C, and each family of linear systems (? t , ε t ) along C t , with ? t invertible, degenerating to (?, ε), the corresponding Weierstrass divisors degenerate to a subscheme whose associated 0-cycle is W. We show that the limit subscheme contains always an “intrinsic” subscheme, canonically associated to (?, ε), but the limit itself depends on the family ? t . 相似文献
70.
《复变函数与椭圆型方程》2012,57(5):409-415
Let $ \cal W $ be the set of entire functions equal to a Weierstrass product of the form $ {f(x)= Ax^q\lim_{r \to \infty} \prod_{|a_j|\leq r}{(1- \fraca {x} {a_j})}} $ where the convergence is uniform in all bounded subsets of $ {\shadC} $ , let $ \cal V $ be the set of $ f\in {\cal W} $ such that $ {\shadC} [\,f]\subset {\cal W} $ , and let $ {\cal H} $ be the $ {\shadC} $ -algebra of entire functions satisfying $ { {\lim_{r\to \infty } } ({\ln M(r,f) / r})=0} $ . Then $ \cal H $ is included in $ {\cal V} $ and strictly contains the set of entire functions of genus zero, (which, itself, strictly contains the $ {\shadC} $ -algebra of entire functions of order 𝜌 < 1). Let $ n, m\in {\shadN} ^* $ satisfy n > m S 3. Let $ a\in {\shadC}^* $ satisfies $ {a^n\not = \fraca{n^n}{(m^m(n-m)^{n-m}})} $ and assume that for every ( n m m )-th root ξ of 1 different from m 1, a satisfies further $ {a^{n}\neq (1+\xi )^{n-m} (\fraca{n^n}{((n-m)^{n-m}m^m}))} $ . Let P ( X ) = X n m aX m + 1 and let T n,m ( a ) be the set of its zeros. Then T n,m ( a ) has n distinct points and is a urs for $ {\cal V} $ . In particular this applies to functions such as sin x and cos x . 相似文献