三维Ⅱ型剖分上的样条空间

三维Ⅱ型剖分上的样条空间施锡泉（大连理工大学数学研究所）ＳＰＬＩＮＥＳＰＡＣＥＳＯＮＴＹＰＥ－２ＴＲＩＡＮＧＵＬＡＴＩＯＮＩＮＲ￣３￥ＳｈｉＸｉ－ｑｕａｎ（Ｉｎｓｔ．ｏｆＭａｔｈ．，ＤａｌｉｎＵｎｉｖ．ｏｆＳｃｉ．ａｎｄＴｅｃｈ．）Ａｂｓｔｒａｃｔ：...     

α-CARLESON MEASURE AND BLOCH FUNCTIONS ON BOUNDED SYMMETRIC DOMAINS OF C~n

α－ＣＡＲＬＥＳＯＮＭＥＡＳＵＲＥＡＮＤＢＬＯＣＨＦＵＮＣＴＩＯＮＳＯＮＢＯＵＮＤＥＤＳＹＭＭＥＴＲＩＣＤＯＭＡＩＮＳＯＦＣ~ｎＯｕｙａｎｇＣａｉｈｅｎｇ（欧阳才衡）（ＷｕｈａｎＩｕｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，ＣｈｉｎｅｓｅＡｃａｄ．ｏｆＳｃｉ．，...     

A KINETIC APPROACH TO SCALAR MULTI-DIMENSIONAL CONSERVATION LAWS

ＡＫＩＮＥＴＩＣＡＰＰＲＯＡＣＨＴＯＳＣＡＬＡＲＭＵＬＴＩ－ＤＩＭＥＮＳＩＯＮＡＬＣＯＮＳＥＲＶＡＴＩＯＮＬＡＷＳ￥ＨａＪｉａｘｉｎ（胡家信）（ＹｏｕｎｇＳｃｉｅｎｔｉｓｔｓＬａｂｏｒａｔｏｒｙｏｆＷｕｈａｎＩｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，Ａｃａｄ...     

THE DISTURBANCE LOCALIZATION PROBLEM FOR SINGULAR SYSTEMS

ＴＨＥＤＩＳＴＵＲＢＡＮＣＥＬＯＣＡＬＩＺＡＴＩＯＮＰＲＯＢＬＥＭＦＯＲＳＩＮＧＵＬＡＲＳＹＳＴＥＭＳＴａｎＬｉａｎｓｈｅｎｇ（ＷｕｈａｎＩｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，Ｃｈｉｎ．Ａｃａｄ．ｏｆＳｃｉ．，Ｗｕｈａｎ４３００７１，Ｃｈｉｎａ．）Ａｂｓ...     

BLOW-UP AT THE BOUNDARY FOR DEGENERATE DIFFUSION EQUATION

ＢＬＯＷ－ＵＰＡＴＴＨＥＢＯＵＮＤＡＲＹＦＯＲＤＥＧＥＮＥＲＡＴＥＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮ￥ＣａｏＺｈｅｎｃｈａｏ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＸｉａｍｅｎＵｎｉｖ．Ｘｉａｍｅｎ３６１００５）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｃｏｎｓｉ...     

L~∞ESTIMATE FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS IN R~N

Ｌ~∞ＥＳＴＩＭＡＴＥＦＯＲＳＯＬＵＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＩＮＲ~ＮＬｉＧｏｎｇｂａｏ（李工宝）（Ｉｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，ＴｈｅＣｈｉｎｅｓｅＡｃａｃｌｅｍｙｏｆＳｃｉｅｎｃｅｓＳｉｎｉｃａ，ＰＯＢ...     

Some results on domination number of products of graphs

ＳＯＭＥＲＥＳＵＬＴＳＯＮＤＯＭＩＮＡＴＩＯＮＮＵＭＢＥＲＯＦＰＲＯＤＵＣＴＳＯＦＧＲＡＰＨＳＳＨＡＮＥＲＦＡＮＧＳＵＮＬＩＡＮＧＡＮＤＫＡＮＧＬＩＹＩＮＧＡｂｓｔｒａｃｔ．ＬｅｔＧ＝（Ｖ,Ｅ）ｂｅａｓｉｍｐｌｅｇｒａｐｈ．ＡｓｕｂｓｅｔＤｏｆＶｉｓ...     

ON INCLUSION RELATIONS BETWEEN BERS-ORLICZ SPACES

ＯＮＩＮＣＬＵＳＩＯＮＲＥＬＡＴＩＯＮＳＢＥＴＷＥＥＮＢＥＲＳ－ＯＲＬＩＣＺＳＰＡＣＥＳＺｈａｏＲｕｈａｎ（赵如汉）（Ｉｎｓｔ．ｏｆＭａｔｈ．Ｓａｃ．，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｄ，Ｗｕｈａｎ４３００７１，Ｃｈｉｎａ）Ａｂｓｔｒａ...     

MAXIMUM TREES OF SUBSETS

ＭＡＸＩＭＵＭＴＲＥＥＳＯＦＳＵＢＳＥＴＳＷｕＳｈｉｑｕａｎ（巫世权）（Ｉｎｓｔ．ｏｆＡｐｐｌ．Ｍａｔｈ．，ＣｈｉｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，ＰＯＢｏｘ２７３４，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：ＬｅｔＸｂｅａｆ...     

ON SOME RESULTS FOR NONLINEAR BEST CHEBYSHEV APPROXIMATION WITH LGH CONDITION

ＯＮＳＯＭＥＲＥＳＵＬＴＳＦＯＲＮＯＮＬＩＮＥＡＲＢＥＳＴＣＨＥＢＹＳＨＥＶＡＰＰＲＯＸＩＭＡＴＩＯＮＷＩＴＨＬＧＨＣＯＮＤＩＴＩＯＮＷｅｉＤａｎ（韦旦）（Ｉｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｗｕｈａｎ...     

How to build all Chebyshevian spline spaces good for geometric design?

In the present work we determine all Chebyshevian spline spaces good for geometric design. By Chebyshevian spline space we mean a space of splines with sections in different Extended Chebyshev spaces and with connection matrices at the knots. We say that such a spline space is good for design when it possesses blossoms. To justify the terminology, let us recall that, in this general framework, existence of blossoms (defined on a restricted set of tuples) makes it possible to develop all the classical geometric design algorithms for splines. Furthermore, existence of blossoms is equivalent to existence of a B-spline bases both in the spline space itself and in all other spline spaces derived from it by insertion of knots. We show that Chebyshevian spline spaces good for design can be described by linear piecewise differential operators associated with systems of piecewise weight functions, with respect to which the connection matrices are identity matrices. Many interesting consequences can be drawn from the latter characterisation: as an example, all Chebsyhevian spline spaces good for design can be built by means of integral recurrence relations.     

一类三角域上的三次样条插值(英文)

In this paper, we consider spaces of cubic C^1-spline on a class of triangulations. By using the inductive algorithm, the posed Lagrange interpolation sets are constructed for cubic spline space. It is shown that the class of triangulations considered in this paper are nonsingular for S1/3 spaces. Moreover, the dimensions of those spaces exactly equal to L. L. Schuraaker＇s low bounds of the dimensions. At the end of this paper, we present an approach to construct triangulations from any scattered planar points, which ensures that the obtained triangulations for S1/3 space are nonsingular.     

Dimensions of spline spaces over non-rectangular T-meshes

Spline spaces over rectangular T-meshes have been discussed in many papers. In this paper, we consider spline spaces over non-rectangular T-meshes. The dimension formulae of spline spaces over special simply connected T-meshes have been obtained. For T-meshes with holes, we discover a new type of dimension instability. We construct a relationship between the dimension of the spline space over a T-mesh \(\mathcal {T}\) with holes and the dimension of the spline space over a simply connected T-mesh associated with \(\mathcal {T}\).     

A normalized representation of super splines of arbitrary degree on Powell–Sabin triangulations

In the paper, a family of bivariate super spline spaces of arbitrary degree defined on a triangulation with Powell–Sabin refinement is introduced. It includes known spaces of arbitrary smoothness r and degree \(3r-1\) but provides also other choices of spline degree for the same r which, in particular, generalize a known space of \(\mathscr {C}^{1}\) cubic super splines. Minimal determining sets of the proposed super spline spaces of arbitrary degree are presented, and the interpolation problems that uniquely specify their elements are provided. Furthermore, a normalized representation of the discussed splines is considered. It is based on the definition of basis functions that have local supports, are nonnegative, and form a partition of unity. The basis functions share numerous similarities with classical univariate B-splines.     

On the Problem of Instability in the Dimensions of Spline Spaces over T-Meshes with T-Cycles

The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a basic problem for the theories and applications of splines. However, the problem of determining the dimension of a spline space is difficult since it heavily depends on the geometric properties of the partition. In many cases, the dimension is unstable. In this paper, we study the instability in the dimensions of spline spaces over T-meshes by using the smoothing cofactor-conformality method. The modified dimension formulas of spline spaces over T-meshes with T-cycles are also presented. Moreover, some examples are given to illustrate the instability in the dimensions of the spline spaces over some special meshes.     

Minimal splines and wavelets

This paper is dedicated to the memory of the prominent mathematician S.G. Mikhlin. Here, Mikhlin’s idea of approximation relations is used for construction of wavelet resolution in the case of spline spaces of zero height. These approximation relations allow one to establish the embedding of the spline spaces corresponding to nested grids. Systems of functionals which are biorthogonal to the basic splines are constructed using the relations; then the systems obtained are used for wavelet decomposition. It is established that, for a fixed pair of grids of which one is embedded into the other and for an arbitrary fixed (on the coarse grid) spline space, there exists a continuum of spline spaces (on the fine grid) which contain the aforementioned spline space on the coarse grid. The wavelet decomposition of such embedding is given and the corresponding formulas of decomposition and formulas of reconstruction are deduced. The space of ( , φ)-splines is introduced with three objects: the full chain of vectors, prescribed infinite grid on real axis and the preassigned vector-function φ with m + 1 components (m is called the order of the splines). Under certain assumptions, the splines belong to the class C ^{m ? 1}. The gauge relations between the basic splines on the coarse grid and the basic splines on the fine grid are deduced. A general method for construction of a biorthogonal system of functionals (to basic spline system) is suggested. In this way, a chain of nested spline spaces is obtained, and the wavelet decomposition of the chain is discussed. The spaces and chains of spaces are completely classified in the terms of manifolds. The manifold of spaces considered is identified with the manifold of complete sequences of points of the direct product of an interval on the real axis and the projective space ? ^m ; the manifold of nested spaces is identified with the manifold of nested sequences of points of the direct product mentioned above.     

Morgan-Scott型剖分上的样条空间的奇异性

Multivariate spline function is an important research object and tool in Computational Geometry. The singularity of multivariate spline spaces is a difficult problem that is ineritable in the research of the structure of multivariate spline spaces. The aim of this paper is to reveal the geometric significance of the singularity of bivariate spline space over Morgan-Scott type triangulation by using some new concepts proposed by the first author such as characteristic ratio, characteristic mapping of lines （or ponits）, and characteristic number of algebraic curve. With these concepts and the relevant results, a polished necessary and sufficient conditions for the singularity of spline space S u＋1^u （△MS^u） are geometrically given for any smoothness u by recursion. Moreover, the famous Pascal＇s theorem is generalized to algebraic plane curves of degree n≥3.     

Spline prewavelets for non-uniform knots

Summary In this paper, we develop a framework suitable for performing a multiresolution analysis using univariate spline spaces of arbitrary degree and with non-uniform knot-sequences. To this end, we show, among other things, the existence of compactly supported prewavelets and of prewavelets that are globally supported, but decay exponentially. In each case we obtain a decomposition of a fine spline space as a sum of a coarse spline space plus a spline space spanned by prewavelets.