A New Bound on the Total Domination Subdivision Number

A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ _t (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. In this paper we prove that for every simple connected graph G of order n ≥ 3,

Analysis of stationary subdivision schemes for curve design based on radial basis function interpolation

This paper provides a large family of interpolatory stationary subdivision schemes based on radial basis functions (RBFs) which are positive definite or conditionally positive definite. A radial basis function considered in this study has a tension parameter λ>0 such that it provides design flexibility. We prove that for a sufficiently large , the proposed 2L-point (L∈N) scheme has the same smoothness as the well-known 2L-point Deslauriers-Dubuc scheme, which is based on 2L-1 degree polynomial interpolation. Some numerical examples are presented to illustrate the performance of the new schemes, adapting subdivision rules on bounded intervals in a way of keeping the same smoothness and accuracy of the pre-existing schemes on R. We observe that, with proper tension parameters, the new scheme can alleviate undesirable artifacts near boundaries, which usually appear to interpolatory schemes with irregularly distributed control points.     

On the non-degeneracy property of the longest-edge trisection of triangles

The longest-edge (LE) trisection of a triangle t is obtained by joining the two equally spaced points of the longest-edge of t with the opposite vertex. In this paper we prove that for any given triangle t with smallest interior angle τ>0, if the minimum interior angle of the three triangles obtained by the LE-trisection of t into three new triangles is denoted by τ₁, then τ₁?τ/c₁, where . Moreover, we show empirical evidence on the non-degeneracy property of the triangular meshes obtained by iterative application of the LE-trisection of triangles. If τ_n denotes the minimum angle of the triangles obtained after n iterative applications of the LE-trisection, then τ_n>τ/c where c is a positive constant independent of n. An experimental estimate of c≈6.7052025350 is provided.     

以Bernstein多项式为规则后件的模糊系统构造及算法

以多元多项式为规则后件的模糊系统是区别于Mamdani型和T-S型的一类模糊系统,在模糊控制器及其应用中具有重要的理论价值.首先,以Bernstein多项式为规则后件建立了一类新的多输入单输出模糊系统,进而证明了该模糊系统对n维单位正方体上的连续函数具有逼近性.其次,利用随机剖分数所确定的Bernstein多项式给出了这类模糊系统的输出算法,并通过实例说明该算法是有效的.     

一种高频响条纹信号细分方法及其误差分析

用两片高速A/D转换器和一片闪速存储器(Flash ROM)构建了高分辨率和高频响的莫尔条纹信号细分电路。光栅信号经A/D转换后只需访问一次只读存储器即可输出细分值。通过修改只读存储器的写入数据,可方便地实现不同的细分倍数。在100倍细分时能够实时处理50kHz的输入信号,最高可处理1MHz的信号。实现了光栅信号高频响和高细分处理的统一。通过计算实际信号与理想信号的数量积的方法分析了直流漂移、非正交误差、等幅性误差和三次谐波对只读存储器细分的影响。为进行误差修正和误差补偿奠定了基础。     

利用TFT-LCD像素结构衍射测试CCD图像采集系统的像素间距

研究了在范德卢格特型光学相关器中利用薄膜晶体管液晶显示器（TFT-LCD）替代靶板实物测试CCD图像采集系统像素间距的原理和方法,对由HN-480型CCD摄像机和OK-C21型图像采集卡组成的图像采集系统像素间距进行了现场测试,并对测试结果进行了误差分析.结果表明,该方法充分利用了光学相关器的现有组件,不需要其它设备,保证了图像采集系统像素间距的测试结果和实际工作性能的一致性,具有很强的实用性和可操作性.     

Multivariate Refinable Functions of High Approximation Order Via Quotient Ideals of Laurent Polynomials

We give an algebraic interpretation of the well-known zero-condition or sum rule for multivariate refinable functions with respect to an arbitrary scaling matrix. The main result is a characterization of these properties in terms of containment in a quotient ideal, however not in the ring of polynomials but in the ring of Laurent polynomials.     

A point set whose space of triangulations is disconnected

By the ``space of triangulations" of a finite point configuration we mean either of the following two objects: the graph of triangulations of , whose vertices are the triangulations of and whose edges are the geometric bistellar operations between them or the partially ordered set (poset) of all polyhedral subdivisions of ordered by coherent refinement. The latter is a modification of the more usual Baues poset of . It is explicitly introduced here for the first time and is of special interest in the theory of toric varieties.

We construct an integer point configuration in dimension 6 and a triangulation of it which admits no geometric bistellar operations. This triangulation is an isolated point in both the graph and the poset, which proves for the first time that these two objects cannot be connected.

     

Pointwise convergence of bounded cascade sequences

The cascade algorithm plays an important role in computer graphics and wavelet analysis. For an initial function , a cascade sequence is constructed by the iteration where is defined by In this paper, under a condition that the sequence is bounded in , we prove that the following three statements are equivalent: (i) converges . (ii) For , there exist a positive constant and a constant such that (iii) For some converges in . An example is presented to illustrate our result.

     

Flabby sheaves of chains for singular homology

Iterating the barycentric subdivision operator in a singular complex, we construct flabby sheaves of chains for singular homology. Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 396–401, March, 1999.