For a graph G = (V,E), a set S ⊆ V is a [1, 2]-set if it is a dominating set for G and each vertex v ∈ V \S is dominated by at most two vertices of S, i.e. 1 ≤ |N(v)∩S| ≤ 2. Moreover a set S ⊆ V is a total [1, 2]-set if for each vertex of V , it is the case that 1 ≤ |N(v)∩S| ≤ 2. The [1, 2]-domination number of G, denoted γ[1,2](G), is the minimum number of vertices in a [1, 2]-set. Every [1, 2...

If V is a nonsingular real algebraic set we say Ht(V;Z2) * s algebraic if it is generated by nonsingular algebraic subsets of V. Let V be a 3-dimensional nonsingular real algebraic set. Then, we prove that any immersed surface in V can be isotoped to an algebraic subset if and only if Ht (V: Z 2 ) / = 1,2 are algebraic. This isotopy above carries the natural stratification of the immersed surfa...

12 Figure 8: Blending using two diierent magnitudes of T 2 i (t) = dC(t) dt n(u(t); v(t)). (a) (b) (c) Figure 9: Spout connection to the Utah teapot rounding using T 2 i (t) = dC(t) dt n(u(t); v(t)). 5 i (t) = (S u (u(t); v(t))r(t) + S v (u(t); v(t))s(t)). method, which is guaranteed to be perpendicular to the rail curves in Euclidean space. Figure 9 shows the original teapot (a), the lleted te...

The conjecture Σuv V(G) dG(u)2 / n(G) ≤ Σuvv E(G) dG(u)dG(v) / m(G) that compares normalized Zagreb indices attracted recently a lot of attention1-9. In this paper we analyze analogous statement in which degree dG(u) of vertex u is replaced by its eccentricity δG(u) in which way we define novel first and second Zagreb eccentricity indices. We show that Σuv V(G) εG(u)2 / n(G) ≥ Σuvv E(G) εG(u)εG...

and po.biu, v), («, v), has been considered by a number of writers. Gergen and Littauer [4, Theorems IV and V] have treated the problem of the boundedness, and convergence in the Pringsheim sense, of ...

In this paper we present catalogs of photometric and spectroscopic data for M81 globular clusters (GCs). The catalogs include B− and V − photometric and reddening data of 95 GCs, and spectroscopic metallicities of 40 GCs in M81. Using these data, we make some statistical correlations. The results show that the distributions of intrinsic B and V colors and metallicities are bimodal, with metalli...

A technique is described that produces symmetric drawings of a graph G in the plane. The method requries that G have a non-trivial automorphism group Aut(G), and that a non-trivial symmetry g ∈ Aut(G) has been selected in some way. The technique is found to be very effective in practice. It forms a part of the Groups & Graphs** software package. 1. Symmetric Cycles Let G be a connected undirect...

Verb-Noun compounds in English can be classified into endocentric compounds and exocentric ones. Among exocentric Verb-Noun compounds, two types of constructions are very common: ‘Verb + Object = Agent’ construction and ‘Verb + Object =Instrument’ construction. Based on the cognitive analysis of endocentric V+N compounds, this paper argues that exocentric V+N compounds can be analyzed in the sa...

Health care organizations face challenges in providing language services for Limited English proficiency (LEP) clients. Supported by a grant from the National Science Foundation, we have been working to develop a technology for proximate simultaneous medical interpretation. In an effort to understand the relative importance of physical proximity, audio cues and visual cues to effective interpre...

To have “full” entropy has been defined in a draft NIST standard to be to have min-entropy very close, proportionally, to the min-entropy of a uniform distribution. A function is uniform if all its preimages have the same size. This report proves that the output of any uniform compression function can fail to have full entropy, even when the input has full entropy.