We identify several new quasicrystal approximants in alloy systems in which quasicrystals have not been previously reported. Some occur in alloys with large size contrast between the constituent elements, either containing small Boron atoms, or large Ca/Eu atoms, leading to quasicrystal structures quite different from currently known systems where the size contrast is smaller. Another group of ...

Parametric CAD supports design explorations through generative methods which compose and transform geometric elements. This paper argues that elementary shape computations do not always correspond to valid compositional shape structures. In many design cases generative rules correspond to compositional structures, but for relatively simple shapes and rules it is not always possible to assign a ...

Theta correspondence y over R is established by Howe (J. Amer. Math. Soc. 2 (1989) 535). In He (J. Funct. Anal. 199 (2003) 92), we prove that y preserves unitarity under certain restrictions, generalizing the result of Li (Invent. Math. 97 (1989) 237). The goal of this paper is to elucidate the idea of constructing unitary representation through the propagation of theta correspondences. We show...

Interaction with web service enabled marketplaces would be greatly facilitated if users were given a high level service request language to express their goals in complex business domains. This could be achieved by using a planning framework which monitors the execution of planned goals against predefined standard business processes and interacts with the user to achieve goal satisfaction. The ...

background: an effective polymer gel dosimeter can be fabricated by varying the composition of its chemical components. materials and methods: the magat gel dosimeter formulations that used different compositions of methacrylic acid (maa) and gelatin were extensively investigated in the present study according to the r2–dose response and r2–dose sensitivity. the irradiation of magat gel was per...

For n ≥ 1, let an count the number of ways one can tile a 1 × n chessboard using 1× 1 square tiles, which come in w colors, and 1× 2 rectangular tiles, which come in t colors. The results for an generalize the Fibonacci numbers and provide generalizations of many of the properties satisfied by the Fibonacci and Lucas numbers. We count the total number of 1× 1 square tiles and 1× 2 rectangular t...

We consider a class of generating functions that appear in the context of Carlitz compositions. In order to combinatorially interpret them, we introduce a combinatorial structures that we name generalized compositions and p-Carlitz compositions of integers. We explain their connection to Carlitz compositions, the relation to other combinatorial structures, and we describe their basic properties...

A tree-composition is a tree-like family that serves to describe the obstacles to k-edge-connected orientability of mixed graphs. Here we derive a structural result on tree-compositions that gives rise to a simple algorithm for computing an obstacle when the orientation does not exist. As another application, we show a min–max theorem on the minimal in-degree of a given node set in a k-edge-con...