We prove that every strictly positive endofunctor on the category of sets generated by Martin-LL of's extensional type theory has an initial algebra. This representation of inductively deened sets uses essentially the wellorderings introduced by Martin-LL of in \Constructive Mathematics and Computer Programming". 1 Background Martin-LL of 10] introduced a general set former for wellorderings in...

Windowing queries answer important questions. Primarily, windowing queries answer information involving a given line segment and a windowing region. Given a set of n line segments S and a query window W := [x : x ]x[y : y ], windowing queries answer which segments in S intersect W. The primary difference between windowing queries and range queries is the data. While range queries are associated...

Let G = (V, E) be a graph and let W:V→N be a non-negative integer weighting of the vertices in V. A nonempty set of vertices S ⊆ V is called a weighted defensive alliance if ∀v ∈ S ,∑u∈N[v]∩S w(u) ≥ ∑x∈N(v)−S w(x). A non-empty set S ⊆ V is a weighted offensive alliance if ∀v ∈ δS ,∑u∈N(v)∩S w(u) ≥ ∑x∈N[v]−S w(x). A weighted alliance which is both defensive and offensive is called a weighted pow...

The study of Hamiltonian graphs began with Dirac’s classic result in 1952. This was followed by that of Ore in 1960. In 1984 Fan generalized both these results with the following result: If G is a 2-connected graph of order n and max{d(u), d(v)}≥n/2 for each pair of vertices u and v with distance d(u, v)=2, then G is Hamiltonian. In 1991 Faudree–Gould–Jacobson–Lesnick proved that if G is a 2-co...

two capillary zone electrophoresis (cze) methods were developed in this study, one using an acidic buffer (sodium citrate ph = 2.5) and the other using a basic buffer (sodium tetraborate ph = 9.8). the two methods were compared on the basis of repeatability and reproducibility of results and the cze method developed with the basic buffer was then selected for further studies. the method was ful...

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BiOCl microflowers were synthesized using bismuth nitrate pentahydrate and sodium chloride by microwave (MW) assisted synthesis method for 23 minutes at 180 W. Scanning electron microscopy (SEM) studies revealed a unique morphology of flower-like assemblies comprised of nanosheets. The X-ray diffraction (XRD) pattern showed that a highly pure and crystalline phase has been obtained. The energy ...