Compact Lie groups appear frequently in algebraic topology, but they are relatively rigid analytic objects, and partially for that reason are a challenge to understand homotopically. Since H. Hopf (and H-spaces) topologists have aspired to escape the analytic straitjacket by finding some homotopy theoretic concept which would capture enough of the idea of “compact Lie group” to lead to rich and...

The goal of the article is to introduce an order on a simple closed curve. To do this, we x two points on the curve and devide it to two arcs. We prove that such a decomposition is unique. Other auxiliary theorems about arcs are proven for preparation of the proof of the above. For simplicity, we use the following convention: a, b, c, s, r are real numbers, n is a natural number, p, q are point...

Graph analytics algorithms leverage quantifiable structural properties of the data to predict interesting concepts and relationships. The same information, however, can be represented using many different structures and the structural properties observed over particular representations do not necessarily hold for alternative structures. Because these algorithms tend to be highly effective over ...

objective: there is no definitive data on the strength of glass fiber and cast posts with different length. this in vitro study was designed to investigate and compare the effect of length on the retentive strength of glass fiber and cast posts. materials and methods: sixty recently extracted intact maxillary canine teeth were cut 1mm above the cej. the specimens were endodontically treated and...

The dynamic response and performance of a micro UAV is greatly influenced by its aerodynamics which in turn is affected by the interactions with features in the environment in close proximity. In the paper we address the modeling of quadrotor robots in different flight conditions that include relative wind velocity and proximity to the ground, the ceiling and other robots. We discuss the incorp...

When FP measurement methods are different between the same functional size projects, FPs are different between them. FP measurement methods are often customized by software vendors. To reinforce accountability for a customer, FP based on a customized method should be transformed to FP based on a standard method. So we proposed two derivation methods of FP transformation formulas. One method is ...

Priebe et al. (2001) introduced the class cover catch digraphs and computed the distribution of the domination number of such digraphs for one dimensional data. In higher dimensions these calculations are extremely difficult due to the geometry of the proximity regions; and only upper-bounds are available. In this article, we introduce a new type of data-random proximity map and the associated ...

Let A and B be nonempty subsets of a metric space X, d . Consider a mapping T : A ∪ B → A ∪ B, T is called a cyclic map if T A ⊆ B and T B ⊆ A. x ∈ A is called a best proximity point of T in A if d x, Tx d A,B is satisfied, where d A,B inf{d x, y : x ∈ A, y ∈ B}. In 2005, Eldred et al. 1 proved the existence of a best proximity point for relatively nonexpansive mappings using the notion of prox...

We fix an error in the proof of a theorem of Van Mill about homeomorphisms between compactifications of ω with small weight. Theorem 4.2. Let aω and bω be compactifications of ω. Assume that (1) there is a retraction r : aω → aω \ ω, (2) there is a retraction s : bω → bω \ ω, (3) f : aω \ ω → bω \ ω is a homeomorphism. If the weight of aω \ ω is less than p, then f can be extended to a homeomor...

We determine the probability that a randomly chosen elliptic curve E/Fp over a randomly chosen prime field Fp has an `-primary part E(Fp)[`∞] isomorphic with a fixed abelian `-group H (`) α,β = Z/` × Z/`. We show that the probability agrees with the one predicted by a natural though unproven equidistribution hypothesis for Frobenius elements in GL(2,Z`). Probabilities for “|E(Fp)| divisible by ...