Recent experiments on the proximity induced supercurrent in mesoscopic normal wires revealed a surprising temperature dependence. They suggest clean-limit behavior although the wires are strongly disordered. We demonstrate that this unexpected scaling is actually contained in the conventional description of diffusive superconductors and find excellent agreement with the experimental results. In...

Let A be a subset of Fp , the n-dimensional linear space over the prime field Fp of size at least δN (N = p), and let Sv = P −1(v) be the level set of a homogeneous polynomial map P : Fp → Fp of degree d, for v ∈ Fp . We show, that under appropriate conditions, the set A contains at least cN |S| arithmetic progressions of length l ≤ d with common difference in Sv, where c is a positive constant...

We study the problem of determining the largest d of a non-Denniston maximal arc of degree 2 generated by a fp; 1g-map in PGð2; 2Þ via a recent construction of Mathon [9]. On one hand, we show that there are fp; 1g-maps that generate non-Denniston maximal arcs of degree 2ðmþ1Þ=2, where md 5 is odd. Together with Mathon’s result [9] in the m even case, this shows that there are always fp; 1g-map...

A characterization of the quotient proximity is given. It is used to find necessary and sufficient conditions for every proximity map on a space to be a topological quotient map. It is shown that a separated proximity space is compact iff every /7-map on X with separated range is a proximity quotient map. Introduction. In 1959 Katetov [3] introduced proximity quotient maps. They have since been...

This handout discusses finite fields: how to construct them, properties of elements in a finite field, and relations between different finite fields (including their Galois groups). We write Z/(p) and Fp interchangeably for the field of size p. Here is an executive summary of the main results. • Every finite field has prime power order. • For every prime power, there is a finite field of that o...

Helicopter landing sites in proximity to the forest fire-risk zones are necessary for the delivery of supplies and fire emergency response teams. In this paper, we initially prepared forest fire risk map using Random Forest algorithm by overlaying the effective factors on fire occurring including vegetation types, physiographic, climatic and human factors. Then, three variants of natural candid...

In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:Crightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we ...

Mussel adhesive proteins (MAPs) have been considered as potential underwater and medical bioadhesives. Previously, we reported a functional expression of recombinant MAP hybrid fp-151, which is a fusion protein with six type 1 (fp-1) decapeptide repeats at each type 5 (fp-5) terminus, with practical properties in Escherichia coli. In the present work, we introduced the Vitreoscilla hemoglobin (...

While Fabry-Pérot (FP) resonances and Moiré superlattices are intensively studied in graphene on hexagonal boron nitride (hBN), the two effects have not been discussed in their coexistence. Here we investigate the FP oscillations in a ballistic pnp-junctions in the presence and absence of a Moiré superlattice. First, we address the effect of the smoothness of the confining potential on the visi...

FP prostanoid receptors are G-protein-coupled receptors whose physiological activator is prostaglandin-F(2alpha) (PGF(2alpha)). PGF(2alpha) has been implicated in wound healing and cardiac hypertrophy, which are both known to involve the induction of the immediate-early response gene, early growth response factor-1 (EGR-1). We hypothesized that activation of the human FP receptor by PGF(2alpha)...