For each integer D ≥ 5 with D ≡ 0 or 1 mod 4, the Weierstrass curve WD is an algebraic curve and a finite volume hyperbolic orbifold which admits an algebraic and isometric immersion into the moduli space of genus two Riemann surfaces. The Weierstrass curves are the main examples of Teichmüller curves in genus two. The primary goal of this paper is to determine the number and type of orbifold p...

This paper introduces a new way of generalizing Hilbert’s two-dimensional space-filling curve to arbitrary dimensions. The new curves, called harmonious Hilbert curves, have the unique property that for any d′ < d, the d-dimensional curve is compatible with the d′-dimensional curve with respect to the order in which the curves visit the points of any d′-dimensional axis-parallel space that cont...

A dosimetric calibration of three types radiochromic films (GafChromicTM HD-V2, MD-V3, and EBT3) was carried out for absorbed doses (D) ranging up to 100 kGy using a 130 TBq Co60 γ-ray source. The optical densities (ODs) the irradiated were acquired with transmission-mode flatbed film scanner EPSON GT-X980. data cross-checked 20-MeV proton beam from azimuthally varying field cyclotron at Resear...

background: electrophysiologic (edx) study is the most valuable method in grading the severity of carpal tunnel syndrome (cts), but it is invasive and painful. we evaluated the efficacy of ultrasound for this purpose. materials and methods: eighty-one wrists of 52 consecutive patients with clinical evidences of cts, confirmed and graded by edx as mild, moderate, and severe, were examined by ult...

We consider the problem vt = ∆v + |v|p−1v in Ω× (0, T ), v = 0 on ∂Ω× (0, T ), v > 0 in Ω× (0, T ). In a domain Ω ⊂ Rd, d ≥ 7 enjoying special symmetries, we find the first example of a solution with type II blow-up for a power p less than the JosephLundgren exponent pJL(d) = { ∞, if 3 ≤ d ≤ 10, 1 + 4 d−4−2 √ d−1 , if d ≥ 11. No type II radial blow-up is present for p < pJL(d). We take p = d+1 ...

We establish a Lefschetz hyperplane theorem for the Berkovich analytifications of Jacobians curves over an algebraically closed non-Archimedean field. Let J be Jacobian curve X, and let $$W_{d} \subset J$$ locus effective divisor classes degree d. show that pair $$(J^{an},W_d^{an})$$ is d-connected, thus in particular inclusion analytification theta $$\Theta ^{an}$$ into $$J^{an}$$ satisfies $$...