Figure 2: Analysis output of localized H-MRS spectra from the right node of patient 9. The in vivo spectrum (thin grey curve) has been estimated with the LCModel output (thick red curve), and the difference of these spectra (residue) is plotted at the top. Cho, choline. Figure 3: Scatterplot displaying Cho/W concentrations (arbitrary units) as function of FDG uptake (g/mL). The linear regressio...

Digital Elevation Models (DEMs) are used to estimate different morphologies, analysis of river profile, delineating drainage basin and drainage pattern associated with lithological and structural changes. The study area is Maroon River located in Khuzestan Province, Iran. In this study geomorphometric analysis based on DEM carried out to understand Maroon river uplift rate and tectonic- erosion...

We investigate bi–Hamiltonian structures and related mKdV hierarchy of solitonic equations generated by (semi) Riemannian metrics and curve flow of non–stretching curves. The corresponding nonholonomic tangent space geometry is defined by canonically induced nonlinear connections, Sasaki type metrics and linear connections. One yields couples of generalized sine–Gordon equations when the corres...

Recently, the first Abel map for a stable curve of genus g ≥ 2 has been constructed. Fix an integer d ≥ 1 and let C be a stable curve of compact type of genus g ≥ 2. We construct two d-th Abel maps for C, having different targets, and we compare the fibers of the two maps. As an application, we get a characterization of hyperelliptic stable curves of compact type with two components via the 2-n...

The breakup of the shearless invariant torus with winding number ω = √ 2 − 1 is studied numerically using Greene’s residue criterion in the standard nontwist map. The residue behavior and parameter scaling at the breakup suggests the existence of a new fixed point of the renormalization group operator (RGO) for area-preserving maps. The unstable eigenvalues of the RGO at this fixed point and th...

Recently, many papers have begun to consider so-called non-QRT birational maps of the plane. Compared to the QRT family of maps which preserve each biquadratic curve in a fibration of the plane, non-QRT maps send a biquadratic curve to another biquadratic curve belonging to the same fibration or to a biquadratic curve from a different fibration of the plane. In this communication, we give the g...

A 2-dimensional space-filling curve, here, is a surjective continuous map from an interval to a 2-dimensional space. To construct a new space-filling curve distinct and much different from Hilbert’s, Peano’s, and the Z-order, we first observe that all three of these curves are based on self-similar fractals–in particular, the recursive definition of the sequences of functions that converge to t...

We define three hard problems in the theory of elliptic divisibility sequences (EDS Association, EDS Residue and EDS Discrete Log), each of which is solvable in subexponential time if and only if the elliptic curve discrete logarithm problem is solvable in sub-exponential time. We also relate the problem of EDS Association to the Tate pairing and the MOV, Frey-Rück and Shipsey EDS attacks on th...