We produce an integral model for the modular curve X(Np) over the ring of integers of a sufficiently ramified extension of Zp whose special fiber is a semistable curve in the sense that its only singularities are normal crossings. This is done by constructing a semistable covering (in the sense of Coleman) of the supersingular part of X(Np), which is a union of copies of a Lubin-Tate curve. In ...

Charles Evans We present an exposition of various results dealing with the total curvature of curves in Euclidean 3-space. There are two primary results: Fenchel’s theorem and the theorem of Fary and Milnor. Fenchel’s theorem states that the total curvature of a simple closed curve is greater than or equal to 2π, with equality if and only if the curve is planar convex. The Fary-Milnor theorem s...

The flicker response curve for the newt Triturus viridescens (water phase) has much the same quantitative structure as that found with various fresh-water teleosts at the same temperature (21.5 degrees ). The variability of critical intensity and of critical flash frequency likewise follows the same rules. The cone portion of the F - log I curve is much more widely spread, however. This, and th...

The functional equation for the motivic integral of Milnor number of a plane curve is derived using the Denef-Loeser formula for the change of variables. Its solution is a function of five auxiliary parameters, it is unique up to the multiplication by the constant and there is a simple algorithm to find its coefficients. The method is universal enough and gives, for example, the equations for t...

We prove that every curve on a separably rationally connected variety is rationally equivalent to a (non-effective) integral sum of rational curves. That is, the Chow group of 1-cycles is generated by rational curves. Applying the same technique, we also show that the Chow group of 1-cycles on a separably rationally connected Fano complete intersections of index at least 2 is generated by lines...

The log-aesthetic curves include the logarithmic (equiangular) spiral, clothoid, and involute curves. Although most of them are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform them and they are expected to be utilized for practical use of industrial and graphical design. However, their input method proposed so far by use of three soc...

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...

Stroeker and Tzanakis gave convincing numerical and heuristic evidence for the fact that in their Ellog method a certain parameter λ plays a decisive role in the size of the final bound for the integral points on elliptic curves. Furthermore, they provided an algorithm to determine the MordellWeil basis of the curve which corresponds to the optimal choice of λ. In this paper we show that workin...