In order to study the shrinkage process of clayey soil, we perform a modified laboratory test allowing to measure simultaneously and continuously the vertical displacement and the weight of natural state specimen. The experiment was conducted on undisturbed clayey specimen. Using the experimental results, and on the basis of the existing relation between the soil water content and its structura...

Abstract Curve shortening in the z -plane which, at a given point on curve, normal velocity of curve is equal to curvature, shown satisfy $$S_tS_z=S_{zz}$$ S t z = zz , where S ( t ) Schwarz funct...

Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...

Let P be a polygonal curve in R of length n, and S be a point set of size k. The Curve/Point Set Matching problem consists of finding a polygonal curve Q on S such that the Fréchet distance from P is less than a given ε. We consider eight variations of the problem based on the distance metric used and the omittability and repeatability of the points. We provide closure to a recent series of com...

Some Definitions and Notations. In this section α : [0, L] → R will denote a curve in R that is parametrized by arclength and is of class C, k ≥ 2. We recall that the unit tangent to α at s is defined by −→t (s) := α′(s). (That it is a unit vector is just the definition of α being parametrized by arclength.) The curvature of α is the non-negative real-valued function k : [0, L] → R defined by k...

Let P be a polygonal curve in R of length n, and S be a point-set of size k. The Curve/Point Set Matching problem consists of finding a polygonal curve Q on S such that the Fréchet distance from P is less than a given ε. We consider eight variations of the problem based on the distance metric used and the omittability or repeatability of the points. We provide closure to a recent series of comp...