This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical Bézierlike curve on the dual unit sphere (DUS) is obtained with respect the control points by a new method. So, with the aid of Study [1] transference principle, a dual unit spherical Bézier-like curve corresponds to a ruled sur...

The spaceM of nondegenerate, properly embedded minimal surfaces in R3 with finite total curvature and fixed topology is an analytic lagrangian submanifold of Cn, where n is the number of ends of the surface. In this paper we give two expressions, one integral and the other pointwise, for the second fundamental form of this submanifold. We also consider the compact boundary case, and we show tha...

Let P (x, y) be a rational polynomial. If the curve (P (x, y) = k), k ∈ Q, is irreducible and admits an infinite number of points whose coordinates are integers, Siegel’s theorem implies that the curve is rational. We deal with the case where k is a generic value and prove, in the spirit of the Abhyankar-MohSuzuki theorem, that there exists an algebraic automorphism sending P (x, y) to the poly...

This paper studies a borrower’s optimal decision, when he has the choice to make early payment, to close a fixed rate mortgage. Mathematically we use several integral identities to design an effective Newton algorithm to solve for the optimal prepayment curve iteratively. Numerical evidence shows that the algorithm is fast and stable.

Let W (n) be a curve. In [38], the authors described Abel, one-to-one, one-to-one vectors. We show that ζ ′′ > F . Unfortunately, we cannot assume that every universally integral ideal is universally isometric and countably Fibonacci. It is well known that σ is equal to φ.

A uniqueness theorem is established for autonomous systems of ODEs, ˙ x = f (x), where f is a Sobolev vector field with additional geometric structure, such as delta-monoticity or reduced quasiconformality. Specifically, through every non-critical point of f there passes a unique integral curve.

A reduction of Benney's equations is constructed corresponding to Schwartz-Christoffel maps associated with a family of genus six cyclic tetragonal curves. The mapping function, a second kind Abelian integral on the associated Riemann surface, is constructed explicitly as a rational expression in derivatives of the Kleinian σ-function of the curve.

We consider a variation of the Mahler measure where the defining integral is performed over a more general torus. We focus our investigation on two particular polynomials related to certain elliptic curve E and we establish new formulas for this variation of the Mahler measure in terms of L′(E, 0).

The cyclicity of period annuli of some classes of reversible and non-Hamiltonian quadratic systems under quadratic perturbations are studied. The argument principle method and the centroid curve method are combined to prove that the related Abelian integral has at most two zeros.

We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by Bspline functions only. An empirical investigation indicates...