Two approaches for determining Hilbert functions of fat point subschemes of P2 are demonstrated. A complete determination of the Hilbert functions which occur for 9 double points is given using the first approach, extending results obtained in a previous paper using the second approach. In addition the second approach is used to obtain a complete determination of the Hilbert functions for n ≥ 9...

Consider the single-facility Euclidean j-centrum location problem in R. This problem is a generalization of the classical Euclidean 1-median problem and 1-center problem. In this paper, we develop two efficient algorithms that are particularly suitable for problems where n is large by using unconstrained optimization techniques. The first algorithm is based on the neural networks smooth approxi...

Kontsevich constructed universal characteristic classes of smooth bundles with fiber a framed odd-dimensional homology sphere, which is known in the 3-dimensional case that they are universal among finite type invariants. The purpose of the present paper is twofold. First, we obtain a bordism invariant of smooth unframed bundles with fiber a 5dimensional homology sphere as a sum of the simplest...

Regulation of membrane ion channels by second messengers is an important mechanism by which gastrointestinal smooth muscle excitability is controlled. Receptor-mediated phosphorylation of Ca(2+) channels has been known for some time; however, recent findings indicate that these channels may also modulate intracellular signaling. The plasmalemma ion channels may also function as a point of conve...

We present a numerical method for computing the signed distance to a piecewise-smooth surface defined as the zero set of a function. It is based on a marching method by Kim [Kim01] and a hybrid discretization of firstand second-order discretizations of the signed distance function equation. If the solution is smooth at a point and at all of the points in the domain of dependence of that point, ...

We study the Rayleigh-Stokes problem for a generalized second-grade fluid which involves a Riemann-Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations. We establish the Sobolev regularity of the homogeneous problem for both smooth and nonsmooth initial data [Formula: see text], including [Formula: ...

Considering the second boundary value problem of Lagrangian mean curvature equation, we obtain existence and uniqueness smooth uniformly convex solution, which generalizes Brendle–Warren’s theorem about minimal diffeomorphism in Euclidean metric space.

This paper focuses on a hydraulic radius separation approach used to calculate the boundary shear stress in terms of bed and wall shear stress proposed in a trapezoidal channel. The average bed and sidewall shear stress in smooth trapezoidal open channels are derived after using Guo & Julien (2005) early equations taking a part of an investigation to cover both rectangular and trapezoidal chann...