We revisit a problem solved in 1963 by Zaanen & Luxemburg in this monthly: what is the largest possible length of the graph of a monotonic function on an interval? And is there such a function that attains this length? This is an interesting and intriguing problem with a somewhat surprising answer, that should be of interest to a broad spectrum of mathematicians starting with upper level underg...

Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load dis...

In this paper we study k-noncrossing RNA structures with arc-length ≥ 3, i.e. RNA molecules in which for any i, the nucleotides labeled i and i + j (j = 1, 2) cannot form a bond and in which there are at most k − 1 mutually crossing arcs. Let S k,3 (n) denote their number. Based on a novel functional equation for the generating function P n≥0 S k,3 (n)z n , we derive for arbitrary k ≥ 3 exponen...

When fitting parametric polynomial curves to sequences of points or derivatives we have to choose suitable parameter values at the interpolation points. This paper investigates the effect of the parameterization on the approximation order of the interpolation. We show that chord length parameter values yield full approximation order when the polynomial degree is at most three. We obtain full ap...

Since the low energy absorption spectrum of a linear polyene is dominated by the strongly allowed 1 Ag→1 Bu transition ~S0 to S2!, it can be reconstructed for any chain length if the 0–0 band excitation energy, the band profile, and intensity are known. From this premise, this paper uses information developed in high resolution experiments on well-defined linear polyenes to extract the distribu...

Nonphotorealistic Rendering (NPR) deals with representing pictures and animation in, as the name suggests, a nonphotorealistic fashion. While there is only one way to render a photorealistic image, in an NPR system we have the freedom to represent it in an unlimited number of ways. By varying the style of rendering, the image composition and the level of detail, by omitting or emphasizing certa...

Techniques are presented for distributing grid points on parametric surfaces and in volumes according to a speci ed distribution of arc length. Interpolation techniques are introduced which permit a given distribution of grid points on the edges of a three-dimensional grid block to be propagated through the surface and volume grids. Examples demonstrate how these methods can be used to improve ...

A quantitative histological study was performed on small intestinal biopsies from eight ambulatory patients with HIV infection (AIDS/AIDS-related complex, ARC) and compared with those from 16 normal subjects. Enteropathy was assessed by measurement of villus area, crypt length and mitotic count, as well as duodenal counts of intraepithelial lymphocytes, mucosal mast cells and goblet cells. Ente...

Studies with artificially generated electrical arcs includes the variation of the length of the arc as an important information. In this paper, it is done a 3D reconstruction (by 3D-snake) followed by the measurement of the length of the arc in evolution based on stereo pairs of images. The accuracy of such measurement depends strongly on the halting of the iterative relaxation process that adj...

1 High Performance Computing Collaboratory, Center for Advanced Vehicular Systems, Graduate Program in Computational Engineering, Mississippi State University, Mississippi State, MS, U.S.A. [email protected] 2 Department of Mathematics and Statistics, Department of Computer Science and Engineering, Center for Computational Sciences, Graduate Program in Computational Engineering, Mississipp...