Discrete strip-concave functions considered in this paper are, in fact, equivalent to an extension of Gelfand-Tsetlin patterns to the case when the pattern has a not necessarily triangular but convex configuration. They arise by releasing one of the three types of rhombus inequalities for discrete concave functions (or “hives”) on a “convex part” of a triangular grid. The paper is devoted to a ...

In this note we shall introduce a simple, effective numerical method for solving partial differential equations for scalar and vector-valued data defined on surfaces. Even though we shall follow the traditional way to approximate the regular surfaces under consideration by triangular meshes, the key idea of our algorithm is to develop an intrinsic and unified way to compute directly the partial...

A technique for generating a triangular net from an implicit surface description is presented. This technique can be applied to 2-order differentiable functions describing the surface and is based on finding the principal curvatures at each generated point. It is therefore well adapted to the shape of the surface, taking more samples in the areas with high curvature. The triangular net is compe...

In a recent paper, I began with four classical results due to Jacobi, Dirichlet and Lorenz which give the number of representations of a number by various forms involving squares in terms of divisor functions. I deduced another sixteen similar representation theorems involving triangular numbers and/or squares, including celebrated results of Legendre and Ramanujan (and omitted a seventeenth, g...

We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such consists in specific scaling similarity transformation that reduces the departure from normality matrix, thus decreasing its norm and general function condition number. It easily be extended to non-triangular provided it is involving prior...

In this paper, a triangular spectral element method using orthogonal rational functions as basis is presented for problems on complex domains.

The fuzzy regression control chart is a functional technique to evaluate the process in which the average has a trend and the data represents a linguistic or approximate value. In this study, the theoretical structure of the “α-level fuzzy midrange for α-cut fuzzy X ~ -regression control chart” is proposed for triangular (TFN) and trapezoidal (TrFN) membership functions. In addition, the real w...