THOMAS, C. E., and PARKESOL, B. R. 1991. Simple, flexible, trigonometric taper equations. Can. J. For. Res. 21: 1132-1137. There have been numerous approaches to modeling stem form in recent decades. The majority have concentrated on the simpler coniferous bole form and have become increasingly complex mathematical expressions. Use of trigonometric equations provides a s imple expression of tap...

We prove the right Lax-type inequality on subarcs of the unit circle of the complex plane for complex algebraic polynomials of degree n having no zeros in the open unit disk. This is done by establishing the right Bernstein-Szegő-Videnskii type inequality for real trigonometric polynomials of degree at most n on intervals shorter than the period. The paper is closely related to recent work by B...

The trigonometric network, introduced in this paper, is a multilayer feedforward neural network with sinusoidal activation functions. Unlike the N-dimensional Fourier series, the basis functions of the proposed trigonometric network have no strict harmonic relationship. An effective training algorithm for the network is developed. It is shown that the trigonometric network performs better than ...

In this paper we introduce the notion of hybrid trigonometric parametrization as a tuple of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials, with the restriction that variables in each block of functions are different. We analyze the main properties of the varieties defined by these parametrizations and we prove that they are exactly the ...

Trigonometric functions are often needed in embedded real-time software. To fulfill concrete resource demands, different implementation strategies of trigonometric functions are possible. In this paper we analyze the resource demands of iterative calculations compared to other implementation strategies, using the trigonometric functions as a case study. By analyzing the worst-case execution tim...

Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known; however, sums with products of trigonometric functions can become complicated, and may not have a simple expression in a number of cases. Some of these sums have interest...

This paper describes a simple and efficient non-stationary subdivision scheme of order 4. This curve scheme unifies known subdivision rules for cubic B-splines, splines-in-tension and a certain class of trigonometric splines capable of reproducing circles. The curves generated by this unified subdivision scheme are C2 splines whose segments are either polynomial, hyperbolic or trigonometric fun...

For a given function u(x) on an interval [a,b] we want to find an approximation p(x) where • either p is a polynomial: p ∈Pn = span{1,x, . . . ,xn} • or p is a trigonometric polynomial: p ∈Tn = span{1,cosx,sinx, . . . ,cos(nx),sin(nx)} We can measure the error in two ways: • (weighted) mean square error ‖u− p‖L2 w 2 = ́ b a (u(x)− p(x)) 2 w(x)dx with a weight function w(x) (e.g., w(x) = 1) • max...

Keyword: Generalized Gregory’s series Trigonometric identities Odd harmonic numbers In this paper the countable family of generalized Gregory’s series (all of which are the power series having the radius of convergence equal to one) is defined. Sums SnðxÞ; n 1⁄4 1;2; . . . of these series are found – first in the definite integral form and next in the form of finite linear combination of arcus ...

Turetzkii [Uchenye Zapiski, Vypusk 1 (149) (1959), 31–55, (English translation in East J. Approx. 11 (2005) 337–359)] considered quadrature rules of interpolatory type with simple nodes, with maximal trigonometric degree of exactness. For that purpose Turetzkii made use of orthogonal trigonometric polynomials of semi–integer degree. Ghizzeti and Ossicini [Quadrature Formulae, Academie-Verlag, B...