in this paper, solution of nonlinear optimal control problems and the controlled duffing oscillator, as a special class of optimal control problems, are considered and an efficient algorithm is proposed. this algorithm is based on state parametrization as a polynomial with unknown coefficients. by this method, the control and state variables can be approximated as a function of time. also, the ...

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

Background: Scoliosis is a health problem that causes a side-to-side curvature in the spine. The curvature may have an “S” or “C” shape. To evaluate scoliosis, the Cobb angle has been commonly used. However, digital image processing allows the Cobb angle to be obtained easily and quickly, several researchers have determined that Cobb angle contains high variations (errors) in the measurements. ...

We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.

Abstract In this research, a radial basis function artificial neural network (RBF-ANN) model was developed to predict the hot deformation flow curves of API X65 pipeline steel. The results of the developed model was compared with the results of a new phenomenological model that has recently been developed based on a power function of Zener-Hollomon parameter and a third order polynomial functio...

The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one...

a function is said to be bi-univalent on the open unit disk d if both the function and its inverse are univalent in d. not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. in this paper we use the faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...

We study multiplicities of jumping numbers multiplier ideals in a smooth variety arbitrary dimension. prove that the multiplicity function is quasi-polynomial, hence proving Poincar\'e series rational function. further when various components quasi-polynomial have highest possible degree and relate it to contributed by Rees valuations. Finally, we special case monomial ideals.

We construct bivariate polynomial approximations of the Lerch function, which for certain specialisations of the variables and parameters turn out to be HermitePadé approximants either of the polylogarithms or of Hurwitz zeta functions. In the former case, we recover known results, while in the latter the results are new and generalise some recent works of Beukers and Prévost. Finally, we make ...

The ‘dollar game’ represents a kind of diffusion process on a graph. Under the rules of the game some configurations are both stable and recurrent, and these are known as critical configurations. The set of critical configurations can be given the structure of an abelian group, and it turns out that the order of the group is the tree-number of the graph. Each critical configuration can be assig...