In this work, a novel method for determining the principal directions (maxima) of the diffusion orientation distribution function (ODF) is proposed. We represent the ODF as a symmetric high-order Cartesian tensor restricted to the unit sphere and show that the extrema of the ODF are solutions to a system of polynomial equations whose coefficients are polynomial functions of the tensor elements....

In this paper we derive new fractional error bounds for polynomial systems with exponents explicitly determined by the dimension of the underlying space and the number/degree of the involved polynomials. Our major result extends the existing error bounds from the system involving only a single polynomial to a general polynomial system and do not require any regularity assumptions. In this way w...

In quasi-static tests, flexible polyurethane foam undergoing large compressive loading and unloading deformation exhibits highly nonlinear and viscoelastic behavior. In particular, the response in the first cycle is significantly different from the response in subsequent cycles. In addition, the stresses in the loading paths are higher than those in unloading paths. It is assumed that this quas...

When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given interval) a function has coefficients that are not exactly representable with a finite number of bits. And yet, the polynomial approximations that are actua...

The Newton-Raphson (N-R) method is useful to find the roots of a polynomial degree n. However, this limited since it diverges for case in which polynomials only have complex if real initial condition taken. In present work, we explain an iterative that created using fractional calculus, will call Fractional (F N-R) Method, has ability enter space numbers given condition, allows us both and unli...

In this paper we propose a Fully Polynomial Time Approximation Scheme (FPTAS) for a class of optimization problems where the feasible region is a polyhedral one and the objective function is the sum or product of linear ratio functions. The class includes the well known ones of Linear (Sum-of-Ratios) Fractional Programming and Multiplicative Programming.

An attempt is made to develop approximate method get solution of system linear Fredholm fractional integro-differential equations using Least squares and Lauguerre polynomial method. The reduced a polynomials. implemented obtain the equations. solutions are simulated Scilab.

In a recent study, we investigate the Burgers–Fisher equation through developed scheme, namely, non-polynomial spline fractional continuity method. The proposed models represent nonlinear optics, chemical physics, gas dynamics, and heat conduction. basic concept of new approach is constructing with instead natural derivative. Furthermore, truncation error analyzed to determine order convergence...

Fractional calculus is a natural extension of the integer order calculus and recently, a large number of applied problems have been formulated on fractional di¤erential equations. Analytical solution of many applications, where the fractional di¤erential equations appear, cannot be established. Therefore, cubic polynomial spline function is considered to …nd approximate solution for fractional ...

We use the recently established higher-level Bailey lemma and Bose–Fermi polynomial identities for the minimal models M(p, p) to demonstrate the existence of a Bailey flow from M(p, p) to the coset models (A (1) 1 )N ×(A (1) 1 )N ′/(A (1) 1 )N+N ′ where N is a positive integer and N ′ is fractional, and to obtain Bose–Fermi identities for these models. The fermionic side of these identities is ...