Articles (Departament de Tecnologies de la Informació i les Comunicacions)
http://hdl.handle.net/10230/5923
Thu, 30 May 2024 09:09:16 GMT2024-05-30T09:09:16ZChildren’s first handwriting productions show a rhythmic structure
http://hdl.handle.net/10230/60263
Children’s first handwriting productions show a rhythmic structure
Pagliarini, Elena; Scocchia, Lisa; Vernice, Mirta; Zoppello, Marina; Balottin, Umberto; Bouamama, Sana; Guasti, Maria Teresa; Stucchi, Natale
Although much research has been concerned with the development of kinematic aspects of handwriting, little is known about the development along with age of two principles that govern its rhythmic organization: Homothety and Isochrony. Homothety states that the ratio between the durations of the single motor events composing a motor act remains invariant and independent from the total duration of the movement. Isochrony refers to the proportional relationship between the speed of movement execution and the length of its trajectory. The current study shows that children comply with both principles since their first grade of primary school. The precocious adherence to these principles suggests that an internal representation of the rhythm of handwriting is available before the age in which handwriting is performed automatically. Overall, these findings suggest that despite being a cultural acquisition, handwriting appears to be shaped by more general constraints on the timing planning of the movements.
Includes supplementary materials for the online appendix.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10230/602632017-01-01T00:00:00ZFractional Newton-Raphson method
http://hdl.handle.net/10230/59958
Fractional Newton-Raphson method
Torres Hernandez, Anthony; Brambila Paz, Fernando
The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real
initial condition is taken. In the present work, we explain an iterative method that is created using the fractional
calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the
space of complex numbers given a real initial condition, which allows us to find both the real and complex roots
of a polynomial unlike the classical Newton-Raphson method.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10230/599582021-01-01T00:00:00ZAn approximation to zeros of the riemann zeta function using fractional calculus
http://hdl.handle.net/10230/59957
An approximation to zeros of the riemann zeta function using fractional calculus
Torres Hernandez, Anthony
In this paper an approximation to the zeros of the Riemann zeta function has been obtained for the first time using a fractional iterative method which originates from a unique feature of the fractional calculus. This iterative method, valid for one and several variables, uses the property that the fractional derivative of constants are not always zero. This allows us to construct a fractional iterative method to find the zeros of functions in which it is possible to avoid expressions that involve hypergeometric functions, Mittag-Leffler functions or infinite series. Furthermore, we can find multiple zeros of a function using a singe initial condition. This partially solves the intrinsic problem of iterative methods, which in general is necessary to provide N initial conditions to find N solutions. Consequently the method is suitable for approximating nontrivial zeros of the Riemann zeta function when the absolute value of its imaginary part tends to infinity. Some examples of its implementation are presented, and finally 53 different values near to the zeros of the Riemann zeta function are shown.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10230/599572021-01-01T00:00:00ZCode of amultidimensional fractional quasi-newton method with an order of convergence at least quadratic using recursive programming
http://hdl.handle.net/10230/59956
Code of amultidimensional fractional quasi-newton method with an order of convergence at least quadratic using recursive programming
Torres Hernandez, Anthony
The following paper presents a way to define and classify a family of fractional iterative methods through a
group of fractional matrix operators, as well as a code written in recursive programming to implement a variant of
the fractional quasi-Newton method, which through minor modifications, can be implemented in any fractional
fixed-point method that allows solving nonlinear algebraic equation systems.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10230/599562022-01-01T00:00:00Z