27 research outputs found
On numerical aspects of pseudo-complex powers in R^3
In this paper we consider a particularly important case of 3D monogenic polynomials that are isomorphic to the integer powers of one complex variable (called pseudo-complex powers or
pseudo-complex polynomials, PCP). The construction of bases for spaces of monogenic polynomials in the framework of Clifford Analysis has been discussed by several authors and from different points of view. Here our main concern are numerical aspects of the implementation of PCP as bases of monogenic polynomials of homogeneous degree k. The representation of the well known Fueter polynomial basis by a particular PCP-basis is subject to a detailed analysis for showing the numerical effciency of the use of PCP. In this context a modiffcation
of the Eisinberg-Fedele algorithm for inverting a Vandermonde matrix is presented.This work was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, the Research Centre of Mathematics of the University of Minho and the Portuguese Foundation for Science and Technology ("FCT - Fundacao para a Ciencia e a Tecnologia"), within projects PEst-OE/MAT/UI4106/2014 and PEstOE/MAT/UI0013/2014
Bifurcation Boundary Conditions for Switching DC-DC Converters Under Constant On-Time Control
Sampled-data analysis and harmonic balance analysis are applied to analyze
switching DC-DC converters under constant on-time control. Design-oriented
boundary conditions for the period-doubling bifurcation and the saddle-node
bifurcation are derived. The required ramp slope to avoid the bifurcations and
the assigned pole locations associated with the ramp are also derived. The
derived boundary conditions are more general and accurate than those recently
obtained. Those recently obtained boundary conditions become special cases
under the general modeling approach presented in this paper. Different analyses
give different perspectives on the system dynamics and complement each other.
Under the sampled-data analysis, the boundary conditions are expressed in terms
of signal slopes and the ramp slope. Under the harmonic balance analysis, the
boundary conditions are expressed in terms of signal harmonics. The derived
boundary conditions are useful for a designer to design a converter to avoid
the occurrence of the period-doubling bifurcation and the saddle-node
bifurcation.Comment: Submitted to International Journal of Circuit Theory and Applications
on August 10, 2011; Manuscript ID: CTA-11-016
Equivalence between non-bilinear spin- Ising model and Wajnflasz model
We propose the mapping of polynomial of degree 2S constructed as a linear
combination of powers of spin- (for simplicity, we called as spin-
polynomial) onto spin-crossover state. The spin- polynomial in general can
be projected onto non-symmetric degenerated spin up (high-spin) and spin down
(low-spin) momenta. The total number of mapping for each general spin- is
given by . As an application of this mapping, we consider a
general non-bilinear spin- Ising model which can be transformed onto
spin-crossover described by Wajnflasz model. Using a further transformation we
obtain the partition function of the effective spin-1/2 Ising model, making a
suitable mapping the non-symmetric contribution leads us to a spin-1/2 Ising
model with a fixed external magnetic field, which in general cannot be solved
exactly. However, for a particular case of non-bilinear spin- Ising model
could become equivalent to an exactly solvable Ising model. The transformed
Ising model exhibits a residual entropy, then it should be understood also as a
frustrated spin model, due to competing parameters coupling of the non-bilinear
spin- Ising model
Discrete orthogonal polynomials on Gauss-Lobatto Chebyshev nodes
Abstract In this paper we present explicit formulas for discrete orthogonal polynomials over the so-called Gauss-Lobatto Chebyshev points. We also give the "three-term recurrence relation" to construct such polynomials. As a numerical application, we apply our formulas to the least-squares problem
On the inversion of Vandermonde matrix,
Abstract The inversion of the Vandermonde matrix has received much attention for its role in the solution of some problems of numerical analysis and control theory. This work deals with the problem of getting an explicit formula for the generic element of the inverse. We derive two algorithms in O(n 2 ) and O(n 3 ) and compare them with the Parker-Traub and the Björck-Pereyra algorithms