The fact that generalized Appell sequences of monogenic polynomials in the setting of hypercomplex function theory also satisfy a corresponding binomial type theorem allows to obtain their explicit structure. Recently...
The fact that generalized Appell sequences of monogenic polynomials in the setting of hypercomplex function theory also satisfy a corresponding binomial type theorem allows to obtain their explicit structure. Recently it has been obtained a complete characterization in the case of paravector valued homogeneous polynomials of three real variables. The aim of this contribution is the study of paravector valued homogeneous polynomials of four real variables, where new types of generalized Appell sequences could be detected.
In this paper we investigate a novel model of concatenation of a pair of two-dimensional (2D) convolutional codes. We consider finite-support 2D convolutional codes and choose the so-called Fornasini-Marchesini input-...
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In this paper we use some classical ideas from linear systems theory to analyse convolutional codes. In particular, we exploit input-state-output representations of periodic linear systems to study periodically time-v...
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作者：
Figueiredo, DanielDepartment of Mathematics
CIDMA - Center for Research and Development in Mathematics and Applications University of Aveiro Campus Universitário de Santiago Aveiro3810-193 Portugal
When studying a biological regulatory network, it is usual to use boolean network models. In these models, boolean variables represent the behavior of each component of the biological system. Taking in account that th...
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It is evident, that the properties of monogenic polynomials in (n + 1)-real variables significantly depend on the generators e1,e2,...,en of the underlying 2n-dimensional Clifford algebra Cℓ0,n over R and their intera...
It is evident, that the properties of monogenic polynomials in (n + 1)-real variables significantly depend on the generators e1,e2,...,en of the underlying 2n-dimensional Clifford algebra Cℓ0,n over R and their interactions under multiplication. The case of n = 3 is studied through the consideration of Pascal's tetrahedron with hypercomplex entries as special case of the general Pascal simplex for arbitrary n, which represents a useful geometric arrangement of all possible products. The different layers ℒk of Pascal's tetrahedron (or pyramid) are built by ordered symmetric products contained in the trinomial expansion of (e1+e2+e3)k,k = 0,1,... .
In continuation of [4], this paper discusses the quaternionic Zernike spherical polynomials (QZSPs), which refine and extend the Zernike polynomials or radial polynomials introduced in the early thirties by F. Zernike...
In continuation of [4], this paper discusses the quaternionic Zernike spherical polynomials (QZSPs), which refine and extend the Zernike polynomials or radial polynomials introduced in the early thirties by F. Zernike's Nobel prize. In particular, the underlying polynomials are of three real variables and take on values in the quaternions (identified with R4 ). QZSPs are complete and orthonormal in the unit ball. The representation of these functions are explicitly given, and a summary of their fundamental properties is also discussed. To the best of our knowledge, this does not appear to have been done in literature before.
This paper presents a model based switching control strategy to drive the neuromuscular blockade (NMB) level of patients undergoing general anesthesia to a predefined reference. A single-input single-output Wiener sys...
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In this paper, two-dimensional convolutional codes constituted by sequences in Fn) Z2 where F is a finite field, are considered. In particular, we restrict to codes with rate 1/n and we investigate the problem of mini...
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The recent introduction of generalized Appell sequences in the framework of Clifford Analysis solved an open question about a suitable construction of power-like monogenic polynomials as generalizations of the integer...
The recent introduction of generalized Appell sequences in the framework of Clifford Analysis solved an open question about a suitable construction of power-like monogenic polynomials as generalizations of the integer powers of a complex variable. The deep connection between Appell sequences and Pascal's triangle called also attention to other number triangles and, at the same time, to the construction of generalized Pascal matrices. Both aspects are considered in this communication.
In continuation of [3], this paper discusses the prolate spheroidal quaternionic wave signals (PSQWSs), which refine and extend the prolate spheroidal wave functions introduced in the early sixties by D. Slepian and H...
In continuation of [3], this paper discusses the prolate spheroidal quaternionic wave signals (PSQWSs), which refine and extend the prolate spheroidal wave functions introduced in the early sixties by D. Slepian and H.O. Pollak. The PSQWSs are ideally suited to study certain questions regarding the relationship between quaternionic functions and their Fourier transforms. The PSQWSs are orthogonal and complete over two different intervals: the space of square integrable functions over a finite interval and the three-dimensional Paley-Wiener space of bandlimited functions. No other system of classical generalized orthogonal functions is known to possess this unique property. We address all the above and explore some basic facts of the arising quaternionic function theory.
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