A conformal mapping in a plane domain locally maps circles to circles. More generally, quasiconformal mappings locally map circles to ellipses of bounded distortion. In this paper the authors study the corresponding s...
A conformal mapping in a plane domain locally maps circles to circles. More generally, quasiconformal mappings locally map circles to ellipses of bounded distortion. In this paper the authors study the corresponding situation for solutions to Stein-Weiss systems in the nD Euclidean space. We add a more precise meaning by pointing out that a generalized holomorphic function asymptotically maps the unit sphere onto explicitly characterized ellipsoids and vice versa. Ultimately, we illustrate our approach using a typical example.
Observability problem for non-autonomous systems is considered. We deduce high-order observability conditions using the techniques developed in [8] and [9] for stabilization problem, and show that the stabilizer const...
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It is well known that the presence of orthogonal decompositions for Hilbert spaces is particularly important to the study of certain boundary value problems of systems of partial differential equations. During the las...
It is well known that the presence of orthogonal decompositions for Hilbert spaces is particularly important to the study of certain boundary value problems of systems of partial differential equations. During the last years, many essential results have been obtained within the framework of real quaternion and Clifford algebras. However, according to our current knowledge central questions concerning the decompositions of the complex quaternion Hilbert space remain untouched so far. In this paper, we introduce a new orthogonal decomposition of the complex quaternion Hilbert space into its subspaces of null solutions of the corresponding Dirac operator invoking orthogonality with complex potential. The corresponding orthoprojections onto the subspaces of this decomposition are studied in detail. We then apply this decomposition to prove the existence and uniqueness, and a representation formula for the solution of related Dirichlet boundary value problems. We end up evaluating the Teodorescu transform from the estimation of its kernel function.
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that ar...
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ISBN:
(纸本)9781467320658
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed classical/fractional Euler-Lagrange extremals. Both Lagrangian and Hamiltonian versions of the Noether theorem are obtained. Finally, we extend our Noether's theorem to more general problems of optimal control with classical and Riemann-Liouville derivatives.
Let σ(x) be a nondecreasing function, such that σ(−∞) = 0,σ(∞) = 1 and let us denote by ℬ the class of functions which can be represented by a Fourier-Stieltjes integral f(t) = ∫ −∞∞eitxdσ(x) . In continuati...
Let σ(x) be a nondecreasing function, such that σ(−∞) = 0,σ(∞) = 1 and let us denote by ℬ the class of functions which can be represented by a Fourier-Stieltjes integral f(t) = ∫ −∞∞eitxdσ(x) . In continuation to [12], we prove a generalization of the classical theorem of Bochner on Fourier integral transforms to quaternion functions belonging to a subclass of ℬ. The underlying functions are continuous functions of bounded variation defined in ℝ2 and taking values on the quaternion algebra. Additionally, we introduce the definition of convolution of quaternion functions of bounded variation.
Complete orthogonal systems of monogenic polynomials over 3D prolate spheroids have been previously introduced and shown to have some important properties. In particular, the underlying functions take on values in the...
Complete orthogonal systems of monogenic polynomials over 3D prolate spheroids have been previously introduced and shown to have some important properties. In particular, the underlying functions take on values in the quaternion algebra (identified with R4 ), and are nullsolutions of the well known Moisil-Théodoresco system. In this paper we introduce a new complete orthogonal system of monogenic polynomials as solutions of this system for the space exterior to 3D prolate spheroids. Additionally, we show how monogenic polynomials for the interior and exterior of a spheroid look like once their values on the surface are prescribed. With the help of these polynomials an explicit expression of the monogenic Szegö kernel function over the surface of 3D spheroids is given.
In this paper a nonlinear positive control law is proposed for reference tracking in multi-input positive systems. This law proves to have a good performance in the control of the depth of anesthesia (DoA) by means of...
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In this paper a nonlinear positive control law is proposed for reference tracking in multi-input positive systems. This law proves to have a good performance in the control of the depth of anesthesia (DoA) by means of...
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In this paper a nonlinear positive control law is proposed for reference tracking in multi-input positive systems. This law proves to have a good performance in the control of the depth of anesthesia (DoA) by means of propofol and remifentanil , which is illustrated by several simulations.
We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green's theorem are proved. These ...
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ISBN:
(纸本)9781467320658
We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green's theorem are proved. These results allow us to obtain a fractional Euler-Lagrange necessary optimality condition for variable order two-dimensional fractional variational problems.
In the clinical practice the concerns about the administration of hypnotics and analgesics for minimally invasive diagnostics and therapeutic procedures have enormously increased in the past years. The automatic detec...
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In the clinical practice the concerns about the administration of hypnotics and analgesics for minimally invasive diagnostics and therapeutic procedures have enormously increased in the past years. The automatic detection of changes in the signals used to evaluate the depth of anesthesia is hence of foremost importance in order to decide how to adapt the doses of hypnotics and analgesics that should be administered to patients. The aim of this work is to online detect drifts in the referred depth of anesthesia signals of patients undergoing general anesthesia. The performance of the proposed method is illustrated using BIS records previously collected from patients subject to abdominal surgery. The results show that the drifts detected by the proposed method are in accordance with the actions of the clinicians in terms of times where a change in the hypnotic or analgesic rates had occurred. This detection was performed under the presence of noise and sensor faults. The presented algorithm was also online validated. The results encourage the inclusion of the proposed algorithm in a decision support system based on depth of anesthesia signals.
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