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.
We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility c...
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We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.
This paper is devoted to the study of variational problems with Hadamard type fractional integrals. We present two approaches to solve such type of variational problems: indirect and direct. In the first case we deriv...
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In this paper we define the property of feasible reachability both for 1D state-space systems evolving over Z and for 2D state-space systems evolving over Z 2 described by Fornasini-Marchesini models. Feasible reachab...
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In this paper we define the property of feasible reachability both for 1D state-space systems evolving over Z and for 2D state-space systems evolving over Z 2 described by Fornasini-Marchesini models. Feasible reachability consists in the reachability of the feasible subspaces associated with those systems. After characterizing these properties in terms of the system matrices, we compare them with behavioral controllability.
In this paper we study the problem of estimation for multidimensional systems within the context of the behavioral approach. We consider the case where there are no disturbances as well as the case where the system dy...
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In this paper we study the problem of estimation for multidimensional systems within the context of the behavioral approach. We consider the case where there are no disturbances as well as the case where the system dynamics is perturbed, and provide necessary conditions for the solvability of the corresponding estimation problems together with the construction of a solution, if it exists. Such solution is an estimator that is asymptotic, in the sense that the error trajectories are stable with respect to a pre-specified nD stability cone.
The stabilization of periodic control systems using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theor...
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A (κ, τ)-regular set is a vertex subset S inducing a κ-regular subgraph such that every vertex out of S has τ neighbors in S. This article is an expository overview of the main results obtained for graphs with (...
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A graph with convex quadratic stability number is a graph for which the stability number is determined by solving a convex quadratic program. Since the very beginning, where a convex quadratic programming upper bound ...
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The calculus of variations is a field of mathematical analysis born in 1687 with Newton’s problem of minimal resistance, which is concerned with the maxima or minima of integral functionals. Finding the solution of s...
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We analyse different kinds of stabilities for the Bessel equation and for the modified Bessel equation with initial conditions. Sufficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, σ-semi-Hyer...
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