This article introduces two new fractional operators with sine ($\sin$) and cosine ($\cos$) kernels, motivated by their fundamental role in modeling AC signals in electrical circuits. The operators are designed to improve the analysis of nonlinear components such as the memristor by transforming certain nonlinear equations into simpler linear forms, particularly in systems with memory effects.
The $ν$-metric used in robust control is computed for control systems with parametric uncertainty, governed by a diffusion equation in a bounded one-dimensional spatial region with boundary control and point observation.
I prove Richard Soland's conjecture that for an efficient solution to a multicriteria optimization problem, there need not exist a continuous, strictly increasing and strictly concave criterion space function that attains its maximum at the vector of criteria values achieved by that solution. I work out an important implication of this result for multicriteria decision making.
Lecture Notes based on the course given at Toulouse School of Economics, on Fall 2024. It contains a quick introduction to the field of bilevel optimization, following a perspective from Variational Analysis.
This work studies a class of singular Volterra integral equations that are (controlled) and can be applied to memory-related problems.For optimum controls, we prove a second-order Pontryagin type maximal principle.
In this paper, we present new applications of our general minimax theorems. In particular, one of them concerns the multiplicity of global minima for the integral functional of the Calculus of Variations.
The multidimensional ($n$-D) systems described by Roesser model are presented in this paper. These $n$-D systems consist of discrete systems and continuous fractional order systems with fractional order $ν$, $0<ν<1$. The stability and Robust stability of such $n$-D systems are investigated.
A variational model for reconstruction of damaged color images is studied, in particular in the case where only finitely many colors are admissible for the reconstructed image. An existence result and regularity properties of minimizers are presented.
The purpose of this paper is to prove the existence of solutions of quasi-equilibrium problems without any generalized monotonicity assumption. Additionally, we give an application to quasi-optimization problems.
Resistive electrical networks constitute a beautiful example of open, interconnected, large-scale systems, giving rise to an elegant classical mathematical theory, still posing open problems and suggesting important extensions.
A class of state models, called Kronecker-Weierstrass models (or, simply, KW-models), is introduced, and the state representation problem for linear differential systems is studied in the context of these models. It is shown, in particular, that there is a canonical one-to-one correspondence between linear differential systems and similarity classes of minimal proper KW-models.
It is known that for convex sets, the KKM condition is equivalent to the finite intersection property. We use this equivalence to obtain a characterisation of monotone operators in terms of convex KKM maps and in terms of the existence of solutions to Minty variational inequalities. The latter result provides a converse to the seminal theorem of Minty.
We introduce a notion of variable quasi-Bregman monotone sequence which unifies the notion of variable metric quasi-Fejér monotone sequences and that of Bregman monotone sequences. The results are applied to analyze the asymptotic behavior of proximal iterations based on variable Bregman distance and of algorithms for solving convex feasibility problems in reflexive real Banach spaces.
Kuhn-Tucker conditions for mathematical programming problems in Banach spaces partially ordered by cone with empty interior are obtained under strong simultaneity condition. If partial ordered cone has interior point, it is proved that Slater and strong simultaneity conditions are equivalent.
Here, necessary optimal condition for Optimistic Bilevel programming problem is obtained in Asplund spaces. Also we have got necessary optimal conditions in finite dimensional spaces, by assuming differentiability on the given functions.
We investigate a limit value of an optimal control problem when the horizon converges to infinity. For this aim, we suppose suitable nonexpansive-like assumptions which does not imply that the limit is independent of the initial state as it is usually done in the literature.
We provide an example proving that there exists no quadratic Lyapunov function for a certain class of linear agreement/consensus algorithms, a fact that had been numerically verified in [5]. We also briefly discuss sufficient conditions for the existence of such a Lyapunov function.
Broer de Groot, Hilary A. Jenkins, Stephen J. Loeb
et al.
Ruthenium(II) complexes of the thiacyclophane ligands 2,5,8-trithia[9]-o-cyclophane (TT[9]OC) and 5-oxa-2,8-dithia[9]-o-cyclophane (ODT[9]OC) were synthesized by ligand displacement reactions employing RuCl2(DMSO)4, RuCl2(PPh3)3, and RuHCl(PPh3)3 as starting materials. X-ray crystal structures of two of these complexes, RuCl2(DMSO)(TT[9]OC) and RuCl2(PPh3)(ODT[9]OC), demonstrate how TT[9]OC and ODT[9]OC bind to Ru(II). RuCl2(DMSO)(TT[9]OC) crystallized as the DMSO solvate in the orthorhombic space group Pbca with a = 19.590(5), b = 16.849(4), c = 13.149(4) Å, V = 4340(3) Å3, and Z = 8. The structure refined to R = 5.27% and Rw = 6.27% for 2472 reflections with Fo2 > 3σ(Fo2). RuCl2(PPh3)(ODT[9]OC) crystallized as a ClCH2CH2Cl solvate in the monoclinic space group P21/c with a = 7.912(1), b = 22.419(5), c = 18.794(3) Å, β = 101.12(1),° V = 3271.2(9) Å3, and Z = 4. The structure refined to R = 4.96% and Rw = 5.14% for 1800 reflections with Fo2 > 3σ(Fo2). Both compounds are octahedral with the thiacyclophane ligand bound through three donor atoms in a facial coordination mode, cis chlorine atoms, and the unique ancillary ligand, DMSO or PPh3, bound trans to the central S or O donor of the macrocycle. The X-ray structures support 1H NMR spectral evidence which shows that the ligands are bound in an "endo" mode for L = DMSO and in an "exo" mode when L = PPh3. The reaction of RuHCl(PPh3)3 with TT[9]OC yields the ruthenium hydride complex RuHCl(PPh3)2(TT[9]OC). 1H and 31P NMR spectroscopy are consistent with an octahedral species for which the macrocycle occupies only two coordination sites acting as a bidentate η2-chelating ligand. Keywords: thioether, macrocycle, hydride, crystal structure.