Exact controllability of infinite dimensional systems persists under small perturbations

This paper studies the concept of controllability for infinite-dimensional linear control systems in Banach spaces. First, we prove that the set of admissible control operators for the semigroup generator is unchanged if we perturb the generator by the Desch–Schappacher perturbations. Second we show that exact controllability is not changed by such perturbations.     

Kinetics and Mechanism of the Nucleophilic Substitution Reaction of Imidazole with Bis(2,4,6-trichlorophenyl) Oxalate and Bis(2,4-dinitrophenyl) Oxalate

The kinetics of the imidazole-catalyzed decomposition of bis(2,4,6-trichlorophenyl) oxalate (TCPO) and bis(2,4-dinitrophenyl) oxalate (DNPO) was investigated by the stopped-flow technique. Pseudo-first-order rate constants were determined as a function imidazole concentration in the temperature range 6-45 degrees C by fitting the temporal changes in absorbance throughout the 245 to 345 nm wavelength range for TCPO and at 420 nm for DNPO. The reaction proceeds by release of two molecules of substituted phenol and formation of 1,1'-oxalyldiimidazole (ODI) for both esters. The identity of ODI was confirmed in the reaction of imidazole with TCPO by its UV absorbance spectrum and (13)C-NMR spectrum. The reaction of imidazole with TCPO has a second-order dependence on imidazole concentration and an observed negative activation energy of -6.2 +/- 0.3 kJ/mol, whereas the DNPO reaction has a first-order dependence on imidazole concentration and an observed positive activation energy of 12.0 +/- 0.6 kJ/mol. The differences in the temperature dependence and order of the reaction with respect to imidazole for the two oxalate esters are explained by a shift in the rate-determining step from addition to the acyl group for DNPO to imidazole-catalyzed release of the phenol leaving group for TCPO. These kinetics results are useful in interpreting the initial reaction steps in peroxyoxalate chemiluminescence.     

On norm continuity,differentiability and compactness of perturbed semigroups

Semigroup Forum - The main purpose of this paper is to treat semigroup properties like norm continuity, compactness and differentiability for perturbed semigroups in Banach spaces. In particular,...     

Kinetics of two pathways in peroxyoxalate chemiluminescence

It has been shown that 1,1'-oxalyldiimidazole (ODI) is formed as an intermediate in the imidazole-catalyzed reaction of oxalate esters with hydrogen peroxide. Therefore, the kinetics of the chemiluminescence reaction of 1,1'-oxalyldiimidazole (ODI) with hydrogen peroxide in the presence of a fluorophore was investigated in order to further elucidate the mechanism of the peroxyoxalate chemiluminescence reaction. The effects of concentrations of ODI, hydrogen peroxide, imidazole (ImH), the general-base catalysts lutidine and collidine, and temperature on the chemiluminescence profile and relative quantum efficiency in the solvent acetonitrile were determined using the stopped-flow technique. Pseudo-first-order rate constant measurements were made for concentrations of either H2O2 or ODI in large excess. All of the reaction kinetics are consistent with a mechanism in which the reaction is initiated by a base-catalyzed substitution of hydrogen peroxide for imidazole in ODI to form an imidazoyl peracid (Im(CO)2OOH). In the presence of a large excess of H2O2, this intermediate rapidly decays with both a zero- and first-order dependence on the H2O2 concentration. It is proposed that the zero-order process reflects a cyclization of this intermediate to form a species capable of exciting a fluorophore via the "chemically initiated electron exchange mechanism" (CIEEL), while the first-order process results from the substitution of an additional molecule of hydrogen peroxide to the imidazoyl peracid to form dihydroperoxyoxalate, reducing the observed quantum yield. Under conditions of a large excess of ODI, the reaction is more than 1 order of magnitude more efficient at producing light, and the quantum yield increases linearly with increasing ODI concentration. Again, it is proposed that the slow initiating step of the reaction involves the substitution of H2O2 for imidazole to form the imidazoyl peracid. This intermediate may decay by either cyclization or by reaction with another ODI molecule to form a cyclic peroxide that is much more efficient at energy transfer with the fluorophore. The reaction kinetics clearly distinguishes two separate pathways for the chemiluminescent reaction.     

Singular functional differential equations of neutral type in Banach spaces

The well-posedness of a large class of singular partial differential equations of neutral type is discussed. Here the term singularity means that the difference operator of such equations is nonatomic at zero. This fact offers many difficulties in applying the usual methods of perturbation theory and Laplace transform technique and thus makes the study interesting. Our approach is new and it is based on functional analysis of semigroup of operators in an essential way, and allows us to introduce a new concept of solutions for such equations. Finally, we study the well-posedness of a singular reaction-diffusion equation of neutral type in weighted Lebesgue's spaces.     

Eventual norm continuity for neutral semigroups on Banach spaces

In this paper we prove, under suitable hypotheses, eventually norm continuity and compactness of the solution semigroups of certain neutral differential equations in Banach spaces. Our approach is based on a general perturbation theorem obtained from closed-loop systems of infinite dimensional control systems with unbounded control and observation operators. In fact, the solution semigroup can be viewed as the semigroup of an appropriate closed-loop system in product state spaces.     

Unbounded Perturbations of C0-Semigroups on Banach Spaces and Applications

In this paper we prove a perturbation result for strongly continuous semigroups extending one of G. Weiss from Hilbert to Banach spaces. This allows us to establish a new variation of constants formula for non-homogeneous perturbed Cauchy problems. From this formula we deduce another new one for non-homogeneous functional differential equations with L^p-phase spaces in terms of Yosida extensions of delay operators.     

Regular linear systems governed by systems with state, input and output delays

^** Email: hadd{at}ucam.ac.ma^*** Email: idrissi{at}ucam.ac.ma In this paper, we give a new reformulation of linear systemswith delays in input, state and output. We show that these systemscan be written as a regular linear system without delays. Thetechnique used here is essentially based on the theory recentlydeveloped by Salamon and Weiss and the shift in semigroup properties.Our framework can be applied, in particular, when the delayoperators are given by Riemann–Stieltjes integrals.     

Regular linear systems governed by neutral FDEs

The aim of this paper is to prove that a class of distributed parameter systems governed by neutral FDEs provides regular linear systems. Employing the well established theory of representation, transfer function and feedback of these later we then give new representations of the state and the output function of the neutral systems.