Boundary controllability of integrodifferential systems in Banach spaces

Sufficient conditions for boundary controllability of integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle. Examples are provided to illustrate the theory.     

Existence of solutions of neutral functional integrodifferential equation in Banach spaces

In this paper we prove the existence of mild solutions for neutral functional integrodifferential equation in a Banach space. The results are obtained by using the Schaefer fixed-point theorem.     

Theory of laser action in scattering gain media

A laser model based on feedback produced by scattering has been developed to explain the narrow linewidth emission and input-output behavior observed in scattering gain media. The model is based on the transient two-level laser equations and includes the detailed spectral properties of the dye gain system. Monte Carlo methods were employed to calculate the threshold gain required for modeling the input-output and linewidth emission characteristics.     

Controllability of nonlinear systems to affine manifolds

Controllability to an affine manifold involves controlling a system to a target defined by the generalized boundary condition x=r, where :C ⁿ R ⁿ is a bounded linear operator on the continuous functions, as defined for ordinary differential equations by Kartsatos. In this paper, sufficient conditions are obtained for such controllability for linear systems and for a class of nonlinear perturbations of linear systems.     

Synthesis,characterization and charge-transfer photochemistry of trans-aquo azido-N,N′-trimethylenebis(naphthylideneiminato)chromium(III)

A new Cr^III complex, viz. trans-[Cr(naphprn)(H₂O)₂]ClO₄·2H₂O, (1) {naphprn=N,N-trimethylenebis(naphthylideneimine)} has been synthesized and characterized. Aquo ligand substitution of ( 1 ) by the azide ligand gave rise to trans-[Cr(naphprn)(N₃)(H₂O)], ( 2 ). Irradiation of ( 2) in DMF gave nitrido(naphprn)chromium(V) ( 3 ). Solutions of ( 3 ) showed e.p.r. spectra at room temperature (g _iso=1.9865). The i.r. spectra showed disappearance of a band at 2067cm^–1 showing the breakdown of NN and appearance of a new band at 1074cm^–1which is assigned to the Cr¹⁴N, stretching frequency indicating the formation of a nitrido chromium(V) complex, ( 3). The u.v.–vis. spectrum of complex ( 3 ) exhibited a d–d band maximum at 553nm (=120M^–1cm^–1). The rate of formation of ( 2 ) was found to be 5.0×10^–3M^–1s^–1 in an aqueous acidic medium at [Cr^III]=0.5×10^–3M; [N₃ ^–]=0.01–0.15M; [H⁺]=0.001M and I=0.2M (LiClO₄). The rate of photo-decomposition of ( 2 ) to give rise to ( 3 ) was found to be 0.15×10^–3s^–1 in DMF.     

Discodermolide/Dictyostatin hybrids: synthesis and biological evaluation

[structure: see text] Two hybrid analogues of discodermolide and dictyostatin (3, 26) have been designed and synthesized. These are the first macrocyclic analogues of discodermolide and biological activities were evaluated and compared with linear discodermolide analogues.     

Mass spectra of partially n-acetylated derivatives of kanamycin a

As part of a program concerned with the chemistry and biochemistry of aminocyclitol antibiotics, a number of selectively N-acetylated kanamycins have been prepared from kanamycin monosulfate and characterized by a study of the electron impact induced fragmentation of two types of derivatives. In one of these, the remaining free amino groups were N-trideuteroacetylated and the N-acylated kanamycins thus obtained, were N.O-methylated. The spectra of these derivatives were useful for the location of the N-acetyl and N-trideu-teroacetyl groups, except in the 2-deoxystreptamine unit. In a second type of derivative, the partially N-acetylated kanamycins were N.O-permethylated converting the free amino groups into dimethylamino groups. In this form, it was possible to locate the site of N-aeelylation on the 2-deoxystreptamine ring. The partially N-acetylated kanamycins have been identified as 1,3,6'-tri-N-acetyl, 3,6',3'-tri-N-acetyl, 3,6'-di-N-acetyl, 1,6'-di-N-acetyl and 6'-N-acetyl kanamycin, from a study of the mass spectra of these two types of derivatives.     

Relation between nonlinear models and gauge ambiguities

We show that the solutions of a class of nonlinear models also generate gauge ambiguities in the vacuum sector of Yang-Mills theories. Our results extend known connections between gauge ambiguities and certain nonlinear -models, and clarify the underlying group theory. For many nonlinear models, we also give a simple, intrinsic parametrization of physical fields (which have values in a homogeneous space of a group).Supported in part by the U.S. Department of Energy.Supported by Fonds zur Förderung der Wissenschaftlichen Forschung in Österreich