Asymptotic distribution of the eigenvalues of the bending-torsion vibration model with fully nondissipative boundary feedback

Asymptotic and spectral results on the initial boundary-value problem for the coupled bending-torsion vibration model (which is important in such areas of engineering sciences as bridge and tall building designs, aerospace and oil pipes modeling, etc.) are presented. The model is given by a system of two hyperbolic partial differential equations equipped with a three-parameter family of non-self-adjoint (linear feedback type) boundary conditions modeling the actions of self-straining actuators. The system is rewritten in the form of the first-order evolution equation in a Hilbert space of a four-component Cauchy data. It is shown that the dynamics generator is a matrix differential operator with compact resolvent, whose discrete spectrum splits asymptotically into two disjoint subsets called the α-branch and the β-branch, respectively. Precise spectral asymptotics for the eigenvalues from each branch as the number of an eigenvalue tends to ∞ have been derived. It is also shown that the leading asymptotical term of the α-branch eigenvalue depends only on the torsion control parameter, while of the β-branch eigenvalue depends on two bending control parameters.     

Methods of Fourier optics in digital holographic microscopy

In this paper, processing methods of Fourier optics implemented in a digital holographic microscopy system are presented. The proposed methodology is based on the possibility of the digital holography in carrying out the whole reconstruction of the recorded wave front and consequently, the determination of the phase and intensity distribution in any arbitrary plane located between the object and the recording plane. In this way, in digital holographic microscopy the field produced by the objective lens can be reconstructed along its propagation, allowing the reconstruction of the back focal plane of the lens, so that the complex amplitudes of the Fraunhofer diffraction, or equivalently the Fourier transform, of the light distribution across the object can be known. The manipulation of Fourier transform plane makes possible the design of digital methods of optical processing and image analysis. The proposed method has a great practical utility and represents a powerful tool in image analysis and data processing. The theoretical aspects of the method are presented, and its validity has been demonstrated using computer generated holograms and images simulations of microscopic objects.     

Commutative ideal theory without finiteness conditions: Primal ideals

Our goal is to establish an efficient decomposition of an ideal of a commutative ring as an intersection of primal ideals. We prove the existence of a canonical primal decomposition: , where the are isolated components of that are primal ideals having distinct and incomparable adjoint primes . For this purpose we define the set of associated primes of the ideal to be those defined and studied by Krull. We determine conditions for the canonical primal decomposition to be irredundant, or residually maximal, or the unique representation of as an irredundant intersection of isolated components of . Using our canonical primal decomposition, we obtain an affirmative answer to a question raised by Fuchs, and also prove for that an ideal is an intersection of -primal ideals if and only if the elements of are prime to . We prove that the following conditions are equivalent: (i) the ring is arithmetical, (ii) every primal ideal of is irreducible, (iii) each proper ideal of is an intersection of its irreducible isolated components. We classify the rings for which the canonical primal decomposition of each proper ideal is an irredundant decomposition of irreducible ideals as precisely the arithmetical rings with Noetherian maximal spectrum. In particular, the integral domains having these equivalent properties are the Prüfer domains possessing a certain property.

     

On a duality of modules over valuation rings

Sunto. Rispondendo ad una questione posta da A. Orsatti in[8], si dà esempio di dualità, non soddisfacente alle proprietà di estensione di caratteri, sopra un anello di valutazione discreto completo e si ottiene una caratterizzazione dei domini noetheriani per cui una tale dualità esiste.

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Entrata in Redazione il 17 maggio 1977.

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This paper has been written while the author was visiting professor in Dept. of Mathematics of Università di Padova.     

On a class of butler groups

A complete classification, both up to quasi isomorphism and up to isomorphism, is given of the strongly indecomposable torsionfree abelian groups that occur as quotients of a finite rank completely decomposable torsionfree group modulo a rank 1 subgroup. This research was done while the second author held a visiting professorship at Tulane University.     

A propos de l'espace des modules de fibrés de rang 2 sur une courbe

Sans résumé

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Partiellement financé par le contrat Science Geometry of Algebraic Varieties, contrat n^o SCI-0398-C     

Coordinating Abilities Towards Sodium of Oxygenated Solvents

Tetracoordination of the sodium cation is indicated by the ²³Na-NMR. chemical shifts for NaClO₄ in binary mixtures of ether and alcohol solvents. Solvent exchange occurs by a sequential process, and involves one or several intermediates. In competition with tetrahydrofurfuryl alcohol, whereas glyme corresponds to monocyclic intermediates, diglyme and triglyme

1 For abbreviations see Table 1.

favor formation of bicyclic intermediates. The relevant conformational factors are analysed, and also serve to explain the better coordinating abilities of diglyme and triglyme, as compared to glyme. The mechanism for solvent exchange is discussed.     

Investigation of benzene-hexafluorobenzene dynamics in liquid binary mixtures

The structure and microscopic dynamics of liquid mixtures of benzene and hexafluorobenzene at room temperature and several compositions have been studied by molecular-dynamics simulations. In this implementation we have rescaled the intermolecular H-F cross potential parameters obtained from the Lorentz-Berthelot combining rules, in order to avoid the substantial overestimation of the energy of mixing predicted by the model when the usual rules are employed. We found that a reduction in the strength of cross H-F interactions by 50% relative to the geometric mean is required in order to get a good agreement with experiments. Radial-angular pair-correlation functions between like and unlike species have been computed and analyzed, by comparing them with the correlations in the corresponding neat liquids. We have also studied the microscopic intermolecular momentum transfer, by computing the time correlation function between the initial velocity of a central molecule and later velocities of neighboring molecules. Structural and dynamical information extracted from the mentioned functions seem to be consistent with the picture of relatively long-lived benzene-hexafluorobenzene (Bz-Hf) complexes present in the mixtures, which would be responsible for the considerable perturbation of the structure in the first shell of like species, and would be moving within the liquid in a parallel face-to-face configuration. Using the tools developed originally to estimate hydrogen-bond lifetimes in liquids, we have computed the lifetimes of the Bz-Hf complexes as a function of the mixture composition, by two different methods: the direct time-averaging scheme and from the autocorrelation function of bond occupation numbers. The obtained lifetimes are strongly dependent on the scheme chosen to compute the characteristic times. We have obtained for the Bz-Hf dimer in solution, at room temperature, lifetimes in the range of 30-40 ps from averaging schemes and around 60-120 ps from autocorrelation function methods. In the latter case, the longest times correspond to the equimolar mixture.     

Inhibition of immediate type hypersensitivity reaction by combined irradiation with ultraviolet and visible light

Recently we found that ultraviolet B (UVB) irradiation in erythematous doses significantly inhibited the immediate type hypersensibility reaction in the skin. In the present study we investigated the effects of different wavelengths on the skin prick test reaction (SPT). The forearm of ragweed allergic patients was irradiated with increasing doses of ultraviolet A (UVA), visible light (VIS) or combined UVB, UVA and VIS light, referred to as mUV/VIS. SPTs were performed 24 h after irradiation both on irradiated and non-irradiated control skin areas using ragweed extract. UVA and VIS irradiation led to a slight, not significant inhibition of allergen-induced wheal formation. Mixed irradiation with mUV/VIS light resulted in a dose-dependent inhibition of the allergen-induced wheal formation. The inhibition was significant already at suberythematous doses. As there is a good correlation between SPT and the nasal symptoms in patients with hay fever these data suggest that phototherapy with mUV/VIS light might be an effective and safe treatment modality for immediate type hypersensibility reactions in the skin and nasal mucosa.