A Lower Bound for the Differences of Powers of Linear Operators

Let T be a bounded linear operator in a Banach space, with σ（T）={1}. In 1983, Esterle-Berkani＇ s conjecture was proposed for the decay of differences （I - T） T^n as follows： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.     

Asymptotic expansion of the logistic midrange

Using the symbolic computation program MAPLE, we compute several terms of an asymptotic expansion for the distribution function of the logistic midrange.     

Synthesis of cationic molybdenum and cobalt diene complexes from neutral allyl compounds by ligand exchange in a strong protic acid

Conclusions The allyl ligand in neutral molybdenum and cobalt complexes is readily exchanged by dienes in the presence of a strong protic acid with the formation of cationic complexes. This exchange is facilitated by an increase in the basicity of the starting compounds.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1655–1657, July, 1987.     

Halogenation of N-substituted para-quinone monoimine and para-quinone monooxime esters: VI. Regular trends in chlorination and bromination of N-arylsulfonyl-1,4-benzoquinone monoimines alkyl-substituted in the quinoid ring

Reactions of halogens with N-arylsulfonyl-1,4-benzoquinone monoimines occur with the formation of a halogenonium ion that either transforms into a carbocation where the first halogen atom adds to the carbon in the ortho-position relative to the carbonyl carbon, or the halogenonium ion adds directly the second halogen atom.     

An improved approach for hydrogen analysis in metal samples using single laser-induced gas plasma and target plasma at helium atmospheric pressure

We report in this paper the results of an experimental study on hydrogen analysis of solid samples in high pressure helium ambient gas employing the basic scheme of laser induced breakdown spectroscopy (LIBS). It is shown that the metastable excited state of helium atom can be utilized to induce delayed excitation of the ablated hydrogen atoms, and thereby avoid the Stark broadening effect as well as overcoming the undesirable mismatch effect, which are responsible for inefficient excitation respectively. It is further demonstrated that for samples of high boiling-point materials such as zircaloy, successful hydrogen analysis can be achieved by a newly introduced double excitation technique employing single laser realized in a modified configuration of the conventional LIBS method. PACS 51-52     

Existence Results for Semilinear Neutral Functional Differential Inclusions via Analytic Semigroups

In this paper we prove existence results for semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.      

Signal recording in acoustooptical imaging of scattering media

An expression for a signal at the ultrasonic frequency from a photodetector arising when diffraction waves at the cathode mix is obtained for the case when the optical and acoustic beams are space-limited and Bragg angles are small. The alternating current generated when the scattering medium is crossed by a focused 3-MHz ultrasonic beam and illuminated by a cw He-Ne laser is measured. Satisfactory agreement between experimental results and those calculated from the formulas obtained indicates that our model treating acoustooptical interaction in the medium in terms of Raman-Nath diffraction is valid. Conditions for measuring the alternating current (which is a parameter of acoustooptical imaging) that are optimal from the viewpoint of maximizing the signal and signal-to-noise ratio are predicted theoretically and corroborated experimentally.     

Characterization and identification of partially blocked electrodes

A new method for the characterization of partially covered electrodes is proposed. It is based on the formal analogy between such electrodes and those having a first-order chemical reaction associated with the charge transfer. It consists in making use of the two linear segments in Z(s^{?$\text{1}\text{2}$} appearing on some specified conditions on the operational impedance spectrum obtained for semi-infinite diffusion. To avoid confusion between these two types of electrode, an identification method is proposed, involving the measurements of diffusion-limiting currents on a RDE. Analysis of the limits of validity of these methods leads to the conclusion that most inhibiting coverages fulfilling the conditions necessary for their characterization should not be mistaken for a chemical reaction.     

The effect of geoacoustic characteristics of the bottom on the long-range sound propagation in an inhomogeneous ocean

The long-range sound propagation from a deep ocean to a receiving system located on the shelf is modeled. The waveguide model is constructed on the basis of the data of an acoustic-oceanographic experiment carried out in the northwestern Pacific. The sensitivity and the frequency dependence of the difference in the sound field levels at the crossing of the frontal zone on the geoacoustic characteristics of the bottom of the shelf and the continental slope are investigated. It is shown that the level difference decreases by 8.2 dB as the velocity of longitudinal waves increases by 100 m/s in the range within 1490–1820 m/s.     

Wave biomechanics of the skeletal muscle

Results of acoustic measurements in skeletal muscle are generalized. It is shown that assessment of the pathologies and functional condition of the muscular system is possible with the use of shear waves. The velocity of these waves in muscles is much smaller than the velocity of sound; therefore, a higher symmetry type is formed for them. In the presence of a preferential direction (along muscle fibers), it is characterized by only two rather than five (as in usual media with the same anisotropy) moduli of elasticity. A covariant form of the corresponding wave equation is presented. It is shown that dissipation properties of skeletal muscles can be controlled by contracting them isometrically. Pulsed loads (shocks) and vibrations are damped differently, depending on their frequency spectrum. Characteristic frequencies on the order of tens and hundreds of hertz are attenuated due to actin-myosin bridges association/dissociation dynamics in the contracted muscle. At higher (kilohertz) frequencies, when the muscle is tensed, viscosity of the tissue increases by a factor of several tens because of the increase in friction experienced by fibrillar structures as they move relative to the surrounding liquid; the tension of the fibers changes the hydrodynamic conditions of the flow around them. Finally, at higher frequencies, the attenuation is associated with the rheological properties of biological molecules, in particular, with their conformational dynamics in the wave field. Models that describe the controlled shock dissipation mechanisms are proposed. Corresponding solutions are found, including those that allow for nonlinear effects.