More on the duality conjecture for entropy numbers

We verify, up to a logarithmic factor, the duality conjecture for entropy numbers in the case where one of the bodies is an ellipsoid. To cite this article: S. Artstein et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Neutrino mass effect on the nuclear muon capture

Multipole expansion of the partial transition amplitude in the nuclear muon capture with massive lefthanded Dirac neutrino has been derived. The multipole amplitudes for the partial nuclear transitions are given as the explicit functions of the neutrino mass parameter. As an example, the capture rate, the recoil asymmetry and the neutrino polarization are investigated in terms of these multipole amplitudes. The transversal neutrino polarization provides a connection between theT-violation and the neutrino mass: ifT-odd component in the neutrino polarization is observed, then neutrino must be a massive particle. It turns out that in the capture rate and recoil polarization, the effects due to very small neutrino mass can be proportional to the square ratio of the neutrino mass to its momentum, while the neutrino transversal polarization is proportional to this ratio only. Under the recent limits on the muon neutrino mass, the observable effects inthe partial transition may be below the order of ?10^?3.     

Note on grammatical translations of logical calculi

It is shown that there exists no grammatical translation into classical (propositional) logic of the modal logics, nor of intuitionistic logic and of the relatedness and dependence logics, as defined in Richard L. Epstein's bookThe Semantic foundations of logic. In the book the result is proved for translations without parameters.Classical propositional logicPC can be translated into other logics. Usually the grammatical structure of propositions is preserved, in the sense of the following definition.     

Laser photolysis of 2-phenylheptamethyltrisilane

Two transient absorptions have been detected in the 266 nm laser photolysis of 2-phenylheptamethyltrisilane in cyclohexane solution at room temperature, and their time evolution was recorded in the presence and absence of air and added trapping agents. The shorter-lived 440 nm transient (t1/2 < 20μs) is tentatively assigned to the silylene :SiMePh and the more persistent 380 nm transient to the disilene MePhSiSiMePh. The reactivity of this silylene is much lower than had been expected.     

Dependence of calculated collective nuclear properties on the form of the potential energy and inertia tensor

A systematic study of the dependence of the collective quantities (energies and matrix elements of the E2, M1 and E0 moments) on the form of approximations to the potential energy V and the inertia tensor B is performed. Various approximations used up to now are tested. Macroscopic-microscopic values for V and cranking results for B are taken as a reference. The collective quantities are calculated by solving the Schrödinger equation corresponding to the collective Bohr hamiltonian. The contribution of all nucleons is explicitly taken into account; no renormalization factors are used. Spherical, transitional and deformed even-even nuclei are considered. The quality of various approximations for V and B used in the boson-expansion method is discussed. Large effects of the microstructure of the inertia tensor B are obtained and commented on.     

Saturating constructions for normed spaces II

We prove several results of the following type: given finite-dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) and (2) every subspace of X, whose dimension is not “too small”, contains a further well-complemented subspace nearly isometric to V. This sheds new light on the structure of large subspaces or quotients of normed spaces (resp., large sections or linear images of convex bodies) and provides definitive solutions to several problems stated in the 1980s by Milman.     

Dye distribution in fluorescent-labeled latex prepared by emulsion polymerization

Emulsion polymerizations were used for preparing fluorescent-labeled polymers. The labeled polymers were analyzed by gel permeation chromatography (GPC) using both fluorescence (FL) and refractive index (RI) as detectors. The uniformity of polymer labeling was measured by the ratio between FL and RI signals, calculated by a computer software, on the basis of each GPC chromatogram. It was found that in emulsion polymerizations, the semicontinuous process can produce a more homogenous dye distribution in the host polymer molecules than the batch method. Uniform labeling of a polymer with various dyes can be achieved by the semi-continuous process. However, experimental conditions for polymerization, such as initiator concentration and the presence of surfactant or chain transfer agent, may influence the uniformity of dye distribution. © 1994 John Wiley & Sons, Inc.     

Vapour—liquid equilibria in binary systems formed by N-Methylpyrrolidone with hydrocarbons and hydroxyl derivatives

The vapour—liquid equilibria (VLE) determined by an ebulliometric total pressure method under isothermal conditions for binary systems formed by N-methylpyrrolidone with hexane (333.25 and 343.15 K), dodecane (393.25 K), cyclohexane (333.25 and 354.15 K), methyl-cyclohexane (354.15 and 373.25 K), benzene (333.25 and 354.15 K), toluene (362.15 and 383.35 K), propylbenzene (352.15 and 373.75 K), butylbenzene (352.15 and 373.75 K), propanol-1 (354.15 K), hexanol-1 (351.75 and 393.35 K) and at 393.55 K for cyclohexanol, 4-methylphenol and 2,4-dimethylphenol are reported. The vapour pressures of the pure substances are given. The least squares analysis of VLE data by means of the Redlich-Kister equation is given.     

Design of shaped piezoelectric modal sensor for beam with arbitrary boundary conditions by using Adomian decomposition method

The theory for designing distributed piezoelectric modal sensors is well established for beam structures. However, the current modal sensor theory is limited in scope in that it can only be applied in the case of classical boundary conditions (i.e., either clamped, free, simply supported or sliding). In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a beam with arbitrary boundary conditions is proposed, using the Adomian decomposition method (ADM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a function of the second spatial derivative of the structural mode shape function. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the second spatial derivative of the mode shapes can be determined. Then the shapes of the designed modal sensors are obtained. Finally, some numerical examples are given to demonstrate the feasibility of the proposed modal sensors. It is shown that, for classical boundary conditions, the shapes of the modal sensors based on the ADM agree well with analytical and numerical results given in the literature. For general boundary conditions it is found that the shape of the modal sensors is influenced by the number of modes of interest because the second spatial derivatives of the mode shapes are not orthogonal to one another. The modal sensors for general boundary conditions can be considered as modal filters within a limited frequency band.