The Möbius Category of Some Combinatorial Inverse Semigroups

\noindent The purpose of this paper is to point out some aspects of the relationship between combinatorial inverse semigroups and their Möbius categories, and to explore combinatorial results arising from combinatorial Brandt semigroups, fundamental simple inverse -semigroups and from the free monogenic inverse semigroup.     

On the invariance of classes under composition

The necessary and sufficient condition for to be in the class for every of that class whose range is in the domain of is that be in .

     

On the intersection of null spaces for matrix substitutions in a non-commutative rational formal power series

For a rational formal power series in N non-commuting indeterminates, with matrix coefficients, we establish the formula which relates the intersection of the null spaces of coefficients to the intersection of the null spaces of values of this series at N-tuples of $n\times n$ matrices, for n large enough. As an application, we formulate the criteria of observability, controllability, and minimality for a recognizable formal power series representation in terms of matrix substitutions. To cite this article: D. Alpay, D.S. Kalyuzhny??-Verbovetzki??, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Quantum tensor product structures are observable induced

It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multipartite tensor product structure of the state space and the associated notion of quantum entanglement are then relative and observable induced. We develop a general algebraic framework aimed to formalize this concept.     

Non-destructive evaluation of elastic material properties in anisotropic circular cylindrical structures

In this paper, non-axisymmetric guided wave propagation in circular cylindrical, anisotropic structures is studied in a frequency range up to 1 MHz. The investigations are carried out with carbon fibre reinforced tubes. The aim is the experimental determination of their effective linear elastic material properties in a non-destructive way. Therefore, an analytical model of the dispersion equation is fitted to the experimentally detected dispersion curves by systematically adjusting the desired material properties. A total least square scheme accompanied by an outlier detection criterion is used for this optimization task. Since the raw data of the measured dispersion curves contain a lot of noise, these outliers have to be detected and excluded, to achieve accurate results. Good agreement is found between the measured curves and the analytically calculated curves based on the estimated parameters. This fact indicates a high accuracy of the determined material properties.     

Initial attempts at directly detecting alpha wave activity in the brain using MRI

The “direct detection” of neuronal activity by MRI could offer improved spatial and temporal resolution compared to the blood oxygenation level-dependent (BOLD) effect. Here we describe initial attempts to use MRI to detect directly the neuronal currents resulting from spontaneous alpha wave activity, which have previously been shown to generate the largest extracranial magnetic fields. Experiments were successfully carried out on four subjects at 3 T. A single slice was imaged at a rate of 25 images per second under two conditions. The first (in darkness with eyes-closed) was chosen to promote alpha wave activity, while the second (eyes-open viewing a visual stimulus) was chosen to suppress it. The fluctuations of the phase and magnitude of the resulting MR image data were frequency analysed, and tested for the signature of both alpha wave activity and neuronal activity evoked by the visual stimulus.

Regions were found that consistently showed elevated power in fluctuations of the phase of the MR signal, in the frequency range of alpha waves, during the eyes-closed condition. It was conservatively assumed that if oscillations occurred at the same frequency in the magnitude signal from the same region or at the same frequency in the phase or magnitude signal from other regions overlying large vessels or cerebrospinal fluid (CSF), then the phase changes were not due to neuronal activity related to alpha waves. Using these criteria the data obtained were consistent with direct detection of alpha wave activity in three of the four volunteers. No significant MR signal fluctuations due to evoked activity were identified.     

A comparative study of myo-inositol quantification using LCmodel at 1.5 T and 3.0 T with 3 D 1H proton spectroscopic imaging of the human brain

Myo-inositol is a strongly coupled system and resonates at four chemical shift positions. At 1.5 T, only the singlet component at 3.57 ppm is detected. However, at 3 T this resonance is resolved into its components at 3.55 ppm and 3.61 ppm. Due to the increased spectral resolution and signal-to-noise ratio, it is anticipated that the quantification of myo-inositol should improve at 3 T. Using data from normal controls and the LCmodel quantification procedure, we found that the quantification precision, reproducibility and detection sensitivity of myo-inositol is significantly better at 3 T relative to 1.5 T.     

RNA interference silencing the transcriptional message

We developed the microbial immobilization particle with curdlan and activated carbon, which has great adsorption capacity. The characteristics of porosity and mechanical strength of these supporting particles are dependent on manufacturing method. The supporting particle showed the best performance when the ratio of curdlan and activated carbon was 30 to 6 g/L. Brumauer-Emmett-Teller (specific surface area) and swelling capacity of the carrier were 52.63 m²/g and 17 (w/w), respectively. The immobilization characteristics of iron-oxidizing bacteria on supporting particles were observed using a scanning electron microscope. The concentration of micro-organism on the surface of supporting particle was increased with reaction time. As the number of iron oxidation batch cycles increased, the iron oxidation rate increased.     

Oxidation of alkylsilane-based monolayers on gold

The oxidation of alkylsilane monolayers on Au has been studied by X-ray photoelectron spectroscopy, reflection-absorption infrared spectroscopy, contact-angle measurements, and scanning tunneling microscopy. Exposure of the monolayers at 298 K to pure O(2) or H(2)O (>5 x 10(-5) Torr and >150 000 L) does not cause oxidation. Ambient atmosphere only causes oxidation if direct sight lines are maintained to the sample. Ozone exposure results in rapid monolayer oxidation. Oxidation initially occurs only at the Si atom, resulting in formation of a cross-linked siloxane monolayer that retains alkyl surface termination. Prolonged ozone exposures result in the oxidation and subsequent loss of the alkyl chain.     

Lattice boltzmann study on the contact angle and contact line dynamics of liquid-vapor interfaces

The moving contact line problem of liquid-vapor interfaces was studied using a mean-field free-energy lattice Boltzmann method recently proposed [Phys. Rev. E 2004, 69, 032602]. We have examined the static and dynamic interfacial behaviors by means of the bubble and capillary wave tests and found that both the Laplace equation of capillarity and the dispersion relation were satisfied. Dynamic contact angles followed the general trend of contact line velocity observed experimentally and can be described by Blake's theory. The velocity fields near the interface were also obtained and are in good agreement with fluid mechanics and molecular dynamics studies. Our simulations demonstrated that incorporating interfacial effects into the lattice Boltzmann model can be a valuable and powerful alternative in interfacial studies.