Scars of the Wigner Function

We propose a picture of Wigner function scars as a sequence of concentric rings along a two-dimensional surface inside a periodic orbit. This is verified for a two-dimensional plane that contains a classical hyperbolic orbit of a Hamiltonian system with 2 degrees of freedom. The stationary wave functions are the familiar mixture of scarred and random waves, but the spectral average of the Wigner functions in part of the plane is nearly that of a harmonic oscillator and individual states are also remarkably regular. These results are interpreted in terms of the semiclassical picture of chords and centers.     

A Synthesis of Fused Butenoudes

It has been shown that tert-butyldimethylsilylated (Z) 2-carboethoxymethylene cycloalkanols are readily desilylated with concomitant cyclization to give the corresponding butenolides. The (E) isomers are desilylated, but not cyclized under these conditions.     

Influence of the anode material on an argon arc

The interaction between the arc and the anode was experimentally studied by means of a transferred arc burning in argon with copper, iron, or steel anodes. Depending on the rate of anode cooling, a stable plasma was obtained just above the anode, established either in pure argon (strong cooling) or in a mixture of argon with metal vapor. Temperature and metal concentration fields were deduced from spectroscopic measurements. Two important results were reached: the arc radius near the anode depends on the nature of the electrode, even without anode erosion; and the presence of metal vapor leads to a cooling of the plasma. The same arc configurations were theoretically simulated by a two-dimensional model. The comparison between experimental and numerical results allows a large proportion of the observed phenomena to be interpreted, in spite of partial discrepancies between predicted and measured values. The dimension of the arc root at the anode depends on the thermal conductivity of the solid metal, whereas the cooling effect due to metal vapor in the plasma is explained by the increases of electrical conductivity and of radiative losses in the presence of the vapor     

On Transfer Operators for Continued Fractions with Restricted Digits

For any non-empty subset I of the natural numbers, let _I denotethose numbers in the unit interval whose continued fractiondigits all lie in I. Define the corresponding transfer operator for , where Re (rß) = _I is the abscissa of convergence of the series . When acting on a certain Hilbert space H_I, rß, weshow that the operator L_I, rß is conjugate to an integraloperator K_I, rß. If furthermore rß is real,then K_I, rß is selfadjoint, so that L_I, rß: H_I, rß H_I, rß has purely real spectrum.It is proved that L_I, rß also has purely real spectrumwhen acting on various Hilbert or Banach spaces of holomorphicfunctions, on the nuclear space C [0, 1], and on the Fréchetspace C [0, 1]. The analytic properties of the map rß L_I, rßare investigated. For certain alphabets I of an arithmetic nature(for example, I = primes, I = squares, I an arithmetic progression,I the set of sums of two squares it is shown that rß L_I, rß admits an analytic continuation beyond thehalf-plane Re rß > _I. 2000 Mathematics SubjectClassification 37D35, 37D20, 30B70.     

Structure and vibrational spectra of Ti(IV) hydroxides and their clusters with expanded titanium coordination. DFT study

Equilibrium structures of H(4-n)Ti(OH)n (n = 2-4) molecules and the Ti(OH)4 dimer and trimers were optimized at the B3LYP level of theory. Theoretical vibrational frequencies of TiO stretching modes obtained with several basis sets were compared with the existing experimental frequencies of these vibrations, and the 6-31+G(d) set was chosen for cluster calculations. Only one energy minimum was found for the [Ti(OH)4](2) dimer, but two isomers without symmetry elements stabilized by internal hydrogen bonds and two isomers, belonging to C(s) and C(i) point groups, with free OH groups were found as minima at the [Ti(OH)4](3) potential energy surface. The structure with the linear arrangement of hexacoordinated titanium atoms in the Ti3O12 skeleton may be proposed for trimeric species observed in liquid titanium alkoxides as the only structure satisfying experimental spectroscopic evidence about the presence of center of inversion in these species. Frequency changes of TiO4 modes which accompany the oligomer formation are predicted and discussed.     

Boron‐Containing Probes for Non‐optical High‐Resolution Imaging of Biological Samples

Boron has been employed in materials science as a marker for imaging specific structures by electron energy loss spectroscopy (EELS) or secondary ion mass spectrometry (SIMS). It has a strong potential in biological analyses as well; however, the specific coupling of a sufficient number of boron atoms to a biological structure has proven challenging. Herein, we synthesize tags containing closo‐1,2‐dicarbadodecaborane, coupled to soluble peptides, which were integrated in specific proteins by click chemistry in mammalian cells and were also coupled to nanobodies for use in immunocytochemistry experiments. The tags were fully functional in biological samples, as demonstrated by nanoSIMS imaging of cell cultures. The boron signal revealed the protein of interest, while other SIMS channels were used for imaging different positive ions, such as the cellular metal ions. This allows, for the first time, the simultaneous imaging of such ions with a protein of interest and will enable new biological applications in the SIMS field.     

Impact of Adding Polysaccharides on the Stability of Egg Yolk/Fish Oil Emulsions under Accelerated Shelf-Life Conditions

Polysaccharides can form interfacial complexes with proteins to form emulsions with enhanced stability. We assessed the effect of adding gum guar or gum arabic to egg yolk/fish oil emulsions. The emulsions were produced using simple or high-pressure homogenization, stored for up to 10 days at 45 °C, and characterized for their particle size and distribution, viscosity, encapsulation efficiency, oxidative stability, and cytotoxicity. Emulsions containing gum guar and/or triglycerides had the highest viscosity. There was no significant difference in the encapsulation efficiency of emulsions regardless of the polysaccharide used. However, emulsions containing gum arabic displayed a bridging flocculation effect, resulting in less stability over time compared to those using gum guar. Emulsions produced using high-pressure homogenization displayed a narrower size distribution and higher stability. The formation of peroxides and propanal was lower in emulsions containing gum guar and was attributed to the surface oil. No significant toxicity toward Caco-2 cells was found from the emulsions over time. On the other hand, after 10 days of storage, nonencapsulated fish oil reduced the cell viability to about 80%. The results showed that gum guar can increase the particle stability of egg yolk/fish oil emulsions and decrease the oxidation rate of omega-3 fatty acids.     

TOPS-MODE based QSARs derived from heterogeneous series of compounds. Applications to the design of new herbicides

A new application of TOPological Sub-structural MOlecular DEsign (TOPS-MODE) was carried out in herbicides using computer-aided molecular design. Two series of compounds, one containing herbicide and the other containing nonherbicide compounds, were processed by a k-Means Cluster Analysis in order to design the training and prediction sets. A linear classification function to discriminate the herbicides from the nonherbicide compounds was developed. The model correctly and clearly classified 88% of active and 94% of inactive compounds in the training set. More specifically, the model showed a good global classification of 91%, i.e., (168 cases out of 185). While in the prediction set, they showed an overall predictability of 91% and 92% for active and inactive compounds, being the global percentage of good classification of 92%. To assess the range of model applicability, a virtual screening of structurally heterogeneous series of herbicidal compounds was carried out. Two hundred eighty-four out of 332 were correctly classified (86%). Furthermore this paper describes a fragment analysis in order to determine the contribution of several fragments toward herbicidal property; also the present of halogens in the selected fragments were analyzed. It seems that the present TOPS-MODE based QSAR is the first alternate general "in silico" technique to experimentation in herbicides discovery.