Contractions with rank one defect operators and truncated CMV matrices

The main issue we address in the present paper are the new models for completely nonunitary contractions with rank one defect operators acting on some Hilbert space of dimension N?∞. These models complement nicely the well-known models of Livšic and Sz.-Nagy-Foias. We show that each such operator acting on some finite-dimensional (respectively, separable infinite-dimensional Hilbert space) is unitarily equivalent to some finite (respectively semi-infinite) truncated CMV matrix obtained from the “full” CMV matrix by deleting the first row and the first column, and acting in CN (respectively ?²(N)). This result can be viewed as a nonunitary version of the famous characterization of unitary operators with a simple spectrum due to Cantero, Moral and Velázquez, as well as an analog for contraction operators of the result from [Yu. Arlinski?, E. Tsekanovski?, Non-self-adjoint Jacobi matrices with a rank-one imaginary part, J. Funct. Anal. 241 (2006) 383-438] concerning dissipative non-self-adjoint operators with a rank one imaginary part. It is shown that another functional model for contractions with rank one defect operators takes the form of the compression f(ζ)→PK(ζf(ζ)) on the Hilbert space L²(T,dμ) with a probability measure μ onto the subspace K=L²(T,dμ)?C. The relationship between characteristic functions of sub-matrices of the truncated CMV matrix with rank one defect operators and the corresponding Schur iterates is established. We develop direct and inverse spectral analysis for finite and semi-infinite truncated CMV matrices. In particular, we study the problem of reconstruction of such matrices from their spectrum or the mixed spectral data involving Schur parameters. It is pointed out that if the mixed spectral data contains zero eigenvalue, then no solution, unique solution or infinitely many solutions may occur in the inverse problem for truncated CMV matrices. The uniqueness theorem for recovered truncated CMV matrix from the given mixed spectral data is established. In this part the paper is closely related to the results of Hochstadt and Gesztesy-Simon obtained for finite self-adjoint Jacobi matrices.     

Ferrocenylalkyl azoles: bioactivity,synthesis, structure

The toxicity of ferrocenylethyl benzotriazole ( 1 ) and other ferrocene compounds including ferrocenylmethyl benzimidazoles ( 4,5,6,11 ), ferricenium salts ( 3,9,10 ) and ferrocenylmethyl adenine ( 7 ), was studied. All ferrocene complexes under investigation showed low or medium toxicities. On the basis of an earlier model of chemical carcinogenesis, the antitumor activity of ferrocenylalkyl azoles 1, 8 and ferricenium salts 9, 10 was studied in vivo in the so‐called sub‐capsular test on human tumors. This effectiveness was compared with that of cisplatin. A series of ferrocenylalkyl azoles were synthesized by interacting azoles either with α‐hydroxyalkyl ferrocenes FcC(OH)R₁R₂ in organic solvent in the presence of aqueous HBF₄ in quantitative yields or with trimethyl(aminomethyl)ferrocene iodide in an aqueous‐basic medium in good yields. The X‐ray determinations of molecular and crystal structures of α‐(1‐benzotriazolyl)ethylferrocene ( 1 ) and α‐(1‐naphthatriazolyl)ethylferrocene ( 12 ) were performed. Copyright © 2008 John Wiley & Sons, Ltd.     

ML-Based Analysis of Particle Distributions in High-Intensity Laser Experiments: Role of Binning Strategy

When entering the phase of big data processing and statistical inferences in experimental physics, the efficient use of machine learning methods may require optimal data preprocessing methods and, in particular, optimal balance between details and noise. In experimental studies of strong-field quantum electrodynamics with intense lasers, this balance concerns data binning for the observed distributions of particles and photons. Here we analyze the aspect of binning with respect to different machine learning methods (Support Vector Machine (SVM), Gradient Boosting Trees (GBT), Fully-Connected Neural Network (FCNN), Convolutional Neural Network (CNN)) using numerical simulations that mimic expected properties of upcoming experiments. We see that binning can crucially affect the performance of SVM and GBT, and, to a less extent, FCNN and CNN. This can be interpreted as the latter methods being able to effectively learn the optimal binning, discarding unnecessary information. Nevertheless, given limited training sets, the results indicate that the efficiency can be increased by optimizing the binning scale along with other hyperparameters. We present specific measurements of accuracy that can be useful for planning of experiments in the specified research area.     

Hydrodynamic formation of stable anisotropic structures in Couette flow of dilute suspensionFormation hydrodynamique pour structures anisotropiques stables dans un flux de Couette d'une suspension diluée

The problem of rotary motion of rigid axially symmetric elongated particles in the Couette flow of dilute suspension with anisotropic carrier fluid is solved. It is shown that the stable stationary solutions of the dynamical set of ordinary differential equations describing the particles rotary motion are possible in the case of forming the stationary anisotropy in the carrier fluid of the suspension. It allows us to detect the stationary orientation of suspended particles and formation of stable anisotropic liquid-crystalline structures in the considered suspension under the action of hydrodynamic forces. The study of rheological properties of such a structured suspension shows that it behaves as a viscoelastic quasi-Newtonian anisotropic liquid medium. To cite this article: E.Yu. Taran et al., C. R. Mecanique 332 (2004).     

Lewis acid catalyzed reactions of donor-acceptor cyclopropanes with 1- and 2-pyrazolines: formation of substituted 2-pyrazolines and 1,2-diazabicyclo[3.3.0]octanes

The reaction of 2-substituted cyclopropane-1,1-dicarboxylates with 1- and 2-pyrazolines is efficiently catalyzed by scandium or ytterbium triflates to give N-substituted 2-pyrazolines or 1,2-diazabicyclo[3.3.0]octanes. The reactions of 2-pyrazolines give diazabicyclooctanes as the major products. In contrast, the reactions starting from 1-pyrazolines predominantly give N-substituted 2-pyrazolines, which become the major compounds obtained if an equimolar amount of GaCl₃ is used. A possible reaction mechanism is suggested.     

Impact of synthesis conditions on surface chemistry and structure of carbide-derived carbons

Carbide-derived carbons produced by chlorination of titanium carbide at 600, 800, or 1100 °C were subjected to a post-treatment at 600 °C in Ar, H₂, or NH₃ atmosphere. Experimental results suggest that the chlorination temperature influences the ordering of carbon in a manner that impacts specific surface area and porosity. Higher chlorination temperatures lead to higher total pore volume and increased ordering, but lower microporosity. The effect of post-treatments on surface chemistry is pronounced only for samples chlorinated at 600 °C; post-treatments in Ar are shown to be less effective for chlorine removal than those performed in H₂ or NH₃. Post-treatments in Ar result in a lower total pore volume compared to the ones in H₂ or NH₃ for the same chlorination temperature. Samples chlorinated at higher temperatures contained less oxygen functionalities than samples chlorinated at 600 °C, and showed correspondingly less desorption of H₂O, possibly due to diminished uptake of ambient water.     

Comparative dissociation of peptide polyanions by electron impact and photo-induced electron detachment

We compare product-ion mass spectra produced by electron detachment dissociation (EDD) and electron photodetachment dissociation (EPD) of multi-deprotonated peptides on a Fourier transform and a linear ion trap mass spectrometer, respectively. Both methods, EDD and EPD, involve the electron emission-induced formation of a radical oxidized species from a multi-deprotonated precursor peptide. Product-ion mass spectra display mainly fragment ions resulting from backbone cleavages of C_α-C bond ruptures yielding a and x ions. Fragment ions originating from N-C_α backbone bond cleavages are also observed, in particular by EPD. Although EDD and EPD methods involve the generation of a charge-reduced radical anion intermediate by electron emission, the product ion abundance distributions are drastically different. Both processes seem to be triggered by the location and the recombination of radicals (both neutral and cation radicals). Therefore, EPD product ions are predominantly formed near tryptophan and histidine residues, whereas in EDD the negative charge solvation sites on the backbone seem to be the most favorable for the nearby bond dissociation.     

AgGaS2- and Al-doped GaSe Crystals for IR Applications

We report a systematic study of AgGaS₂- and Al-doped GaSe crystals in comparison with pure GaSe and S-doped GaSe crystals. AgGaS₂-doped GaSe (GaSe:AgGaS₂) crystal was grown by Bridgman technique from the melt of GaSe:AgGaS₂ (10.6 wt.%). Its real composition was identified as GaSe:S (2 wt.%). Al-doped GaSe (GaSe:Al) crystals were grown from the melt of GaSe and 0.01, 0.05, 0.1, 0.5, 1, 2 mass % of aluminium. Al content in the grown crystals is too small to be measured. The hardness of GaSe:S (2 wt.%) crystal grown from the melt of GaSe:AgGaS₂ is 25% higher than that of GaSe:S (2 wt.%) crystal grown by a conventional S-doping technique and 1.5- to 1.9-times higher than that of pure GaSe. GaSe:Al crystals are characterized by 2.5- to 3-times higher hardness than that of pure GaSe and by extremely low conductivity of ≤ 10^− 7 Om^− 1 cm^− 1. A comparative experiment on SHG in AgGaS₂-, Al-, S-doped GaSe and pure GaSe is carried out under the pumps of 2.12-2.9 μm fs OPA and 9.2−10.8 μm ns CO₂ laser. It was found that GaSe:S crystals possess the best physical properties for mid-IR applications among these doped GaSe crystals. GaSe:Al crystals have relatively low conductivity which have strong potential for THz application.     

On the complexity of the (r|p)-centroid problem in the plane

In the (r∣p)-centroid problem, two players, called leader and follower, open facilities to service clients. We assume that clients are identified with their location on the Euclidean plane, and facilities can be opened anywhere in the plane. The leader opens p facilities. Later on, the follower opens r facilities. Each client patronizes the closest facility. In case of ties, the leader’s facility is preferred. The goal is to find p facilities for the leader to maximize his market share. We show that this Stackelberg game is \(\varSigma_{2}^{P}\) -hard. Moreover, we strengthen the previous results for the discrete case and networks. We show that the game is \(\varSigma_{2}^{P}\) -hard even for planar graphs for which the weights of the edges are Euclidean distances between vertices.