Identification of chaos in a cutting process by the 0–1 test

We have examined the cutting process by using a two degrees of freedom non-smooth model with a friction component. Instead of the standard Lyapunov exponent treatment a statistical ‘0–1’ test based on the asymptotic properties of a non-harmonic Brownian motion chain has been successively applied to reveal the nature of the cutting process. In this test we calculated the control parameter K which is approaching asymptotically to 0 or 1 for regular and chaotic motions, respectively. The presented approach is independent on the integration procedure as we defined a characteristic distance between the points forming the time series used in the test separately.     

On some properties ofJ-convex stochastic processes

Summary We present some results on the differentiability of convex stochastic processes. Furthermore, the stochastic version of a theorem onJ-convex functions majorized byJ-concave functions is given.     

Maximum Spin Polarization in Chromium Dimer Cations as Demonstrated by X‐ray Magnetic Circular Dichroism Spectroscopy

X‐ray magnetic circular dichroism spectroscopy has been used to characterize the electronic structure and magnetic moment of Cr₂⁺. Our results indicate that the removal of a single electron from the 4sσ_g bonding orbital of Cr₂ drastically changes the preferred coupling of the 3d electronic spins. While the neutral molecule has a zero‐spin ground state with a very short bond length, the molecular cation exhibits a ferromagnetically coupled ground state with the highest possible spin of S=11/2, and almost twice the bond length of the neutral molecule. This spin configuration can be interpreted as a result of indirect exchange coupling between the 3d electrons of the two atoms that is mediated by the single 4s electron through a strong intraatomic 3d‐4s exchange interaction. Our finding allows an estimate of the relative energies of two states that are often discussed as ground‐state candidates, the ferromagnetically coupled ¹²Σ and the low‐spin ²Σ state.     

Cutting process dynamics by nonlinear time series and wavelet analysis

We have modeled the dynamics of a cutting process by a two-degree-of-freedom mass-spring system with dry friction. Using nonlinear time series and wavelet analysis, we have investigated the vibrational instabilities of the system for different values of the cutting force. By constructing the phase portraits and calculating the Lyapunov exponents we have delineated the conditions for which a periodic or chaotic motion can occur. The results are verified by means of a time-scale representation of the wavelet power spectrum.     

Controlled spacing of cationic gold nanoparticles by nanocrown RNA

Using atomic force microscopy, we describe the linear arrangement of cationic gold nanoparticles directed by programmable self-assembling RNA ladders and demonstrate that the regular spacing of nanoparticles is controlled by the RNA architecture acting as nanocrown scaffoldings. Thus, precise positioning of molecular components can be accomplished with RNA not only through electrostatic but also via size and shape recognitions.     

Visible‐Light Photoactive,Highly Efficient Triplet Sensitizers Based on Iodinated Aza‐BODIPYs: Synthesis,Photophysics and Redox Properties

A series of novel iodinated NO₂‐substituted aza‐BODIPYs have been synthesized and characterized. Highly desirable photophysical and photochemical properties were induced in NO₂‐substituted aza‐BODIPYs by iodination of the pyrrole rings. In particular, high values of singlet oxygen quantum yields (Φ_Δ) ranging from 0.79 to 0.85 were measured. The photooxygenation process proceeds via a Type II mechanism under the experimental conditions applied. The compounds studied exhibited an absorption band within the so‐called “therapeutic window”, with λ_max located between 645 nm to 672 nm. They were non‐fluorescent at room temperature with excited singlet‐state lifetimes within the picosecond range as measured by femtosecond transient absorption. Nanosecond laser flash photolysis experiments revealed T₁→T_n absorption spanning from ca. 400 nm to ca. 500 nm and allowed determination of the triplet‐state lifetimes. The estimated triplet lifetimes (τ_T) in deaerated acetonitrile ranged between 2.74 μs and 3.50 μs. As estimated by CV/DPV measurements, all iodinated aza‐BODIPYs studied exhibited one irreversible oxidation and two quasi‐reversible reductions processes. Estimation of the E_HOMO gave the value of ?6.06 to ?6.26 eV while the E_LUMO was found to be located at ca. ?4.6 eV. Thermogravimetric (TGA) analysis revealed that iodinated aza‐BODIPYs were stable up to approximately 300 °C. All compounds studied exhibit high photostability in toluene solution.     

Spectrophotometric determination of boron in human hair with azomethine H

Summary Investigation of methods of hair sample mineralization was made. The most profitable method of hair mineralization was by combustion in oxygen. Boron was determined spectrophotometrically with azomethine H as a spectrophotometric reagent. Boron in hair was determined in the range of 0–5 g/g.     

Study of the shock-induced acceleration of hexane droplets

An experimental study of the interaction of a shock wave with a hexane droplet is presented. The main goal of the experiments was to record images of the process and measure basic parameters describing movement, dispersion and evaporation of the droplets engulfed by a shock wave propagating in air. A shock tube with a visualization section was used for this research. Photography of the process allowed one to measure the positions, velocities and sizes of mist clouds created by the interaction processes. Analysis of the pictures shows that there is no qualitative difference between cases for different size droplets, but shock Mach number had a significant effect on the process. Quantitative analysis shows that under certain conditions, a catastrophic breakup mechanism of dispersion occurred. The droplets are shattered into a mist cloud before they achieve mechanical equilibrium with the surrounding gas. The approximate time for the complete dispersion and acceleration of the fuel droplet varies from 300 to 500 μs, and depends both on the droplet diameter and shock velocity. The dispersion time is controlled principally by the droplet diameter, and to a lesser extent, the shock Mach number. This paper is based on work that was presented at the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems, Montreal, Canada, July 31–August 5, 2005.     

Towards More Photostable,Brighter, and Less Phototoxic Chromophores: Synthesis and Properties of Porphyrins Functionalized with Cyclooctatetraene

Free base and zinc porphyrins functionalized with cyclooctatetraene (COT), a molecule known as a good triplet-state quencher, have been obtained and characterized in detail by structural, spectral, and photophysical techniques. Substitution with COT leads to a dramatic decrease of the intrinsic lifetime of the porphyrin triplet. As a result, photostability in oxygen-free solution increases by two to three orders of magnitude. In non-degassed solutions, improvement of photostability is about tenfold for zinc porphyrins, but the free bases become less photostable. Similar quantum yields of photodegradation in free base and zinc porphyrins containing the COT moiety indicate a common mechanism of photochemical decomposition. The new porphyrins are expected to be much less phototoxic, since the quantum yield of singlet oxygen formation strongly decreases because of the shorter triplet lifetime. The reduction of triplet lifetime should also enhance the brightness and reduce blinking in porphyrin chromophores emitting in single-molecule regime, since the duration of dark OFF states will be shorter.     

Correction to: Unexpected Z/E isomerism of N-methyl-O-phosphothioyl benzohydroxamic acids,their oxyphilic reactivity and inertness to amines

Structural Chemistry - A Correction to this paper has been published: https://doi.org/10.1007/s11224-021-01744-8