Dominant matrices and max algebra

We study the class of so-called totally dominant matrices in the usual algebra and in the max algebra in which the sum is the maximum and the multiplication is usual. It turns out that this class coincides with the well known class of positive matrices having positive the determinants of all 2×2 submatrices. The closure of this class is closed not only with respect to the usual but also with respect to the max multiplication. Further properties analogous to those of totally positive matrices are proved and some connections to Monge matrices are mentioned.     

Congruence openings of additive Green’s relations on a semiring

In a series of papers, Green’s relations on the additive and multiplicative reducts of a semiring proved to be a very useful tool in the study of semirings. However, in the vast majority of cases, Green’s relations are not congruences, and we show that in such cases it is much more convenient to use the congruence openings of Green’s relations, instead of the Green’s relations themselves. By means of these congruence openings we define and study several very interesting operators on the lattices of varieties of semirings and additively idempotent semirings, and, in particular, we establish order embeddings of the lattice of varieties of additively idempotent semirings into the direct products of the lattices of open (resp. closed) varieties with respect to two opening (resp. closure) operators on this lattice that we introduced.     

Novel polycarbonate-based polyurethane elastomers: Composition–property relationship

Novel all-aliphatic polycarbonate-based polyurethane (PC-PU) elastomers, as well as PC-PU nanocomposites filled with organic-modified clays were synthesized, characterized and studied. It was found that they have very attractive mechanical properties (e.g., elongation at break between 600% and 800%). The prepared PC-PUs possess a distinctly segmented structure, which is the key prerequisite for their behavior as strong physical rubbery networks. All synthesized materials melt at elevated temperatures (between 110 and 200 °C) and hence can be processed like normal thermoplastics. The dispersion of the clay nanofiller was achieved by its one day swelling in the alcohol and a brief successive stirring. This procedure is very successful and leads to a partial exfoliation of the clay (documented by X-ray diffraction and TEM). The best nanocomposites with very good tensile properties, particularly with significantly increased moduli were obtained using the bentonite nanofiller. The study shows that the nanofiller interacts strongly with the hard domains and influences their melting temperature (DMTA and DSC), but it does not affect the glass transition temperature of soft domains. While Cloisite 15A was found to interact preferentially with the hard domains, the organic modified bentonite shows a strong interaction with both soft and hard segments, behaving as a blending agent. Hard domains in neat matrices, formed by hydrogen bonding of hard segments, were practically invisible by X-ray or TEM, but were successfully detected by AFM. Besides excellent mechanical properties, the prepared elastomers and their nanocomposites showed an interesting phase behavior (which was studied by combining DMTA and modulated DSC).     

Clay‐supported 2‐phenyl‐1H‐imidazole derivatives for heterogeneous catalysis of Henry reaction

Six derivatives ( 1 , 2 , 3 , 4 , 5 , 6 ) of 2‐phenyl‐1H‐imidazole were tested as catalysts of Henry reaction. Three new ( 4 , 5 , 6 ) 2‐phenyl‐1H‐imidazole derivatives, differently substituted (thio)ureas, were synthesized and determined by ¹H NMR and IR spectroscopy and elemental analysis. Two types of catalysis, homogeneous and heterogeneous, were examined and compared. Clay minerals Ca‐MMT and Cu‐MMT were used as solid supports for heterogeneous catalysis. The best results were obtained using compound 2 under conditions of heterogeneous method D from the point of view of yield and reaction time. J. Heterocyclic Chem., (2011)     

Relativistic effects in low-lying electronic states of iron

Excited electronic states of Fe I have been calculated using the MRCI Douglas?CKroll?CHess method. Average spin-free excitation energies of the eight lowest even electronic terms ( $\hbox{a}^5\hbox{D}, \hbox{a}^5\hbox{F}, \hbox{a}^3\hbox{F}, \hbox{a}^5\hbox{P}, \hbox{a}^3\hbox{P2}, \hbox{a}^3\hbox{H}, \hbox{b}^3\hbox{F2}, \hbox{and a}^3\hbox{G}$ ) are reported. The RASSI method was employed for calculation of individual J levels of the four lowest terms. All reported values are in good agreement with experiment. Our study pointed out significant relativistic effects even in relatively light element like iron.     

Application of colloidal palladium nanoparticles for labeling in electron microscopy

The application of palladium nanoparticles as electron-dense markers for labeling in both transmission and scanning electron microscopy requires their conjugation to a specific protein. The conjugation protocol described here includes the dihydrolipoic acid (DHLA) capping of Pd nanoparticles (8 nm equivalent diameter) and their subsequent covalent attachment to functional protein molecules such as streptavidin, protein A, or avidin. The single-step reaction was mediated using the cross-linking agent ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC). The final Pd conjugates were fully functional, as demonstrated by labeling of ultrathin resin sections of either bovine serum albumin or secretory granules of the salivary gland isolated from the partially fed female Ixodes ricinus tick. The results of bovine serum labeling were quantified, statistically evaluated, and compared with results obtained using commercially available gold particle conjugates (10 nm diameter). The highest values of labeling density were achieved using both streptavidin-Pd (106 ± 7 particles/μm2) and protein A-Au conjugates (130 ± 18 particles/μm2) compared to a commercial streptavidin-Au (66 ± 16 particles/μm2) and protein A-Pd conjugates (70 ± 11 particles/μm2). The concentrations of both DHLA and EDC, pH during conjugation, and finally thorough washing away of unbound proteins crucially influenced conjugation.     

Wavelength-modulated femtosecond stimulated Raman spectroscopy-approach towards automatic data processing

A new wavelength modulator based on a custom-made chopper blade and a slit placed in the Fourier plane of a pulse shaper was used to detect explicitly the first derivative of the time-resolved femtosecond stimulated Raman spectroscopy (FSRS) signals. This approach resulted in an unprecedented reduction of the non-coherent background that results from population transfer by the Raman pump inherent to FSRS experiments. The method of Fourier peak filtering was implemented as a powerful tool for reducing both the remaining non-coherent and coherent background associated with FSRS experiments. The method was demonstrated on β-carotene and a similar synthetic aryl carotenoid. The experiments confirm earlier FSRS results on β-carotene but suggest some reinterpretation. Strong bleaching signals of ground state vibrations were observed and interpreted as an inseparable part of the time-resolved FSRS experiment. New long-lived Raman features were observed in β-carotene and the synthetic aryl carotenoid and assigned to a combination of conformational changes and solvent rearrangement. More complex wavelength modulation methods are proposed in the development of more robust FSRS experiments.     

Extended viologen as a source of electric oscillations

A long organic molecule 1 with five bipyridinium functions separated by benzene rings (extended viologen) undergoes a reversible multi-step electron transfer. Here we show that this decacation accepts electrons at the heterogeneous interface with the occurrence of the periodically changing electric reduction currents. According to the applied bias voltage the observed current-time dependence changes from chaotic through periodic and irregular to sinusoidal and finally to monotonous. A careful choice of the controlling parameters yields the sustained periodic sinusoidal currents lasting for a prolonged time. Oscillations stem from a mutual interplay of the heterogeneous supply of electrons and the homogeneous redox reactions (disproportionation) between the transient redox forms. In difference to many other electrochemical oscillating systems the described oscillations do not require any additional external impedance. The principle of these oscillatory currents may serve as a model of a truly 'molecular oscillator'.     

Preconditioning trace coupled 3d‐1d systems using fractional Laplacian

Multiscale or multiphysics problems often involve coupling of partial differential equations posed on domains of different dimensionality. In this work, we consider a simplified model problem of a 3d‐1d coupling and the main objective is to construct algorithms that may utilize standard multilevel algorithms for the 3d domain, which has the dominating computational complexity. Preconditioning for a system of two elliptic problems posed, respectively, in a three‐dimensional domain and an embedded one dimensional curve and coupled by the trace constraint is discussed. Investigating numerically the properties of the well‐defined discrete trace operator, it is found that negative fractional Sobolev norms are suitable preconditioners for the Schur complement of the system. The norms are employed to construct a robust block diagonal preconditioner for the coupled problem.