Photophysics of a Ruthenium 4H‐Imidazole Panchromatic Dye in Interaction with Titanium Dioxide

The photophysics of bis(4,4′‐di‐tert‐butyl‐2,2′‐bipyridine‐κ²N,N′)[2‐(4‐carboxyphenyl)‐4,5‐bis(p‐tolylimino‐κN)imidazolato]ruthenium(II) hexafluorophosphate is investigated, both in solution and attached to a nanocrystalline TiO₂ film. The studied substitution pattern of the 4H‐imidazole ligand is observed to block a photoinduced structural reorganization pathway within the 4H‐imidazole ligand that has been previously investigated. Protonation at the 4H‐imidazole ring decreases the excited‐state lifetime in solution. When the unprotonated dye is anchored to TiO₂, photoinduced electron injection occurs from thermally nonrelaxed triplet metal‐to‐ligand charge transfer (³MLCT) states with a characteristic time constant of 0.5 ps and an injection efficiency of roughly 25 %. Electron injection from the subsequently populated thermalized ³MLCT state of the dye does not take place. The energy of this state seems to be lower than the conduction band edge of TiO₂.     

Sol‐to‐Gel Transition in Fast Evaporating Systems Observed by in Situ Time‐Resolved Infrared Spectroscopy

The in situ observation of a sol‐to‐gel transition in fast evaporating systems is a challenging task and the lack of a suitable experimental design, which includes the chemistry and the analytical method, has limited the observations. We synthesise an acidic sol, employing only tetraethylorthosilicate, SiCl₄ as catalyst and deuterated water; the absence of water added to the sol allows us to follow the absorption from the external environment and the evaporation of deuterated water. The time‐resolved data, obtained by attenuated total reflection infrared spectroscopy on an evaporating droplet, enables us to identify four different stages during evaporation. They are linked to specific hydrolysis and condensation rates that affect the uptake of water from external environment. The second stage is characterized by a decrease in hydroxyl content, a fast rise of condensation rate and an almost stationary absorption of water. This stage has been associated with the sol‐to‐gel transition.     

Multi‐constituent determination and fingerprint analysis of Scutellaria indica L. using ultra high performance liquid chromatography coupled with quadrupole time‐of‐flight mass spectrometry

An ultra‐performance liquid chromatography coupled with quadrupole time‐of‐flight mass spectrometry method integrating multi‐constituent determination and fingerprint analysis has been established for quality assessment and control of Scutellaria indica L. The optimized method possesses the advantages of speediness, efficiency, and allows multi‐constituents determination and fingerprint analysis in one chromatographic run within 11 min. 36 compounds were detected, and 23 of them were unequivocally identified or tentatively assigned. The established fingerprint method was applied to the analysis of ten S. indica samples from different geographic locations. The quality assessment was achieved by using principal component analysis. The proposed method is useful and reliable for the characterization of multi‐constituents in a complex chemical system and the overall quality assessment of S. indica.     

Pseudo‐differential operators in a Gelfand–Shilov setting

We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand–Shilov spaces. Moreover, we deduce composition and certain invariance properties of these classes.     

Interlacing of Hurwitz series

In this paper, we introduce the notion of interlacing of Hurwitz series. We begin by reviewing some important properties of the ring of Hurwitz series over a commutative ring A of arbitrary characteristic, and we introduce and investigate properties of the maps exp and log. We show that solutions of linear homogeneous differential equations with constant coefficients from the ring A can be described simply as interlacings of solutions of a first order system of differential equations. We give several examples to illustrate this result, and we conclude by defining and investigating properties of trigonometric functions using interlacings of Hurwitz series.     

On maximal subalgebras and a generalized Jordan–Hölder theorem for Lie algebras

The purpose of this paper is to continue the study of chief factors of a Lie algebra and to prove a further strengthening of the Jordan–Hölder theorem for chief series.     

Relationships between the canonical ascending and descending central series of ideals of an associative algebra

We consider the canonical descending and ascending central series of ideals of an associative algebra. In particular, we prove that some ideal in the descending central series is finite-dimensional if and only if some ideal in the ascending central series is finite-codimensional. This result is the associative algebra analogue of results due to Reinhold Baer and Philip Hall in group theory and Ian Stewart in Lie algebra. We also prove various related results.     

On primeness of general skew inverse Laurent series ring

Ever since the introduction, skew inverse Laurent series rings have kept growing in importance, as researchers characterized their properties (such as Noetherianness, Armendarizness, McCoyness, etc.) in terms of intrinsic properties of the base ring and studied their relations with other fields of mathematics, as for example quantum mechanics theory. The goal of our paper is to study the primeness and semiprimeness of general skew inverse Laurent series rings R((x^?1;σ,δ)), where R is an associative ring equipped with an automorphism σ and a σ-derivation δ.     

Lowest priority waiting time distribution in an accumulating priority Lévy queue

We derive the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive Lévy input. The priority of an infinitesimal customer (particle) is a function of their class and waiting time in the system, and the particles with the highest AP are the next to be processed. To this end we introduce a new method that relies on the construction of a workload overtaking process and solving a first-passage problem using an appropriate stopping time.     

On the distribution of cumulative Parisian ruin

We introduce the concept of cumulative Parisian ruin, which is based on the time spent in the red by the underlying surplus process. Our main result is an explicit representation for the distribution of the occupation time, over a finite-time horizon, for a compound Poisson process with drift and exponential claims. The Brownian ruin model is also studied in details. Finally, we analyse for a general framework the relationships between cumulative Parisian ruin and classical ruin, as well as with Parisian ruin based on exponential implementation delays.