Spectralizable Operators

We introduce the notion of spectralizable operators. A closed operator A in a Hilbert space is called spectralizable if there exists a non-constant polynomial p such that the operator p(A) is a scalar spectral operator in the sense of Dunford. We show that such operators belongs to the class of generalized spectral operators and give some examples where spectralizable operators occur naturally. Vladimir Strauss gratefully acknowledges support by DFG, Grant No. TR 903/3-1.     

ESR‐Vis/NIR Spectroelectrochemical Study of C70(CF3)2−. and C70(C2F5)2−. Radical Anions

A spectroelectrochemical study of the two isostructural asymmetric perfluoroalkyl derivatives C₁‐7,24‐C₇₀(CF₃)₂ and C₁‐7,24‐C₇₀(C₂F₅)₂ is presented. Reversible formation of their stable monoanion radicals is monitored by cyclic voltammetry and by in situ ESR‐Vis‐NIR spectroelectrochemistry. The ESR spectrum of the C₇₀(CF₃)₂^?. radical is a 1:3:3:1 quartet with a ¹⁹F hyperfine coupling constant (a(F)) of 0.323(4) G, demonstrating that the unpaired spin is coupled to only one of the two CF₃ groups. The ¹³C satellites are assigned to specific carbon atoms. The ESR spectrum of the C₇₀(C₂F₅)₂^?. radical is an apparent octet with an apparent a(F) value of 0.83(2) G. DFT calculations suggest that this pattern is due to the superposition of spectra for four nearly isoenergetic C₇₀(C₂F₅)₂^?. conformers. Time‐dependent DFT calculations suggest that the NIR band at 1090 nm exhibited by both C₇₀(R_f)₂^?. radical anions is assigned to the SOMO→LUMO+3 transition. The analogous NIR band exhibited by the closed‐shell C₇₀(CF₃)₂^2? dianion was blue‐shifted to 1000 nm.     

Some new results in multiplicative and additive Ramsey theory

There are several notions of largeness that make sense in any semigroup, and others such as the various kinds of density that make sense in sufficiently well-behaved semigroups including and . It was recently shown that sets in which are multiplicatively large must contain arbitrarily large geoarithmetic progressions, that is, sets of the form , as well as sets of the form . Consequently, given a finite partition of , one cell must contain such configurations. In the partition case we show that we can get substantially stronger conclusions. We establish some combined additive and multiplicative Ramsey theoretic consequences of known algebraic results in the semigroups and , derive some new algebraic results, and derive consequences of them involving geoarithmetic progressions. For example, we show that given any finite partition of there must be, for each , sets of the form together with , the arithmetic progression , and the geometric progression in one cell of the partition. More generally, we show that, if is a commutative semigroup and a partition regular family of finite subsets of , then for any finite partition of and any , there exist and such that is contained in a cell of the partition. Also, we show that for certain partition regular families and of subsets of , given any finite partition of some cell contains structures of the form for some .

     

Analysis of size-classified fine and ultrafine particulate matter on substrates with laser-induced breakdown spectroscopy

Airborne particulate matter in the fine (0.1 µm–2.5 µm) and ultrafine (≤ 0.1 µm) size range is supposed to affect human health significantly. Smaller particles intrude more deeply into the lungs, so that an organism directly absorbs toxic compounds. Therefore, knowledge of the size-dependent composition of airborne particles is required to determine their health hazard. In this paper, we demonstrate the application of laser-induced breakdown spectroscopy to directly analyze size-classified particulate matter samples without any sample preparation. Samples analyzed are collected on filter substrates using a cascade impactor. Greased aluminum foils are used as filter substrate. To reduce ablation of the substrate material, low pulse energies of 0.6 mJ are used for plasma excitation. The plasma light is observed using an Echelle spectrometer. The effect of ambient gas and pressure on the line intensities is studied. Calibration samples for 14 elements relevant for human health were produced, and the system was calibrated for concentration ranges up to four orders of magnitude. Finally, the collected samples of particulate originating from steel-making processes were analyzed. The measurements show that the composition of these particles depends strongly on their size. For example, the elements lead, cadmium and copper are enriched within particles of about 200 nm diameter.     

High-Entropy Lithium Argyrodite Solid Electrolytes Enabling Stable All-Solid-State Batteries

Superionic solid electrolytes (SEs) are essential for bulk-type solid-state battery (SSB) applications. Multicomponent SEs are recently attracting attention for their favorable charge-transport properties, however a thorough understanding of how configurational entropy (ΔS_conf) affects ionic conductivity is lacking. Here, we successfully synthesized a series of halogen-rich lithium argyrodites with the general formula Li_5.5PS_4.5Cl_xBr_1.5-x (0≤x≤1.5). Using neutron powder diffraction and ³¹P magic-angle spinning nuclear magnetic resonance spectroscopy, the S²⁻/Cl⁻/Br⁻ occupancy on the anion sublattice was quantitatively analyzed. We show that disorder positively affects Li-ion dynamics, leading to a room-temperature ionic conductivity of 22.7 mS cm⁻¹ (9.6 mS cm⁻¹ in cold-pressed state) for Li_5.5PS_4.5Cl_0.8Br_0.7 (ΔS_conf=1.98R). To the best of our knowledge, this is the first experimental evidence that configurational entropy of the anion sublattice correlates with ion mobility. Our results indicate the possibility of improving ionic conductivity in ceramic ion conductors by tailoring the degree of compositional complexity. Moreover, the Li_5.5PS_4.5Cl_0.8Br_0.7 SE allowed for stable cycling of single-crystal LiNi_0.9Co_0.06Mn_0.04O₂ (s-NCM90) composite cathodes in SSB cells, emphasizing that dual-substituted lithium argyrodites hold great promise in enabling high-performance electrochemical energy storage.     

Electronic structure of CO--an exercise in modern chemical bonding theory

This paper discusses recent progress that has been made in the understanding of the electronic structure and bonding situation of carbon monoxide which was analyzed using modern quantum chemical methods. The new results are compared with standard models of chemical bonding. The electronic charge distribution and the dipole moment, the nature of the HOMO and the bond dissociation energy are discussed in detail.     

Study of latent and etched tracks by a charged particle transmission technique

A recently suggested technique for non-destructive investigation of inhomogeneities in thin objects, which is based on the measurement of the energy spectra of charged particles transmitted through the object, is used for the study of thermal annealing of 10–20 μm thick polyethylene terephtalate, polypropylene and polycarbonate foils irradiated with 1–10 MeV/amu heavy ions. At elevated temperature a foil linear contraction is observed on pristine and irradiated material. Also the foil roughness increases with increasing temperature. On the same foils with etched pores 0.5–1.0 μm in diameter, the thermal annealing results in gradual closing of the pores up to about 30% of their initial diameter at the temperatures of 150–175°C. At higher temperatures the pore diameter increases and achieves its initial value.     

Simultaneously Definitizable and Spectralizable Operators in Krein Space

We study the spectral properties of a self–adjoint operator in Krein space such that one of its natural powers is J–non–negative and some other power is a spectral operator in the Dunford sense.