Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA × DSA cross-correlation

Paramagnetic metal ions with fast-relaxing electronic spin and anisotropic susceptibility tensor provide a rich source of structural information that can be derived from pseudo-contact shifts, residual dipolar couplings, dipole-dipole Curie spin cross-correlation, and paramagnetic relaxation enhancements. The present study draws attention to a cross-correlation effect between nuclear relaxation due to anisotropic chemical shielding (CSA) and due to the anisotropic dipolar shielding (DSA) caused by the electronic Curie spin. This CSA x DSA cross-correlation contribution seems to have been overlooked in previous interpretations of paramagnetic relaxation enhancements. It is shown to be sufficiently large to compromise the 1/r6 distance dependence usually assumed. The effect cannot experimentally be separated from auto-correlated DSA relaxation. It can increase or decrease the observed paramagnetic relaxation enhancement. Under certain conditions, the effect can dominate the entire paramagnetic relaxation, resulting in nuclear resonances narrower than in the absence of the paramagnetic center. CSAxDSA cross-correlation becomes important when paramagnetic relaxation is predominantly due to the Curie rather than the Solomon mechanism. Therefore the effect is most pronounced for relaxation by metal ions with large magnetic susceptibility and fast-relaxing electron spin. It most strongly affects paramagnetic enhancements of transverse relaxation in macromolecules and of longitudinal relaxation in small molecules.     

Astrogeometry: Toward mathematical foundations

Inimage processing (e.g., inastronomy), the desired black-and-white image is, from the mathematical viewpoint, aset. Hence, to process images, we need to process sets. To define a generic set, we need infinitely many parameters; therefore, if we want to represent and process sets in the computer, we must restrict ourselves to finite-parameter families of sets that will be used to approximate the desired sets. The wrong choice of a family can lead to longer computations and worse approximation. Hence, it is desirable to find the family that it isthe best in some reasonable sense. In this paper, we show how the problems of choosing the optimal family of sets can be formalized and solved. As a result of the described general methodology, forastronomical images, we get exactly the geometric shapes that have been empirically used by astronomers and astrophysicists; thus, we have atheoretical explanation for these shapes.     

Balance constraints reduction of large-scale linear programming problems

This paper describes a method and the corresponding algorithms for simplification of large-scale linear programming models. It consists of the elimination of the balance constraints (i.e. constraints with zero RHS term). The idea is to apply some linear transformations to the original problem in order to nullify the balance constraints. These transformations are able to simultaneously eliminate more balance rows. The core of this contribution is the introduction of the reduction matrix and the associated theorems on the equivalent linear programs (original and reduced). The numerical experiments with this method of simplification proved this approach to be beneficial for a large class of LP problems.This research work was done while the first author was at Duisburg University, Mess-, Steuer und Regelungstechnik, Germany, under the greatly appreciated financial assistance given by the Alexander-von-Humboldt Foundation.     

Rank, term rank, and chromatic number

Let G be a graph with a nonempty edge set, and with rank rk(G), term rank Rk(G), and chromatic number χ(G). We characterize Rk(G) as being the maximum number of colors in certain proper colorings of G. In particular, we observe that χ(G)Rk(G), with equality holding if and only if (besides isolated vertices) G is either complete or a star. For a twin-free graph G, we observe the bound and we show that this bound is sharp.     

A common generalization for MV-algebras and Łukasiewicz–Moisil algebras

We introduce the notion of n-nuanced MV-algebra by performing a Łukasiewicz–Moisil nuancing construction on top of MV-algebras. These structures extend both MV-algebras and Łukasiewicz–Moisil algebras, thus unifying two important types of structures in the algebra of logic. On a logical level, n-nuanced MV-algebras amalgamate two distinct approaches to many valuedness: that of the infinitely valued Łukasiewicz logic, more related in spirit to the fuzzy approach, and that of Moisil n-nuanced logic, which is more concerned with nuances of truth rather than truth degree. We study n-nuanced MV-algebras mainly from the algebraic and categorical points of view, and also consider some basic model-theoretic aspects. The relationship with a suitable notion of n-nuanced ordered group via an extension of the Γ construction is also analyzed.     

Singlet versus triplet dynamics of β-carotene studied by quantum control spectroscopy

Biomolecules very often present complex energy deactivation networks with overlapping electronic absorption bands, making their study a difficult task. This can be especially true in transient absorption spectroscopy when signals from bleach, excited state absorption and stimulated emission contribute to the signal. However, quantum control spectroscopy can be used to discriminate specific electronic states of interest by applying specifically designed laser pulses. Recently, we have shown the control of energy flow in bacterial light-harvesting using shaped pump pulses in the visible and the selective population of pathways in carotenoids using an additional depletion pulse in the transient absorption technique. Here, we apply a closed-loop optimization approach to β-carotene using a spatial light modulator to decipher the energy flow network after a multiphoton excitation with a shaped ultrashort pulse in the near-IR. After excitation, two overlapping bands were detected and identified as the S₁ state and the first triplet state T₁. Using the transient absorption signal at a specific probe delay as feedback, the triplet signal could be optimized over the singlet contribution.     

Bubble point pressure estimates from Gibbs ensemble simulations

Bubble pressure points of ethanol–1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea refrigerant) mixtures from the third Industrial Fluid Properties Simulation Challenge are computed using publicly available molecular simulation software. Several published force fields are compared against the known answers provided in the contest guidelines and the best force fields are used to make predictions for the unknown results.     

Synthese und Eigenschaften von Sr3Mo1.5Zn0.5O7‐δ, einer Phase mit perowskitverwandter Schichtstruktur

Synthesis and Properties of the Layered Perovskite Phase Sr₃Mo_1.5Zn_0.5O_7‐δ The new layered perovskite phase Sr₃Mo_1.5Zn_0.5O_7‐δ was synthesized by solid state reaction using a Zn/ZnO oxygen buffer. The crystal structure was refined from X‐ray powder pattern by the Rietveld method. The compound crystallizes tetragonal in the space group I4/mmm (no. 139) with the lattice parameters a = 3.9631(3) Å, c = 20.583(1) Å. An oxygen deficiency corresponding to δ ≈ 0.25 was determinated, indicating the presence of molybdenum in mixed valence (Mo⁴⁺ and Mo⁶⁺).     

Resonance multiplicities in a hadron transport approach

In this article we focus on the multiplicities of resonances, ratios of resonant over non-resonant states and rescattering processes in heavy ion collisions. Therefore we utilize a hadron transport model (UrQMD v1.3). We find that rescattering of decay particles is of great importance when studying resonances in a hadronic medium.