The Existence of Zeros of Multivalued Functionals,Coincidence Points,and Fixed Points in $$f$$ -Quasimetric Spaces

Mathematical Notes - The notion of a $$\lambda$$ -generalized-search multivalued functional on an $$f$$ -quasimetric space is introduced. An existence theorem for zeros of such functionals is...     

Operator Interpolation and Systems of Linear Equations and Inequalities in Euclidean Spaces

Ukrainian Mathematical Journal - We establish new criteria of compatibility for a linear system of equations (equivalent to the Kronecker–Capelli theorem) or inequalities (equivalent to the...     

Restricted testing conditions for the multilinear maximal operator

Restricted testing conditions were considered recently. For the maximal operator, Hytönen, Li and Sawyer [8] first obtained parental testing condition. Later, they [9] showed that it suffices to restrict testing to doubling cubes. Chen and Lacey [3] gave a similar restricted testing condition. In our paper, we discuss a version of the latter in the multilinear setting.

     

Polycrystallinity in Gallium Arsenide Crystals Grown by the Czochralski Method

Crystallography Reports - The specific features of the formation of crystallites in gallium arsenide crystals grown by the Czochralski method have been investigated. The crystallites are found to...     

Sensitive CE-MS method for monitoring of riociguat and desmethylriociguat levels in human serum

Riociguat is novel antihypertensive drug for treatment of pulmonary hypertension. As such, it is still being tested in many clinical and pharmacokinetic trials. Existing methods that determine serum riociguat and desmethylriociguat (DMR) are based solely on liquid chromatography with mass spectrometry. Therefore, we present a novel capillary electrophoresis with mass spectrometry method (CE-MS) for their determination in human serum as alternative method for ongoing trials. Complete resolution of both analytes was achieved by means of pH optimization of ammonium formate background electrolytes that are fully compatible with ESI/MS detection. Simple liquid-liquid extraction was used as sample pretreatment. The calibration dependence of the method was linear (in the range of 10–1000 ng/mL), with adequate accuracy (90.1–114.9%) and precision (13.4%). LOD and LOQ were arbitrarily set at 10 ng/mL for both analytes. Clinical applicability was validated using serum samples from patients treated with riociguat in pharmacokinetic study and the results corresponded with reference HPLC-MS/MS values. Capillary electrophoresis proved to be sensitive and selective tool for the analysis of riociguat and DMR.     

Dynamics of Bacteriorhodopsin in the Dark-Adapted State from Solution Nuclear Magnetic Resonance Spectroscopy

To achieve efficient proton pumping in the light-driven proton pump bacteriorhodopsin (bR), the protein must be tightly coupled to the retinal to rapidly convert retinal isomerization into protein structural rearrangements. Methyl group dynamics of bR embedded in lipid nanodiscs were determined in the dark-adapted state, and were found to be mostly well ordered at the cytosolic side. Methyl groups in the M145A mutant of bR, which displays only 10 % residual proton pumping activity, are less well ordered, suggesting a link between side-chain dynamics on the cytosolic side of the bR cavity and proton pumping activity. In addition, slow conformational exchange, attributed to low frequency motions of aromatic rings, was indirectly observed for residues on the extracellular side of the bR cavity. This may be related to reorganization of the water network. These observations provide a detailed picture of previously undescribed equilibrium dynamics on different time scales for ground-state bR.     

The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.     

Formation of Finely Dispersed Structures in Alloys of Aluminum with Cobalt and Zirconium

Russian Journal of Physical Chemistry A - Rapidly quenched alloys of aluminum with cobalt and zirconium are investigated using a combination of means of physicochemical analysis to study the...