Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities.

For a family of self-adjoint Dirac operators subject to generalized MIT bag boundary conditions on domains in , it is shown that the nonrelativistic limit in the norm resolvent sense is the Dirichlet Laplacian. This allows to transfer spectral geometry results for Dirichlet Laplacians to Dirac operators for large .

Scoping review and evidence mapping of interventions aimed at improving reproducible and replicable science: Protocol.

Background: Many interventions, especially those linked to open science, have been proposed to improve reproducibility in science. To what extent these propositions are based on scientific evidence from empirical evaluations is not clear.

Aims: The primary objective is to identify Open Science interventions that have been formally investigated regarding their influence on reproducibility and replicability.

Homo and heteromultimetallic complexes containing a group 8 transition metal and μ-diphosphine bridging ligands involved in anticancer research: A review.

Herein, we present a comprehensive review focusing on synthetic strategies, detailed structural analysis, and anticancer activity investigations of complexes following the general formula [LM(μ-diphosphine)M'L] where M = group 8 metal; M' = any transition metal; μ-diphosphine = bridging ligand; L and L = ligand spheres). Both homo- and heteromultimetallic complexes will be discussed in detail. We review in vitro, in vivo and in silico anticancer activity investigations, in an attempt to draw comparisons between the various complexes and derive structure-activity relationships (SAR).

Diastereoselective Dearomatizing Cyclizations of 5-Arylpentan-2-ones by Samarium Diiodide - A Computational Analysis.

This study analyzes the samarium diiodide-promoted cyclizations of 5-arylpentan-2-ones to dearomatized bicyclic products utilizing density functional theory. The reaction involves a single electron transfer to the carbonyl group, which occurs synchronously with the rate determining cyclization event, and a second subsequent proton-coupled electron transfer. These redox reactions are accurately computed employing small core pseudo potentials explicitly involving all f-electrons of samarium.

On the Single Layer Boundary Integral Operator for the Dirac Equation.

This paper is devoted to the analysis of the single layer boundary integral operator for the Dirac equation in the two- and three-dimensional situation. The map is the strongly singular integral operator having the integral kernel of the resolvent of the free Dirac operator and belongs to the resolvent set of . In the case of smooth boundaries fine mapping properties and a decomposition of in a 'positive' and 'negative' part are analyzed.

Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations.

Let be a valuation ring of a global field . We show that for all positive integers and there exists an integer-valued polynomial on , that is, an element of , which has precisely essentially different factorizations into irreducible elements of whose lengths are exactly . In fact, we show more, namely that the same result holds true for every discrete valuation domain with finite residue field such that the quotient field of admits a valuation ring independent of whose maximal ideal is principal or whose residue field is finite.

Fabrication of Amorphous Silicon-Carbon Hybrid Films Using Single-Source Precursors.

The aim of this study was the preparation of different amorphous silicon-carbon hybrid thin-layer materials according to the liquid phase deposition (LPD) process using single-source precursors. In our study, 2-methyl-2-silyltrisilane (methylisotetrasilane; ), 1,1,1-trimethyl-2,2-disilyltrisilane (trimethylsilylisotetrasilane; ), 2-phenyl-2-silyltrisilane (phenylisotetrasilane; ), and 1,1,2,2,4,4,5,5-octamethyl-3,3,6,6-tetrasilylcyclohexasilane (cyclohexasilane; ) were utilized as precursor materials and compared with the parent compound 2,2-disilyltrisilane (neopentasilane; ). Compounds - were successfully oligomerized at λ = 365 nm with catalytic amounts of the neopentasilane oligomer ().

Selective synthesis of germasila-adamantanes through germanium-silicon shift processes.

The regioselective synthesis of germasila-adamantanes with the germanium atoms in the bridgehead positions is described starting from cyclic precursors by a cationic sila-Wagner-Meerwein (SWM) rearrangement reaction. The SWM rearrangement allows also a deliberate shift of germanium atoms from the periphery and within the cage structures into the bridgehead positions. This opens the possibility for a synthesis of germasila-adamantanes of defined germanium content and controlled regiochemistry.

Schrödinger Operators with Oblique Transmission Conditions in .

In this paper we study the spectrum of self-adjoint Schrödinger operators in with a new type of transmission conditions along a smooth closed curve . Although these transmission conditions are formally similar to -conditions on (instead of the normal derivative here the Wirtinger derivative is used) the spectral properties are significantly different: it turns out that for attractive interaction strengths the discrete spectrum is always unbounded from below. Besides this unexpected spectral effect we also identify the essential spectrum, and we prove a Krein-type resolvent formula and a Birman-Schwinger principle.

Magnetostructural Properties of Some Doubly-Bridged Phenoxido Copper(II) Complexes.

Three new tripod tetradentate phenolate-amines (, and ), together with seven more already related published ligands, were synthesized, and characterized. With these ligands, two new dinuclear doubly-bridged-phenoxido copper(II) complexes (, ), and six more complexes (, , -), a new trinuclear complex () with an alternative doubly-bridged-phenoxido and -methoxido, as well as the 1D polymer () were synthesized, and their molecular structures were characterized by spectroscopic methods and X-ray single crystal crystallography. The Cu(II) centers in these complexes exhibit distorted square-pyramidal arrangement in -, mixed square pyramidal and square planar in , , and , and distorted octahedral (5+1) arrangements in and .

[Digital futures of the university: Scenarios of sociotechnical change].

For the university, digital technologies proved to be a central element of crisis management during the COVID-19 pandemic. This is especially true for teaching. From a "multi-level perspective" (Geels 2004), the disruptive effects of the pandemic open a "window of opportunity" for profound and lasting sociotechnical change.

Dinuclear doubly bridged phenoxido copper(II) complexes as efficient anticancer agents.

Two cationic [Cu(L)](ClO) (1, 2), and four neutral doubly bridged-phenoxido-copper(II) complexes [Cu(L)] (3, 4) and [Cu(L)(HO)]‧2HO (5, 6) as well as 1D polymeric catena-[Cu(L)] (7), where HL and HL represent tripodal tetradentate pyridyl or aliphatic-amino groups based 2,4-disubstituted phenolates, were synthesized and thoroughly characterized by various spectroscopic methods and single crystal X-ray analysis. The molecular structures of the complexes exhibited diverse geometrical environments around the central Cu(II) atoms. The in vitro antiproliferative activity of the isolated complexes and selected parent free ligands were screened against some human cancer cell lines (A2780, A2780R, PC-3, 22Rv1, MCF-7).

Metallacyclosilanes of Calcium, Yttrium, and Iron.

Utilizing a choice of α,ω-oligosilanylene diides, it is possible to synthesize a number of heterocyclosilanes with heteroelements of calcium, yttrium, and iron by metathesis reactions with respective metal halides CaI, YCl, and FeBr. Si NMR spectroscopic analysis of the calcacyclosilanes suggests that these compounds retain a strong oligosilanylene dianion character, which is more pronounced than in the analogous magnesacyclosilanes. As the electronegativity of calcium lies between potassium and magnesium, silyl calcium reagents should be considered as building blocks with an attractive reactivity profile.

Dirac operator spectrum in tubes and layers with a zigzag-type boundary.

We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in and of tube or layer shapes with a zigzag-type boundary using the corresponding properties of the Dirichlet Laplacian.

Spectral Transition for Dirac Operators with Electrostatic -Shell Potentials Supported on the Straight Line.

In this note the two dimensional Dirac operator with an electrostatic -shell interaction of strength supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths the continuous spectrum of inside the spectral gap of the free Dirac operator collapses abruptly to a single point.

Microsensor in Microbioreactors: Full Bioprocess Characterization in a Novel Capillary-Wave Microbioreactor.

Microbioreactors (MBRs) with a volume below 1 mL are promising alternatives to established cultivation platforms such as shake flasks, lab-scale bioreactors and microtiter plates. Their main advantages are simple automatization and parallelization and the saving of expensive media components and test substances. These advantages are particularly pronounced in small-scale MBRs with a volume below 10 µL.

Insights into the Spin Dynamics of Mononuclear Cerium(III) Single-Molecule Magnets.

Four novel Ce mononuclear complexes of formulas [Ce(ntfa)(MeOH)] (), [Ce(ntfa)(5,5'-Mebipy)] (), [Ce(ntfa)(terpy)] (), and [Ce(ntfa)(bipy)] (), where ntfa = 4,4,4-trifluoro-1-(naphthalen-2-yl)butane-1,3-dionato, 5,5'-Mebipy = 5,5'-dimethyl-2,2'-dipyridyl, terpy = 2,2':6',2″-terpyridine, and bipy = 2,2'-bipyridine, have been synthesized and structurally characterized with Ce displaying coordination numbers of 8, 8, 9, and 10, respectively. Magnetic measurements indicate that all the complexes show a field-induced single-ion magnet behavior under a small applied dc field. The magnetic analysis shows the relevance of the different spin relaxation mechanisms in the magnetic relaxation of the Ce compounds, with special emphasis on the local-mode process.

A unified approach to Schrödinger evolution of superoscillations and supershifts.

Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time-dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of superoscillations during the evolution is the (more general) supershift property of the solution.

A Bayesian Approach to the Estimation of Parameters and Their Interdependencies in Environmental Modeling.

We present a case study for Bayesian analysis and proper representation of distributions and dependence among parameters when calibrating process-oriented environmental models. A simple water quality model for the Elbe River (Germany) is referred to as an example, but the approach is applicable to a wide range of environmental models with time-series output. Model parameters are estimated by Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling.

Silole allylic anions instead of silanides.

Reaction of a 3,4-diphenylsilole with two neopentasilanyl groups attached to the 2- and 5-positions with one equivalent of KOBu did not result in the expected silanide formation but yielded a silole allylic anion instead. The initially formed silanide added to a neighboring phenyl group, which then transfers a proton to the 2-position of the silole ring.

Improved approximate rips filtrations with shifted integer lattices and cubical complexes.

Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes is expensive because of a combinatorial explosion in the complex size. For points in , we present a scheme to construct a 2-approximation of the filtration of the Rips complex in the -norm, which extends to a -approximation in the Euclidean case.

Electronic spectra of ytterbium fluoride from relativistic electronic structure calculations.

We report an investigation of the low-lying excited states of the YbF molecule-a candidate molecule for experimental measurements of the electron electric dipole moment-with 2-component based multi-reference configuration interaction (MRCI), equation of motion coupled cluster (EOM-CCSD) and the extrapolated intermediate Hamiltonian Fock-space coupled cluster (XIHFS-CCSD). Specifically, we address the question of the nature of these low-lying states in terms of configurations containing filled or partially-filled Yb 4f shells. We show that while it does not appear possible to carry out calculations with both kinds of configurations contained in the same active space, reliable information can be extracted from different sectors of Fock space-that is, by performing electron attachment and detachment IHFS-CCSD and EOM-CCSD calculation on the closed-shell YbF and YbF species, respectively.

Electronic Properties of Tetraazaperopyrene Derivatives on Au(111): Energy-Level Alignment and Interfacial Band Formation.

N-heteropolycyclic aromatic compounds are promising organic electron-transporting semiconductors for applications in field-effect transistors. Here, we investigated the electronic properties of 1,3,8,10-tetraazaperopyrene derivatives adsorbed on Au(111) using a complementary experimental approach, namely, scanning tunneling spectroscopy and two-photon photoemission combined with state-of-the-art density functional theory. We find signatures of weak physisorption of the molecular layers, such as the absence of charge transfer, a nearly unperturbed surface state, and an intact herringbone reconstruction underneath the molecular layer.