Spin–orbit coupling in biradicals. 5. Zero-field splitting in triplet dimethylnitrenium,dimethylphosphenium and dimethylarsenium cations

The spin dipole–spin dipole and spin–orbit coupling contributions to the zero-field splitting parameters D and E of [CH₃–N–CH₃]⁺, [CH₃–P–CH₃]⁺, and [CH₃–As–CH₃]⁺ have been calculated from CASSCF(14,14)/cc-pVTZ wave functions and the Breit–Pauli Hamiltonian at T₁ B3LYP/cc-pVTZ optimized geometries. The spin–orbit coupling contributions represent a minor correction for the dimethylnitrenium cation, which has a triplet ground state. They dominate the spin–spin terms by an order of magnitude in the dimethylphosphenium cation and by more than two orders of magnitude in the dimethylarsenium cation, both of which have a singlet ground state. The properties of all these biradicaloids follow expectations based on the simple algebraic 2-in-2 model of biradical structure.     

A calculator‐based computational approach Part 3. The differentiation

This paper extends the themes on the computational approach discussed in Parts 1 and 2 to the differentiation of functions. One theme is that constructing diagrams for programs using a calculator helps students to visualize processes and thus acquire the concepts involved. The ability to construct diagrams for a given problem is identical to that of programming a calculator to solve the problem. However, in this case constructing the diagram for derivatives from the diagram of the function also represents the ability to teach a calculator how to perform formal differentiation. A second theme is that the approach promotes sequential or procedural thinking which is important in both programming and mathematics. A third theme is that the approach permits the generation of many subproblems, thereby encouraging one to pose questions rather than merely to solve those set by others. Consequently, it becomes clear that the approach has wider applications in the learning of mathematics.     

On a Relation Between Potentials for Pluriharmonic Maps and Para-Pluriharmonic Maps

In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between pluriharmonic maps and para-pluriharmonic maps. Moreover, we investigate the relation among CMC-surfaces by use of such maps.     

Direct synthesis of inverse hexagonally ordered diblock copolymer/polyoxometalate nanocomposite films

Nanostructured inverse hexagonal polyoxometalate composite films were cast directly from solution using poly(butadiene-block-2-(dimethylamino)ethyl methacrylate) (PB-b-PDMAEMA) diblock copolymers as structure directing agents for phosphomolybdic acid (H(3)[PMo(12)O(40)], H(3)PMo). H(3)PMo units are selectively incorporated into the PDMAEMA domains due to electrostatic interactions between protonated PDMAEMA and PMo(3-) anions. Long solvophilic PB chains stabilized the PDMAEMA/H(3)PMo aggregates in solution and reliably prevented macrophase separation. The choice of solvent is crucial. It appears that all three components, both blocks of the diblock copolymer as well as H(3)PMo, have to be soluble in the same solvent which turned out to be tetrahydrofuran, THF. Evaporation induced self-assembly resulted in highly ordered inverse hexagonal nanocomposite films as observed from transmission electron microscopy and small-angle X-ray scattering. This one-pot synthesis may represent a generally applicable strategy for integrating polyoxometalates into functional architectures and devices.     

Chemoenzymatic synthesis of O-mannosylpeptides in solution and on solid phase

O-mannosyl glycans are known to play an important role in regulating the function of α-dystroglycan (α-DG), as defective glycosylation is associated with various phenotypes of congenital muscular dystrophy. Despite the well-established biological significance of these glycans, questions regarding their precise molecular function remain unanswered. Further biological investigation will require synthetic methods for the generation of pure samples of homogeneous glycopeptides with diverse sequences. Here we describe the first total syntheses of glycopeptides containing the tetrasaccharide NeuNAcα2-3Galβ1-4GlcNAcβ1-2Manα, which is reported to be the most abundant O-mannosyl glycan on α-DG. Our approach is based on biomimetic stepwise assembly from the reducing end and also gives access to the naturally occurring mono-, di-, and trisaccharide substructures. In addition to the total synthesis, we have developed a "one-pot" enzymatic cascade leading to the rapid synthesis of the target tetrasaccharide. Finally, solid-phase synthesis of the desired glycopeptides directly on a gold microarray platform is described.     

Ultrafast dynamics of a spiropyran in water

The reversible switching of a water-soluble spiropyran compound is recorded over 1 ns by means of femtosecond vis-pump/vis- and IR-probe spectroscopy under aqueous conditions. Our investigations reveal that the photochemical conversion from the closed spiropyran to the open merocyanine takes 1.6 ps whereas the reversed photoreaction is accomplished within 25 ps. The combination of time-resolved and steady-state observations allows us to reveal central parts of the reaction pathway leading to either form. The enhanced water solubility, its fast and efficient switching behavior, and its stability against hydrolysis over a time range of several weeks make this compound an attractive and versatile tool for biological applications.     

Multicriteria approaches for ranking of efficient units in DEA models

Data envelopment analysis models usually split decision making units into two basic groups, efficient and inefficient. Efficiency score of inefficient units allows their ranking but efficient units cannot be ranked directly because of their maximum efficiency. That is why there are formulated several models for ranking of efficient units. The paper presents two original models for ranking of efficient units in data envelopment analysis—they are based on multiple criteria decision making techniques—goal programming and analytic hierarchy process. The first model uses goal programming methodology and minimizes either the sum of undesirable deviations or maximal undesirable deviation from the efficient frontier. The second approach is analytic hierarchy process model for ranking of efficient units. The two presented models are compared with several super-efficiency models and other approaches for ranking decision making units in DEA models including definitions based on distances from optimistic and pessimistic envelopes and cross efficiency evaluation models. The results of the analysis by all presented models are illustrated on a real data set—evaluation of 194 bank branches of one of the Czech commercial banks.     

Study of the thermal stability of Zerodur glass ceramics suitable for a scanning probe microscope frame

The work presents measurements of the length stability of Zerodur glass ceramic with temperature change. Measurement of this thermal characteristic is necessary for determination of the optimal temperature at which the Zerodur glass ceramic has a coefficient of thermal expansion close to zero. The principle of the measurement is to monitor the length changes using an optical resonator with a cavity mirror spacer made from the Zerodur material to be studied. The resonator is placed inside a vacuum chamber with a temperature control. A tunable laser diode is locked to a certain optical mode of the resonator to monitor the optical frequency of this mode. A beat-note signal from optical mixing between the laser and a stabilized femtosecond frequency comb is detected and processed. The temperature dependence of the glass ceramics was determined and analyzed. The resolution of the length measurement of the experimental set-up is on the order of 0.1 nm.