Über eine allgemeine Methode zur mathematischen Analyse empirischer Reihen

Ohne ZusammenfassungGerhard Kowalewski zum 60. Geburtstage am 27. März 1936 gewidmet     

Primordial <Superscript>4</Superscript>He Abundance Constrains the Possible Time Variation of the Higgs Vacuum Expectation Value

We constrain the possible time variation of the Higgs vacuum expectation value (v) by recent results on the primordial ⁴He abundance (Y _P ). For that, we use an analytic approach which enables us to take important issues into consideration, that have been ignored by previous works, like the v-dependence of the relevant cross sections of deuterium production and photodisintegration, including the full Klein–Nishina cross section. Furthermore, we take a non-equilibrium Ansatz for the freeze-out concentration of neutrons and protons and incorporate the latest results on the neutron decay. Finally, we approximate the key-parameters of the primordial ⁴He production (the mean lifetime of the free neutron and the binding energy of the deuteron) by terms of (where v ₀ denotes the present theoretical estimate). Eventually, we derive the relation and the most stringent limit on a possible time variation of v is given by: .     

Non‐thermal plasma‐induced apoptosis in yeast Saccharomyces cerevisiae

The effect of non‐thermal plasma generated by the direct current (DC) corona discharge in the mode of transition spark is studied on a yeast Saccharomyces cerevisiae. The exposure to plasma increases production of reactive oxygen species (ROS) in cells, possibly causing the induction of apoptosis. To clarify the mechanism of apoptosis, its induction is tested not only on a wild strain of S. cerevisiae, but also on mutant strains: A deletion mutant Δyca1 without yeast metacaspase proves that in S. cerevisiae the apoptosis occurs partly by the caspase‐independent pathway. A petite strains with mutation in the mitochondria do not show pronounced ROS formation, but in spite of this, apoptosis is detected. Hence, mitochondrial ROS probably do not play an important role in induction of apoptosis.     

Thiophenylazobenzene: An Alternative Photoisomerization Controlled by Lone-Pair⋅⋅⋅π Interaction

Azoheteroarene photoswitches have attracted attention due to their unique properties. We present the stationary photochromism and ultrafast photoisomerization mechanism of thiophenylazobenzene (TphAB). It demonstrates impressive fatigue resistance and photoisomerization efficiency, and shows favorably separated (E)- and (Z)-isomer absorption bands, allowing for highly selective photoconversion. The (Z)-isomer of TphAB adopts an unusual orthogonal geometry where the thiophenyl group is perfectly perpendicular to the phenyl group. This geometry is stabilized by a rare lone-pair⋅⋅⋅π interaction between the S atom and the phenyl group. The photoisomerization of TphAB occurs on the sub-ps to ps timescale and is governed by this interaction. Therefore, the adoption and disruption of the orthogonal geometry requires significant movement along the inversion reaction coordinates (CNN and NNC angles). Our results establish TphAB as an excellent photoswitch with versatile properties that expand the application possibilities of AB derivatives.     

Catalytically Active Hollow Fiber Membranes with Enzyme-Embedded Metal–Organic Framework Coating

Metal–organic frameworks (MOFs) are suitable enzyme immobilization matrices. Reported here is the in situ biomineralization of glucose oxidase (GOD) into MOF crystals (ZIF-8) by interfacial crystallization. This method is effective for the selective coating of porous polyethersulfone microfiltration hollow fibers on the shell side in a straightforward one-step process. MOF layers with a thickness of 8 μm were synthesized, and fluorescence microscopy and a colorimetric protein assay revealed the successful inclusion of GOD into the ZIF-8 layer with an enzyme concentration of 29±3 μg cm⁻². Enzymatic activity tests revealed that 50 % of the enzyme activity is preserved. Continuous enzymatic reactions, by the permeation of β-d -glucose through the GOD@ZIF-8 membranes, showed a 50 % increased activity compared to batch experiments, emphasizing the importance of the convective transport of educts and products to and from the enzymatic active centers.     

Direct Introduction of an Alkylsulfonamido Group on C-sites of Isomeric Dicarba-closo-dodecaboranes: The Influence of Stereochemistry on Inhibitory Activity against the Cancer-Associated Carbonic Anhydrase IX Isoenzyme

Carbonic anhydrase IX (CA IX), a tumor-associated metalloenzyme, represents a validated target for cancer therapy and diagnostics. Herein, we report the inhibition properties of isomeric families of sulfonamidopropyl-dicarba-closo-dodecaboranes group(s) prepared using a new direct five-step synthesis from the corresponding parent cages. The protocol offers a reliable solution for synthesis of singly and doubly substituted dicarba-closo-dodecaboranes with a different geometric position of carbon atoms. The closo-compounds from the ortho- and meta-series were then degraded to corresponding 11-vertex dicarba-nido-undecaborate(1−) anions. All compounds show in vitro enzymatic activity against CA IX in the low nanomolar or subnanomolar range. This is accompanied by clear isomer dependence of the inhibition constant (K_i) and selectivity towards CA IX. Decreasing trends in K_i and selectivity index (S_I) values are observed with increasing separation of the cage carbon atoms. Interactions of compounds with the active sites of CA IX were explored with X-ray crystallography, and eight high-resolution crystal structures uncovered the structural basis of inhibition potency and selectivity.     

Surfaces of prescribed mean curvature in a cone

We show existence of surfaces of prescribed mean curvature in central projection for such values of the mean curvature for which estimates for the corresponding Euler–Lagrange equations are generally not known. This is achieved by extending the variational problem to the space \({BV(\Omega)}\), where graphs in a cone must satisfy a side condition, and using variational methods. Moreover, we give an example of a solution in \({BV(\Omega)}\) which does not solve the Dirichlet problem for the Euler-Lagrange equation.