On the first birth and the last death in a generation in a multi-type Markov branching process

In a multi-type continuous time Markov branching process the asymptotic distribution of the first birth in and the last death (extinction) of the kth generation can be determined from the asymptotic behavior of the probability generating function of the vector Z(^k)(t), the size of the kth generation at time t, as t tends to zero or as t tends to infinity, respectively. Apart from an appropriate transformation of the time scale, for a large initial population the generations emerge according to an independent sum of compound multi-dimensional Poisson processes and become extinct like a vector of independent reversed Poisson processes. In the first birth case the results also hold for a multi-type Bellman-Harris process if the life span distributions are differentiable at zero.     

Aufeinanderfolgende Elemente in multiplikativen Zahlenmengen

LetM be a multiplicative set with 1M andmnM if and only ifmM,nM for (m,n)=1. It is shown by elementary means that there exists the asymptotic density of the setM(M–1) for every multiplicative setM. The density is positive if and only ifM possesses a positive density and 2M for some . This result is slightly generalized to sums over multiplicative functionsf with |f|1.     

Current Interruption at Powers up to 1 GW with Crossed-Field Tubes

This paper describes the current interruption and voltage holdoff capabilities of a wide range of crossed-field tubes (XFTs). The XFTs investigated have active electrode areas ranging from 96 to 8000 cm2 with mean diameters from 2 to 56 cm. For the larger XFTs, currents up to 10 kA have been interrupted at voltages up to 100 kV, corresponding to a switched power of 1 GW. Experiments have shown the peak interruptible current to vary linearly with tube radius. The mechanism responsible for the limitation may be related to the self-generated magnetic field, but other factors are also shown to play a role.     

On meson resonances and chiral symmetry

We study meson resonances with quantum numbers J^P=1⁺ in terms of the chiral SU(3) Lagrangian. At leading order a parameter-free prediction is obtained for the scattering of Goldstone bosons off vector mesons with J^P=1⁻ once we insist on approximate crossing symmetry of the unitarized scattering amplitude. A resonance spectrum arises that is remarkably close to the empirical pattern. In particular, we find that the strangeness-zero resonances h₁(1380), f₁(1285) and b₁(1235) are formed due to strong and channels. This leads to large coupling constants of those resonances to the latter states.     

Glycopeptides by Linch-Pin C−H Activations for Peptide-Carbohydrate Conjugation by Manganese(I)-Catalysis

Late-stage C−H glycosylations of structurally complex amino acids and peptides were accomplished by means of racemization-free manganese(I)-catalyzed C−H activation. Thus, glycosylative modifications proved to be viable by a linch-pin approach, featuring chemo- and site-selective C−H transformations. The peptide–saccharide conjugation provided modular access to structurally complex glycopeptides, likewise enabling the assembly of fluorescent-labelled glycopeptides.     

Directing-Group-Free C7-Alkylations of N-Alkylindoles Mediated by Cationic Zirconium Complexes: Role of Brønsted Acid for Catalytic Manifold

Highly position selective alkylations of N-alkylindoles at C7-positions have been enabled by cationic zirconium complexes. The strategy provides a straightforward access to install alkyl groups at C7-positions of indoles without a complex directing group. Mechanistic studies provided support for the importance of Brønsted acids in the catalytic manifold.     

Enantioselective C−H Activation with Earth‐Abundant 3d Transition Metals

Molecular syntheses largely rely on time‐ and labour‐intensive prefunctionalization strategies. In contrast, C?H activation represents an increasingly powerful approach that avoids lengthy syntheses of prefunctionalized substrates, with great potential for drug discovery, the pharmaceutical industry, material sciences, and crop protection, among others. The enantioselective functionalization of omnipresent C?H bonds has emerged as a transformative tool for the step‐ and atom‐economical generation of chiral molecular complexity. However, this rapidly growing research area remains dominated by noble transition metals, prominently featuring toxic palladium, iridium and rhodium catalysts. Indeed, despite significant achievements, the use of inexpensive and sustainable 3d metals in asymmetric C?H activations is still clearly in its infancy. Herein, we discuss the remarkable recent progress in enantioselective transformations via organometallic C?H activation by 3d base metals up to April 2019.