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For a bounded real-valued function V on R , we consider two Schrodinger operators [Please download the PDF to view the mathematical expression] and [Please download the PDF to view the mathematical expression]. We prove that if the negative spectra [H.sub.+] and H-are discrete and the negative eigenvalues of [H.sub.+] and H- tend to zero sufficiently fast, then the absolutely continuous spectra cover the positive half-line [0, oo). Bibliography: 7 titles. Illustrations: 1 figure. Dedicated to the 85th birthday of Vladimir Maz'ya, 1 The Main Results Being discrete and being continuous are two opposite properties of a set in the plane. However, there are situations in which the fact that one part [...]

In the article, the joint analysis of the Bernoulli equations for compressible gas, variations of the supersonic flow parameters of the Prandtl-Meyer expansion fan and the hypothesis of aerofoil dynamic curvature were used to develop linear and nonlinear mathematical models describing the occurrence of transonic flutter of aerodynamic control surfaces of supersonic aircraft. The analysis of the obtained mathematical models confirms a theoretical possibility of the occurrence of transonic flutter of aerodynamic control surfaces of supersonic aircraft which is due to the peculiarities of the interaction of shock waves with the angular velocity of elastic bending oscillations of aerodynamic control surfaces. [ABSTRACT FROM AUTHOR]

Due to their long lifespan, trees and bushes develop higher order of branches in a perennial manner. In contrast to a tall tree, with a clearly defined main stem and branching order, a bush is shorter and has a less apparent main stem and branching pattern. To address the developmental basis of these two forms, we studied several naturally occurring architectural variants in silver birch ( Betula pendula ). Using a candidate gene approach, we identified a bushy kanttarelli variant with a loss-of-function mutation in the BpMAX1 gene required for strigolactone (SL) biosynthesis. While kanttarelli is shorter than the wild type (WT), it has the same number of primary branches, whereas the number of secondary branches is increased, contributing to its bush-like phenotype. To confirm that the identified mutation was responsible for the phenotype, we phenocopied kanttarelli in transgenic BpMAX1::RNAi birch lines. SL profiling confirmed that both kanttarelli and the transgenic lines produced very limited amounts of SL. Interestingly, the auxin (IAA) distribution along the main stem differed between WT and BpMAX1::RNAi . In the WT, the auxin concentration formed a gradient, being higher in the uppermost internodes and decreasing toward the basal part of the stem, whereas in the transgenic line, this gradient was not observed. Through modeling, we showed that the different IAA distribution patterns may result from the difference in the number of higher-order branches and plant height. Future studies will determine whether the IAA gradient itself regulates aspects of plant architecture., Competing Interests: Competing interests statement:The authors declare no competing interest.

A stop codon within the mRNA facilitates coordinated termination of protein synthesis, releasing the nascent polypeptide from the ribosome. This essential step in gene expression is impeded with transcripts lacking a stop codon, generating nonstop ribosome complexes. Here, we use deep sequencing to investigate sources of nonstop mRNAs generated from the human mitochondrial genome. We identify diverse types of nonstop mRNAs on mitochondrial ribosomes that are resistant to translation termination by canonical release factors. Failure to resolve these aberrations by the mitochondrial release factor in rescue (MTRFR) imparts a negative regulatory effect on protein synthesis that is associated with human disease. Our findings reveal a source of underlying noise in mitochondrial gene expression and the importance of responsive ribosome quality control mechanisms for cell fitness and human health.