Maximization of the total population in a reaction–diffusion model with logistic growth

This paper is concerned with a nonlinear optimization problem that naturally arises in population biology. We consider the effect of spatial heterogeneity on the total population of a biological species at a steady state, using a reaction–diffusion logistic model. Our objective is to maximize the total population when resources are distributed in the habitat to control the intrinsic growth rate, but the total amount of resources is limited. It is shown that under some conditions, any local maximizer must be of “bang–bang” type, which gives a partial answer to the conjecture addressed by Ding et al. (Nonlinear Anal Real World Appl 11(2):688–704, 2010). To this purpose, we compute the first and second variations of the total population. When the growth rate is not of bang–bang type, it is shown in some cases that the first variation becomes nonzero and hence the resource distribution is not a local maximizer. When the first variation becomes zero, we prove that the second variation is positive. These results implies that the bang–bang property is essential for the maximization of total population.     

New synthetic routes to optically active alpha-quaternary alpha-aryl amino acid derivatives via the diastereoselective Stevens and Sommelet-Hauser rearrangements

The Stevens rearrangement of N-allylic alpha-aryl amino acid-derived ammonium salts and the Sommelet-Hauser rearrangement of N-benzylic alpha-alkyl amino acid-derived ammonium salts are shown to proceed with remarkably high levels of diastereoselectivity. The methods presented in this work provide new routes to optically active alpha-quaternary alpha-aryl amino acid derivatives.     

Dynamic Lone Pair Expression as Chemical Bonding Origin of Giant Phonon Anharmonicity in Thermoelectric InTe

Loosely bonded (“rattling”) atoms with s² lone pair electrons are usually associated with strong anharmonicity and unexpectedly low thermal conductivity, yet their detailed correlation remains largely unknown. Here we resolve this correlation in thermoelectric InTe by combining chemical bonding analysis, inelastic X-ray and neutron scattering, and first principles phonon calculations. We successfully probe soft low-lying transverse phonons dominated by large In¹⁺ z-axis motions, and their giant anharmonicity. We show that the highly anharmonic phonons arise from the dynamic lone pair expression with unstable occupied antibonding states induced by the covalency between delocalized In¹⁺ 5s² lone pair electrons and Te 5p states. This work pinpoints the microscopic origin of strong anharmonicity driven by rattling atoms with stereochemical lone pair activity, important for designing efficient materials for thermoelectric energy conversion.     

Double helical oligoresorcinols specifically recognize oligosaccharides via heteroduplex formation through noncovalent interactions in water

We report on the oligosaccharide recognition through noncovalent interactions in water based on a unique supramolecular homoduplex-to-heteroduplex transformation of the oligoresorcinol nonamer as a fully artificial receptor. The oligoresorcinol forms a double helix in water, which unravels and entwines upon complexation with specific oligosaccharides with a particular chain length and glucosidic linkage pattern, thus generating the heteroduplex with an excess one-handed helical conformation that can be readily monitored and further quantified by absorption, circular dichroism, and NMR spectroscopies.     

Structure of the monoclinic-form misfit-layer compound, (Ca0.85OH)2alpha CoO2 (alpha approximately 0.57822)

The incommensurate modulated crystal structure of the new misfit-layer calcium cobalt oxide (Ca0.85OH)2alphaCoO2 was investigated using a superspace-group formalism with synchrotron X-ray diffraction data. The compound is a kind of composite crystal that consists of two interpenetrating subsystems, [CoO2]infinity layers containing triangular lattices formed by edge-sharing CoO6 octahedra, separated from each other by [2Ca0.85OH]infinity double-layered rock-salt-type slabs. Both the subsystems are monoclinic lattices with the unit cell parameters, a1 = 2.8180(4) A, b = 4.8938(6) A, c = 8.810(1) A, alpha0 = 95.75(3) degrees , and alpha(=|q|=a1/a2) = 0.57822(8), viz., a2 = 4.8736 A, with Z = 2. A possible superspace group is C2/m(alpha10)s0-C21/m(alpha(-1)10) for the respective subsystems. The atomic positions deviate from the average positions of the fundamental structure due to the incommensurable periodic interaction between the subsystems. A significant structural modulation was found in the [2Ca0.85OH] subsystem, whereas the modulation in the [CoO2] subsystem is less than in [2Ca0.85OH], due to the tight bonding of the close-packed CoO6 octahedra. The degree of modulation in the CoO2 layers, i.e., the potential modulation, is almost the same as those of other compounds of the misfit-layer cobalt oxides. Flattened CoO6 octahedra indicate hole doping into the CoO2 layers. The [2Ca0.85OH] blocks act as the charge reservoir layers, and the defect Ca ions are presumably the source of the holes.     

Construction of Helical Structures with Multiple Fused Anthracenes: Structures and Properties of Long Expanded Helicenes

Polycyclic aromatic compounds consisting of four or five fused anthracene units were synthesized by PtCl₂-catalyzed cycloisomerization as novel long expanded helicenes. These compounds have helical structures with significant stacking of the terminal anthracene moieties at 0.33 nm interlayer distance. In the UV-vis and fluorescence spectra, the absorption and emission bands were red-shifted as the number of fused anthracene units was increased. The characteristic broad and long-lived emission bands of the long analogues are explained by the excimer-like stabilization of the excited state. These photophysical data as well as their cyclic voltammetric data are discussed on the basis of the π-conjugation and interlayer π⋅⋅⋅π interactions in the molecular structures and the molecular orbitals. The barrier and mechanism of helical inversion are also reported.     

Massenspektren der von Aminosäuren bzw. Peptiden abgeleiteten Triazin-Derivate

A mass spectrometric study of about 30 triazine derivatives from amino acids and peptides is reported. These derivatives incorporated the C-terminal of amino acids and peptides in the ring. In contrast to the mass spectra of amino acids and peptide esters reported previously, they always showed characteristic fragments, denoting the presence of the terminal triazine ring. By using this peak as a marker, it is easy to estimate the C-terminal of peptides. In dipeptides, the N-terminal and C-terminal are determined simultaneously.     

Specific isolation of N-terminal fragments from proteins and their high-fidelity de novo sequencing

A new method to determine N-terminal amino acid sequences of multiple proteins at low pmol level by a parallel processing has been developed. The method contains the following five steps: (1) reduction, S-alkylation and guanidination for targeted proteins; (2) coupling with sulfosucccimidyl-2-(biotinamido)ethyl-1,3-dithiopropionate(sulfo-NHS-SS-biotin) to N(alpha)-amino groups of proteins; (3) digestion of the modified proteins by an appropriate protease; (4) specific isolation of N-terminal fragments of proteins by affinity capture using the biotin-avidin system; (5) de novo sequence analysis of peptides by MALDI-TOF-/MALDI-TOF-PSD mass spectrometry with effective utilization of the CAF (chemically assisted fragmentation) method.1 This method is also effective for N-terminal sequencing of each protein in a mixture of several proteins, and for sequencing components of a multiprotein complex. It is expected to become an essential proteomics tool for identifying proteins, especially when used in combination with a C-terminal sequencing method.     

Graphite–boron composite heater in a Kawai-type apparatus: the inhibitory effect of boron oxide and countermeasures

We have investigated the performance of a graphite–boron composite (GBC) with 3?wt % boron as a precursor for a boron-doped diamond heater in a Kawai-type apparatus at 15?GPa. We first tested a machinable cylinder of GBC sintered at 1000°C in Ar/H₂ gas (99:1 molar ratio). Boron oxide (B₂O₃) formed during sintering frequently hindered the GBC heater from stable operation at temperatures higher than 1400°C by producing melt throughout the heater together with oxide and/or silicates. We then rinsed the GBC heater in hydrochloric acid to remove B₂O₃. After rinsing, we succeeded in stably generating temperatures higher than 2000°C. We also improved a molding process of different-sized GBC tubes for convenient use and tested the molded GBC heater. It was free from the B₂O₃ problem. The electromotive force of the W/Re thermocouple was successfully monitored up to 2400°C.     

The Change of Grip Strength in a Patient with Congenital Myotonic Dystrophy Over a 4-year Period

Myotonic dystrophy (MyD) is a neuromuscular disease that is autosomal dominant and the most common form of muscular dystrophy affecting adults. The clinical features of MyD include a multisystemic disorder characterized by myotonia, progressive muscle weakness and wasting, cataracts, premature balding and mental retardation. The most severe type of MyD is classified as congenital MyD (CMyD). The muscle weakness in CMyD is very severe, but muscle development can be observed in the period of growth. However, no clinical case of this type has been reported yet. Therefore, we report on a girl with CMyD who had an increase in muscle strength over a four-year period. The girl with CMyD participated in this study from the age of 9 to the age of 12. The measurement of muscle strength was recorded as the maximum score of grip strength with the use of dynamometers. Grip strength was assessed once a year by the same two physical therapists. Grip strength of CMyD for each year was markedly weak when compared with the normal controls, but muscle strength changed within some specific growth areas. The muscle weakness in CMyD was remarkable, but the result showed that specific muscle strength of CMyD in childhood was actually increased.