Dynamics of a pair of coupled nonlinear oscillators

A pair of coupled classical oscillators with a general potential and general form of coupling is investigated. For general potentials, the single-frequency solution is shown to be stable for small excitations. For special potentials, such system remains stable for an arbitrary excitation. In both cases, the stability does not depend on the form of coupling. Transition to the instability regime follows from the way how nonlinear potential entrains the energy transfer between the oscillators. Relation between the existence of multi-frequency quasi-periodic or periodic solutions and the instability of single-frequency ones is discussed.     

Geometric separation and exact solutions for the parameterized independent set problem on disk graphs

We consider the parameterized problem, whether for a given set  of n disks (of bounded radius ratio) in the Euclidean plane there exists a set of k non-intersecting disks. For this problem, we expose an algorithm running in time that is—to our knowledge—the first algorithm with running time bounded by an exponential with a sublinear exponent. For λ-precision disk graphs of bounded radius ratio, we show that the problem is fixed parameter tractable with a running time  . The results are based on problem kernelization and a new “geometric ( -separator) theorem” which holds for all disk graphs of bounded radius ratio. The presented algorithm then performs, in a first step, a “geometric problem kernelization” and, in a second step, uses divide-and-conquer based on our new “geometric separator theorem.”     

Early reactions of light-induced protochlorophyllide and chlorophyllide transformations analyzed in vivo at room temperature with a diode array spectrofluorometer

The steps of protochlorophyllide (Pchlide) photoreduction and subsequent chlorophyllide (Chlide) transformations which occur in the seconds to minutes time-scale were studied using a diode array spectrofluorometer in dark-grown barley leaves. The intensity of the excitation light was varied between 3 and 2,500 micromol m(-2) s(-1) and a series of fluorescence spectra were recorded at room temperature in the seconds and minutes time scales. In certain experiments, 77-K emission spectra were measured with the same equipment. The high quality of the spectra allowed us to run spectral resolution studies which proved the occurrence, at room temperature, of multiple Pchlide and Chlide forms found previously in 77-K spectra. The comparison of the 77-K and room-temperature spectra showed that the fluorescence yields of the nonphotoactive 633-nm Pchlide form and of the Chlide product emitting at 678 nm were temperature independent. The fluorescence intensity of aggregated NADPH-pigment-POR complexes (photoactive 656-nm Pchlide and 693-nm Chlide forms) were strongly increased at 77 K, while that of the NADP(+)-Chlide-POR (684-686-nm Chlide form) was much less affected by temperature. Information was obtained also about the dynamics of the transformation of pigment forms in the light at different photon densities. At low light intensities, the phototransformation of the 642-644-nm Pchlide form was faster than that of the 654-656-nm form. The relative amplitudes of Gaussian components related to different Chlide forms found after exposure to a constant amount of photons strongly depended on the light intensity used. Strong quenching of all Chlide components occurred upon prolonged exposure to high intensity light. These effects are discussed by considering the interconversion processes between different forms of the pigment-protein complexes, their relative fluorescence yields and energy migration processes.     

Enantioselective Preparation of 2‐Aminomethyl Carboxylic Acid Derivatives: Solving the β2‐Amino Acid Problem with the Chiral Auxiliary 4‐Isopropyl‐5,5‐diphenyloxazolidin‐2‐one (DIOZ). Preliminary Communication

Multigram amounts of suitably protected β²‐amino acids with 17 of the 20 proteinogenic side chains are prepared by diastereoselective reactions of Li, B, or Ti enolates of the corresponding 3‐acyl‐4‐isopropyl‐5,5‐diphenyloxazolidin‐2‐ones (acyl‐DIOZ; 1 ) with appropriate electrophiles (amidomethylation, hydroxyalkylation, (benzyloxycarbonyl)methylation) in yields of 55–90% and with diastereoselectivities of 80 to >97% (Scheme). The primary products 2 – 8 thus obtained are converted to protected β²‐amino acids by standard procedures (Table 1). Many of the DIOZ derivatives are highly crystalline compounds (31 X‐ray crystal structures in Table 2). The chiral auxiliary DIOZ, readily prepared in either enantiomeric form, is recovered with high yield.     

OXYGEN QUENCHING OF CHLOROPHYLL FLUORESCENCE IN CHLOROPLASTS

Abstract— Three phases of chlorophyll a fluorescence quenching by O₂ are observed in green plants. The effects of various inhibitors on photosynthetic partial processes in chloroplasts were investigated in attempts to (1) localize the O₂-quenching sites and (2) assess possible physiological significance of O₂-quenching. Our results localize the most sensitive (and presumably functionally important) phase to a site between plastoquinone and the photosystem I acceptor, chlorophyll (P₇₀₀), possibly plastocyanin. It is suggested that PC may transfer electrons to oxygen in addition to P₇₀₀.     

“Integer-making” theorems

Let X = {x₁, x₂,…} be a finite set and associate to every x_i a real number α_i. Let f(n) [g (n)] be the least value such that given any family $\text{F}$ of subsets of X having maximum degree n [cardinality n], one can find integers α_i, i=1,2,… so that α_i ? α_i|<1 and

$\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{a}{}_{\mathrm{i}}\text{?}\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{α}{}_{\mathrm{i}}\text{≤?(n)}\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{a}{}_{\mathrm{i}}\text{?}\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{α}{}_{\mathrm{i}}\text{≤}\text{g(n)}$

for all $\text{E ?}\text{F}$. We prove

$\text{f(n)≤n ? 1 and g(n)≤c(n}\text{log}\text{n)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$

.     

In-bone protein digestion followed by LC-MS/MS peptide analysis as a new way towards the routine proteomic characterization of human maxillary and mandibular bone tissue in oral surgery

Proteomic characterization of alveolar bones in oral surgery represents an analytical challenge due to their insoluble character. The implementation of a straightforward technique could lead to the routine use of proteomics in this field. This work thus developed a simple technique for the characterization of bone tissue for human maxillary and mandibular bones. It is based on the direct in-bone tryptic digestion of proteins in both healthy and pathological human maxillary and mandibular bone samples. The released peptides were then identified by the LC-MS/MS. Using this approach, a total of 1120 proteins were identified in the maxillary bone and 1151 proteins in the mandibular bone. The subsequent partial least squares–discrimination analysis (PLS-DA) of protein data made it possible to reach 100% discrimination between the samples of healthy alveolar bones and those of the bone tissue surrounding the inflammatory focus. These results indicate that the in-bone protein digestion followed by the LC-MS/MS and subsequent statistical analysis can provide a deeper insight into the field of oral surgery at the molecular level. Furthermore, it could also have a diagnostic potential in the differentiation between the proteomic patterns of healthy and pathological alveolar bone tissue. Data are available via ProteomeXchange with the identifier PXD026775.     

Analytical Performance of Clay Paste Electrode and Graphene Paste Electrode-Comparative Study

The analytical performance of the clay paste electrode and graphene paste electrode was compared using square wave voltammetry (SWV) and cyclic voltammetry (CV). The comparison was made on the basis of a paracetamol (PA) determination on both working electrodes. The influence of pH and SWV parameters was investigated. The linear concentration ranges were found to be 6.0 × 10⁻⁷–3.0 × 10⁻⁵ and 2.0 × 10⁻⁶–8.0 × 10⁻⁵ mol L⁻¹ for clay paste electrode (ClPE) and graphene paste electrode (GrPE), respectively. The detection and quantification limits were calculated as 1.4 × 10⁻⁷ and 4.7 ×10⁻⁷ mol L⁻¹ for ClPE and 3.7 × 10⁻⁷ and 1.2 × 10⁻⁶ mol L⁻¹ for GrPE, respectively. Developed methods were successfully applied to pharmaceutical formulations analyses. Scanning electron microscopy and energy-dispersive X-ray spectroscopy were used to characterize ClPE and GrPE surfaces. Clay composition was examined with wavelength dispersive X-ray (WDXRF).