Frequency modules and nonexistence of quasi-periodic solutions of nonlinear evolution equations

This paper gives lower estimates for the frequency modules of almost periodic solutions to equations of the form , where A generates a strongly continuous semigroup in a Banach space , F(t,x) is 2π-periodic in t and continuous in (t,x), and f is almost periodic. We show that the frequency module ℳ(u) of any almost periodic mild solution u of (*) and the frequency module ℳ(f) of f satisfy the estimate e ^{2π iℳ(f)}⊂e ^{2π iℳ(u)}. If F is independent of t, then the estimate can be improved: ℳ(f)⊂ℳ(u). Applications to the nonexistence of quasi-periodic solutions are also given.     

On the Kolmogorov complexity of continuous real functions

Kolmogorov complexity was originally defined for finitely-representable objects. Later, the definition was extended to real numbers based on the asymptotic behaviour of the sequence of the Kolmogorov complexities of the finitely-representable objects—such as rational numbers—used to approximate them.This idea will be taken further here by extending the definition to continuous functions over real numbers, based on the fact that every continuous real function can be represented as the limit of a sequence of finitely-representable enclosures, such as polynomials with rational coefficients.Based on this definition, we will prove that for any growth rate imaginable, there are real functions whose Kolmogorov complexities have higher growth rates. In fact, using the concept of prevalence, we will prove that ‘almost every’ continuous real function has such a high-growth Kolmogorov complexity. An asymptotic bound on the Kolmogorov complexities of total single-valued computable real functions will be presented as well.     

Assessment model of classroom acoustics criteria for enhancing speech intelligibility and learning quality

In this paper, a new classroom acoustics assessment model (CAAM) based on analytic hierarchy process (AHP) for enhancing speech intelligibility and learning quality is proposed. The model is based on five main criteria that affect the learning process and related to classrooms acoustical properties. These include classroom specifications, noise sources inside and outside the classroom, teaching style, and vocal effort. The priority and weights of these major criteria along with their alternatives are identified using the views of students, staff, education consultants, and expertise by using a developed questionnaire, and the AHP methodology. This model can be considered as a helpful framework enabling universities decision makers to take effective decisions on classroom acoustics treatment issues. It also provides colleges’ higher authorities the suitable guidelines that help for determining necessary requirements that help to raise the quality and efficiency of the educational environment; in order to reach an excellent learning environment; and hence increasing students learning outcomes.     

Optical and current transport properties of CuO/ZnO nanocoral p–n heterostructure hydrothermally synthesized at low temperature

We demonstrate the synthesis and investigate the electrical and optical characteristics of ‘nanocorals’ (NCs) composed of CuO/ZnO grown at low temperature through the hydrothermal approach. High-density CuO nanostructures (NSs) were selectively grown on ZnO nanorods (NRs). The synthesized NCs were used to fabricate p–n heterojunctions that were investigated by the current density–voltage (J–V) and the capacitance–voltage (C–V) techniques. It was found that the NC heterojunctions exhibit a well-defined diode behavior with a threshold voltage of about 1.52 V and relatively high rectification factor of ～760. The detailed forward J–V characteristics revealed that the current transport is controlled by an ohmic behavior for V≤0.15 V, whereas at moderate voltages 1.46≤V<1.5 the current follows a J? α?exp(βV) relationship. At higher voltages (≥1.5 V) the current follows the relation J? α? V ², indicating that the space-charge-limited current mechanism is the dominant current transport. The C–V measurement indicated that the NC diode has an abrupt junction. The grown CuO/ZnO NCs exhibited a broad light absorption range that is covering the UV and the entire visible parts of the spectrum.     

Methods of multivariate data analysis applied to the investigation of fen soils

Fen soils from two sites of the Rhin-Havel-Luch, a peatland in the north-east of Germany, have been investigated. The samples have been collected in two horizons, representing different degrees of degradation and mineralisation of peat. Gravimetric measurements, energy dispersive X-ray fluorescence (EDXRF), elemental analysis, and ¹H low resolution nuclear magnetic resonance (LR-NMR) of the fen soil samples have been performed. By multivariate analysis of all the experimental data, especially by the principal component analysis (PCA) and by the cluster analysis, respectively, it was possible to classify the fen soils, to identify their characteristic properties, to detect temporal and local variations, and to prove representative field sampling. Furthermore, the correlation between variables of the applied analytical methods could be interpreted in context to the composition of fen soils and mutual influences of their properties.     

Recent Advances in the Chemistry and Therapeutic Evaluation of Naturally Occurring and Synthetic Withanolides

Natural products are a major source of biologically active compounds that make promising lead molecules for developing efficacious drug-like molecules. Natural withanolides are found in many flora and fauna, including plants, algae, and corals, that traditionally have shown multiple health benefits and are known for their anti-cancer, anti-inflammatory, anti-bacterial, anti-leishmaniasis, and many other medicinal properties. Structures of these withanolides possess a few reactive sites that can be exploited to design and synthesize more potent and safe analogs. In this review, we discuss the literature evidence related to the medicinal implications, particularly anticancer properties of natural withanolides and their synthetic analogs, and provide perspectives on the translational potential of these promising compounds.     

A Convenient Synthesis of β-Amino Acid

We have reported the reductive cleavage of azlactones¹ and phenylhydrazones² of carbonyl compounds in the presence of a suitable catalyst. In this paper a general method involving a one step synthesis of β-amino acid^3,4, in good yield, through catalytic reduction of oximes of α-β-unsaturated acid is reported. This method involves the reaction of α, β-unsaturated acid with hydroxylamine hydrochloride in the presence of sodium acetate. Markovnikov's rule is followed in the synthesis of oximes of α, β-unsaturated acids.     

Luciferin‐Regenerating Enzyme Mediates Firefly Luciferase Activation Through Direct Effects of D‐Cysteine on Luciferase Structure and Activity

Luciferin‐regenerating enzyme (LRE) contributes to in vitro recycling of D‐luciferin. In this study, reinvestigation of the luciferase‐based LRE assay is reported. Here, using quick change site‐directed mutagenesis seven T‐LRE (Lampyris turkestanicusLRE) mutants were constructed and the most functional mutant of T‐LRE (T⁶⁹R) was selected for this research and the effects of D‐ and L‐cysteine on T⁶⁹R T‐LRE‐luciferase‐coupled assay are examined. Our results demonstrate that bioluminescent signal of T⁶⁹R T‐LRE‐luciferase‐coupled assay increases and then reach equilibrium state in the presence of 5 mm D‐cysteine. In addition, results reveal that 5 mm D‐ and L‐cysteine in the absence of T⁶⁹R T‐LRE cause a significant increase in bioluminescence intensity of luciferase over a long time as well as decrease in decay rate. Based on activity measurements, far‐UV CD analysis, ANS fluorescence and DLS (Dynamic light scattering) results, D‐cysteine increases the activity of luciferase due to weak redox potential, antiaggregatory effects, induction of changes in conformational structure and kinetics properties. In conclusion, in spite of previous reports on the effect of LRE on luciferase bioluminescent intensity, the majority of increase in luciferase light output and time‐course originate from the direct effects of D‐cysteine on structure and activity of firefly luciferase.     

Gut microbiota, diet, and heart disease

Modulation of the gut microbiota is an area of growing interest, particularly for its link to improving and maintaining the systemic health of the host. It has been suggested to have potential to reduce risk factors associated with chronic diseases, such as elevated cholesterol levels in coronary heart disease (CHD). Diets of our evolutionary ancestors were largely based on plant foods, high in dietary fiber and fermentable substrate, and our gut microbiota has evolved against a background of such diets. Therapeutic diets that mimic plant-based diets from the early phases of human evolution may result in drug-like cholesterol reductions. In contrast, typical Western diets low in dietary fiber and fermentable substrate, and high in saturated and trans fatty acids, are likely contributors to the increased need for pharmacological agents for cholesterol reduction. The gut microbiota of those consuming a Western diet are likely underutilized and depleted of metabolic fuels, resulting in a less than optimal gut microbial profile. As a result, this diet is mismatched to our archaic gut microbiota and, therefore, to our genome, which has changed relatively little since humans first appeared. While the exact mechanism by which the gut microbiota may modulate cholesterol levels still remains uncertain, end products of bacterial fermentation, particularly the short chain fatty acids (i.e., propionate), have been suggested as potential candidates. While more research is required to clarify the potential link between gut microbiota and CHD risk reduction, consuming a therapeutic diet rich in plant foods, dietary fiber, and fermentable substrate would be a useful strategy for improving systemic health, possibly by altering the gut microbiota.     

Anti-angiogenic activity of Morinda citrifolia extracts and its chemical constituents

Morinda citrifolia L. has been used for the treatment of a wide variety of diseases, including cancer. This study was undertaken to evaluate the anti-angiogenic effect of M. citrifolia fruits and leaves. Anti-angiogenic activity was evaluated in?vivo using the chick chorioallantoic membrane assay. Bioactivity-guided fractionation and isolation were performed to identify the active constituent, and high-performance liquid chromatography analysis was then used to quantify the amount of this active constituent in the active extracts and fraction. The methanol extracts of fruits and leaves of M. citrifolia and the subsequent chloroform fraction of the fruit methanolic extract were found to have potential anti-angiogenic activity and were more potent compared to suramin. Scopoletin was identified as one of the chemical constituents that may be partly responsible for the anti-angiogenic activity of M. citrifolia fruits. The present findings further support the use of M. citrifolia in cancer or other pathological conditions related to angiogenesis.