Limit sets of dynamical systems on the space of probability measures

Let m be a dynamical system on the space of probability measures $\text{M}$₁(R^d), and let Λ + (?) be the positive limit set for ? ∈ $\text{M}$₁(R^d), where ? has compact support K ?R^d. The main result of this paper states that support of Λ⁺(?) ?

,support of Λ + (δ_x), where δ_x is the Dirac measure at point x.     

A TIN-119 Mössbauer and electrical conductivity study of the system SnxGe1-xSe (0 ⩽ x ⩽ 1)

¹¹⁹Sn Mössbauer parameters and electrical conductivity data for phases in the system Sn_xGe_1-xSe (0 ? x ? 1) are reported. The Mössbauer data for the material Sn_0.8Ge_0.2Se show that the electron distribution around the Sn at this composition is anomalous. There is, however, little indication of the presence of such an anomaly in the electrical conductivity and Hall Effect data. The implications of these observations are discussed.     

Analysis of chaotic saddles in high-dimensional dynamical systems: the Kuramoto-Sivashinsky equation

This paper presents a methodology to study the role played by nonattracting chaotic sets called chaotic saddles in chaotic transitions of high-dimensional dynamical systems. Our methodology is applied to the Kuramoto-Sivashinsky equation, a reaction-diffusion partial differential equation. The paper describes a novel technique that uses the stable manifold of a chaotic saddle to characterize the homoclinic tangency responsible for an interior crisis, a chaotic transition that results in the enlargement of a chaotic attractor. The numerical techniques explained here are important to improve the understanding of the connection between low-dimensional chaotic systems and spatiotemporal systems which exhibit temporal chaos and spatial coherence.     

Computational titration analysis of a multiprotic HIV-1 protease-ligand complex

A new computational method for analyzing the protonation states of protein-ligand complexes with multiple ionizable groups is applied to the structurally characterized complex between the peptide Glu-Asp-Leu and HIV-1 protease. This complex has eight ionizable groups at the active site: four from the ligand and four Asp residues on the protein. Correlation, with an error of ca. 0.6 kcal mol-1, is made between the calculated titration curve and the experimental titration curve. The analysis suggests that between four and five of the eight ionizable groups are protonated at the pH of crystallization.     

Determination of McGowan volumes for ions and correlation with van der Waals volumes

The McGowan volume has been widely used for the analysis of physicochemical and biochemical properties in chemistry and drug industry. Because McGowan volumes are not available for ions, its application is limited to only neutral compounds. Pauling radii of metallic ions have been collected and studied to obtain McGowan volumes for ions. Regression analysis was carried out between Pauling radii (R(p)) and McGowan radii (R(x)) for a wide range of compounds. It was found that Pauling radii and McGowan radii derived from McGowan volumes by using a volume-radius formula are linearly related (R(x) = 1.115R(p) + 0.0623, r(2) = 0.995). This equation is then used to calculate McGowan volumes for various ions and charged groups. McGowan volumes have been calculated for inorganic, organic, and organometallic compounds and correlated with van der Waals volumes. Results show that McGowan volumes (V(x)) are entirely equivalent to computer-calculated van der Waals volumes.     

Intrinsic fluorescence polarization of amniotic fluid: evaluation of human fetal lung maturity

This article reports a novel approach for the evaluation of fetal lung maturity based on fluorescence polarization (FP). The technique determines the intrinsic fluorescence polarization ratio (IFPR) of the amniotic fluid (AF). In vitro measurements of the IFPR indicate a clear dichotomy: high values for young pregnancies and low values for mature pregnancies. The new method has the potential to be a noninvasive procedure because the excitation of the AF and the collection of its fluorescence emission can be performed through the intact cervical amniotic membranes.     

Ab initio structure study from in-house powder diffraction of a novel ZnS(EN)0.5 structure with layered wurtzite ZnS fragment

The solvothermal reaction of elemental zinc with sulfur in ethylenediamine (en) as solvent yields [ZnS-0.5(NH2CH2CH2NH2)], 1, an unprecedented ethylenediamine pillared ZnS layered compound, containing two dimensional (2-D) boat-type 6-membered rings, which was characterized by ab initio structure solution from powder diffraction data (SDPD).     

The Bifurcation Approach to Hyperbolic Geometry

The Thomas precession of relativity physics gives rise to important isometries in hyperbolic geometry that expose analogies with Euclidean geometry. These, in turn, suggest our bifurcation approach to hyperbolic geometry, according to which Euclidean geometry bifurcates into two mutually dual branches of hyperbolic geometry in its transition to non-Euclidean geometry. One of the two resulting branches turns out to be the standard hyperbolic geometry of Bolyai and Lobachevsky. The corresponding bifurcation of Newtonian mechanics in the transition to Einsteinian mechanics indicates that there are two, mutually dual, kinds of uniform accelerations. Furthermore, while current hyperbolic geometry does not use the notion of vector at all (I. M. Yaglom, Geometric Transformations III, p. 135, trans. by Abe Shenitzer, Random House, New York, 1973), our bifurcation approach exposes the elusive hyperbolic vectors, that we call gyrovectors.     

Bioguided Fractionation of Local Plants against Matrix Metalloproteinase9 and Its Cytotoxicity against Breast Cancer Cell Models: In Silico and In Vitro Study (Part II)

In our previous work, the partitions (1 mg/mL) of Ageratum conyzoides (AC) aerial parts and Ixora coccinea (IC) leaves showed inhibitions of 94% and 96%, respectively, whereas their fractions showed IC₅₀ 43 and 116 µg/mL, respectively, toward Matrix Metalloproteinase9 (MMP9), an enzyme that catalyzes a proteolysis of extracellular matrix. In this present study, we performed IC₅₀ determinations for AC n-hexane, IC n-hexane, and IC ethylacetate partitions, followed by the cytotoxicity study of individual partitions against MDA-MB-231, 4T1, T47D, MCF7, and Vero cell lines. Successive fractionations from AC n-hexane and IC ethylacetate partitions led to the isolation of two compounds, oxytetracycline (OTC) and dioctyl phthalate (DOP). The result showed that AC n-hexane, IC n-hexane, and IC ethylacetate partitions inhibit MMP9 with their respective IC₅₀ as follows: 246.1 µg/mL, 5.66 µg/mL, and 2.75 × 10⁻² µg/mL. Toward MDA-MB-231, 4T1, T47D, and MCF7, AC n-hexane demonstrated IC₅₀ 2.05, 265, 109.70, and 2.11 µg/mL, respectively, whereas IC ethylacetate showed IC₅₀ 1.92, 57.5, 371.5, and 2.01 µg/mL, respectively. The inhibitions toward MMP9 by OTC were indicated by its IC₅₀ 18.69 µM, whereas DOP was inactive. A molecular docking study suggested that OTC prefers to bind to PEX9 rather than its catalytic domain. Against 4T1, OTC showed inhibition with IC₅₀ 414.20 µM. In conclusion, this study furtherly supports the previous finding that AC and IC are two herbals with potential to be developed as triple-negative anti-breast cancer agents.     

Effect of Cryostructuring Treatment on Some Properties of Xanthan and Karaya Cryogels for Food Applications

Cryogels are novel materials because the manufacturing process known as cryostructuring allows biopolymers to change their properties as a result of repeated controlled freeze–thaw cycles. Hydrogels of xanthan and karaya gums were evaluated after undergoing up to four controlled freeze–thaw cycles in indirect contact with liquid nitrogen (up to −150 °C) to form cryogels. Changes in structural, molecular, rheological, and thermal properties were evaluated and compared to those of their respective hydrogels. Samples were also analyzed by Scanning Electron Microscopy (SEM), Fourier Transform Infrared Spectroscopy with Attenuated Total Reflection (FTIR-ATR), Rotational Rheology (RR), Modulated Differential Scanning Calorimetry (MDSC) and zeta potential (ζ). In general, significant differences (p < 0.05) between the numbers of freeze–thaw cycles were found. Karaya cryogels were not stable to repeated cycles of cryostructuring such as the three-cycle xanthan cryogel, which has the best structural order (95.55%), molecular interactions, and thermal stability, which allows the generation of a novel material with improved thermal and structural properties that can be used as an alternative in food preservation.