On Isomorphic K-Rational Groups of Isogenous Elliptic Curves Over Finite Fields

It is well known that two elliptic curves are isogenous if and only if they have same number of rational points. In fact, isogenous curves can even have isomorphic groups of rational points in certain cases. In this paper, we consolidate all the current literature on this relationship and give a extensive classification of the conditions in which this relationship arises. First we prove two ordinary isogenous elliptic curves have isomorphic groups of rational points when they have the same $j$-invariant. Then, we extend this result to certain isogenous supersingular elliptic curves, namely those with equal $j$-invariant of either 0 or 1728, using Vl\u{a}du\c{t}\u27s characterization of the group structure of rational points

Pressure- and Temperature-Dependent Crystallization Kinetics of Isotactic Polypropylene under Process Relevant Conditions

In this study, a non-nucleated homopolymer (HP) and random copolymer (RACO), as well as a nucleated HP and heterophasic copolymer (HECO) were investigated regarding their crystallization kinetics. Using pvT-measurements and fast scanning chip calorimetry (FSC), the crystallization behavior was analyzed as a function of pressure, cooling rate and temperature. It is shown that pressure and cooling rate have an opposite influence on the crystallization temperature of the materials. Furthermore, the addition of nucleating agents to the material has a significant effect on the maximum cooling rate at which the formation of α-crystals is still possible. The non-nucleated HP and RACO materials show significant differences that can be related to the sterically hindering effect of the comonomer units of RACO on crystallization, while the nucleated materials HP and HECO show similar crystallization kinetics despite their different structures. The pressure-dependent shift factor of the crystallization temperature is independent of the material. The results contribute to the description of the relationship between the crystallization kinetics of the material and the process parameters influencing the injection-molding induced morphology. This is required to realize process control in injection molding in order to produce pre-defined morphologies and to design material properties

Process induced skin-core morphology in injection molded polyamide 66

Polyamide 66 (PA 66) was injection-molded to obtain samples with a structure gradient between skin and core, as it was revealed by analysis of the semi-crystalline morphology using polarized-light optical microscopy (POM). Wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS) were employed to characterize thin sections with a thickness in the order of magnitude of 50 µm, allowing detection of crystals of different perfection, as a function of the distance from the surface. It was found that the transparent and non-spherulitic skin layer contains rather imperfect α-crystals while the perfection of α-crystals continuously increases with extending distance from the surface. Since variation of the molding conditions allows tailoring the skin-core morphology, the present study was performed to suggest a reliable route to map the presence of specific semi-crystalline morphologies in such sample

Correlation between Processing Parameters, Morphology, and Properties of Injection-Molded Polylactid Acid (PLA) Specimens at Different Length Scales

Polylactic acid (PLA) is one of the most promising bioplastic representatives that finds application in many different areas, e.g., as single-use products in the packaging industry, in the form of mulch film for agriculture, or in medical devices. For the development of new areas, especially in terms of long-term applications and the production of recyclable products, the material properties controlled by processing must be known. The state of the art is investigations at the global scale (integral values) without consideration of local structure inhomogeneities and their influence on the material properties. In this work, morphological, thermal, and mechanical properties of injection-molded PLA tensile bars are investigated at different length scales (global and local) as a function of processing parameters. In addition to the processing parameters, such as melt temperature, mold temperature, and cooling time in the mold, the influence of the D-isomer content on the crystallization behavior and the resulting material properties are investigated. The material was found to form crystalline structures only when cooled in a mold tempered above Tg. In addition, PLA with a lower content of D-isomer was found to have a higher degree of crystallinity. Since the mechanical properties obtained by tensile tests could not be correlated with the degree of crystallinity, detailed analysis were performed showing a characteristic inhomogeneous morphology within the tensile bars. By means of micromechanical investigations on samples with different microstructure ranges, the relationship between local morphology and failure behavior could be explained

Vancomycin-resistant enterococci outside the health-care setting: prevalence, sources, and public health implications.

Although nosocomial acquisition and subsequent colonization of vancomycin-resistant enterococci (VRE), an emerging international threat to public health, has been emphasized in the United States, colonization among nonhospitalized persons has been infrequently documented. In contrast, in Europe, colonization appears to occur frequently in persons outside the health-care setting. An important factor associated with VRE in the community in Europe has been avoparcin, a glycopeptide antimicrobial drug used for years in many European nations at subtherapeutic doses as a growth promoter in food-producing animals. In Europe, evidence suggests that foodborne VRE may cause human colonization. Although avoparcin has never been approved for use in the United States, undetected community VRE transmission may be occurring at low levels. Further studies of community transmission of VRE in the United States are urgently needed. If transmission with VRE from unrecognized community sources can be identified and controlled, increased incidence of colonization and infection among hospitalized patients may be prevented

Water softening using a light-responsive, spiropyran-modified nanofiltration membrane

A novel technique for the covalent attachment of a light-responsive spiropyran onto polyamide thin film composite nanofiltration (NF) membranes in a one-step reaction using low-energy electron beam technology is described. The effect of illumination of the immobilized spiropyran was studied, as well as the resulting membrane properties with respect to MgSO4 retention, water permeability rate, and chlorine resistance. Electron beam irradiation showed a direct effect on the transformation of the rough PA NF membrane surface into a ridge-and-valley structure. Upon UV light irradiation, the spiropyran transformed into zwitterionic merocyanine, which had shown MgSO4 removal of >95% with water permeation rates of 6.5 L/(m2·h·bar). Alternatively, visible light was used to convert merocyanine to spiropyran, which achieved >95% of MgSO4 retention with a water flux of around 5.25 L/(m2·h·bar). The modified NF membranes showed higher chlorine resistance as well as a higher normalized water flux as compared to the reference membrane, without a loss of ion retention. All the NF membranes were characterized by scanning electron microscopy and X-ray photoelectron spectroscopy. This study demonstrates a simple and inexpensive method for the immobilization of molecules onto polymeric membranes, which may be applied in water softening

Dynactin-dependent cortical dynein and spherical spindle shape correlate temporally with meiotic spindle rotation in Caenorhabditis elegans.

Oocyte meiotic spindles orient with one pole juxtaposed to the cortex to facilitate extrusion of chromosomes into polar bodies. In Caenorhabditis elegans, these acentriolar spindles initially orient parallel to the cortex and then rotate to the perpendicular orientation. To understand the mechanism of spindle rotation, we characterized events that correlated temporally with rotation, including shortening of the spindle in the pole-to pole axis, which resulted in a nearly spherical spindle at rotation. By analyzing large spindles of polyploid C. elegans and a related nematode species, we found that spindle rotation initiated at a defined spherical shape rather than at a defined spindle length. In addition, dynein accumulated on the cortex just before rotation, and microtubules grew from the spindle with plus ends outward during rotation. Dynactin depletion prevented accumulation of dynein on the cortex and prevented spindle rotation independently of effects on spindle shape. These results support a cortical pulling model in which spindle shape might facilitate rotation because a sphere can rotate without deforming the adjacent elastic cytoplasm. We also present evidence that activation of spindle rotation is promoted by dephosphorylation of the basic domain of p150 dynactin