Discrete Laplace Cycles of Period Four

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of corresponding points form a discrete W-congruence. We derive some properties of discrete Laplace cycles of period four and describe two explicit methods for their construction

RAFT-based polystyrene and polyacrylate melts under thermal and mechanical stress

Although controlled/living radical polymerization processes have significantly facilitated the synthesis of well-defined low polydispersity polymers with specific functionalities, a detailed and systematic knowledge of the thermal stability of the products-highly important for most industrial processes-is not available. Linear polystyrene (PS) carrying a trithiocarbonate mid-chain functionality (thus emulating the structure of the Z-group approach via reversible addition-fragmentation chain transfer (RAFT) based macromolecular architectures) with various chain lengths (20 kDa ≤ Mn,SEC ≤ 150 kDa, 1.27 ≤ Crossed D sign = Mw/Mn ≤ 1.72) and chain-end functionality were synthesized via RAFT polymerization. The thermal stability behavior of the polymers was studied at temperatures ranging from 100 to 200 C for up to 504 h (3 weeks). The thermally treated polymers were analyzed via size exclusion chromatography (SEC) to obtain the dependence of the polymer molecular weight distribution on time at a specific temperature under air or inert atmospheres. Cleavage rate coefficients of the mid-chain functional polymers in inert atmosphere were deduced as a function of temperature, resulting in activation parameters for two disparate Mn starting materials (Ea = 115 ± 4 kJ·mol-1, A = 0.85 × 109 ± 1 × 109 s-1, M n,SEC = 21 kDa and Ea = 116 ± 4 kJ·mol -1, A = 6.24 × 109 ± 1 × 109 s-1, Mn,SEC = 102 kDa). Interestingly, the degradation proceeds significantly faster with increasing chain length, an observation possibly associated with entropic effects. The degradation mechanism was explored in detail via SEC-ESI-MS for acrylate based polymers and theoretical calculations suggesting a Chugaev-type cleavage process. Processing of the RAFT polymers via small scale extrusion as well as a rheological assessment at variable temperatures allowed a correlation of the processing conditions with the thermal degradation properties of the polystyrenes and polyacrylates in the melt. © 2013 American Chemical Society.C.B.-K and M.W. gratefully acknowledge financial support from the German Research Council (DFG). M.L.C gratefully acknowledges generous allocations of supercomputing time from the Australian National Computing Facility, financial support from the Australian Research Council (ARC) Centre of Excellence for Free-radical Chemistry and Biotechnology and an ARC Future Fellowship. C.B.-K. acknowledges additional funding from the Karlsruhe Institute of Technology (KIT) in the context of the Helmholtz programs

Zero Frequency Current Noise for the Double Tunnel Junction Coulomb Blockade

We compute the zero frequency current noise numerically and in several limits analytically for the coulomb blockade problem consisting of two tunnel junctions connected in series. At low temperatures over a wide range of voltages, capacitances, and resistances it is shown that the noise measures the variance in the number of electrons in the region between the two tunnel junctions. The average current, on the other hand, only measures the mean number of electrons. Thus, the noise provides additional information about transport in these devices which is not available from measuring the current alone.Comment: 33 pages, 10 figure

Signaling via interleukin-4, receptor alpha chain is required for successful vaccination against schistosomiasis in BALB/c mice

Radiation-attenuated (RA) schistosome larvae are potent stimulators of innate immune responses at the skin site of exposure (pinna) that are likely to be important factors in the development of Th1-mediated protective immunity. In addition to causing an influx of neutrophils, macrophages, and dendritic cells (DCs) into the dermis, RA larvae induced a cascade of chemokine and cytokine secretion following in vitro culture of pinna biopsy samples. While macrophage inflammatory protein 1 and interleukin-1 (IL-1) were produced transiently within the first few days, the Th1-promoting cytokines IL-12 and IL-18 were secreted at high levels until at least day 14. Assay of C3H/HeJ mice confirmed that IL-12 secretion was not due to lipopolysaccharide contaminants binding Toll-like receptor 4. Significantly, IL-12 p40 secretion was sustained in pinnae from vaccinated mice but not in those from nonprotected infected mice. In contrast, IL-10 was produced from both vaccinated and infected mice. This cytokine regulates IL-12-associated dermal inflammation, since in vaccinated IL-10/ mice, pinna thickness was greatly increased concurrent with elevated levels of IL-12 p40. A significant number of IL-12 p40 cells were detected as emigrants from in vitro-cultured pinnae, and most were within a population of rare large granular cells that were Ia, consistent with their being antigen-presenting cells. Labeling of IL-12 cells for CD11c, CD205, CD8, CD11b, and F4/80 indicated that the majority were myeloid DCs, although a proportion were CD11c F4/80, suggesting that macrophages were an additional source of IL-12 in the skin

Children use one-to-one correspondence to establish equality after learning tocount

Humans make frequent and powerful use of external symbolsto express number exactly, leading some to question whetherexact number concepts are only available through the acqui-sition of symbolic number systems. Although prior work hasaddressed this longstanding debate on the relationship betweenlanguage and thought in innumerate populations and semi-numerate children, it has frequently produced conflicting re-sults, leaving the origin of exact number concepts unclear.Here, we return to this question by replicating methods pre-viously used to assess exact number knowledge in innumer-ate groups, such as the Pirah ̃a, with a large sample of semi-numerate US toddlers. We replicate previous findings fromboth innumerate cultures and developmental studies showingthat numeracy is linked to the concept of exact number. How-ever, we also find evidence that this knowledge is surprisinglyfragile even amongst numerate children, suggesting that nu-meracy alone does not guarantee a full understanding of exact-ness