Bernoulli数模2r和3r的同余式

设{Bn}为Bernoulli数,m、n为自然数,本文证明了同余式(2-22n)B2n≡1-4n ∑mk=1(2n)/(2k)24kB2k (mod 24m 3)与(3-32n)B2n≡2-6n 2∑mk=1(2n)/(2k)32kB2k (mod 32m 1).取m=1,2,得到[5]中宣布的(2-22n)B2n(mod 27)与(3-32n)B2n(mod 35)的简单同余式.     

Eicosapentaenoic acid in tissue lipids ofPieris brassicae

Summary Larvae of the cabbage white butterfly,Pieris brassicae, have a dietary requirement for linolenic acid (C183n3) and were found to accumulate two other members of the n-3 family, C203n3 and C205n3 (eicosapentaenoic acid) especially in testicular phospholipids. Arachidonic acid was observed in trace amounts only. During diapause the relative titer of eicosapentaenoic acid increased in testicular phospholipids to about 4.2% of the fatty acids. Eicosapentaenoic acid is a possible precursor of prostaglandins, suggesting that prostaglandins of the 3-series predominate in this insect.     

Sex pheromone of the pine sawflyDiprion pini (Hymenoptera: Diprionidae): Chemical identification,synthesis and biological activity

The main component of the sex pheromone secretion of femaleDiprion pini L. (Hymenoptera: Diprionidae) from insects collected both in Finland and in France has been identified as athreo-3,7-dimethyl-2-tridecanol (8 ng per female) stereoisomer by GC-MS and synthesis. The secretion also contains lower and higher homologues in small amounts (1–4% of the main component). Combined gas chromatographic-electroantennographic detection showed activity in both natural and esterified extracts (acetates and propionates); the esters of the main component gave the largest responses. The acetates and propionates of the eight stereoisomers of 3,7-dimethyl-2-tridecanol were synthesized from enantiomerically highly enriched (>99% ee) building blocks. The stereochemistry of the main component was established to be (2S,3R,7R)-3,7-dimethyl-2-tridecanol by GC analysis of the natural material. It was purified by liquid chromatography prior to the GC analysis of both its pentafluorobenzoates and its isopropylcarbamates on a non-chiral polar column (ECD) and a chiral column (NPD), respectively. Field tests demonstrated that both the acetate and propionate of the main component (100 g of each applied on cotton roll dispensers) were active in attracting males, with or without the presence of several of the minor compounds. Experiments with smaller amounts of the acetate and the propionate (1 g in France and 50 g in Finland) demonstrated that the propionate was more active than the acetate, and that it also caught more males than a blend of the two compounds.     

Birefringence signals and tension development in single frog muscle fibres at short stimulus intervals

Summary The early large birefringence signal and mechanical activity were studied together in isolated single fibres of frog skeletal muscle with double stimulation at short stimulus intervals (2–60 msec) at room temperature and at 4–6°C. In all fibres tested, extra tension and additional birefringence signal in response to the second stimulus appeared simultaneously and suddenly upon increasing the stimulus interval. The shape of the stimulus-interval versus tension-development curve makes it highly improbable that subthreshold calcium release occurs at shorter stimulus intervals; therefore, tension development reliably reflects Ca-release in these experiments. In contrast to the report by Suarez-Kurtz and Parker, birefringence signal and calcium release are shown not to be dissociated by double stimulation. This result supports the hypothesis that the early large birefringence signal is an intrinsic indicator of calcium release from the sr during EC-coupling in skeletal muscle.     

In vitro inactivation of corpora allata of the bugOncopeltus fasciatus by precocene II

Summary Corpora allata fromOncopeltus fasciatus incubated in vitro in medium containing 10^–5.35 M (1 g/ml) of precocene II lose their ability to secrete juvenile hormone when reimplanted into last instar larvae.Acknowledgments. We thank Mr K. Dorn, Mrs L. Dolezal, Mrs V. Nötzli-Graf, Mr K.H. Trautmann and Mr A. Schuler for technical help, Dr W. Vogel and Dr A. Dübendorfer for valuable discussions.     

Liquid marbles.

The transport of a small amount of liquid on a solid is not a simple process, owing to the nature of the contact between the two phases. Setting a liquid droplet in motion requires non-negligible forces (because the contact-angle hysteresis generates a force opposing the motion), and often results in the deposition of liquid behind the drop. Different methods of levitation-electrostatic, electromagnetic, acoustic, or even simpler aerodynamic techniques-have been proposed to avoid this wetting problem, but all have proved to be rather cumbersome. Here we propose a simple alternative, which consists of encapsulating an aqueous liquid droplet with a hydrophobic powder. The resulting 'liquid marbles' are found to behave like a soft solid, and show dramatically reduced adhesion to a solid surface. As a result, motion can be generated using gravitational, electrical and magnetic fields. Moreover, because the viscous friction associated with motion is very small, we can achieve quick displacements of the droplets without any leaks. All of these features are of potential benefit in microfluidic applications, and also permit the study of a drop in a non-wetting situation-an issue of renewed interest following the recent achievement of super-hydrophobic substrates.     

Superconductivity in CaCuO2 as a result of field-effect doping.

Understanding the doping mechanisms in the simplest superconducting copper oxide-the infinite-layer compound ACuO2 (where A is an alkaline earth metal)-is an excellent way of investigating the pairing mechanism in high-transition-temperature (high-Tc) superconductors more generally. Gate-induced modulation of the carrier concentration to obtain superconductivity is a powerful means of achieving such understanding: it minimizes the effects of potential scattering by impurities, and of structural modifications arising from chemical dopants. Here we report the transport properties of thin films of the infinite-layer compound CaCuO2 using field-effect doping. At high hole- and electron-doping levels, superconductivity is induced in the nominally insulating material. Maximum values of Tc of 89 K and 34 K are observed respectively for hole- and electron-type doping of around 0.15 charge carriers per CuO2. We can explore the whole doping diagram of the CuO2 plane while changing only a single electric parameter, the gate voltage.     

Novel neurotrophic factor CDNF protects and rescues midbrain dopamine neurons in vivo

In Parkinson's disease, brain dopamine neurons degenerate most prominently in the substantia nigra. Neurotrophic factors promote survival, differentiation and maintenance of neurons in developing and adult vertebrate nervous system. The most potent neurotrophic factor for dopamine neurons described so far is the glial-cell-line-derived neurotrophic factor (GDNF). Here we have identified a conserved dopamine neurotrophic factor (CDNF) as a trophic factor for dopamine neurons. CDNF, together with its previously described vertebrate and invertebrate homologue the mesencephalic-astrocyte-derived neurotrophic factor, is a secreted protein with eight conserved cysteine residues, predicting a unique protein fold and defining a new, evolutionarily conserved protein family. CDNF (Armetl1) is expressed in several tissues of mouse and human, including the mouse embryonic and postnatal brain. In vivo, CDNF prevented the 6-hydroxydopamine (6-OHDA)-induced degeneration of dopaminergic neurons in a rat experimental model of Parkinson's disease. A single injection of CDNF before 6-OHDA delivery into the striatum significantly reduced amphetamine-induced ipsilateral turning behaviour and almost completely rescued dopaminergic tyrosine-hydroxylase-positive cells in the substantia nigra. When administered four weeks after 6-OHDA, intrastriatal injection of CDNF was able to restore the dopaminergic function and prevent the degeneration of dopaminergic neurons in substantia nigra. Thus, CDNF was at least as efficient as GDNF in both experimental settings. Our results suggest that CDNF might be beneficial for the treatment of Parkinson's disease.     

Visualizing single-molecule diffusion in mesoporous materials

Periodic mesoporous materials formed through the cooperative self-assembly of surfactants and framework building blocks can assume a variety of structures, and their widely tuneable properties make them attractive hosts for numerous applications. Because the molecular movement in the pore system is the most important and defining characteristic of porous materials, it is of interest to learn about this behaviour as a function of local structure. Generally, individual fluorescent dye molecules can be used as molecular beacons with which to explore the structure of--and the dynamics within--these porous hosts, and single-molecule fluorescence techniques provide detailed insights into the dynamics of various processes, ranging from biology to heterogeneous catalysis. However, optical microscopy methods cannot directly image the mesoporous structure of the host system accommodating the diffusing molecules, whereas transmission electron microscopy provides detailed images of the porous structure, but no dynamic information. It has therefore not been possible to 'see' how molecules diffuse in a real nanoscale pore structure. Here we present a combination of electron microscopic mapping and optical single-molecule tracking experiments to reveal how a single luminescent dye molecule travels through linear or strongly curved sections of a mesoporous channel system. In our approach we directly correlate porous structures detected by transmission electron microscopy with the diffusion dynamics of single molecules detected by optical microscopy. This opens up new ways of understanding the interactions of host and guest.     

Lanthanide contraction and magnetism in the heavy rare earth elements

The heavy rare earth elements crystallize into hexagonally close packed (h.c.p.) structures and share a common outer electronic configuration, differing only in the number of 4f electrons they have. These chemically inert 4f electrons set up localized magnetic moments, which are coupled via an indirect exchange interaction involving the conduction electrons. This leads to the formation of a wide variety of magnetic structures, the periodicities of which are often incommensurate with the underlying crystal lattice. Such incommensurate ordering is associated with a 'webbed' topology of the momentum space surface separating the occupied and unoccupied electron states (the Fermi surface). The shape of this surface-and hence the magnetic structure-for the heavy rare earth elements is known to depend on the ratio of the interplanar spacing c and the interatomic, intraplanar spacing a of the h.c.p. lattice. A theoretical understanding of this problem is, however, far from complete. Here, using gadolinium as a prototype for all the heavy rare earth elements, we generate a unified magnetic phase diagram, which unequivocally links the magnetic structures of the heavy rare earths to their lattice parameters. In addition to verifying the importance of the c/a ratio, we find that the atomic unit cell volume plays a separate, distinct role in determining the magnetic properties: we show that the trend from ferromagnetism to incommensurate ordering as atomic number increases is connected to the concomitant decrease in unit cell volume. This volume decrease occurs because of the so-called lanthanide contraction, where the addition of electrons to the poorly shielding 4f orbitals leads to an increase in effective nuclear charge and, correspondingly, a decrease in ionic radii.