Fractional Operators, Dirichlet Averages, and Splines

Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose of this paper to show that there are deep and interesting relationships between these three areas. First a brief introduction to fractional differential and integral operators defined on Lizorkin spaces is presented and some of their main properties exhibited. This particular approach has the advantage that several definitions of fractional derivatives and integrals coincide. We then introduce Dirichlet averages and extend their definition to an infinite-dimensional setting that is needed to exhibit the relationships to splines of complex order. Finally, we focus on splines of complex order and, in particular, on cardinal B-splines of complex order. The fundamental connections to fractional derivatives and integrals as well as Dirichlet averages are presented

B-mode and colour Doppler sonographic examination of the milk vein and musculophrenic vein in dry cows and cows with a milk yield of 10 and 20 kg

BACKGROUND: This study investigated the effect of milk yield on blood flow variables in the milk vein and musculophrenic vein in dairy cows. METHODS: Five healthy dry cows, five cows with a daily milk yield of 10 kg and five others with a daily milk yield of 20 kg underwent B-mode and colour Doppler sonographic examination. The diameter of the veins, blood flow velocities and blood flow volumes were measured on both sides in standing, non-sedated cows using a 7.5 MHz linear transducer. RESULTS: Lactating cows had significantly higher blood flow velocities in the milk vein than dry cows; the maximum blood flow velocity of dry cows and those with a daily milk yield of 10 and 20 kg were 14.04, 38.77 and 39.49 cm/s, respectively, the minimum velocities were 0.63, 3.02 and 2.64 cm/s, respectively, and the mean maximum velocities were 8.21, 26.67 und 28.22 cm/s, respectively. Cows producing 20 kg of milk a day had a blood flow volume of 3.09 l/min, which was significantly higher than 0.79 l/min recorded in dry cows. Lactating cows had significantly higher mean maximum blood flow velocities in the musculophrenic vein than dry cows. Blood flow variables of both veins did not differ significantly between the left and right side. CONCLUSION: This study showed that milk yield has a profound effect on blood flow variables in the milk vein and to a lesser extent the musculophrenic vein. This must be taken into consideration in future Doppler sonographic studies of these veins and possibly other vessels. Furthermore, measurements on one side are representative of both sides

EHEC – kein spezifisches Problem nachhaltiger Landwirtschaft - [EHEC – A problem not specific to sustainable agriculture] [La EHEC – no es un problema específico de la agricultura sostenible] - [EHEC – Non è un problema specifi-co dell’agricoltura biologica] - [ECEH n’est pas un problème dû à l’agriculture durable] - [EHEC – nem speciálisan a fenntartható mezőgazdaság gondja] - [ECEH n’est pas un problème dû à l’agriculture durable]

DEUTSCH Über den EHEC-Erreger, der in Deutschland zu über dreissig tragischen Todesfällen geführt hat, ist viel spekuliert worden. Unterdessen konnten die Verbreitungswege nahezu aufgeklärt werden, während die Entstehung des Krankheitserregers noch weitgehend unklar ist. Im Zusammenhang mit dem EHEC-Ausbruch wurde auch die Frage erörtert, ob bestimmte Landwirtschaftsmethoden (zum Beispiel gemischte Betriebe mit Tierhaltung und Pflanzenbau oder die organische Düngung von Gemüse) oder ob gewisse Hygienisierungsmethoden für frische, konsumfähige Produkte(wie zum Beispiel die Verwendung von schonenden, weniger Rückstände verursachenden organischen Säuren) das Risiko erhöhen könnten. Diese Dokumentation geht nicht auf die aktuellen Fälle von EHEC in Norddeutschland ein, sondern liefert an diesem Beispiel Hintergrundinformationen zur Frage, wie nachhaltige, in Kreisläufen arbeitende Landwirtschaftsmethoden mit vom Tier auf den Menschen übertragbare Krankheitserreger (Zoonosen) umgehen. ENGLISH There has been much speculation about the pathogenic EHEC bacterial strain that has tragically claimed the lives of more than 30 people so far in Germany. Meanwhile, the transmission pathways have for the most part been identified. The origin of the pathogen, however, is largely unclear. In the context of the EHEC outbreak there have been debates as to whether certain agriculturalmethods (e.g. mixed holdings including both livestock and crop production, or the use of organic fertilizers for vegetable production) or certain sanitization methods for fresh consumable products (such as the use of organic acids, a mild treatment that leaves fewer residues) may increase the risk of infection. This document does not address the current epidemiological situation of the outbreak in northern Germany. Its purpose is rather to provide background information on the question of how sustainable agricultural methods based on nutrient cycling deal with pathogens that can be transmitted from animals to humans (zoonoses). CASTELLANO Mucho se ha especulado sobre la bacteria patógena Escherichia coli enterohemorrágica (ECEH), que ha ocasionado más de treinta muertes trágicas en Alemania. Hasta ahora casi se ha podido esclarecer la via de su propagación, mientras que sigue estando poco claro como ha aparecido el agente patógeno. Con el brote de la ECEH se ha cuestionado si determinadas prácticas agrícolas (por ejemplo, mantener explotaciones mixtas con ganado y cultivos, o la fertilización orgánica de los vegetales) o si los métodos de higiene para productos frescos, listos para el consumo (como por ejemplo, el uso de ácidos orgánicos menos agresivos y con menor riesgo de dejar residudos), pudieran incrementar los riesgos. Esta documento no se refiere sólo a los casos actuales de ECEH en el norte de Alemania, sino que proporciona, información básica de fondo, aprovechando este ejemplo, sobre como los métodos de producción agraria de ciclos cerrados con animales evitan forma sostenible que los patógenos generadores de enfermedades contagiosas (zoonosis) trasmisibles al ser humano. ITALIANO A proposito dell’insorgenza di EHEC è stata sollevata la questione se determinati metodi agricoli (per esempio aziende miste con allevamento di animali e produzione vegetale o la concimazione organica di ortaggi) oppure se determinati metodi di igienizzazione per pro-dotti freschi adatti al consumo (come per esempio l’impiego di acidi organici che provocano meno residui) possano aumentare i rischi. La presente documentazione non entra nei particolari degli attuali casi di EHEC nella Ger-mania settentrionale bensì fornisce informazioni d’approfondimento su come i me-todi agri-coli sostenibili basati sui cicli degli elementi nutritivi trattano la questione degli agenti pato-geni trasmissibili dagli animali all’uomo (zoonosi). HUNGARIAN Sok a spekuláció az EHEC kórokozót illetően, amely Németországban harmincnál is több tragikus halálesethez vezetett. Időközben a terjedés útját már csaknem teljesen felderítették, míg a kórokozó létrejöttéről még szinte semmit sem tudunk. Az EHEC fertőzés kitörése kapcsán az a kérdés is felmerült, hogy bizonyos mezőgazdasági módszerek (pl. a vegyes üzemek, melyek egyaránt foglalkoznak növénytermesztéssel és állattenyésztéssel, vagy a zöldségek szerves trágyázása), ill. a friss, fogyasztásra kész termékek egyes fertőtlenítési módszerei (így pl. a kímélőbb, kevesebb hulladékot eredményező szerves savak alkalmazása) nem növelhetik-e a kockázatot. A jelen tanulmány nem a Németország északi részén kialakult aktuális EHEC esetekkel foglalkozik, hanem háttér-információval szolgál arról, hogy a körforgásos működésű, fenntartható mezőgazdasági módszerek milyen kapcsolatban lehetnek az állatról emberre terjedő betegségekkel, az ún. zoonózisokkal. FRANCAIS ECEH n’est pas un problème dû à l’agriculture durabl

Domain wall mobility in nanowires: transverse versus vortex walls

The motion of domain walls in ferromagnetic, cylindrical nanowires is investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a classical spin model in which energy contributions from exchange, crystalline anisotropy, dipole-dipole interaction, and a driving magnetic field are considered. Depending on the diameter, either transverse domain walls or vortex walls are found. The transverse domain wall is observed for diameters smaller than the exchange length of the given material. Here, the system behaves effectively one-dimensional and the domain wall mobility agrees with a result derived for a one-dimensional wall by Slonczewski. For low damping the domain wall mobility decreases with decreasing damping constant. With increasing diameter, a crossover to a vortex wall sets in which enhances the domain wall mobility drastically. For a vortex wall the domain wall mobility is described by the Walker-formula, with a domain wall width depending on the diameter of the wire. The main difference is the dependence on damping: for a vortex wall the domain wall mobility can be drastically increased for small values of the damping constant up to a factor of $1/\alpha^2$.Comment: 5 pages, 6 figure

Relative humidity and its effect on aerosol optical depth in the vicinity of convective clouds

The hygroscopic growth of aerosols is controlled by the relative humidity (RH) and changes the aerosols' physical and hence optical properties. Observational studies of aerosol–cloud interactions evaluate the aerosol concentration using optical parameters, such as the aerosol optical depth (AOD), which can be affected by aerosol humidification. In this study we evaluate the RH background and variance values, in the lower cloudy atmosphere, an additional source of variance in AOD values beside the natural changes in aerosol concentration. In addition, we estimate the bias in RH and AOD, related to cloud thickness. This provides the much needed range of RH-related biases in studies of aerosol–cloud interaction. Twelve years of radiosonde measurements (June–August) in thirteen globally distributed stations are analyzed. The estimated non-biased AOD variance due to day-to-day changes in RH is found to be around 20% and the biases linked to cloud development around 10%. Such an effect is important and should be considered in direct and indirect aerosol effect estimations but it is inadequate to account for most of the AOD trend found in observational studies of aerosol–cloud interactions

Quantum Statistics of Interacting Dimer Spin Systems

The compound TlCuCl3 represents a model system of dimerized quantum spins with strong interdimer interactions. We investigate the triplet dispersion as a function of temperature by inelastic neutron scattering experiments on single crystals. By comparison with a number of theoretical approaches we demonstrate that the description of Troyer, Tsunetsugu, and Wuertz [Phys. Rev. B 50, 13515 (1994)] provides an appropriate quantum statistical model for dimer spin systems at finite temperatures, where many-body correlations become particularly important.Comment: 4 pages, 4 figures, to appear in Physical Review Letter

Lifetimes of C-60(2-) and C-70(2-) dianions in a storage ring

C-60(2-) and C-70(2-) dianions have been produced by electrospray of the monoanions and subsequent electron pickup in a Na vapor cell. The dianions were stored in an electrostatic ring and their decay by electron emission was measured up to 1 s after injection. While C-70(2-) ions are stable on this time scale, except for a small fraction of the ions which have been excited by gas collisions, most of the C-60(2-) ions decay on a millisecond time scale, with a lifetime depending strongly on their internal temperature. The results can be modeled as decay by electron tunneling through a Coulomb barrier, mainly from thermally populated triplet states about 120 meV above a singlet ground state. At times longer than about 100 ms, the absorption of blackbody radiation plays an important role for the decay of initially cold ions. The tunneling rates obtained from the modeling, combined with WKB estimates of the barrier penetration, give a ground-state energy 200 +/- 30 meV above the energy of the monoanion plus a free electron and a ground-state lifetime of the order of 20 s. (c) 2006 American Institute of Physics

Molecular Hydrodynamics: Vortex Formation and Sound Wave Propagation

In the present study, quantitative feasibility tests of the hydrodynamic description of a two-dimensional fluid at the molecular level are performed, both with respect to length and time scales. Using high-resolution fluid velocity data obtained from extensive molecular dynamics simulations, we computed the transverse and longitudinal components of the velocity field by the Helmholtz decomposition and compared them with those obtained from the linearized Navier-Stokes (LNS) equations with time-dependent transport coefficients. By investigating the vortex dynamics and the sound wave propagation in terms of these field components, we confirm the validity of the LNS description for times comparable to or larger than several mean collision times. The LNS description still reproduces the transverse velocity field accurately at smaller times, but it fails to predict characteristic patterns of molecular origin visible in the longitudinal velocity field. Based on these observations, we validate the main assumptions of the mode-coupling approach. The assumption that the velocity autocorrelation function can be expressed in terms of the fluid velocity field and the tagged particle distribution is found to be remarkably accurate even for times comparable to or smaller than the mean collision time. This suggests that the hydrodynamic-mode description remains valid down to the molecular scale

The Supercooling of a Nematic Liquid Crystal

We investigate the supercooling of a nematic liquid crystal using fluctuating non-linear hydrodynamic equations. The Martin-Siggia-Rose formalism is used to calculate renormalized transport coefficients to one-loop order. Similar theories for isotropic liquids have shown substantial increases of the viscosities as the liquid is supercooled or compressed due to feedback from the density fluctuations which are freezing. We find similar results here for the longitudinal and various shear viscosities of the nematic. However, the two viscosities associated with the nematic director motion do not grow in any dramatic way; i.e.\ there is no apparent freezing of the director modes within this hydrodynamic formalism. Instead a glassy state of the nematic may arise from a ``random anisotropy" coupling of the director to the frozen density.Comment: Late

Effect of side-chain asymmetry on the intermolecular structure and order-disorder transition in alkyl-substituted polyfluorenes

We study relations among the side-chain asymmetry, structure, and order-disorder transition (ODT) in hairy-rod-type poly(9,9-dihexylfluorene) (PF6) with two identical side chains and atactic poly(9-octyl-9-methylfluorene) (PF1-8) with two different side chains per repeat. PF6 and PF1-8 organize into alternating side-chain and backbone layers that transform into an isotropic phase at T-ODT(PF6) and T-bi(ODT)(PF1-8). We interpret polymers in terms of monodisperse and bidisperse brushes and predict scenarios T-ODT <T-bi(ODT) and T-ODT similar to T-bi(ODT) for high and low grafting densities (the side-chain length above or below the average grafting distance). Calorimetry and x-ray scattering indicate the condition T-ODT(PF6) similar to T-bi(ODT)(PF1-8) following the low grafting prediction. PF6 side chains coming from the alternating backbone layers appear as two separate layers with thickness H(PF6), whereas PF1-8 side chains appear as an indistinguishable bilayer with a half thickness H-bilayer(PF1-8)/2 approximate to H(PF6). The low grafting density region is structurally possible but not certain for PF6 and confirmed for PF1-8.Peer reviewe