Galerkin FEM for fractional order parabolic equations with initial data in H−s, 0<s≤1H^{-s},~0 < s \le 1

We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that $\Omega\subset \mathbb{R}^d$, $d=1,2,3$ is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in $L_2$- and $H^1$-norms for initial data in $H^{-s}(\Omega),~0\le s \le 1$. We confirm our theoretical findings with a number of numerical tests that include initial data $v$ being a Dirac $\delta$-function supported on a $(d-1)$-dimensional manifold.Comment: 13 pages, 3 figure

Non-Newtonian fluid flow through three-dimensional disordered porous media

We investigate the flow of various non-Newtonian fluids through three-dimensional disordered porous media by direct numerical simulation of momentum transport and continuity equations. Remarkably, our results for power-law (PL) fluids indicate that the flow, when quantified in terms of a properly modified permeability-like index and Reynolds number, can be successfully described by a single (universal) curve over a broad range of Reynolds conditions and power-law exponents. We also study the flow behavior of Bingham fluids described in terms of the Herschel-Bulkley model. In this case, our simulations reveal that the interplay of ({\it i}) the disordered geometry of the pore space, ({\it ii}) the fluid rheological properties, and ({\it iii}) the inertial effects on the flow is responsible for a substantial enhancement of the macroscopic hydraulic conductance of the system at intermediate Reynolds conditions. This anomalous condition of ``enhanced transport'' represents a novel feature for flow in porous materials.Comment: 5 pages, 5 figures. This article appears also in Physical Review Letters 103 194502 (2009

Infrared spectroscopy of diatomic molecules - a fractional calculus approach

The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically solving the fractional Schr\"odinger equation based on the Riemann and Caputo definition of a fractional derivative. The fractional approach allows a smooth transition between vibrational and rotational type spectra, which is shown to be an appropriate tool to analyze IR spectra of diatomic molecules.Comment: revised + extended version, 9 pages, 6 figure

Universal Rights and Wrongs

This paper argues for the important role of customers as a source of competitive advantage and firm growth, an issue which has been largely neglected in the resource-based view of the firm. It conceptualizes Penrose’s (1959) notion of an ‘inside track’ and illustrates how in-depth knowledge about established customers combines with joint problem-solving activities and the rapid assimilation of new and previously unexploited skills and resources. It is suggested that the inside track represents a distinct and perhaps underestimated way of generating rents and securing long-term growth. This also implies that the sources of sustainable competitive advantage in important respects can be sought in idiosyncratic interfirm relationships rather than within the firm itself

Human Mas-related G protein-coupled receptors-X1 induce chemokine receptor 2 expression in rat dorsal root ganglia neurons and release of chemokine ligand 2 from the human LAD-2 mast cell line

Primate-specific Mas-related G protein-coupled receptors-X1 (MRGPR-X1) are highly enriched in dorsal root ganglia (DRG) neurons and induce acute pain. Herein, we analyzed effects of MRGPR-X1 on serum response factors (SRF) or nuclear factors of activated T cells (NFAT), which control expression of various markers of chronic pain. Using HEK293, DRG neuron-derived F11 cells and cultured rat DRG neurons recombinantly expressing human MRGPR-X1, we found activation of a SRF reporter gene construct and induction of the early growth response protein-1 via extracellular signal-regulated kinases-1/2 known to play a significant role in the development of inflammatory pain. Furthermore, we observed MRGPR-X1-induced up-regulation of the chemokine receptor 2 (CCR2) via NFAT, which is considered as a key event in the onset of neuropathic pain and, so far, has not yet been described for any endogenous neuropeptide. Up-regulation of CCR2 is often associated with increased release of its endogenous agonist chemokine ligand 2 (CCL2). We also found MRGPR-X1-promoted release of CCL2 in a human connective tissue mast cell line endogenously expressing MRGPR-X1. Thus, we provide first evidence to suggest that MRGPR-X1 induce expression of chronic pain markers in DRG neurons and propose a so far unidentified signaling circuit that enhances chemokine signaling by acting on two distinct yet functionally co-operating cell types. Given the important role of chemokine signaling in pain chronification, we propose that interruption of this signaling circuit might be a promising new strategy to alleviate chemokine-promoted pain

Inclusive V0V^0 Production Cross Sections from 920 GeV Fixed Target Proton-Nucleus Collisions

Inclusive differential cross sections $d\sigma_{pA}/dx_F$ and $d\sigma_{pA}/dp_t^2$ for the production of \kzeros, \lambdazero, and \antilambda particles are measured at HERA in proton-induced reactions on C, Al, Ti, and W targets. The incident beam energy is 920 GeV, corresponding to $\sqrt {s} = 41.6$ GeV in the proton-nucleon system. The ratios of differential cross sections \rklpa and \rllpa are measured to be $6.2\pm 0.5$ and $0.66\pm 0.07$, respectively, for \xf $\approx-0.06$. No significant dependence upon the target material is observed. Within errors, the slopes of the transverse momentum distributions $d\sigma_{pA}/dp_t^2$ also show no significant dependence upon the target material. The dependence of the extrapolated total cross sections $\sigma_{pA}$ on the atomic mass $A$ of the target material is discussed, and the deduced cross sections per nucleon $\sigma_{pN}$ are compared with results obtained at other energies.Comment: 17 pages, 7 figures, 5 table

Circuit dissection of the role of somatostatin in itch and pain

Stimuli that elicit itch are detected by sensory neurons that innervate the skin. This information is processed by the spinal cord; however, the way in which this occurs is still poorly understood. Here we investigated the neuronal pathways for itch neurotransmission, particularly the contribution of the neuropeptide somatostatin. We find that in the periphery, somatostatin is exclusively expressed in Nppb+ neurons, and we demonstrate that Nppb+somatostatin+ cells function as pruriceptors. Employing chemogenetics, pharmacology and cell-specific ablation methods, we demonstrate that somatostatin potentiates itch by inhibiting inhibitory dynorphin neurons, which results in disinhibition of GRPR+ neurons. Furthermore, elimination of somatostatin from primary afferents and/or from spinal interneurons demonstrates differential involvement of the peptide released from these sources in itch and pain. Our results define the neural circuit underlying somatostatin-induced itch and characterize a contrasting antinociceptive role for the peptide

Neuronal circuitry for pain processing in the dorsal horn

Neurons in the spinal dorsal horn process sensory information, which is then transmitted to several brain regions, including those responsible for pain perception. The dorsal horn provides numerous potential targets for the development of novel analgesics and is thought to undergo changes that contribute to the exaggerated pain felt after nerve injury and inflammation. Despite its obvious importance, we still know little about the neuronal circuits that process sensory information, mainly because of the heterogeneity of the various neuronal components that make up these circuits. Recent studies have begun to shed light on the neuronal organization and circuitry of this complex region

Effect of Long-Term Zinc Pollution on Soil Microbial Community Resistance to Repeated Contamination

The aim of the study was to compare the effects of stress (contamination trials) on the microorganisms in zinc-polluted soil (5,018 mg Zn kg−1 soil dry weight) and unpolluted soil (141 mg Zn kg−1 soil dw), measured as soil respiration rate. In the laboratory, soils were subjected to copper contamination (0, 500, 1,500 and 4,500 mg kg−1 soil dw), and then a bactericide (oxytetracycline) combined with a fungicide (captan) along with glucose (10 mg g−1 soil dw each) were added. There was a highly significant effect of soil type, copper treatment and oxytetracycline/captan treatment. The initial respiration rate of chronically zinc-polluted soil was higher than that of unpolluted soil, but in the copper treatment it showed a greater decline. Microorganisms in copper-treated soil were more susceptible to oxytetracycline/captan contamination. After the successive soil contamination trials the decline of soil respiration was greater in zinc-polluted soil than in unpolluted soil