Chebyshev Type Inequalities Involving the Fractional Integral Operator Containing Multi-Index Mittag-Leffler Function in the Kernel

Recently, several authors have investigated Chebyshev type inequalities for numerous fractional integral operators. Being motivated by the work done by earlier researchers and their numerous applications in probability, transform theory, numerical quadrature, statistical problems and its significance in fractional boundary value problems. We aim to evaluate Chebyshev type inequalities involving fractional integral operator containing multi-index Mittag-Leffler function in the kernel. Admissible connections of the results mentioned in this article to those associated with previously established familiar fractional integral operators have been pointed out

Signal Transduction Pathways in the Pentameric Ligand-Gated Ion Channels

The mechanisms of allosteric action within pentameric ligand-gated ion channels (pLGICs) remain to be determined. Using crystallography, site-directed mutagenesis, and two-electrode voltage clamp measurements, we identified two functionally relevant sites in the extracellular (EC) domain of the bacterial pLGIC from Gloeobacter violaceus (GLIC). One site is at the C-loop region, where the NQN mutation (D91N, E177Q, and D178N) eliminated inter-subunit salt bridges in the open-channel GLIC structure and thereby shifted the channel activation to a higher agonist concentration. The other site is below the C-loop, where binding of the anesthetic ketamine inhibited GLIC currents in a concentration dependent manner. To understand how a perturbation signal in the EC domain, either resulting from the NQN mutation or ketamine binding, is transduced to the channel gate, we have used the Perturbation-based Markovian Transmission (PMT) model to determine dynamic responses of the GLIC channel and signaling pathways upon initial perturbations in the EC domain of GLIC. Despite the existence of many possible routes for the initial perturbation signal to reach the channel gate, the PMT model in combination with Yen's algorithm revealed that perturbation signals with the highest probability flow travel either via the β1-β2 loop or through pre-TM1. The β1-β2 loop occurs in either intra- or inter-subunit pathways, while pre-TM1 occurs exclusively in inter-subunit pathways. Residues involved in both types of pathways are well supported by previous experimental data on nAChR. The direct coupling between pre-TM1 and TM2 of the adjacent subunit adds new insight into the allosteric signaling mechanism in pLGICs. © 2013 Mowrey et al

Gating at the Mouth of the Acetylcholine Receptor Channel: Energetic Consequences of Mutations in the αM2-Cap

Gating of nicotinic acetylcholine receptors from a C(losed) to an O(pen) conformation is the initial event in the postsynaptic signaling cascade at the vertebrate nerve-muscle junction. Studies of receptor structure and function show that many residues in this large, five-subunit membrane protein contribute to the energy difference between C and O. Of special interest are amino acids located at the two transmitter binding sites and in the narrow region of the channel, where C↔O gating motions generate a low↔high change in the affinity for agonists and in the ionic conductance, respectively. We have measured the energy changes and relative timing of gating movements for residues that lie between these two locations, in the C-terminus of the pore-lining M2 helix of the α subunit (‘αM2-cap’). This region contains a binding site for non-competitive inhibitors and a charged ring that influences the conductance of the open pore. αM2-cap mutations have large effects on gating but much smaller effects on agonist binding, channel conductance, channel block and desensitization. Three αM2-cap residues (αI260, αP265 and αS268) appear to move at the outset of channel-opening, about at the same time as those at the transmitter binding site. The results suggest that the αM2-cap changes its secondary structure to link gating motions in the extracellular domain with those in the channel that regulate ionic conductance

Experimental evidence for a light and broad scalar resonance in D+→π−π+π+D^+\to \pi^-\pi^+\pi^+ decay

From a sample of $1172 \pm 61$ $D^+ \to \pi^- \pi^+ \pi^+$ decay, we find $\Gamma (D^+ \to \pi^- \pi^+ \pi^+) / \Gamma (D^+ \to K^- \pi^+ \pi^+) = 0.0311 \pm 0.0018 ^{+0.0016}_{-0.0026}$. Using a coherent amplitude analysis to fit the Dalitz plot of this decays, we find strong evidence that a scalar resonance of mass $478^{+24}_{-23} \pm 17$ MeV/$c^2$ and width $324^{+42}_{-40} \pm 21$ MeV/$c^2$ accounts for approximately half of all decays.Comment: 10 pages, 3 eps figure

Fermilab E791

Fermilab E791, a very high statistics charm particle experiment, recently completed its data taking at Fermilab's Tagged Photon Laboratory. Over 20 billion events were recorded through a loose transverse energy trigger and written to 8mm tape in the the 1991-92 fixed target run at Fermilab. This unprecedented data sample containing charm is being analysed on many-thousand MIP RISC computing farms set up at sites in the collaboration. A glimpse of the data taking and analysis effort is presented. We also show some preliminary results for common charm decay modes. Our present analysis indicates a very rich yield of over 200K reconstructed charm decays.Comment: 4 pages, 1 figure, LaTe

Dalitz Plot Analysis of the Decay D^+ --> K^- pi^+ pi^+ and Indication of a Low-Mass Scalar K pi Resonance

We study the Dalitz plot of the decay D^+ --> K^- pi^+ pi^+ with a sample of 15090 events from Fermilab experiment E791. Modeling the decay amplitude as the coherent sum of known K pi resonances and a uniform nonresonant term, we do not obtain an acceptable fit. If we allow the mass and width of the K^*_0(1430) to float, we obtain values consistent with those from PDG but the chi^2 per degree of freedom of the fit is still unsatisfactory. A good fit is found when we allow for the presence of an additional scalar resonance, with mass 797 +/- 19 +/- 43 MeV/c^2 and width 410 +/- 43 +/- 87 MeV/c^2. The mass and width of the K^*_0(1430) become 1459 +/- 7 +/- 5 MeV/c^2 and 175 +/- 12 +/- 12 MeV/c^2, respectively. Our results provide new information on the scalar sector in hadron spectroscopy.Comment: Accepted for publication in Physical Review Letter