Painlev\'e V and time dependent Jacobi polynomials

In this paper we study the simplest deformation on a sequence of orthogonal polynomials, namely, replacing the original (or reference) weight $w_0(x)$ defined on an interval by $w_0(x)e^{-tx}.$ It is a well-known fact that under such a deformation the recurrence coefficients denoted as $\alpha_n$ and $\beta_n$ evolve in $t$ according to the Toda equations, giving rise to the time dependent orthogonal polynomials, using Sogo's terminology. The resulting "time-dependent" Jacobi polynomials satisfy a linear second order ode. We will show that the coefficients of this ode are intimately related to a particular Painlev\'e V. In addition, we show that the coefficient of $z^{n-1}$ of the monic orthogonal polynomials associated with the "time-dependent" Jacobi weight, satisfies, up to a translation in $t,$ the Jimbo-Miwa $\sigma$-form of the same $P_{V};$ while a recurrence coefficient $\alpha_n(t),$ is up to a translation in $t$ and a linear fractional transformation $P_{V}(\alpha^2/2,-\beta^2/2, 2n+1+\alpha+\beta,-1/2).$ These results are found from combining a pair of non-linear difference equations and a pair of Toda equations. This will in turn allow us to show that a certain Fredholm determinant related to a class of Toeplitz plus Hankel operators has a connection to a Painlev\'e equation

On the Inverse Problem Relative to Dynamics of the w Function

In this paper we shall study the inverse problem relative to dynamics of the w function which is a special arithmetic function and shall get some results.Comment: 11 page

Pair Correlation Function of Wilson Loops

We give a path integral prescription for the pair correlation function of Wilson loops lying in the worldvolume of Dbranes in the bosonic open and closed string theory. The results can be applied both in ordinary flat spacetime in the critical dimension d or in the presence of a generic background for the Liouville field. We compute the potential between heavy nonrelativistic sources in an abelian gauge theory in relative collinear motion with velocity v = tanh(u), probing length scales down to r_min^2 = 2 \pi \alpha' u. We predict a universal -(d-2)/r static interaction at short distances. We show that the velocity dependent corrections to the short distance potential in the bosonic string take the form of an infinite power series in the dimensionless variables z = r_min^2/r^2, uz/\pi, and u^2.Comment: 16 pages, 1 figure, Revtex. Corrected factor of two in potential. Some changes in discussio

Ground resonance analysis using a substructure modeling approach

A convenient and versatile procedure for modeling and analyzing ground resonance phenomena is described and illustrated. A computer program is used which dynamically couples differential equations with nonlinear and time dependent coefficients. Each set of differential equations may represent a component such as a rotor, fuselage, landing gear, or a failed damper. Arbitrary combinations of such components may be formulated into a model of a system. When the coupled equations are formed, a procedure is executed which uses a Floquet analysis to determine the stability of the system. Illustrations of the use of the procedures along with the numerical examples are presented

Superconductivity in the Two-Dimensional tt-JJ Model at Low Hole Doping

By combining a generalized Lanczos scheme with the variational Monte Carlo method we can optimize the short- and long-range properties of the groundstate separately. This allows us to measure the long-range order of the groundstate of the $t$-$J$ model as a function of the coupling constant $J/t$, and identify a region of finite d-wave superconducting long-range order. With a lattice size of 50 sites we can reliably examine hole densities down to 0.16.Comment: 12 pages and 4 PostScript figures, ReVTeX 3.0, ETH-TH/94-1

Accessibility of referent information influences sentence planning : An eye-tracking study

Acknowledgments We thank Phoebe Ye and Gouming Martens for help with data collection for Experiment 1 and 2, respectively. This research was supported by the European Research Council for the ERC Starting Grant (206198) to YC.Peer reviewedPublisher PD

Heterodimerization of apelin receptor and neurotensin receptor 1 induces phosphorylation of ERK1/2 and cell proliferation via Gαq-mediated mechanism

Dimerization of G protein-coupled receptors (GPCRs) is crucial for receptor function including agonist affinity, efficacy, trafficking and specificity of signal transduction, including G protein coupling. Emerging data suggest that the cardiovascular system is the main target of apelin, which exerts an overall neuroprotective role, and is a positive regulator of angiotensin-converting enzyme 2 (ACE2) in heart failure. Moreover, ACE2 cleaves off C-terminal residues of vasoactive peptides including apelin-13, and neurotensin that activate the apelin receptor (APJ) and neurotensin receptor 1 (NTSR1) respectively, that belong to the A class of GPCRs. Therefore, based on the similar mode of modification by ACE2 at peptide level, the homology at amino acid level and the capability of forming dimers with other GPCRs, we have been suggested that APJ and NTSR1 can form a functional heterodimer. Using co-immunoprecipitation, BRET and FRET, we provided conclusive evidence of heterodimerization between APJ and NTSR1 in a constitutive and induced form. Upon agonist stimulation, hetrodimerization enhanced ERK1/2 activation and increased proliferation via activation of Gq α-subunits. These novel data provide evidence for a physiological role of APJ/NTSR1 heterodimers in terms of ERK1/2 activation and increased intracellular calcium and induced cell proliferation and provide potential new pharmaceutical targets for cardiovascular disease. © 2014 The Authors

Synthetic biology: advancing biological frontiers by building synthetic systems

Advances in synthetic biology are contributing to diverse research areas, from basic biology to biomanufacturing and disease therapy. We discuss the theoretical foundation, applications, and potential of this emerging field