Calculation of some determinants using the s-shifted factorial

Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a generalization for non-negative integers of the power function, the rising factorial (or Pochammer's symbol) and the falling factorial. It is a special case of polynomial sequence of the binomial type studied in combinatorics theory. In terms of the gamma function, an extension is defined for negative integers and even complex values. Properties, mainly composition laws and binomial formulae, are given. They are used to evaluate families of generalized Vandermonde determinants with s-shifted factorials as elements, instead of power functions.Comment: 25 pages; added section 5 for some examples of application

Fuels treatment and wildfire effects on runoff from Sierra Nevada mixed-conifer forests

We applied an eco-hydrologic model (Regional Hydro-Ecologic Simulation System [RHESSys]), constrained with spatially distributed field measurements, to assess the impacts of forest-fuel treatments and wildfire on hydrologic fluxes in two Sierra Nevada firesheds. Strategically placed fuels treatments were implemented during 2011–2012 in the upper American River in the central Sierra Nevada (43 km2) and in the upper Fresno River in the southern Sierra Nevada (24 km2). This study used the measured vegetation changes from mechanical treatments and modelled vegetation change from wildfire to determine impacts on the water balance. The well-constrained headwater model was transferred to larger catchments based on geologic and hydrologic similarities. Fuels treatments covered 18% of the American and 29% of the Lewis catchment. Averaged over the entire catchment, treatments in the wetter central Sierra Nevada resulted in a relatively light vegetation decrease (8%), leading to a 12% runoff increase, averaged over wet and dry years. Wildfire with and without forest treatments reduced vegetation by 38% and 50% and increased runoff by 55% and 67%, respectively. Treatments in the drier southern Sierra Nevada also reduced the spatially averaged vegetation by 8%, but the runoff response was limited to an increase of less than 3% compared with no treatment. Wildfire following treatments reduced vegetation by 40%, increasing runoff by 13%. Changes to catchment-scale water-balance simulations were more sensitive to canopy cover than to leaf area index, indicating that the pattern as well as amount of vegetation treatment is important to hydrologic response

Partial order and a T0T_0-topology in a set of finite quantum systems

A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states, density matrices, etc) into their counterparts in the supersystem $\Sigma (n)$ (for $m|n$). The compatibility of these embeddings is studied. The concept of ubiquity is introduced for quantities which fit with this structure. It is shown that various entropic quantities are ubiquitous. The sets of various quantities become $T_0$-topological spaces with the divisor topology, which encapsulates fundamental physical properties. These sets can be converted into directed-complete partial orders (dcpo), by adding `top elements'. The continuity of various maps among these sets is studied

Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system

We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor, and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2

Green's function of a finite chain and the discrete Fourier transform

A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is considered as an example. Comparison to Bethe ansatz clarifies the relation between the two approaches.Comment: preprint of the paper published in Int. J. Modern Physics B Vol. 20, No. 5 (2006) 593-60

Universal low-energy properties of three two-dimensional particles

Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pair-wise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is expanded in a set of eigenfunctions on the hypersphere and the system of hyper-radial equations is used to obtain analytical and numerical results. Within the framework of this method, exact analytical expressions are derived for the eigenpotentials and the coupling terms of hyper-radial equations. The derivation of the coupling terms is generally applicable to a variety of three-body problems provided the interaction is described by the boundary condition model. The asymptotic form of the total wave function at a small and a large hyper-radius $\rho$ is studied and the universal logarithmic dependence $\sim \ln^3 \rho$ in the vicinity of the triple-collision point is derived. Precise three-body binding energies and the $2 + 1$ scattering length are calculated.Comment: 30 pages with 13 figure

Two Pfam protein families characterized by a crystal structure of protein lpg2210 from Legionella pneumophila.

BackgroundEvery genome contains a large number of uncharacterized proteins that may encode entirely novel biological systems. Many of these uncharacterized proteins fall into related sequence families. By applying sequence and structural analysis we hope to provide insight into novel biology.ResultsWe analyze a previously uncharacterized Pfam protein family called DUF4424 [Pfam:PF14415]. The recently solved three-dimensional structure of the protein lpg2210 from Legionella pneumophila provides the first structural information pertaining to this family. This protein additionally includes the first representative structure of another Pfam family called the YARHG domain [Pfam:PF13308]. The Pfam family DUF4424 adopts a 19-stranded beta-sandwich fold that shows similarity to the N-terminal domain of leukotriene A-4 hydrolase. The YARHG domain forms an all-helical domain at the C-terminus. Structure analysis allows us to recognize distant similarities between the DUF4424 domain and individual domains of M1 aminopeptidases and tricorn proteases, which form massive proteasome-like capsids in both archaea and bacteria.ConclusionsBased on our analyses we hypothesize that the DUF4424 domain may have a role in forming large, multi-component enzyme complexes. We suggest that the YARGH domain may play a role in binding a moiety in proximity with peptidoglycan, such as a hydrophobic outer membrane lipid or lipopolysaccharide

Analytical model for laser-assisted recombination of hydrogenic atoms

We introduce a new method that allows one to obtain an analytical cross section for the laser-assisted electron-ion collision in a closed form. As an example we perform a calculation for the hydrogen laser-assisted recombination. The $S$-matrix element for the process is constructed from an exact electron Coulomb-Volkov wave function and an approximate laser modified hydrogen state. An explicit expression for the field-enhancement coefficient of the process is expressed in terms of the dimensionless parameter $\kappa= |{e\epsilon_{0}}/{q\omega_{0}}|^{2}$, where $e$ and $q$ are the electron charge and momentum respectively, and $\epsilon_{0}$ and $\omega_{0}$ are the amplitude and frequency of the laser field respectively. The simplified version of the cross section of the process is derived and analyzed within a soft photon approximation.Comment: 10 page

Bound and resonant impurity states in a narrow gaped armchair graphene nanoribbon

An analytical study of discrete and resonant impurity quasi-Coulomb states in a narrow gaped armchair graphene nanoribbon (GNR) is performed. We employ the adiabatic approximation assuming that the motions parallel ("slow") and perpendicular ("fast") to the boundaries of the ribbon are separated adiabatically. The energy spectrum comprises a sequence of series of quasi-Rydberg levels relevant to the "slow" motion adjacent from the low energies to the size-quantized levels associated with the "fast" motion. Only the series attributed to the ground size-quantized sub-band is really discrete, while others corresponding to the excited sub-bands consist of quasi-discrete (Fano resonant) levels of non-zero energetic widths, caused by the coupling with the states of the continuous spectrum branching from the low lying sub-bands. In the two- and three-subband approximation the spectrum of the complex energies of the impurity electron is derived in an explicit form. Narrowing the GNR leads to an increase of the binding energy and the resonant width both induced by the finite width of the ribbon. Displacing the impurity centre from the mid-point of the GNR causes the binding energy to decrease while the resonant width of the first excited Rydberg series increases. As for the second excited series their widths become narrower with the shift of the impurity. A successful comparison of our analytical results with those obtained by other theoretical and experimental methods is presented. Estimates of the binding energies and the resonant widths taken for the parameters of typical GNRs show that not only the strictly discrete but also the some resonant states are quite stable and could be studied experimentally in doped GNRs

Nonrelativistic Chern-Simons Vortices on the Torus

A classification of all periodic self-dual static vortex solutions of the Jackiw-Pi model is given. Physically acceptable solutions of the Liouville equation are related to a class of functions which we term Omega-quasi-elliptic. This class includes, in particular, the elliptic functions and also contains a function previously investigated by Olesen. Some examples of solutions are studied numerically and we point out a peculiar phenomenon of lost vortex charge in the limit where the period lengths tend to infinity, that is, in the planar limit.Comment: 25 pages, 2+3 figures; improved exposition, corrected typos, added one referenc