Search results for "Integer"
showing 10 items of 250 documents
The sunset diagram in SU(3) chiral perturbation theory
1996
A general procedure for the calculation of a class of two-loop Feynman diagrams is described. These are two-point functions containing three massive propagators, raised to integer powers, in the denominator, and arbitrary polynomials of the loop momenta in the numerator. The ultraviolet divergent parts are calculated analytically, while the remaining finite parts are obtained by a one-dimensional numerical integration, both below and above the threshold. Integrals of this type occur, for example, in chiral perturbation theory at order p^6.
Ultrarelativistic (Cauchy) spectral problem in the infinite well
2016
We analyze spectral properties of the ultrarelativistic (Cauchy) operator $|\Delta |^{1/2}$, provided its action is constrained exclusively to the interior of the interval $[-1,1] \subset R$. To this end both analytic and numerical methods are employed. New high-accuracy spectral data are obtained. A direct analytic proof is given that trigonometric functions $\cos(n\pi x/2)$ and $\sin(n\pi x)$, for integer $n$ are {\it not} the eigenfunctions of $|\Delta |_D^{1/2}$, $D=(-1,1)$. This clearly demonstrates that the traditional Fourier multiplier representation of $|\Delta |^{1/2}$ becomes defective, while passing from $R$ to a bounded spatial domain $D\subset R$.
Billiards in magnetic fields: A molecular dynamics approach
2009
We present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows to treat arbitrary geometries and several interacting particles. We test the scheme for rectangular single-particle billiards in magnetic fields and find a sequence of regularity islands at integer aspect ratios. In the case of two Coulomb-interacting particles the dynamics is dominated by chaotic behavior. However, signatures of quasiperiodicity can be identified at weak interactions, as well as regular trajectories at strong magnetic fields. Our scheme provides a promising tool to monitor the classical limit of many-electron semiconductor…
Electromagnetically induced transparency with standing-wave drive in the frequency up-conversion regime
2003
We study Electromagnetically Induced Transparency in Doppler-broadened three-level media for probe to drive field frequency ratio R<1 and moderate drive intensities. We show that in this regime a standing-wave drive is more efficient than a travelling-wave one, specially when R is close to half integer values.
Analytic density functionals with initial-state dependence and memory
2013
We analytically construct the wave function that, for a given initial state, produces a prescribed density for a quantum ring with two non-interacting particles in a singlet state. In this case the initial state is completely determined by the initial density, the initial time-derivative of the density and a single integer that characterizes the (angular) momentum of the system. We then give an exact analytic expression for the exchange-correlation potential that relates two non-interacting systems with different initial states. This is used to demonstrate how the Kohn-Sham procedure predicts the density of a reference system without the need of solving the reference system's Schr\"odinger …
Rational solutions to the KPI equation and multi rogue waves
2016
Abstract We construct here rational solutions to the Kadomtsev–Petviashvili equation (KPI) as a quotient of two polynomials in x , y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2 N ( N + 1 ) in x , y and t depending on 2 N − 2 real parameters for each positive integer N . We give explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the ( x , y ) plane for different values of time t and parameters.
Atomic Coherence Effects in Doppler-Broadened Three-Level Systems with Standing-Wave Drive
2001
We study atomic coherence effects (e.g., electromagnetically induced transparency, EIT, and amplification without inversion, AWI) for a probe travelling-wave (TW) laser field in closed Doppler-broadened three-level systems driven by a standingwave (SW) laser field of moderate intensity (its Rabi frequencies are smaller than the Doppler width of the driven transition). We show that probe windows of transparency occur only for values of the probe to drive field frequency ratio R close to half integer values. For optical transitions and typical values of Doppler broadening for atoms in a vapor cell, we show that for R > 1 a SW drive field is appreciably more efficient than a TW drive in induci…
Effect of rootstock on growth, yield and fruit characteristics in cv 'Bianca' pistachio (Pistacia vera L.) trees
2005
This paper, following preliminary field evaluation trials started in 1993, reports a study on the effect of eight different in vitro-propagated clonal rootstocks (P. atlantica and P. integerrima) and one seedling rootstock (P. terebinthus) on the vegetative and productive behaviour of pistachio cultivar 'Bianca'. The trees, budded in 1991, were grown using standard cultural practices for dry-land farming in a sandy clay loam soil, located inland in Sicily. On average, clones of P. integerrima (I-6 and I-2) were the most vigorous rootstocks. Clones of P. atlantica had intermediate vigour. Rootstock significantly affect yield but not fruit weight, kernel to nut ratio, splitting and blanking p…
Root vacuolar sequestration and suberization are prominent responses of Pistacia spp. rootstocks during salinity stress
2021
Abstract Understanding the mechanisms of stress tolerance in diverse species is needed to enhance crop performance under conditions such as high salinity. Plant roots, in particular in grafted agricultural crops, can function as a boundary against external stresses in order to maintain plant fitness. However, limited information exists for salinity stress responses of woody species and their rootstocks. Pistachio (Pistacia spp.) is a tree nut crop with relatively high salinity tolerance as well as high genetic heterogeneity. In this study, we used a microscopy‐based approach to investigate the cellular and structural responses to salinity stress in the roots of two pistachio rootstocks, Pis…
Minimal Absent Words in Rooted and Unrooted Trees
2019
We extend the theory of minimal absent words to (rooted and unrooted) trees, having edges labeled by letters from an alphabet \(\varSigma \) of cardinality \(\sigma \). We show that the set \(\text {MAW}(T)\) of minimal absent words of a rooted (resp. unrooted) tree T with n nodes has cardinality \(O(n\sigma )\) (resp. \(O(n^{2}\sigma )\)), and we show that these bounds are realized. Then, we exhibit algorithms to compute all minimal absent words in a rooted (resp. unrooted) tree in output-sensitive time \(O(n+|\text {MAW}(T)|)\) (resp. \(O(n^{2}+|\text {MAW}(T)|)\) assuming an integer alphabet of size polynomial in n.