On Some Perturbation Approaches to Population Dynamics

We show that the Adomian decomposition method, the time--series expansion, the homotopy--perturbation method, and the variational--iteration method completely fail to provide a reasonable description of the dynamics of the simplest prey--predator system

A new perturbation method in quantum mechanics

We investigate the convergence properties of a perturbation method proposed some time ago and reveal some of it most interesting features. Anharmonic oscillators in the strong--coupling limit prove to be appropriate illustrative examples and benchmark.Comment: 10 pages, 1 figur

EBL constraints with VERITAS gamma-ray observations

The extragalactic background light (EBL) contains all the radiation emitted by nuclear and accretion processes since the epoch of recombination. Direct measurements of the EBL in the near-IR to mid-IR waveband are extremely difficult due mainly to the zodiacal foreground light. Instead, gamma-ray astronomy offers the possibility to indirectly set limits on the EBL by studying the effects of gamma-ray absorption in the spectra of detected sources in the very high energy range (VHE: $>$100 GeV). These effects can be generally seen in the spectra of VHE blazars as a softening (steepening) of the spectrum and/or abrupt changes in the spectral index or breaks. In this work we use recent VERITAS data of a group of blazars and apply two methods to derive constraints for the EBL spectral properties. We present preliminary results that will be completed with new observations in the near future to enhance the limits on the EBL.Comment: 3 pages, 3 figure

Homotopy perturbation method: when infinity equals five

I discuss a recent application of homotopy perturbation method to a heat transfer problem. I show that the authors make infinity equal five and analyze the consequences of that magic

About homotopy perturbation method for solving heat-like and wave-like equations with variable coefficients

We analyze a recent application of homotopy perturbation method to some heat-like and wave-like models and show that its main results are merely the Taylor expansions of exponential and hyperbolic functions. Besides, the authors require more boundary conditions than those already necessary for the solution of the problem by means of power series

Perturbation approaches and Taylor series

We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian decomposition method (ADM). As an illustrative example we choose a recent application of the HPM to a dynamic system of anisotropic elasticity

Perturbation Theory for Population Dynamics

We prove that a recently proposed homotopy perturbation method for the treatment of population dynamics is just the Taylor expansion of the population variables about initial time. Our results show that this perturbation method fails to provide the global features of the ecosystem dynamics

Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve

We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine monomial curve. We also describe the irregularity complex of such a system with respect to its singular support. We use restriction and some results in D-module theory to reduce our study to the two dimensional case.Comment: Most of the results of this paper are contained in arXiv:0804.0809v2 [math.AG]. Some references added. Corrected typo

Gevrey solutions of irregular hypergeometric systems in two variables

We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine plane monomial curve. We also describe the irregularity complex of such a system with respect to its singular support.Comment: Most of the results of this paper are contained in arXiv:0804.0809v2 [math.AG

Impact of single-particle compressibility on the fluid-solid phase transition for ionic microgel suspensions

We study ionic microgel suspensions composed of swollen particles for various single-particle stiffnesses. We measure the osmotic pressure $\pi$ of these suspensions and show that it is dominated by the contribution of free ions in solution. As this ionic osmotic pressure depends on the volume fraction of the suspension $\phi$, we can determine $\phi$ from $\pi$, even at volume fractions so high that the microgel particles are compressed. We find that the width of the fluid-solid phase coexistence, measured using $\phi$, is larger than its hard-sphere value for the stiffer microgels that we study and progressively decreases for softer microgels. For sufficiently soft microgels, the suspensions are fluid-like, irrespective of volume fraction. By calculating the dependence on $\phi$ of the mean volume of a microgel particle, we show that the behavior of the phase-coexistence width correlates with whether or not the microgel particles are compressed at the volume fractions corresponding to fluid-solid coexistence.Comment: 5 pages, 3 figure