115 research outputs found
Asymptotic and exact series representations for the incomplete Gamma function
Using a variational approach, two new series representations for the
incomplete Gamma function are derived: the first is an asymptotic series, which
contains and improves over the standard asymptotic expansion; the second is a
uniformly convergent series, completely analytical, which can be used to obtain
arbitrarily accurate estimates of for any value of or .
Applications of these formulas are discussed.Comment: 8 pages, 4 figure
Non perturbative regularization of one loop integrals at finite temperature
A method devised by the author is used to calculate analytical expressions
for one loop integrals at finite temperature. A non-perturbative regularization
of the integrals is performed, yielding expressions of non-polynomial nature. A
comparison with previuosly published results is presented and the advantages of
the present technique are discussed.Comment: 7 pages, 2 figures, 2 tables; corrected some typos and simplified eq.
(8
Systematic perturbation calculation of integrals with applications to physics
In this paper we generalize and improve a method for calculating the period
of a classical oscillator and other integrals of physical interest, which was
recently developed by some of the authors. We derive analytical expressions
that prove to be more accurate than those commonly found in the literature, and
test the convergence of the series produced by the approach.Comment: 11 pages, 5 figure
Inversion of perturbation series
We investigate the inversion of perturbation series and its resummation, and
prove that it is related to a recently developed parametric perturbation
theory. Results for some illustrative examples show that in some cases series
reversion may improve the accuracy of the results
Optimized Perturbation Theory for Wave Functions of Quantum Systems
The notion of the optimized perturbation, which has been successfully applied
to energy eigenvalues, is generalized to treat wave functions of quantum
systems. The key ingredient is to construct an envelope of a set of
perturbative wave functions. This leads to a condition similar to that obtained
from the principle of minimal sensitivity. Applications of the method to
quantum anharmonic oscillator and the double well potential show that uniformly
valid wave functions with correct asymptotic behavior are obtained in the
first-order optimized perturbation even for strong couplings.Comment: 11 pages, RevTeX, three ps figure
Non-Hermitian matrix description of the PT symmetric anharmonic oscillators
Schroedinger equation H \psi=E \psi with PT - symmetric differential operator
H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on
L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at
a>0. The proof of this non-variational construction is given. Our Taylor series
form of \psi complements and completes the recent terminating solutions as
obtained for certain couplings \delta at the less common negative a.Comment: 18 pages, latex, no figures, thoroughly revised (incl. title), J.
Phys. A: Math. Gen., to appea
Theory of continuum percolation III. Low density expansion
We use a previously introduced mapping between the continuum percolation
model and the Potts fluid (a system of interacting s-states spins which are
free to move in the continuum) to derive the low density expansion of the pair
connectedness and the mean cluster size. We prove that given an adequate
identification of functions, the result is equivalent to the density expansion
derived from a completely different point of view by Coniglio et al. [J. Phys A
10, 1123 (1977)] to describe physical clustering in a gas. We then apply our
expansion to a system of hypercubes with a hard core interaction. The
calculated critical density is within approximately 5% of the results of
simulations, and is thus much more precise than previous theoretical results
which were based on integral equations. We suggest that this is because
integral equations smooth out overly the partition function (i.e., they
describe predominantly its analytical part), while our method targets instead
the part which describes the phase transition (i.e., the singular part).Comment: 42 pages, Revtex, includes 5 EncapsulatedPostscript figures,
submitted to Phys Rev
Asymptotically exact expression for the energies of the S-3(e) Rydberg series in a two-electron system
Osmoregulators proline and glycine betaine counteract salinity stress in canola
Salt inundation leads to increased salinization of arable land in many arid and semi-arid regions. Until genetic solutions are found farmers and growers must either abandon salt-affected fields or use agronomic treatments that alleviate salt stress symptoms. Here, field experiments were carried out to study the effect of the osmoregulators proline at 200 mg L-1 and glycine betaine at 400 mg L-1 in counteracting the harmful effect of soil salinity stress on canola plants grown in Egypt. We assessed growth characteristics, yield and biochemical constituents. Results show first that all growth characters decreased with increasing salinity stress but applied osmoregulators alleviated these negative effects. Second, salinity stress decreased photosynthetic pigments, K and P contents, whilst increasing proline, soluble sugars, ascorbic acid, Na and Cl contents. Third, application of osmoregulators without salt stress increased photosynthetic pigments, proline, soluble sugars, N, K and P contents whilst decreasing Na and Cl contents. It is concluded that the exogenously applied osmoregulators glycine betaine and proline can fully or partially counteract the harmful effect of salinity stress on growth and yield of canola.© INRA and Springer-Verlag, France 2012
Preparation and bactericidal effect of composites based on crosslinked copolymers containing silver nanoparticles
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