We study the problem of the asymptotic expansion of the ratio of two gamma functions Γ(x+α)/Γ(x+β) as x→+∞, α,β⩾0. In particular, an alternate asymptotic formula with respect to the ones known in ...literature is given.
The article is devoted to the construction and investigation of various types of difference schemes relevant to nonlocal boundary value problems stated for multidimensional elliptic equations. ...Suitable tools for performing the investigation are developed, including difference analogue of Green's formula and inequalities corresponding to nonlocal boundary conditions.
The interior and exterior Neumann problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on ...normal-polar domains whose boundaries are defined by the so called “superformula” introduced by Gielis. A dedicated numerical procedure based on a computer algebra system is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to classical ones, are obtained. Computed results are found to be in good agreement with theoretical findings on Fourier series expansion presented by Carleson.
We develop some extensions of the classical Bell polynomials, previously obtained, by introducing a further class of these polynomials called multidimensional Bell polynomials of higher order. They ...arise considering the derivatives of functions
f in several variables φ
(
i)
, (
i = 1, 2, …,
m), where φ
(
i)
are composite functions of different orders, i.e. φ
(
i)
(
t) =
(
i,1)
(
(
i,2)
(… (
(
i,r
i
)
(
t))), (
i = 1, 2, …,
m). We show that these new polynomials are always expressible in terms of the ordinary Bell polynomials, by means of suitable recurrence relations or formal multinomial expansions. Moreover, we give a recurrence relation for their computation.
Olive oil is the principal source of fats in the Mediterranean diet and it has been postulated that the components in olive oil can contribute to a lower incidence of coronary heart disease and ...cancers (prostate, colon, breast, and skin). The positive effects on human health can be attributed to the high level of phenolic compounds present in olive oil, the major ones being oleuropein, hydroxytyrosol and tyrosol. The aim of the present study was to evaluate the effect of oleuropein on enzymes involved in specific pathways of metabolism of proteins, carbohydrates and lipids.
In particular, the effects of oleuropein on enzymes, such as trypsin, pepsin, lipase, glycerol dehydrogenase, glycerol-3-phosphate dehydrogenase, and glycerokinase, were investigated.
Results demonstrate that oleuropein is able to activate pepsin and shows an inhibitory effect toward all the other enzymes tested, which suggests a new role for this polyphenol. In addition, a new method for lipase activity assay is presented.
An extension of the bell polynomials Natalini, P; Ricci, P.E
Computers & mathematics with applications (1987),
02/2004, Letnik:
47, Številka:
4
Journal Article
Recenzirano
Odprti dostop
After recalling the most important properties and applications of the Bell polynomials, we introduce an extension of this special class of functions. More precisely, we consider the case of ...multicomposite functions, and we show connections with the ordinary Bell polynomials.
LAGUERRE-TYPE BELL POLYNOMIALS Natalini, P.; Ricci, P. E.
International Journal of Mathematics and Mathematical Sciences,
2006, Letnik:
2006
Journal Article
Recenzirano
Odprti dostop
We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute ...the
n
th Laguerre-type derivatives of a composite function. Incidentally, we generalize a result considered by L. Carlitz in order to obtain explicit relationships between Bessel functions and generalized hypergeometric functions.
On some Turán-type inequalities Laforgia, A; Natalini, P
Journal of inequalities and applications,
2006-Apr-20, Letnik:
2006, Številka:
1
Journal Article
Recenzirano
Odprti dostop
: We prove Turán-type inequalities for some special functions by using a generalization of the Schwarz inequality.
: We denote by
and
the gamma and the incomplete gamma functions, respectively. In this paper we prove some monotonicity results for the gamma function and extend, to
, a lower bound established by ...Elbert and Laforgia (2000) for the function
, with
, only for
.
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