Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Is there an absolutely continuous random variable with equal probability density and cumulative distribution functions in its support? Is it unique? …
2014
This paper inquires about the existence and uniqueness of a univariate continuous random variable for which both cumulative distribution and density functions are equal and asks about the conditions under which a possible extrapolation of the solution to the discrete case is possible. The issue is presented and solved as a problem and allows to obtain a new family of probability distributions. The different approaches followed to reach the solution could also serve to warn about some properties of density and cumulative functions that usually go unnoticed, helping to deepen the understanding of some of the weapons of the mathematical statistician’s arsenal.
On the use of fractional calculus for the probabilistic characterization of random variables
2009
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the characteristic function (CF). The CF can be further expressed by a Taylor series involving the moments of the random variable. However, in some circumstances, the moments do not exist and the Taylor expansion of the CF is useless. This happens for example in the case of $\alpha$--stable random variables. Here, the problem of representing the CF or the PDF of random variables (r.vs) is examined by introducing fractional calculus. Two very remarkable results are o…
A method for the probabilistic analysis of nonlinear systems
1995
Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an a…
Perturbations of symmetric elliptic Hamiltonians of degree four
2006
AbstractIn this paper four-parameter unfoldings Xλ of symmetric elliptic Hamiltonians of degree four are studied. We prove that in a compact region of the period annulus of X0 the displacement function of Xλ is sign equivalent to its principal part, which is given by a family induced by a Chebychev system; and we describe the bifurcation diagram of Xλ in a full neighborhood of the origin in the parameter space, where at most two limit cycles can exist for the corresponding systems.
Approximate Osher–Solomon schemes for hyperbolic systems
2016
This paper is concerned with a new kind of Riemann solvers for hyperbolic systems, which can be applied both in the conservative and nonconservative cases. In particular, the proposed schemes constitute a simple version of the classical Osher-Solomon Riemann solver, and extend in some sense the schemes proposed in Dumbser and Toro (2011) 19,20. The viscosity matrix of the numerical flux is constructed as a linear combination of functional evaluations of the Jacobian of the flux at several quadrature points. Some families of functions have been proposed to this end: Chebyshev polynomials and rational-type functions. Our schemes have been tested with different initial value Riemann problems f…
A True Extension of the Markov Inequality to Negative Random Variables
2020
The Markov inequality is a classical nice result in statistics that serves to demonstrate other important results as the Chebyshev inequality and the weak law of large numbers, and that has useful applications in the real world, when the random variable is unspecified, to know an upper bound for the probability that an variable differs from its expectation. However, the Markov inequality has one main flaw: its validity is limited to nonnegative random variables. In the very short note, we propose an extension of the Markov inequality to any non specified random variable. This result is completely new.
Three simultaneous dissolution profiles on a solid pharmaceutical formulation by a FIA manifold provided with a single spectrophotometric detector.
2003
This article deals with the simultaneous determination of three dissolution profiles in the same pharmaceutical formulation. The officially proposed procedure from the pharmacopoeias is adapted to the FIA methodology to obtain the officially recommended profile or "global profile", and two "individual" profiles, corresponding to dissolution rate of two different active principles present in the formulation; both drugs have overlapped UV-vis spectra. The simultaneous determination of several profiles is based on the derivative spectra and the zero crossing mathematical procedure for the "individual" profiles of an active principle; the "global" profile of the formulation is obtained from the…
Hydrodynamics of a co-current three-phase solid-bed reactor for foaming systems
2001
The objective of the present study was to evaluate the parameters, which characterize the pulsing flow of the gas and liquid through a bed, namely the frequency of pulsation, the velocity of the pulses and the pulse structure, for foaming systems. The paper presents the results of experiments aimed at determining the effect of the foaming power and the surface tension of liquid phase on the values of the measured parameters.
Dithionite bleaching of thermomechanical pulp: factors having effects on bleaching efficiency
2000
The efficiency of dithionite bleaching of Norway spruce (Picea abies) thermomechanical pulp was studied by applying various multivariate data analysis techniques to analytical data (temperature, pH, ion chromatographic and energy-dispersive X-ray fluorescence data). In addition, modeling the residual sulfur content of bleached pulp by means of diffuse reflectance UV-vis spectral data from laboratory-scale bleaching experiments was attempted. The results indicated that this lignin-preserving bleaching process could be evaluated by means of the analytical data using either PCR or PLS models. These models also indicated that wavelengths below 400 nm should not be used in measuring the pulp bri…
Transfer coefficients for the liquid–vapor interface of a two-component mixture
2011
Abstract We present the excess entropy production for heat and mass transport across an interface of a non-ideal two-component mixture, using as interface variables the excess densities proposed by Gibbs. With the help of these variables we define the interface as an autonomous system in local equilibrium and study its transport properties. The entropy production determines the conjugate fluxes and forces, and equivalent forms are given. The forms contain finite differences of intensive variables into and across the surface as driving forces. These expressions for the fluxes serve as boundary conditions for integration across heterogeneous systems that are far from global equilibrium. The r…