Search results for "Variable"
showing 10 items of 1674 documents
Nonlocal (Pair Site) Reactivity from Second-Order Static Density Response Function: Gas- and Solution-Phase Reactivity of the Acetaldehyde Enolate a…
1999
A nonlocal (pair site) reactivity scheme is developed and tested. The theory is cast in terms of the first-order Fukui response function f(r,r‘), previously proposed by Fuentealba and Parr [J. Chem. Phys. 1991, 94, 5559]. A change of variables is introduced by using the softness s(r) and t(r) = [∂s(r)/∂N]υ(r) (the variation of softness with respect to the changes in the total number of electrons N at constant external potential υ(r)) that leads to a simple expression for the variation of the Fukui function at site k, namely = − for an electrophilic attack. The first term describes a local contribution, proportional to the variation of the electrostatic potential that can be induced, for exa…
Infinite lie groups of point transformations leaving invariant the linear equation which describes in the hodograph plane the isentropic one-dimensio…
1991
Abstract The group analysis of the hodograph equation which is equivalent to the non-linear system of one-dimensional isentropic gas dynamics reveals the existence of infinite groups of symmetry in correspondence with particular pressure laws. These turn out to be polytropes with selected indices, as is expected, as well as a new type of pressure. In all these cases the hodograph equation can be transformed, by a suitable change of variables, into the wave equationψ ζ = 0.
Stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations
2009
In this paper, the problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear perturbations are addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free weighting matrices and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be easily solved by existing convex optimizat…
A remark on differentiable functions with partial derivatives in Lp
2004
AbstractWe consider a definition of p,δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p,δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.
Statistical properties of the capacity of multipath fading channels
2009
It is well known that a frequency-nonselective multipath fading channel can be modeled by a sum of complex sinusoids, also called sum-of-cisoids (SOC). By using the SOC, we can efficiently model the scattered component of the received signal in non-isotropic scattering environments. Such SOC-based multipath channel models provide the flexibility of having correlated in-phase and quadrature phase components of the received signal. This paper presents the derivation and analysis of the statistical properties of the capacity of multipath fading channels under LOS conditions. As an appropriate stochastic model for the multipath fading channel, we have adopted the SOC model. We have derived the …
Analog joint source-channel Multiple Description coding scheme over AWGN parallel channels
2011
We propose a low complexity analog joint source channel coding Multiple Description (MD) scheme for transmitting the symbols of a Gaussian source across a pair of independent AWGN channels. The outputs of these channels have each a separated receiver, whereas a third receiver has both outputs available. At the transmitter side, a pair of bandwidth-reduction analog mappings are used for joint source-channel coding. The presented scheme has the inherent advantage over digital MD schemes based on separation, that coding and decoding can be performed by using a single-letter (or symbol), a strategy that is very suitable for applications where latency originated by the digital compression and th…
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…
Uniformization with infinitesimally metric measures
2019
We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces $X$ homeomorphic to $\mathbb R^2$. Given a measure $\mu$ on such a space, we introduce $\mu$-quasiconformal maps $f:X \to \mathbb R^2$, whose definition involves deforming lengths of curves by $\mu$. We show that if $\mu$ is an infinitesimally metric measure, i.e., it satisfies an infinitesimal version of the metric doubling measure condition of David and Semmes, then such a $\mu$-quasiconformal map exists. We apply this result to give a characterization of the metric spaces admitting an infinitesimally quasisymmetric parametrization.