Search results for "Linear"

Comments on `A new efficient method for calculating perturbation energies using functions which are not quadratically integrable'

1996

The recently proposed method of calculating perturbation energies using a non-normalizable wavefunction by Skala and Cizek is analysed and rigorously proved.

Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term

2006

We study existence and regularity of distributional solutions for possibly degenerate quasi-linear parabolic problems having a first order term which grows quadratically in the gradient. The model problem we refer to is the following (1){ut−div(α(u)∇u)=β(u)|∇u|2+f(x,t),in Ω×]0,T[;u(x,t)=0,on ∂Ω×]0,T[;u(x,0)=u0(x),in Ω. Here Ω is a bounded open set in RN, T>0. The unknown function u=u(x,t) depends on x∈Ω and t∈]0,T[. The symbol ∇u denotes the gradient of u with respect to x. The real functions α, β are continuous; moreover α is positive, bounded and may vanish at ±∞. As far as the data are concerned, we require the following assumptions: ∫ΩΦ(u0(x))dx<∞ where Φ is a convenient function which …

On the accurate determination of nonisolated solutions of nonlinear equations

1981

A simple but efficient method to obtain accurate solutions of a system of nonlinear equations with a singular Jacobian at the solution is presented. This is achieved by enlarging the system to a higher dimensional one whose solution in question is isolated. Thus it can be computed e. g. by Newton's method, which is locally at least quadratically convergent and selfcorrecting, so that high accuracy is attainable.

Quantum walk on the line through potential barriers

2015

Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the particle may need to tunnel through a potential barrier to hop, and a naive calculation suggests this could eliminate the ballistic transport. We show by explicit calculation, however, that such a loss does not occur. Rather, the $\Theta(t)$ dispersion is retained, with only the coefficient changing, which additionally gives a way to detect and quantify the hopping errors in experiments.

Reply to 'The super-quadratic growth of high-harmonic signal as a function of pressure'

2010

A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets

2004

We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modeling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions is shown by extending the monotonicity method of Frehse. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution. The in influence of the non-tradable state variables on the optimal value function is illustrated by a numerical example.

Quasilinear elliptic equations with singular quadratic growth terms

2011

In this paper, we deal with positive solutions for singular quasilinear problems whose model is [Formula: see text] where Ω is a bounded open set of ℝN, g ≥ 0 is a function in some Lebesgue space, and γ &gt; 0. We prove both existence and nonexistence of solutions depending on the value of γ and on the size of g.

Why benchmark-quality computations are needed to reproduce 1-adamantyl cation NMR chemical shifts accurately.

2011

While the experimental (1)H NMR chemical shiftsof the 1-adamantyl cation can be computed within reasonably small error bounds, the usual Hartree-Fock and density functional quantum-chemical computations, as well as those based on rather elaborate second-order Møller-Plesset perturbation theory, fail to reproduce its experimental (13)C NMR chemical shifts satisfactorily. This also is true even if the NMR shielding calculations treat electron correlation adequately by the coupled-cluster singles and doubles model augmented by a perturbative correction for triple excitations (i.e., at the CCSD(T) level) with quadruple-ζ basis sets. We demonstrate that good agreement can be achieved if highly a…

Comparison of quantitative analysis techniques for the determination of heat seal lacquer layers on aluminum blister foils

2010

For decades a gravimetric method has been common standard for the determination of heat seal lacquers on aluminum blister foils. With the availability of appropriate techniques such as interferometric, infrared reflection absorption spectroscopic (IRRAS), beta backscatter, impedance spectroscopic and eddy current techniques respectively, more efficient determinations can be foreseen which are subject of the present communication. The different methods were compared to each other regarding parameters required for validation of analytical procedures according to the ICH guidelines Q2 (R1) such as linearity, precision, accuracy, robustness and quantitation limits. The interferometric, IRRAS an…

Monitoring of chicken meat freshness by means of a colorimetric sensor array

2012

A new optoelectronic nose to monitor chicken meat ageing has been developed. It is based on 16 pigments prepared by the incorporation of different dyes (pH indicators, Lewis acids, hydrogenbonding derivatives, selective probes and natural dyes) into inorganic materials (UVM-7, silica and alumina). The colour changes of the sensor array were characteristic of chicken ageing in a modi¿ed packaging atmosphere (30% CO2¿70% N2). The chromogenic array data were processed with qualitative (PCA) and quantitative (PLS) tools. The PCA statistical analysis showed a high degree of dispersion, with nine dimensions required to explain 95% of variance. Despite this high dimensionality, a tridimensional re…