Search results for "wt"

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.

Unitary decoupling treatment of a quadratic bimodal cavity quantum electrodynamics model

2013

We consider a two-photon quantum model of radiation–matter interaction between a single two-level atom and a degenerate bimodal high-Q cavity field. Within this tripartite system, the explicit construction of two collective radiation modes, one of which is freely evolving and the other one quadratically coupled to the matter subsystem, is reported. The meaning and advantages of such a decoupling treatment are carefully discussed.

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.

Quadratically Tight Relations for Randomized Query Complexity

2020

In this work we investigate the problem of quadratically tightly approximating the randomized query complexity of Boolean functions R(f). The certificate complexity C(f) is such a complexity measure for the zero-error randomized query complexity R0(f): C(f) ≤R0(f) ≤C(f)2. In the first part of the paper we introduce a new complexity measure, expectational certificate complexity EC(f), which is also a quadratically tight bound on R0(f): EC(f) ≤R0(f) = O(EC(f)2). For R(f), we prove that EC2/3 ≤R(f). We then prove that EC(f) ≤C(f) ≤EC(f)2 and show that there is a quadratic separation between the two, thus EC(f) gives a tighter upper bound for R0(f). The measure is also related to the fractional…

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.

Use of polarography as a quality-control method for determining diacetyl in citrus and vegetable juices, yoghurt and butter

2002

The determination of diacetyl permits the detection of microbial growth in the processing of citrus fruit before the appearance of other organoleptic, chemical or microbiological changes. It also makes it possible to detect a break in the cold chain during distribution and sale. The study proposed a polarographic method for the determination of diacetyl that allowed routine analysis with the aim of detecting possible contamination in the citrus juice manufacturing chain (orange and orange-carrot). The analytical performance of the method in terms of a linearity from 0 to 960 microg ml(-1), a recovery of 97 to 98%, a precision of 3.2 to 4.8%, and a sensitivity of 0.2 ng ml(-1) for juices ind…