If a d-dimensional integral involves an integrand ofthe functional form F (II (x I) + f2(X2) + ... ), then one can introduce an integral transform (Fourier or Laplace or variants on those) which allows all the integrals over the coordinates XI to factor. Thus a d-dimensional integral is reduced to a one-dimensional integral over the transform variable. This is shown to be a very powerful and pr...

The liquid crystalline model biomembrane system consisting of a stack of interacting membranes is studied in the realistic soft confinement regime by the newly developed Fourier Monte Carlo simulation technique. In this regime experiment and simulations show that the functional form of the fluctuation pressure is more nearly exponential rather than the power law valid for the hard confinement r...

The striate cortex transforms the topographic representation of visual space in the lateral geniculate body into a Fourier transform or frequency representation at the complex cell level via the intermediary simple cell stage of "strip integration." Each of these three stages contains essentially the same amount of information, which expresses a conservation of information principle; however, t...

Every Jacobi cusp form of weight k and index m over SL2(Z) Z 2 is in correspondence with 2m Dirichlet series constructed with its Fourier coefficients. The standard way to get from one to the other is by a variation of the Mellin transform. In this paper, we introduce a set of integral kernels which yield the 2m Dirichlet series via the Petersson inner product. We show that those kernels are Ja...

This paper proposes a new test based on a Fourier series expansion to approximate the unknown functional form of a nonlinear time-series model. The test speci...cally allows for structural breaks, seasonal parameters and time-varying parameters. The test is shown to have very good size and power properties. However, it is not especially good in detecting nonlinearity in variables. As such, the ...

We provide a new framework for modeling trends and periodic patterns in high-frequency financial data. Seeking adaptivity to ever-changing market conditions, we enlarge the Fourier flexible form into a richer functional class: both our smooth trend and the seasonality are non-parametrically time-varying and evolve in real time. We provide the associated estimators and use simulations to show th...

Signal-dependent time-frequency representations, by adapting their functional form to t the signal being analyzed, ooer many performance advantages over conventional representations. In this paper, we propose a simple, eecient technique for continuously adapting time-frequency representations over time. The procedure computes a short-time quality measure of the representation for a range of val...

The paper develops a unit-root test that allows for an unknown number of structural breaks with unknown functional forms. The test is based on the fact that the behavior of such series can often be captured using a single frequency component of a Fourier approximation. Hence, instead of selecting specific break dates, the number of breaks, and the form of the breaks, the specification problem i...

Pd nanoparticles were fabricated on graphene oxide (GO) using a deposition-precipitation method with a glow discharge plasma reduction at room temperature. Argon was employed as the plasma-generating gas. The novel plasma method selectively reduces the metal ions. The graphene oxide has no change with this plasma reduction according to the Fourier transform infrared analysis. The Pd nanoparticl...

Abstract We prove that if F is a nonzero (possibly noncuspidal) vector-valued Siegel modular form of any degree, then it has infinitely many Fourier coefficients which are indexed by half-integral matrices having odd, square-free (and thus fundamental) discriminant. The proof uses an induction argument in the setting forms. Further, as application variant our result and complementing work A. Po...