Search results for "Mathematica"
showing 10 items of 7971 documents
Shift-and-scale-invariant pattern recognition using an elliptic coordinate-transformed phase-only filter
1992
A shift-and-scale-invariant elliptic coordinate-transformed phase-only filter in proposed. The filter is built in three steps: the complex conjugate of a basic-size target spectrum is calculated, its phase-only part is taken, and then the elliptic coordinate transformation is made. In the extreme case the scale ratio of recognizable objects equals 1:1.5, permitting good recognition of object sizes S within the range 0.83/= S/= 1.25. Discrimination abilities and relative Horner efficiencies of a few versions of the filter are calculated.
A Lebesgue-type decomposition for non-positive sesquilinear forms
2018
A Lebesgue-type decomposition of a (non necessarily non-negative) sesquilinear form with respect to a non-negative one is studied. This decomposition consists of a sum of three parts: two are dominated by an absolutely continuous form and a singular non-negative one, respectively, and the latter is majorized by the product of an absolutely continuous and a singular non-negative forms. The Lebesgue decomposition of a complex measure is given as application.
Extension of The Stochastic Differential Calculus To Complex Processes
1996
In structural engineering complex processes arise to predict the first excursion failure, fatigue failure, etc. Indeed to solve these problems the envelope function, which is the modulus of a complex process, is usually introduced. In this paper the statistics of the complex response process related to the envelope statistics of linear systems subjected to parametric stationary normal white noise input are evaluated by using extensively the properties of stochastic differential calculus.
Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array
2014
In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous int…
Singularity formation for Prandtl’s equations
2009
Abstract We consider Prandtl’s equations for an impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method. We classify Van Dommelen and Shen’s singularity as a cubic root singularity. We introduce a class of initial data, uniformly bounded in H 1 , which have a dipole singularity in the complex plane. These data lead to a solution blow-up whose time can be made arbitrarily short within the class. This is numerical evidence of the ill-posedness of the Prandtl equations in H 1 . The presence of a small viscosity in the streamwise direction changes the behavior of the singularities. They stabilize at a distanc…
Complex singularities in KdV solutions
2016
In the small dispersion regime, the KdV solution exhibits rapid oscillations in its spatio-temporal dependence. We show that these oscillations are caused by the presence of complex singularities that approach the real axis. We give a numerical estimate of the asymptotic dynamics of the poles.
Determining a Random Schrödinger Operator : Both Potential and Source are Random
2020
We study an inverse scattering problem associated with a Schr\"odinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We then derive two unique recovery results in determining the rough strengths of the random source and the random potential, by using the corresponding far-field data. The first recovery result shows that a single realization of the passive scattering measurements uniquely recovers the rough strength of the random source. The second one shows that, by a single realization of the backscattering data, the rough strength of the random potential can be recovered…
An example of cancellation of infinities in the star-quantization of fields
1993
Within the *-quantization framework, it is shown how to remove some of the divergences occurring in theλo 2 4 -theory by introducing aλ-dependent *-product cohomologically equivalent to the normal *-product.
The impact of learning difficulties and socioemotional and behavioural problems on transition to postsecondary education or work life in Finland: a f…
2016
AbstractLearning difficulties have been found to dilute the possibilities that young adults have in their educational careers. However, during the last few decades, education has become increasingly important for employment and overall life satisfaction. In the present study, we were interested in the effects of mathematical and reading difficulties and socioemotional and behavioural problems (measured at age 16) on three educational situations at age 21: delayed graduation from upper secondary education, short educational trajectory and not being engaged in education, employment or training (NEET). The participants (N = 597; 304 females, 293 males) were one age cohort of ninth graders in g…
On the Conditions of Price Consistency in the Input-Output Model
2013
The input-ouput model remains the basis of most SAM or CGE models. It actually uses two periods: the prices indexes solve it with the current period coefficients; the corresponding physical model is monoperiodic: the current prices solve it with the base period coefficients. The Leontief model is not consistent --- both models diverge generally --- unless the interindustry matrix of direct and indirect quantities of labor is stable over time. This implies that the vertically integrated labor coefficients are stable. This assumption is satisfied when the physical production coefficients and the physical labor coefficients are stable over time, two very strong assumptions.