Search results for "Names"
showing 10 items of 6843 documents
Error Bounds for the Numerical Evaluation of Integrals with Weights
1988
This paper is concerned with a procedure of obtaining error bounds for numerically evaluated integrals with weights. If \( - \infty \mathop < \limits_ = a < b\mathop < \limits_ = \infty \), w integrable over [a,b] and positive almost everywhere, then an approximation of \({I_W}f: = \int\limits_a^b {w\left( t \right)f\left( t \right)dt} \) by a quadrature rule \({Q_n}f: = \sum\limits_{i = 0}^n {{\alpha _i}f\left( {{t_i}} \right)} \) is leading to the error Enf ≔ Iwf ‒ Qnf. An algorithm is derived for the computation of bounds for |Enf| depending on the smoothness of the integrand f and on the degree of exactness of Q. As initial values this algorithm needs moments of the weighting function w…
Dusting Off the Turing Test
2012
Hold up both hands and spread your fingers apart. Now put your palms together and fold your two middle fingers down till the knuckles on both fingers touch each other. While holding this position, one after the other, open and close each pair of opposing fingers by an inch or so. Notice anything? Of course you did. But could a computer without a body and without human experiences ever answer that question or a million others like it? And even if recent revolutionary advances in collecting, storing, retrieving, and analyzing data lead to such a computer, would this machine qualify as “intelligent”?
Weak commutation relations of unbounded operators and applications
2011
Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.
A comparison theorem for the mean exit time from a domain in a K�hler manifold
1992
Let M be a Kahler manifold with Ricci and antiholomorphic Ricci curvature bounded from below. Let ω be a domain in M with some bounds on the mean and JN-mean curvatures of its boundary ∂ω. The main result of this paper is a comparison theorem between the Mean Exit Time function defined on ω and the Mean Exit Time from a geodesic ball of the complex projective space ℂℙ n (λ) which involves a characterization of the geodesic balls among the domain ω. In order to achieve this, we prove a comparison theorem for the mean curvatures of hypersurfaces parallel to the boundary of ω, using the Index Lemma for Submanifolds.
Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality
2018
This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg’s uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for “incompatible questions” used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions …
Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction
2020
We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Caratheodory terms. One is parametric, $$(p-1)$$-sublinear with a partially concave nonlinearity near zero. The other is $$(p-1)$$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $$\lambda >0$$ varies.
Seasonal and daily variation in physical activity among three-year-old Finnish preschool children
2013
The purposes of this study were to assess seasonal, daily, and gender variations in children’s physical activity (PA). ActiGraph GT3X accelerometers were used to record the three-year-old children’s PA levels for five consecutive days in autumn and winter. Complete data for both seasons were obtained for 47 children. Despite a significant difference in seasonal temperatures (p < .001), differences were only found for weekdays light PA (p = .021). No difference in PA was observed between weekdays and weekend days. Only 20% of the sample had ≥120 minutes light-to-vigorous PA (LMVPA), and 46% of children had ≥60 minutes moderate-to-vigorous PA (MVPA). Boys spent more minutes in LMVPA (p = .001…
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.
Shift and scale-invariant correlator using a radially stretched phase-only filter
1995
A radial stretching of the phase only filter depending on the energy angular distribution of the target spectrum is used to perform shift and scale invariant pattern recognition. The complex conjugate of a basic size target Fourier transform and the cumulative energy angular distribution are calculated. Then the radially stretched filter providing the same energy contribution to the correlation peak independent on the target size is prepared and used in a conventional correlator, with spherical-wave illumination. The maximum scale ratio of recognizable objects equals 1:1.5. Computer simulations and experimental results, showing the performance of the filter are presented.
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.