# Gaussian Sentence Examples

It may be assumed that the planes I' and II' are drawn where the images of the planes I and II are formed by rays near the axis by the ordinary

**Gaussian**rules; and by an extension of these rules, not, however, corresponding to reality, the Gauss image point 0', with co-ordinates 'o, of the point 0 at some distance from the axis could be constructed.If all three constants of reproduction be achromatized, then the

**Gaussian**image for all distances of objects is the same for the two colours, and the system is said to be in " stable achromatism."The

**Gaussian**theory is only an approximation; monochromatic or spherical aberrations still occur, which will be different for different colours; and should they be compensated for one colour, the image of another colour would prove disturbing.**Gaussian**logarithms are intended to facilitate the finding of the logarithms of the sum and difference of two numbers whose logarithms are known, the numbers themselves being unknown; and on this account they are frequently called addition and subtraction logarithms. The object of the table is in fact to give log (a =b) by only one entry when log a and log b are given.The

**Gaussian**theory, however, is only true so long as the angles made by all rays with the optical axis (the symmetrical axis of the system) are infinitely small, i.e.AdvertisementConsequently the

**Gaussian**theory only supplies a convenient method of approximating to reality; and no constructor would attempt to realize this unattainable ideal.If, in the first place, monochromatic aberrations be neglected - in other words, the

**Gaussian**theory be accepted - then every reproduction is determined by the positions of the focal planes, and the magnitude of the focal lengths, or if the focal lengths, as ordinarily happens, be equal, by three constants of reproduction.The above approximation for the error bars rests on a

**gaussian**approximation which assumes that the Hessian A is positive definite.First of all the image is smoothed by

**Gaussian**convolution.Seed surface patches are formed by grouping neighboring pixels whose mean and

**Gaussian**curvature have the same sign.AdvertisementThis is unlike approaches such as discriminatively trained

**Gaussian**mixture models or other discriminative classifiers that discriminate at the frame-level only.The models for atmospheric dispersion are based on the

**Gaussian**plume model.We recommend using randomize for this, as the above steps are very unlikely to generate nice

**Gaussian**distributions in the data.We use a

**gaussian**kernel with a covariance matrix equal to that of the original data set,, ie.The approach is based on a stopping time argument that produces a normalizing transformation facilitating the use of a

**Gaussian**likelihood.AdvertisementThese maps are assessed for significantly modulated voxels using a

**Gaussian**Mixture Model for the distribution of intensity values.Consider a data set { x } modeled as coming from a

**Gaussian**distribution of mean mu and s.d. sigma.The surfaces ' points have been corrupted with a

**Gaussian**noise of 2 mm variance.Projection steps in the EP iteration that cannot be done analytically are done using

**Gaussian**quadrature.**Gaussian**quadrature is used to obtain a 2-D expression covering all points on the tooth face.AdvertisementWe report equal error rates on the PolyVar database that are 34% lower than a baseline

**Gaussian**mixture model likelihood ratio approach.With the same probability,

**Gaussian**noise is added to the tolerance value (mean 0, standard deviation 0.01 ).Abstract Within inverted optical tweezers we measure both the lateral and axial trapping efficiency obtained with

**Gaussian**and high-order Laguerre-**Gaussian**beams.If the angle u l be very small, O', is the

**Gaussian**image; and 0', 0' 2 is termed the " longitudinal aberration," and 0'1R the " lateral aberration " of the pencils with aperture u 2.The fitted

**Gaussian**dropped to of the peak value from the center, implying an RMS readout noise of.AdvertisementIn these plots the deviation of the skew

**gaussian**from the mlla predictions at the 1% level can be seen.With the same probability,

**Gaussian**noise is added to the tolerance value (mean 0, standard deviation 0.01).This ray, named by Abbe a " principal ray " (not to be confused with the " principal rays " of the

**Gaussian**theory), passes through the centre of the entrance pupil before the first refraction, and the centre of the exit pupil after the last refraction.