Sentence examples for dimensional over from inspiring English sources

The enclosure used was essentially two dimensional over the frequency range of interest and was only lightly damped.

An outline of this correspondence can be found in the Introductions of [9, 11], wherein one can also find an explanation of why the description of which Lie bialgebras structures exists on the Lie algebra ({mathfrak g}otimes _k k t)),) with ({mathfrak g}) simple finite dimensional over an algebraically closed field k of characteristic 0,  arise naturally in the classification of quantum groups.

The equation f x, y) = 0 determines y as a function of x at all but a finite number of points of C. Since x takes values in the complex numbers, which are two-dimensional over the real numbers, the curve C is two-dimensional over the real numbers near most of its points.

Since the complex numbers involve two real parameters, a surface, which is two-dimensional over the real numbers, has only one complex dimension and is sometimes called a complex curve.

Schlieren and smoke flow visualization indicate that the flow field remains two-dimensional over a significant part of the flame vortex interaction.

Since K is algebraically closed and n-dimensional over (mathsf{K}^{sigma}), non-constant polynomials in (mathsf{K}^{sigma}[y]) can all be factored into a product of polynomials of degree at most n.

Most authors still prefer standard two-dimensional over three-dimensional fast spin echo sequences and over gradient echo sequences, because the former provide classic, well-known T1-, T2-, and intermediate-weighted contrast information and enable detection of subtle abnormalities of the meniscus and ligaments.

Remark 1.2 A thorough description of the G -dimension can be found in [9], but for our purposes here let us just mention that this result implies that the Bergman space is infinite-dimensional over C as any space of positive G -dimension is infinite-dimensional over C.

A thorough description of the G-dimension can be found in [9], but for our purposes here let us just mention that this result implies that the Bergman space is infinite-dimensional over C as any space of positive G-dimension is infinite-dimensional over C.

Vater A, Ritter K, Strunz S, Ronningstam EF, Renneberg B, Roepke S. Stability of narcissistic personality disorder: tracking categorical and dimensional rating systems over a two-year period.

These lift motors and directional motors enable the three dimensional control over the airship.