Sentence examples for extended in Geometry of from inspiring English sources

Young inequality, extended in (Geometry of Orlicz Spaces, 1986; Geometry of Orlicz Spaces, 1996), has extensive use and great effort in mathematical analysis.

That is true in "Geometry of Quiet," too.

While this geometry is classical in X-ray optics [33], it is here extended, in combination with one of the world most brilliant X-ray sources, to an unprecedented spatial resolution and photon density.

Existing string theories proceed by quantizing classical theories of basic entities that are extended in one or more dimensions of a space that has 6 or 7 tiny compact dimensions in addition to the three spatial dimensions of ordinary geometry.

Alternatively, geometries with smaller interboard gaps produce a single, nonsplit ion packet extended in the transversal direction.

The latter can be extended to deduce the geometry of a nanopore without high resolution crystallographic information.

With the invention of the theory of fractal geometry, Dr Mandelbrot thus extended geometry so that it could be applied to complex rough objects as well as simple smooth ones.This solved a number of troublesome problems in mathematics, such as the existence of objects that could not be classified as one-, two- or three-dimensional, but seemed to fall somewhere in between.

The layers extend in the x-y directions; hence, 2D cross-section model is a reasonable simulation geometry of the device.

Newton thought the only way of rendering limits rigorous lay in extending geometry to incorporate them, a view that went entirely against the tide in the development of mathematics in the eighteenth and nineteenth ceturies.

In this study, the ideal turntable model was extended to determine the observation geometry of near-circular LEO objects.

The present generalized model may easily be extended to other geometries and hence may be used in the design of two-phase cooling devices.