differential topology

differential topology

[‚dif·ə′ren·chəl tə′päl·ə·jē]
(mathematics)
The branch of mathematics dealing with differentiable manifolds.
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Subfields of topology include algebraic topology, geometric topology, differential topology, manifold topology.
They introduce and analyze the underlying topological structures, then work out the connection to the spin condition in differential topology. They illustrate the constructions in many simple examples such as the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system, and the curvature singularly of the Schwarzschild space-time.
There are two types of differential LNA topology--single-to-differential topology and fully differential topology. Figure 9 illustrates a single-to-differential LNA topology designed for a digital TV tuner.
Recall that string topology is the study of the algebraic and differential topology of the spaces of paths and loops in compact and oriented manifolds.
A previous or concurrent course in differential topology would also be useful to a few sections.
A common practice of ring-VCO implementation in CMOS process is accomplished by either single-ended or differential topology of delay cell.
On the other hand, a differential topology is usually constructed by the load (active or passive) with a NMOS differential pair.
His research interests include differential topology and geometry and applied mathematics, and he has written undergraduate mathematics texts on linear algebra and multivariable calculus.
However, the geometric vein of our method runs much deeper that the mere interpretation of images as manifolds: The density of the sampling points is a function of the curvature of the manifold, while at the reconstruction stage classical techniques of differential topology [44] and differential geometry [45] are employed.
Four subsequent chapters develop the mathematics in a simple and direct style, assuming that readers are acquainted with basic ideas of differential topology. Chapter 2 covers manifolds, with special emphasis on aspects relevant to degree theory, such as regular values of differentiable mappings and tubular neighborhoods.

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