Branch point area methods in conformal mapping

Capacitive Sensor Design Utilizing Conformal Mapping Methods

In this work we demonstrate the advantages of conformal mapping methods for the design of capacitive sensor setups. If the setups are modeled appropriately, the respective Laplace equations can be solved utilizing conformal mapping methods. These methods yield the equations describing the electric field of the sensor setups. The field equations contain the distinct geometric properties of the s...

Conformal Mapping Methods for Interfacial Dynamics

Conformal Mapping by Computationally Efficient Methods

Dimensionality reduction is the process by which a set of data points in a higher dimensional space are mapped to a lower dimension while maintaining certain properties of these points relative to each other. One important property is the preservation of the three angles formed by a triangle consisting of three neighboring points in the high dimensional space. If this property is maintained for...

Precise branch point mapping and quantification of splicing intermediates.

Lariat intermediates of a group II intron were investigated via RT-PCR. Several reverse transcriptases appeared capable of reading through a branched nucleotide. A new method has been established that yields precise information about the location of the branch point within an intron. As an extension of our approach, antisense transcripts of the previously cloned PCR products were successfully u...

Breakthrough in Conformal Mapping

Few analytical techniques are better known to students of applied mathematics than conformal mapping. It is the classical method for solving problems in continuum mechanics, electrostatics, and other fields involving the two-dimensional Laplace and Poisson equations. To employ the method, one needs an explicit mapping function from some standard domain— such as the unit disk or upper half plane...