Conformal mappings are invaluable for solving prob- lems in engineering and physics that can be expressed in terms of functions of a complex variable, but that ex- hibit inconvenient geometries. By choosing an appropri- ate mapping, the analyst can transform the inconvenient geometry into a much more convenient one.
Definition: A map w = f (z) is said to be conformal if it preserves angel between oriented curves in magnitude as well as in orientation. if f is analytic and f (z) = 0 for any z then f is conformal. The converse of this statement is also true. Let f (z) = ez .
May 2, 2023A complex function w=f(z) is hard to graph because it takes 4 dimensions: 2 for z and 2 for w. So, to visualize them we will think of complex
May 2, 2023Example 1.8.1 The mapping w=z2. We visualize this by putting the z-plane on the left and the w-plane on the right. We then draw various curves
Complex analysis mapping examples
Complex traits, also known as quantitative traits, are traits that do not behave according to simple Mendelian inheritance laws. More specifically, their inheritance cannot be explained by the genetic segregation of a single gene. Such traits show a continuous range of variation and are influenced by both environmental and genetic factors. Compared to strictly Mendelian traits, complex traits are far more common, and because they can be hugely polygenic, they are studied using statistical techniques such as quantitative genetics and quantitative trait loci (QTL) mapping rather than classical genetics methods. Examples of complex traits include height, circadian rhythms, enzyme kinetics, and many diseases including diabetes and Parkinson's disease. One major goal of genetic research today is to better understand the molecular mechanisms through which genetic variants act to influence complex traits.
Gene mapping
Process of locating specific genes
Gene mapping or genome mapping describes the methods used to identify the location of a gene on a chromosome and the distances between genes. Gene mapping can also describe the distances between different sites within a gene.
Network mapping
Study of a computer network's physical connections
Network mapping is the study of the physical connectivity of networks e.g. the Internet. Network mapping discovers the devices on the network and their connectivity. It is not to be confused with network discovery or network enumerating which discovers devices on the network and their characteristics such as. The field of automated network mapping has taken on greater importance as networks become more dynamic and complex in nature.
