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...techniques. Genetics, environmental factors, and dysfunction of the individual’s immune system are important in the development of both Crohn’s disease and ulcerative colitis. In addition, recent research has shown that many individuals with IBD have dysbiosis, which may be a key step in the early development of the disease. Dysbiosis in the gut microbiome leads to...

...technique is to split the exponential function exp of x plus i times y equals e super x times left parenthesis cosine of y plus i times sine of y right parenthesis into its real and imaginary parts: u of x comma y equals e super x times cosine of y and v of x comma y equals e super x times sine of y comma each of which is a real-valued function of the real variables x and...

...techniques that make it much harder to create copies, as well as by trying to persuade users of the benefits of the original product. Such attempts at persuasion can look very threatening, as I noticed on a recently purchased CD that has the following printed on the back cover: FBI Anti-piracy Warning: Unauthorized copying is punishable under federal law. Several...

...techniques that make it easier to work with vectors. Instead of working with vectors geometrically, it is much more efficient to work with them in component form. When vectors are represented according to their components, engineering problems involving vectors can be solved by carrying out standard algebraic operations. This foundation in manipulating and working with...