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Questions regarding the well-definedness of a function often arise when the defining equation of a function refers not only to the arguments themselves, but also to elements of the arguments, serving as representatives. This is sometimes unavoidable when the arguments are cosets and when the equation refers to coset representatives. The result ...
Depending on the type of singularity in the integrand f, the Cauchy principal value is defined according to the following rules: . For a singularity at a finite number b + [() + + ()] with < < and where b is the difficult point, at which the behavior of the function f is such that = for any < and = for any >.
Today, any formal statement or calculation that exhibits this quality of well-definedness is termed computable, while the statement or calculation itself is referred to as a computation. Turing's definition apportioned "well-definedness" to a very large class of mathematical statements, including all well-formed algebraic statements , and all ...
Scholars distinguish between well-defined and ill-defined problems. Briggs and Reinig defined a well-defined solution in terms of space solution space. Pretz, Naples, and Sternberg defined a well-defined problem as one for which the parts of the solution are closely related or clearly based on the information given.
Hence the functional calculus is well-defined. Consequently, if f 1 and f 2 are two holomorphic functions defined on neighborhoods D 1 and D 2 of σ(T) and they are equal on an open set containing σ(T), then f 1 (T) = f 2 (T). Moreover, even though the D 1 may not be D 2, the operator (f 1 + f 2) (T) is well-defined. Same holds for the ...
of the crucible of tyrants, as well as histories of how dictators came to power in the last century. I had to reread the stories of the making and the unmaking of freedom. The more I read these his-tories, the more disturbed I became. I give you the lessons we can learn from them in this pamphlet form because of the crisis we face.
Eating Well. Why you should make a pot of soup every week, according to a food editor. Food. Allrecipes. The sweet and spicy condiment you need in your kitchen. Lighter Side. Lighter Side.
(The Center Square) – The Georgia Court of Appeals removed Fulton County District Attorney Fani Willis from prosecuting the election interference case against Donald J. Trump and others. The ...