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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 ...
For example, we can prove by induction that all positive integers of the form 2n − 1 are odd. Let P(n) represent "2n − 1 is odd": (i) For n = 1, 2n − 1 = 2(1) − 1 = 1, and 1 is odd, since it leaves a remainder of 1 when divided by 2. Thus P(1) is true.
The positive definiteness of a Hermitian covariance matrix ensures the well-definedness of multivariate distributions. [3] Hermitian matrices are applied in the design and analysis of communications system, especially in the field of multiple-input multiple-output (MIMO) systems. Channel matrices in MIMO systems often exhibit Hermitian properties.
A Washington, D.C. man has been arrested for threatening flight attendants on a United Airlines plane traveling from Houston to New Jersey. Kedus Yacob Damtew, 38, was charged with one count of ...
Manifest Your Goals. Taking time on New Year's Eve to truly meditate and reflect on the year ahead is an excellent way to head into the new year with a focused, clear mindset.Try breaking your ...
Youth Services International confronted a potentially expensive situation. It was early 2004, only three months into the private prison company’s $9.5 million contract to run Thompson Academy, a juvenile prison in Florida, and already the facility had become a scene of documented violence and neglect.