This is a mathematical tool of which I had not been familiar during my younger days, and which most folks would have difficulty understanding at all, given that the word “transfinite” itself starts with Cantor’s discovery that there are sets which are so large that they are “uncountable”...
Visconti, to "show to (the) Physicist that his discussions are sometimes unfinished in their logical structure, and to make the Mathematician aware of certain advantages to the scientific community if he changed his methods of exposition so as to become more easily understandable to his colleague ...
(Note that while the wrapping is defined here in terms of a given normal component quantization value n, in most implementations the wrapping would be applied after the current component values and delta values have been normalized into the greatest allowed values, e.g., n = 6.) B...
Once you hit play on that memory you automatically run through the whole thing. This is why Euclid is needlessly talking about areas in the proof of Proposition 5, even though that serves no logical function whatsoever. He is mimicking word for word the phrasing of the previous proposition, ...
with compact support ofX(w). In our proof of the main theorem, in addition to considering the Demazure–Hansen smooth compactifications ofX(w), we show that a similar class of constructions provide smooth compactifications ofX(w) in the case of. Furthermore, we show in the appendix that ...
with appropriate constants aij. The representation is not unique but we have for any such representation that the discriminantD = det(sij) of g(x) is equal to det(A2) =(det(aij))2. Thus we get the following theorem. For each homogeneous positive definite quadratic form g(x) with discri...
(Patrizi thinks that bodies are, in themselves, completely impenetrable and inelastic, and could not be compressed in the absence of a void); secondly, the coacervated void, that of perceptible size (here Patrizi presents the reader with some experiments with clepsydrae); and thirdly, the ...
Remark. We use the word differentiable for what is sometimes called infinitely differentiable (or of class C∞). Our usage should not be confused with the usage of elementary calculus, where a function is called differentiable if its first derivative exists 。 It is an important fact that when...
A【regular curve】 in R3 is a subset C⊂R3 with the following property: For each point p∈C there is a neighborhood V of p in R3 and a differentiable homeomorphism α:I ⊂R-->V∩C such that the differentiable dαt is one-to-one for each t∈I ...
ofG. Anarea assignmentis a real-valued functionA:F→R+. We say that a drawingG′isA-realizing, ifG′is a straight-line drawing equivalent toGin which the area of eachf∈Fis exactlyA(f). IfGhas anA-realizing drawing, we say thatAisrealizable. A plane graphGisarea-universalif every area...