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Properties on the unit circle of polynomials with unimodular coefficients - Newman, Giroux - 1990 () Citation Context ...shows that this polynomial has almost constant modulus (in an asymptotic sense) except on a set of size cn −1/2+δ . Here ω is a primitive nth root of unity. ...
Wall's formula | Inequality properties of integration |Periodic Properties View Solution Cauchy Schwartz inequality || Properties OF Cross product || vector product and Illustration View Solution Triangle - Inequality | cube root and nth roots of Unity | Roots of any Complex-Number Questions View So...
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If n\ge 2, then the only solutions Y, Z\in {{\mathbb {C}}}[x] of (4.1) are Y(x)=\zeta x, Z(x)=\xi (x+1), where \zeta and \xi are arbitrary (n+1)th roots of unity. Proof We invoke the Mason–Stothers theorem, which says that the equality A+B=C, with A, B,...
The crystallite size (D) of magnetron sputtered thin films of copper oxide was calculated using the Scherrer formula [40]:(1)D=kλBcosθwhere: k = 0.89 (close to unity) is the shape factor, λ– the CuKα1 X-ray radiation wavelength, B – full width at half maximum intensity of ...
Although 1X/1Xc, or similar indices of branching in more complex network forming systems such as vulcanizates, can locally exceed unity, its average over an infinite graph cannot. Theories of networks are nevertheless based on tree-like models of average or crosslinking indices larger than unity...
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For a stretch that results in perfect shape retention, the CAR will be unity. For any deviation from perfect shape retention, the CAR will be a positive number less than unity. For any particular film, CAR will differ from unity by an amount that depends at least on the shape of the ...