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The polynomial version of this was taken up by Adams and Straus in [AS]. Theorem 5.1. (Adams and Straus) If f and g are two non-constant polynomials over an algebraically closed ?eld of characteristic zero such that f ?1 (0) = g ?1 (0) and f ?1 (1) = g ?1 (1), then ...
With the notion of weighted sharing of values we investigate the possible relation between two meromorphic functions when [equation] and [equation]share a non-zero polynomial. The results obtained...doi:10.1007/s40590-016-0156-0Abhijit Banerjee...
Footnote 3 Having Taylor’s theorem in mind, one can say that a real function \(\pi (r)\) is p-regular if the first p odd-order coefficients of its Taylor polynomial around \(r=0\) are zero. In this sense, an analytic function \(\pi (r)\) is \(\infty \)-regular if and ...
number zero? A zero of a transfer function is a root of the numerator polynomial of the transfer function, and thus is a real or complex number. When the transfer function is asymptotically stable, that is, when all of the roots of the denominator polynomial are in the open left half pla...
where we use (or or ) to denote the bound for some constant ; sometimes one wishes to also obtain the matching lower bound, thus obtaining or where is synonymous with . Finally, one may wish to obtain a more precise bound, such as where is a quantity that goes to zero as the ...
Show that there must be a nonzero polynomial p∈Pn2 such that p(B) =On. 9. This exercise explores bases for special subspaces of P5. (a) Show that B = {(x − 2),x(x − 2),x2(x − 2),x3(x − 2),x4(x − 2)} is a basis for V=p∈P5p(2)=0. ⋆(b) ...
Zero-Knowledge Sets We show how a polynomial-time prover can commit to an arbitrary finite set S of strings so that, later on, he can, for any string x, reveal with a proof wh... S Micali,J Kilian - IEEE Symposium on Foundations of Computer Science 被引量: 178发表: 0年 Secret-Key...
For any arbitrary \sigma >0, we apply Lemma 3 with the choice \delta :=\frac{\sigma }{4C}, where C>0 is the constant obtained in the estimates above. We deduce that there exists \bar{\varepsilon }=\bar{\varepsilon }_\sigma and C_\sigma >0 such that...
A key application of our method is the worst-case analysis of recursive programs. Our procedure can synthesize non-polynomial bounds of the formO(nlogn), as well asO(nr), whereris not an integer. We show the applicability of our technique to obtain worst-case complexity bounds for sever...