In this paper, we show that the conditional expectation operators corresponding to a family of source-channel models, defined by natural exponential families with quadratic variance functions and ...

Karl Dilcher, Rob Noble, and Chris Smyth, Minimal polynomials of algebraic numbers with rational parameters. Acta Arith. 148 (2011), no. 3, 281-308. John B. Cosgrave, and Karl Dilcher, Mod p 3 ...

Discover how the binomial theorem can streamline polynomial expansions for more efficient Business Intelligence analysis and modeling.

Discover key strategies for efficiently expanding binomials, enhancing your business strategy and decision-making with faster calculations.

In particular, for polynomials the function's change is calculated via Binomial expansion. This manuscript provides another approach to reach polynomial's function change as a limit of certain ...

We generalize recent linear lower bounds for Polynomial Calculus based on binomial ideals. We produce a general hardness criterion (that we call immunity) which is satisfied by a random function and ...

Rethinking questions and chasing patterns led Newton to find the connection between curves and infinite sums.

Multivariate polynomials are also utilized to model nonlinear continuous functions. However, this approach suffers from an exponential increase in the number of coefficients with the degree of the ...

Based on the variant measurement model, this paper uses the combined transformation method to convert the binomial coefficients into a polynomial combination counting formula which contains quaternary ...