Gaussian polynomials and invertibility

Gaussian structures and orthogonal polynomials

When asked to mention one statistical distribution, most people would probably come up with the normal distribution, also known as the Gaussian distribution after the legendary German mathematician Carl Friedrich Gauß (1777–1855). A large number of objects in life are usually considered normally distributed, for example the IQ of adult humans, the error made when measuring the mass of a protein...

Gaussian Polynomials and Content Ideals

We prove that every regular Gaussian polynomial over a locally Noetherian ring has invertible content ideal. We do this by first proving that Gaussian polynomials over an approximately Gorenstein local ring have principal content ideal. We also show over locally Noetherian rings that a regular polynomial f of degree n is Gaussian if c(fg) = c(f)c(g) for polynomials g of degree at most n. Introd...

Gaussian random polynomials and analytic functions

Orthogonal polynomials, Gaussian quadratures, and PDEs

them particularly important in solvinG physical problems. Also, Gaussian integration provides a highly accurate and efficient algorithm for integrating functions. The value of the methods I describe in this installment of “Computing Prescriptions” depends on the basic assumption that a finite-order polynomial can effectively approximate a function. Therefore, a finite sum of orthogonal polynomi...

On the average number of sharp crossings of certain Gaussian random polynomials