One can compute the local $\mathbb{A}^1$-degree at points with separable residue field by base changing, working rationally, and post-composing trace. We show that for endomorphisms of affine line, one inseparable taking a suitable lift polynomial transferring its degree. also discuss general set-up strategy in terms six functor formalism. As an application, we trace forms number fields are $\m...

This paper presents an outlier detection technique for univariate normal datasets. Outliers are observations that lips abnormal distance from the mean. Outlier is a useful in such areas as fraud detection, financial analysis, health monitoring and Statistical modelling. Many recent approaches detect outliers according to reasonable, pre-defined concepts of outlier. Methods Gaussian method have ...

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged. The nearby points are chosen to maximize the variance reduction. We study in detail the case of univariate local linear regression. While ...

We describe an algorithm for solving systems of univariate p-adic constraints. In analogy with univariate real constraints, we formalize univariate p-adic constraints as univariate polynomial equations and order comparisons between p-adic values of univariate polynomials. Systems of constraints are arbitrary boolean combinations of such constraints. Our method combines techniques of Presburger ...