Estimating heights using auxiliary functions

Estimating Heights Using Auxiliary Functions

Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to problems involving the Weil height. The height appears as a solution to a certain extremal problem involving polynomials. We further generalize the above techniques...

Estimating Document Similarity using Auxiliary Category Information

We have developed a novel approach to determine the similarity of documents using probabilistic latent semantic indexing. For each document a probability vector of latent factors is estimated which on the one hand takes into account the distribution of words in the text and on the other hand the distribution of category values. The emphasis can be freely shifted between both aspects and therefo...

estimating claims reserves using ibnr reserves

شرکت های بیمه در قبال بیمه گذاران متعهد می شوند که به ازای دریافت حق بیمه، خسارت وارده به بیمه گذاران را جبران نمایند. بنابراین بیمه گر همیشه مبالغی را بر عهده دارد که متعلق به بیمه گذاران است و مربوط به تعهدات آینده می باشد. این مبالغ را ذخایر فنی یا technical reserves گویند. بیمه گر موظف است در پایان سال مالی، هنگام بستن حساب ها، ذخایر فنی را محاسبه و نگهداری کند. پس از وقوع خسارت، بیمه گذار ...

Optimising nested functions using auxiliary coordinates

Auxiliary functions in transcendence proofs

We discuss the role of auxiliary functions in the development of transcendental number theory. Earlier auxiliary functions were completely explicit (§ 1). The earliest transcendence proof is due to Liouville (§ 1.1), who produced the first explicit examples of transcendental numbers at a time where their existence was not yet known; in his proof, the auxiliary function is just a polynomial in o...