“We don’t know how they do the actual creative task because what goes on inside the neural network layers is way too complex for us to decipher, at least today,” said Dean Thompson, a former chief technology
Is the Fibonacci sequence arithmetic? Let \{ F_n \} denote the sequence of Fibonacci numbers F_{1} = 1, F_{2} = 1, F_{3} = 2, ..., where F_{n+1} = F_{n} + F_{n-1}. For n \geq 3 let a_{n} = ( F_{2n - 5} )/( F_{2n - 3} ). Show that...
What is the formula for Tn in a geometric sequence? Geometric sequence : A geometric sequence is a sequence of numbers in which each term is obtained by multiplying a fixed number with the previous term, except the first term. In other words, the ratio of any two consecutive numbers in a...
The Weighted Average Cost of Capital (WACC) is a comprehensive measure of financial performance that is essential in the field of corporate finance. It defines a company’s expected mean rate of return for all of its investors, cautiously accounting for contributions from both equity and debt cap...
Kaisa Matomäki, Maksym Radziwill, Fernando Xuancheng Shao, Joni Teräväinen, and myself have (finally) uploaded to the arXiv our paper “Higher uniformity of arithmetic functions in short intervals II. Almost all intervals“. This is a sequel to our previous paper from 2022. In that pa...
arithmetic example from Sect.1.1. However, the structuralist literature seems to have largely left this issue aside and a definitive account of identity conditions on structures is yet to appear. Such an equivalence relation may help with the example in Sect.2.2.1, but it will not work for ...
To point out this “heuristical aspect” of the philosophy of mathematics is another aim of this article. For those who are interested in the philosophy of mathematics in general, and its heuristical aspects in particular, the text can serve as an “appetizer” with several suggestions for ...
The section Relative Error and Ulps describes how it is measured. Since most floating-point calculations have rounding error anyway, does it matter if the basic arithmetic operations introduce a little bit more rounding error than necessary? That question is a main theme throughout this section. ...
What Is Excluded From the Operating Profit? Revenue created through the sale of assets is not included in the operating profit figure, except for any items created for the explicit purpose of being sold as part of the core business. In addition, interest earned from cash such as checking or...
A key target here is the density hypothesis that asserts that for all (this is in some sense sharp because the Riemann-von Mangoldt formula implies that ); this hypothesis is currently known for and , but the known bounds are not strong enough to establish this hypothesis in the remaining ...