相关论文: A connection between tests for absolute convergenc…
Among the techniques for determining the convergence of a series, Raabe's Test remains relatively unfamiliar to most mathematicians. We present several results relating to Raabe's Test that do not seem to be widely known, making the case…
The classical D'Alembert's Ratio Test is a powerful test that we learn from calculus to determine convergence for a series of positive terms. Its range of applicability and ease of computation makes this test extremely appealing. However,…
Integration at a point is a new kind of integration derived from integration over an interval in infinitesimal and infinity domains which are spaces larger than the reals. Consider a continuous monotonic divergent function that is…
We provide evidence that a root-mean-square test of goodness-of-fit can be significantly more powerful than state-of-the-art exact tests in detecting deviations from Hardy-Weinberg equilibrium. Unlike Pearson's chi-square test, the…
Testing convergence of infinite series is an important part of mathematics. A very basic test of convergence is to upper-bound a given series with a known series, term by term. In $19^{th}$ century, Kummer proposed a test of convergence for…
This paper focuses on the study of the order of power series that are linear combinations of a given finite set of power series. The order of a formal power series, known as $\textrm{ord}(f)$, is defined as the minimum exponent of $x$ that…
There are many tests for determining the convergence or divergence of series. The test of Raabe and the test of Betrand are relatively unknown and do not appear in most classical courses of analysis. Also, the link between these tests and…
In this paper we prove an $n$th root test for series as well as a Cauchy-Hadamard type formula and Abel's' theorem for power series on universally complete Archimedean complex vector lattices. These results are aimed at developing an…
Suppose that we are given a formal power series of many variables with coefficients in $\mathbb{R}$ (or $\mathbb{C}$) and we want to compute its $n$-th (multiplicative) root. As can be expected coefficients of the root have to satisfy a…
Adversarial training has been shown to be reliable in improving robustness against adversarial samples. However, the problem of adversarial training in terms of fairness has not yet been properly studied, and the relationship between…
Software fairness testing is a central method for evaluating AI systems, yet the meaning of fairness is often treated as fixed and universally applicable. This vision paper positions fairness testing as culturally situated and examines the…
Even though the Rao's score tests are classical tests, such as the likelihood ratio tests, their application has been avoided until now in a multivariate framework, in particular high-dimensional setting. We consider they could play an…
Cauchy's condensation test allows to determine the convergence of a monotone series by looking at a weighted subseries that only involves terms of the original series indexed by the powers of two. It is natural to ask whether the converse…
The recursive relation starts to appear by putting a function $y(x)=\sum_{n=0}^{\infty }d_n x^n$ into a linear ordinary differential equation (ODE). There can be $d$-term of sequences in the recurrence relation of a power series where…
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…
In this paper we study sequences, series, power series and uniform convergence in the $\mathcal{A}$-Calculus. Here $\mathcal{A}$ denotes an associative unital real algebra. We say a function is $\mathcal{A}$-differentiable if it is real…
Centrality measures are widely used to assign importance to graph-structured data. Recently, understanding the principles of such measures has attracted a lot of attention. Given that measures are diverse, this research has usually focused…
An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
Software testing ensures that a system functions correctly, meets specified requirements, and maintains high quality. As artificial intelligence and machine learning (ML) technologies become integral to software systems, testing has evolved…