This paper considers the birth of algebraic proof by looking at the works of Cardano, Viète, Harriot and Pell. The transition from geometric to algebraic proof was mediated by appeals to the Eudoxan theory of proportions in book V of Euclid. The crucial notational innovation was the development of brackets. By the middle of the seventeenth century, geometric proof was unsustainable as the sole ...
We show that, for a finite set A of real numbers, the size of the set A + A A + A = { a + b c + d : a, b, c, d ∈ A, c + d 6= 0 } is bounded from below by ∣∣∣∣A + A A + A ∣∣∣∣ |A|2+1/4 |A/A|1/8 log |A| . This improves a result of Roche-Newton (2016).
The exact order of deterministic, stochastic and average error bounds of multidimensional quadrature formulas for anisotropic Sobolev class W r pðIÞ; Nikolskii class H pðIÞ and their periodic analogue is obtained. It is proved that if p41; then the stochastic and average error bounds are essentially smaller than the deterministic error bounds. Nonlinear methods, adaptive methods, or even method...
Regarding the importance of handmade carpet advertising, variety of advertising tools and financial resources limit, prioritization of the tools by expert opinion can be effective in programming and planning on carpet artisan. Two main objectives are to be achieved in this research. The first objective determining importance factor of evaluation indices of handmade carpet advertising tools and ...
Carlos Fernández-LlatasJuan-Pablo LázaroJosé-Miguel Benedí
The handmade human behavior modeling requires too many human resources and for too long a time. In addition, the final result does probably not reflect the current status of the person due to the influence of time. The use on Workflow Mining techniques to infer human behavior models from past executions of actions can be a solution to this problem. In this paper, a Human Behavior modeling metho...
This paper compares different measures of graphemic similarity applied to the task of bilingual lexicon induction between a Swiss German dialect and Standard German. The measures have been adapted to this particular language pair by training stochastic transducers with the ExpectationMaximisation algorithm or by using handmade transduction rules. These adaptive metrics show up to 11% F-measure ...