Propriedade do valor intermédio vs. continuidade
A definicao de continuidade nem sempre foi a que aceitamos actualmente e, em particular, chegou a confundir-se com a propriedade do valor intermedio. Esclarecidas as duas nocoes, certo e que a…
Low Degree Testing over the Reals
- Mathematics, Computer ScienceArXiv
The problem of testing whether a function f : R n → R is a polynomial of degree at most d in the distribution-free testing model is studied and a new stability theorem for multivariate polynomials that may be of independent interest is proved.
Generalized uncertainty principle or curved momentum space?
- PhysicsPhysical Review D
The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on…
The Mahler measure of a three-variable family and an application to the Boyd–Lawton formula
We prove a formula relating the Mahler measure of an infinite family of three-variable polynomials to a combination of the Riemann zeta function at $$s=3$$ s = 3 and special values of the…
The range of a self-similar additive gamma process is a scale invariant Poisson point process
It is shown that for a non-decreasing self-similar stochastic process T with independent increments, the range of T forms a Poisson point process with σ -ﬁnite intensity if and only if the…
“He was poking holes …” A case study on figuring out metadiscursive rules through primary sources
Contribution of Italian Mathematicians to Real Analysis in the last Decades of Nineteenth Century
In (Biacino 2018) the evolution of the concept of real function of a real variable at the beginning of 1900 is outlined, reporting the discussions and the polemics, in which some young French…
TRIUMPHS Student Projects: Detailed Descriptions TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources
F 01. A Genetic Context for Understanding the Trigonometric Functions In this project, we explore the genesis of the trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.…
A Functional Equation Characterization of Archimedean Ordered Fields
- MathematicsAm. Math. Mon.
Abstract We prove that an ordered field is Archimedean if and only if every continuous additive function from the field to itself is linear over the field.