Suchergebnisse
Suchergebnisse:
Vor 3 Tagen · Searching for linear structures in the failure of the Stone-Weierstrass theorem. Marc Caballer, Sheldon Dantas, Daniel L. Rodríguez-Vidanes. We analyze the existence of vector spaces of large dimension inside the set $\mathcal {C} (L, \K) \setminus \overline {\mathcal {A}}$, where L is a compact Hausdorff space and A is a self-adjoint ...
Vor einem Tag · The well-known Weierstrass approximation theorem says that polynomials are dense in C [0, 1]. That is, given any continuous function f on the unit interval, and any ε > 0, you can find a polynomial P such that f and P are never more than ε apart. This means that linear combinations of the polynomials. 1, x, x², x³, …
Vor 3 Tagen · Introduction. A formal power series can be loosely thought of as an object that is like a polynomial, but with infinitely many terms.Alternatively, for those familiar with power series (or Taylor series), one may think of a formal power series as a power series in which we ignore questions of convergence by not assuming that the variable X denotes any numerical value (not even an unknown value).
Vor 3 Tagen · Title: Searching for linear structures in the failure of the Stone-Weierstrass theorem. Authors: Marc Caballer, Sheldon Dantas, Daniel L. Rodríguez-Vidanes (Submitted on 10 May 2024) Abstract: We analyze the existence of vector spaces of ...
Vor 6 Tagen · The greatest triumph of transcendental number theory was the Lindemann-Weierstrauss theorem: If \(\alpha_1, \alpha_2, \ldots, \alpha_n\) are algebraic numbers that are linearly independent over \(\mathbb{Q}\), then \(\{e^{\alpha_1}, e^{\alpha_2}, \ldots, e^{\alpha_n}\}\) are algebraically independent over \(\mathbb{Q}\), meaning that the set is ...
Vor 3 Tagen · In this paper, a new combined approximation technique is developed to solve the Fitz-Hugh–Nagumo (FHN) equation. This combined technique is based on Taylor’s expansion which discretizes the time derivative and the Bernstein polynomials which are utilized for space derivatives. The FHN equation reduces to a system of linear algebraic equations for each time step via some suitable ...
But when I come out the other end, the beauty is looking back at it all. There were 3 things that stood out to me that made the real analysis experience meaningful and unique (mostly because they weren't really present in any other math class I have taken so far): 1. Real analysis forced me to challenge my preconceptions on familiar material ...
