Zobrazeno 1 - 10
of 269
pro vyhledávání: '"26A27"'
Copulas, in particular Archimedean copulas are commonly viewed as analytically nice and regular objects. Motivated by a recently established result sta\-ting that the first partial derivatives of bivariate copulas can exhibit surprisingly pathologica
Externí odkaz:
http://arxiv.org/abs/2411.07113
With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality and intermittency of the family of generalized Riemann's non-differentiable functions \begin{equation} R_{x_0}(t) = \sum_{n \neq 0} \frac{e^{2\pi i ( n^
Externí odkaz:
http://arxiv.org/abs/2309.08114
We construct an algebra of dimension $2^{\aleph_0}$ consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain functions
Externí odkaz:
http://arxiv.org/abs/2307.11738
Autor:
Kalinin, Alexander
We show that the derivatives in the sense of Fr\'echet and G\^ateaux can be viewed as derivatives oriented towards a star convex set with the origin as center. The resulting oriented differential calculus extends the mean value theorem, the chain rul
Externí odkaz:
http://arxiv.org/abs/2307.10104
Publikováno v:
Ergod. Th. Dynam. Sys. 44 (2024) 2361-2398
We show that the Hausdorff dimension of any slice of the graph of the Takagi function is bounded above by the Assouad dimension of the graph minus one, and that the bound is sharp. The result is deduced from a statement on more general self-affine se
Externí odkaz:
http://arxiv.org/abs/2305.08181
Autor:
Cellarosi, Francesco, Selk, Zachary
Rough paths theory allows for a pathwise theory of solutions to differential equations driven by highly irregular signals. The fundamental observation of rough paths theory is that if one can define "iterated integrals" above a signal, then one can c
Externí odkaz:
http://arxiv.org/abs/2304.11646
We provide a suitable generalisation of Pansu's differentiability theorem to general Radon measures on Carnot groups and we show that if Lipschitz maps between Carnot groups are Pansu-differentiable almost everywhere for some Radon measures $\mu$, th
Externí odkaz:
http://arxiv.org/abs/2211.06081
Autor:
Jung, Kiyuob, Oh, Jehan
In this paper, we construct the transport equation and the wave equation with specular derivatives and solve these equations in one-dimension. To solve these equations, we introduce new function spaces, which we term specular spaces, consisting of ce
Externí odkaz:
http://arxiv.org/abs/2210.06933
Autor:
Jung, Kiyuob, Oh, Jehan
In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Fundamental Theorem of Calculus in light of the specular derivative. We als
Externí odkaz:
http://arxiv.org/abs/2210.06062
Autor:
Ash, J. Marshall, Catoiu, Stefan
J. Marcinkiewicz and A. Zygmund proved in 1936 that the special $n$-th generalized Riemann derivative ${_2}D_nf(x)$ with nodes $0,1,2,2^2,\ldots, 2^{n-1}$, is equivalent to the $n$-th Peano derivative $f_{(n)}(x)$, for all $n-1$ times Peano different
Externí odkaz:
http://arxiv.org/abs/2209.04095