相关论文: Multifractal Formalism and Inequality involving Pa…
We correct a small gap found in the authors' paper 'On bounds for the effective differential Nullstellensatz' (J Algebra 449:1-21, 2016). This gap is due to an inequality that does not generally hold. However, under one additional…
A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a…
We consider various inequalities for polynomials, with an emphasis on the most fundamental inequalities of approximation theory. In the sequel a key role is played by the generalized Minkowski functional \alpha(K,x), already being used by…
Let $X=\bigcup\varphi_{i}X$ be a strongly separated self-affine set in $\mathbb{R}^2$ (or one satisfying the strong open set condition). Under mild non-compactness and irreducibility assumptions on the matrix parts of the $\varphi_{i}$, we…
In this paper, we first introduce some new classes of weighted amalgam spaces. Then we give the weighted strong-type and weak-type estimates for fractional integral operators $I_\gamma$ on these new function spaces. Furthermore, the…
We study the nature of the phase transition in the multifractal formalism of the harmonic measure of Diffusion Limited Aggregates (DLA). Contrary to previous work that relied on random walk simulations or ad-hoc models to estimate the low…
This paper studies the diameter of the numerical range of bounded operators on Hilbert space and the induced seminorm, called the numerical diameter, on bounded linear maps between operator systems which is sensible in the case of unital…
We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \mathbb R $ endowed with a measure which needs not to be doubling.
We first formulate an inverse problem for a linear fractional Lam\'e system. We determine the Lam\'e parameters from exterior partial measurements of the Dirichlet-to-Neumann map. We further study an inverse obstacle problem as well as an…
In this paper we compute the multifractal analysis for local dimensions of Bernoulli measures supported on the self-affine carpets introduced by Bedford-McMullen. This extends the work of King where the multifractal analysis is computed…
We prove a Carleman-type estimate for Dirichlet-stationary multivalued functions and apply it to give a different proof of the optimal dimension of the singular set of Dir-minimizing multivalued functions, originally due to Almgren and to…
In this paper, we give a characterization of the two weight strong and weak type norm inequalities for the bilinear fractional integrals. Namely, we give the characterization of the following inequalities, \[ \|\mathcal I_\alpha…
Motivated by the existence problem of Fourier frames on fractal measures, we introduce Bessel and frame measures for a given finite measure on $\br^d$, as extensions of the notions of Bessel and frame spectra that correspond to bases of…
Let $\mu$ be a doubling measure in $\mathbb{R}^n$. We investigate quantitative relations between the rectifiability of $\mu$ and its distance to flat measures. More precisely, for $x$ in the support $\Sigma$ of $\mu$ and $r > 0$, we…
In this paper the classical Euler-Bernoulli beam (CEBB) theory is reformulated utilising fractional calculus. Such generalisation is called fractional Euler-Bernoulli beams (FEBB) and results in non-local spatial description. The parameters…
The article is devoted to finding conditions for the packing dimension preservation by distribution functions of random variables with independent $\tilde{Q}$-digits. The notion of "faithfulness of fine packing systems for packing dimension…
We establish some new properties of the Dunkl-Wiener amalgam spaces defined on the real line. These results allow us to obtain the boundedness of Dunkl-type fractional integral and fractional maximal operators in the Dunkl-Fofana spaces.
The deployment of Large Language Models (LLMs) in high-stakes medical settings poses a critical AI alignment challenge, as models can inherit and amplify societal biases, leading to significant disparities. Existing fairness evaluation…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately.…