相关论文: About the general chain rule for functions of boun…

The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions $d$. Calculations of the universal function of a conformal invariant $\xi$ which appears in…

The main objective of this article is to present $\nu$-fractional derivative $\mu$-differentiable functions by considering 4-parameters extended Mittag-Leffler function (MLF). We investigate that the new $\nu$-fractional derivative…

Birkhoff's variety theorem, a fundamental theorem of universal algebra, asserts that a subclass of a given algebra is definable by equations if and only if it satisfies specific closure properties. In a generalized version of this theorem,…

We provide some necessary and sufficient conditions for a proper lower semicontinuous convex function, defined on a real Banach space, to be locally or globally Lipschitz continuous. Our criteria rely on the existence of a bounded selection…

Atar, Chowdhary and Dupuis have recently exhibited a variational formula for exponential integrals of bounded measurable functions in terms of R\'enyi divergences. We develop a variational characterization of the R\'enyi divergences between…

We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. We give two types of learning bounds, both distribution-dependent and valid for general families, in…

In this paper, we obtain additional results for a fractional counting process introduced and studied by Di Crescenzo et al. (2016). For convenience, we call it the generalized fractional counting process (GFCP). It is shown that the…

Let $f$ be a measurable, real function defined in a neighbourhood of infinity. The function $f$ is said to be of generalised regular variation if there exist functions $h \not\equiv 0$ and $g > 0$ such that $f(xt) - f(t) = h(x) g(t) +…

The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…

We prove a global fractional differentiability result via the fractional Caccioppoli-type estimate for solutions to nonlinear elliptic problems with measure data. This work is in fact inspired by the recent paper [B. Avelin, T. Kuusi, G.…

The chain rule for derivatives of a function of a function is extended to a function of a statistical functional, and applied to obtain approximations to the cumulants, distribution and quantiles of functions of sample moments, and so to…

We consider the class $PW(\mathbb R^n)$ of functions in $L^2(\mathbb R^n)$, whose Fourier transform has bounded support. We obtain a description of continuous maps $\varphi : \mathbb R^m\rightarrow\mathbb R^n$ such that $f\circ\varphi\in…

We prove necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative. The fractional basic problem of the calculus of variations with free…

Fixed-order perturbative calculations for differential cross sections can suffer from non-physical artifacts: they can be non-positive, non-normalizable, and non-finite, none of which occur in experimental measurements. We propose a…

This article is centered around generalizing a previous implicit function theorem of the author to be applicable for maps f:E sqcap F to F which can be lifted to Keller C^k_pi maps f_i:E sqcap F_i to F_i with F_i Banach and F=projlim F_i .…

The problem of adversarial examples has highlighted the need for a theory of regularisation that is general enough to apply to exotic function classes, such as universal approximators. In response, we give a very general equality result…

Recently, the authors Khalil, R., Al Horani, M., Yousef. A. and Sababheh, M., in " A new Denition Of Fractional Derivative, J. Comput. Appl. Math. 264. pp. 6570, 2014. " introduced a new simple well-behaved definition of the fractional…

We study a linear-fractional Bienaym\'e-Galton-Watson process with a general type space. The corresponding tree contour process is described by an alternating random walk with the downward jumps having a geometric distribution. This leads…

We consider a derivation $\mathsf{D}$ on the ring $\Lambda$ of symmetric functions and investigate its combinatorial, algebraic and geometric properties. More precisely, we show that $\mathsf{D}$ restricts to a quasi-isometry, with respect…

Given a sequence of complex square matrices, $a_n$, consider the sequence of their partial products, defined by $p_n=p_{n-1}a_{n}$. What can be said about the asymptotics as $n\to\infty$ of the sequence $f(p_n)$, where $f$ is a continuous…