Related papers: Variations on Barbalat's Lemma
Let $X=\{X_n: n\in\mathbb{N}\}$ be a linear process in which the coefficients are of the form $a_i=i^{-1}\ell(i)$ with $\ell$ being a slowly varying function at the infinity and the innovations are independent and identically distributed…
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Law-invariant functionals are central to risk management and assign identical values to random prospects sharing the same distribution under an atomless reference probability measure. This measure is typically assumed fixed. Here, we adopt…
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Obtaining explicit stability estimates in classical functional inequalities like the Sobolev inequality has been an essentially open question for 30 years, after the celebrated but non-constructive result of G. Bianchi and H. Egnell in…
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Fermat's statement is equivalent to say that if $x$, $y$, $z$, $n$ are integers and $n>2$, then $z^{n}\gtrless x^{n}+y^{n}$. This is proved with the aid of numbers $\lambda $'s, of the form $\lambda =z/\rho $, with $1<\rho<z$, named…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
The Lebesgue dominated convergence theorem of the measure theory implies that the Riemann integral of a bounded sequence of continuous functions over the interval [ 0,1] pointwise converging to zero, also converges to zero. The validity of…
We claim that if by a choice of the couplings the theory can be made conformally invariant (vanishing of the beta functions) it is automatically finite and vice versa. This is demonstrated by explicit example in supersymmetric gauge theory.…
This is the third installment in a series of papers concerning the Bounded Real Lemma for infinite-dimensional discrete-time linear input/state/output systems. In this setting, under appropriate conditions, the lemma characterizes when the…
A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of…
Herbrand's Theorem is a fundamental result in mathematical logic which provides a reduction of first-order formulas satisfied by a universal class to formulas free of existential quantifiers. In this work, a simpler and self-contained…
The Riemann Hypothesis has been of central interest to mathematicians for a long time and many unsuccessful attempts have been made to either prove or disprove it. Since the Riemann zeta function is defined as a sum of the infinite number…
Strong typicality and the Markov lemma have been used in the proofs of several multiterminal source coding theorems. Since these two tools can be applied to finite alphabets only, the results proved by them are subject to the same…
Safety and liveness are elementary concepts of computation, and the foundation of many verification paradigms. The safety-liveness classification of boolean properties characterizes whether a given property can be falsified by observing a…
We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analytic functions. Examples are given concerning polynomial and…
The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic…