Abstract Conjecture II.3.6 of Spohn in [47] and Lecture 7 Jensen–Yau [35] ask for a general derivation universal fluctuations hydrodynamic limits large-scale stochastic interacting particle systems. However, the past few decades have witnessed only minimal progress according to [26]. In this paper, we develop method deriving so-called Boltzmann–Gibbs principle family nonintegrable nonstationary...

We present a simplified derivation of the fact that the complexity-theoretic lower bound of comparison-based sorting algorithms, both for the worst-case and for the average-case time measure, is Ω(nlogn). The standard proofs typically are directly presented over decision trees. The proof for the average-case however relies on differential calculus, which presents a main hurdle in undergraduate ...

Let $R$ be a 2-torsion free ring and $U$ be a square closed Lie ideal of $R$. Suppose that $alpha, beta$ are automorphisms of $R$. An additive mapping $delta: R longrightarrow R$ is said to be a Jordan left $(alpha,beta)$-derivation of $R$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin R$. In this paper it is established that if $R$ admits an additive mapping $G : Rlongrigh...

We study the Hyers-Ulam stability theory of a four-variate Jensen-type functional equation by considering the approximate remainder φ and obtain the corresponding error formulas. We bring to light the close relation between the β-homogeneity of the norm on F *-spaces and the approximate remainder φ, where we allow p, q, r , and s to be different in their Hyers-Ulam-Rassias stability.

and Applied Analysis 3 Theorem 2.2. A mapping f : X ×X → Y satisfies 1.1 if and only if it satisfies 1.2 . Proof. If f satisfies 1.1 , then we get