We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of d-dimensional bounded monotonic functions under L norms. It is interesting to see that both the metric entropy and bracketing entropy have different behaviors for p < d/(d − 1) and p > d/(d − 1). We apply the new bounds for bracketing entropy to establish a global rate of convergence of the MLE of ...

While voluminous studies have attributed the continuing decline of institutional trust to political corruption, the link between corruption and institutional trust in Asia has yet been explored systematically. Testing the effect of corruption on institutional trust is theoretically important and empirically challenging, since many suggests that contextual factors in Asia such as political cultu...

We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set X in a metric space, it is proved the existence of an almost periodic sequence {ψk}k∈Z such that {ψk; k ∈ Z} = X and ψk = ψk+lq(k), l ∈ Z for all...

In this note we show the spectral mapping theorem for the evolution semigroup on L p ((; ; X), 1 p < 1, associated with a strongly continuous cocycle on a Banach space over a continuous ow on a locally compact metric space.

In 2013, Masson and Siljander determined a method to prove that the minimal p-weak upper gradient $$g_{f_\varepsilon }$$ for time mollification $$f_\varepsilon $$ , $$\varepsilon >0$$ of parabolic Newton–Sobolev function $$f\in L^p_\mathrm {loc}(0,\tau ;N^{1,p}_\mathrm {loc}(\Omega ))$$ with $$\tau $$\Omega open domain in doubling metric measure space $$(\mathbb {X},d,\mu )$$ supporting weak (1...

We develop a metric for probability distributions with applications to biological sequence analysis. Our distance metric is obtained by minimizing a functional defined on the class of paths over probability measures on N categories. The underlying mathematical theory is connected to a constrained problem in the calculus of variations. The solution presented is a numerical solution, which approx...