Abstract. We survey half-linear dynamic equations on time scales. These contain the well-known half-linear differential and half-linear difference equations as special cases, but also other kinds of half-linear equations. Special cases of half-linear equations are the well-studied linear equations of second order. We discuss existence and uniqueness of solutions of corresponding initial value p...

Abstract We give Hardy–Stein and Douglas identities for nonlinear nonlocal Sobolev–Bregman integral forms with unimodal Lévy measures. prove that the corresponding Poisson defines an extension operator spaces. As application, we obtain boundedness of Dirichlet-to-Neumann on weighted $$L^p$$ L p</mml:mi...

We obtain Sturmian comparison results for the nonnegative solutions to Dirichlet problems associated with p-Laplacian operators. From Picone-type identities [4, 9], we obtain results comparing solutions of two types of equations. We also present results related to those operators using Piconetype identities.

Length-Constrained N-Gram Analysis by, Joe Picone, Tom Staples, Kazz Kondo, and Nozomi Arai Tsukuba Research and Development Center Texas Instruments Tsukuba, Japan Abstract A common problem in speech processing is the conversion of the written form of a language to a set of phonetic symbols representing the pronunciation. In this paper we focus on an aspect of this problem specific to the Japa...

We establish a generalization of Sturm–Picone comparison theorem for pair fractional nonlocal equations: $$\begin{aligned} (-div. (A_1(x)\nabla ))^{s} u= & {} C_{1}(x) u \,\,\,\text { in }\,\,\Omega ,\\ 0 \,\,\,\,\text on }\,\,\,\,\,\partial \Omega , \end{aligned}$$ and (A_2(x)\nabla v= C_{2}(x) v in}\,\,\Omega on}\,\,\,\,\,\partial where $$\Omega \subset \mathbb {R}^n$$ is an open bounded subs...