A case of localized lichen planopilaris over the face, extending to the scalp is presented.This case highlights the different variations, which can occur in the presentation of localized lichen planus. The case was unique because of the extension of the lesions into the scalp. We also wanted to demonstrate the peculiar dermoscopic patterns of active lichen planopilaris when occurring over the f...

In this paper, we study the Landis-type conjecture, i.e., unique continuation property from infinity, of fractional Schr\"{o}dinger equation with drift and potential terms. We show that if any solution decays at a certain exponential rate, then it must be trivial. The main ingredients our proof are Caffarelli-Silvestre extension Armitage's Liouville-type theorem.

We consider the minimal average action (Mather's β function) for area preserving twist maps of annulus. The regularity properties this function share interesting relations with dynamics system. prove that β-function associated to a standard-like map admits unique C1-holomorphic (canonical) complex extension, which coincides on set real diophantine frequencies. In particular, we deduce uniquenes...

We prove that every Lipschitz function from a subset of a locally compact length space to a metric tree has a unique absolutely minimal Lipschitz extension (AMLE). We relate these extensions to a stochastic game called Politics — a generalization of a game called Tug of War that has been used in [42] to study real-valued AMLEs.

We introduce the measurement idea in domain theory and then apply it to establish two fixed point theorems. The first is an extension of the Scott fixed point theorem which applies to nonmonotonic mappings. The second is a contraction principle for monotone maps that guarantees the existence of unique fixed points.

In this paper we describe a computational approach to the optimal output feedback control of multi-model systems by means of a unique constant output feedback matrix. Extension of the method to output feedback control of multi-model periodic systems is also presented. The power of the proposed approach is illustrated by the simultaneous stabilization and optimization of a helicopter multi-model.

In this paper we examine an extension of the fictitious play process for bimatrix games to stochastic games. We show that the fictitious play process does not necessarily converge, not even in the 2 × 2 × 2 case with a unique equilibrium in stationary strategies. Here 2 × 2 × 2 stands for 2 players, 2 states, 2 actions for each player in each state.

A. Let f be a function on the set of diagonal n × n matrices, and let˜f be the unique extension of f to the set of symmetric n × n matrices invariant with respect to conjugation by orthogonal matrices. We show that˜f has the same regularity properties as f.

We describe a rare variant of mirror hand in a 20-year-old man who presented with multiple fingers. Radiographs revealed two ulnae (one vestigial) and a radius. There was duplication of the humeral head. The unique features of this case are the age of patient before the start of treatment and extension of the duplication proximal to the elbow.

This paper contributes to two debates: (i) the debate about whether or not ancient Greek has Free Indirect Discourse (FID), and (ii) the debate about how we should analyze FID semantically. We do this by showing that there is a distinction between FID and what we call Unembedded Indirect Discourse (UID). The semantic analysis that we develop for the latter shows that the two phenomena, though s...