We focus on rational solutions or nearly-feasible that serve as certificates of feasibility for polynomial optimization problems. show that, under some separability conditions, certain cubic polynomially constrained sets admit solutions. However, we in other cases it is NP Hard to detect if exist they any reasonable size. extend this idea various settings including near feasible, but super opti...

The essay is a partial investigation into the semantics of the explanatory connective ‘because’. After three independently plausible assumptions about ‘because’ are presented in some detail, it is shown how their interaction generates a puzzle about ‘because’, once they are combined with a common view on conceptual analysis. Four possible solutions to the puzzle are considered.

The role of Painlevé equations in nonlinear world is well recognized. Originally Painlevé derived these equations to find new transcendental functions, and irreducibility of the solutions has been established in general by Umemura [1]. However, classical solutions of the Painlevé equations have attractive and mysterious properties. Recently, such properties of rational solutions have been studi...

We review the recently developed program for constructing and studying solutions of the Einstein constraint equations using gluing techniques. We discuss what we believe are sharp conditions sufficient for a pair of solutions to admit gluing via a connected sum or “wormhole”, and describe how one carries out the gluing. We also discuss a number of useful applications.

It is generally accepted that failure to reason correctly during the early stages of software development causes developers to make incorrect decisions which can lead to the introduction of faults or anomalies in systems. Most key development decisions are usually made at the early system speci cation stage of a software project and developers do not receive feedback on their accuracy until nea...

Willingness to communicate (WTC) construct plays an important role in second language (L2) teaching and learning. Almost any second language learner is likely to respond to a direct question, but many will not continue or initiate communication. The present study investigates Pakistani undergraduate students' perception of their willingness to initiate communication in English across four types...

Abstract According to an influential view, when it comes representing reality, some words are better suited for the job than others. This is elitism. There reason believe that set of best, or elite, should not be redundant arbitrary. However, we often forced choose between these two theoretical vices, especially in cases involving theories seem mere notational variants. riddle redundancy: both ...