In this article we show that there exist measurable sets W ⊂ R2 with finite measure that tile R2 in a measurable way under the action of a expansive matrix A, an affine Weyl group f W, and a full rank lattice e Γ ⊂ R2. This note is follow-up research to the earlier article ”Coxeter groups and wavelet sets” by the first and second authors, and is also relevant to the earlier article ”Coxeter gro...

To state our results precisely, we introduce some notation. Throughout this paper, let F be a given Boolean function over N variables, and we assume that it is given as a CNF formula with M clauses and that it has P2N satisfying assignments, where P will be referred as the sat. assignment ratio of F . Furthermore, we introduce two parameters1 δ > 0 and ε > 0, and consider the following situatio...

The main objective of this Workshop was to bring together in Banff eminent and emerging researchers from the three main branches of Convex Geometry: Discrete, Analytical and Applied. There has not been such a unifying conference in the past fifteen years. The organizers believe that this objective was met during the week of March 4 9. First, of the thirty-nine participants, one third represente...

Mobile Augmented Reality (MAR) has predominantly been used in locative games and playful experiences for the presentation on virtual game objects in conjunction with separate 2-D maps for navigation. This distinct switch in interaction modalities can detract from the game play experience and will arguably be less relevant for AR glasses. Therefore this research considers the application techniq...

We consider the problem of counting the number of lattice vectors of a given length and prove several results regarding its computational complexity. We show that the problem is ♯Pcomplete resolving an open problem. Furthermore, we show that the problem is at least as hard as integer factorization even for lattices of bounded rank or lattices generated by vectors of bounded norm. Next, we discu...

There has been extensive discussion on the need to use corrective feedback in writing within foreign language learning. Essentially, is one of important tools improving students’ skills learning a language. This study aims find out preference and justification written (WCF) through Google Docs among instructors students higher institute. The effects direct indirect with metalinguistic comments ...

This study examined the role of error-type and working memory (WM) in effectiveness direct-metalinguistic indirect written corrective feedback (WCF) on self error-correction first-language writing. Fifty-one French first-year psychology students volunteered to participate experiment. They carried out a task after receiving WCF typographical, orthographic, grammatical, semantic errors. Results i...

This article – originating from a paper presented at the Conference “Pandemic Perspectives 2021: Reflections on Post-Covid World” has twofold aim. Firstly, it seeks to identify and discuss ways in which readers, writers, cultural organisations have used digital platforms re-create literary practices throughout pandemic. Here, encompass attendance festival events, fact of monitoring one’s readin...

Effectively communicating science and linking it to the 'real world' has important benefits for both scientists and society. Here we share our experience at Pint of Science, an initiative that encourages researchers to discuss their findings with the public and to engage in conversation in a relaxed setting. We discuss strategies towards organizing a scientific outreach event - big or small - a...

Edinburgh, Scotland’s capital city, is host for this year’s conference. Edinburgh is an ancient city built on seven hills beside the Firth of Forth. Responsible for the Scottish Reformation and Enlightenment, it is now both a UNESCO world heritage site and one of the UK’s strongest economies. It is home to the world’s largest arts festival and is regularly voted as the best place to live in the...