A Note on Pseudo-reflections

In this note, we show that if V is a finite dimensional vector space equipped with a non-degenerate bilinear form, and one has a set of pseudo-reflections on V, preserving the form and having no non-zero common fixed vector, then the group G generated by this set is ‘sufficiently large’ in the sense that for every linear transformation T : V → V, there exists an element g ∈ G such that g − G is invertible

Picard groups of punctured spectra of dimension three local hypersurfaces are torsion-free

Let (R,m) be a local ring and U_R=Spec(R) -{m} be the punctured spectrum of R. Gabber conjectured that if R is a complete intersection of dimension 3, then the abelian group Pic(U_R) is torsion-free. In this note we prove Gabber's statement for the hypersurface case. We also point out certain connections between Gabber's Conjecture, Van den Bergh's notion of non-commutative crepant resolutions and some well-studied questions in homological algebra over local rings.Comment: Some statements/typos fixed thanks to corrections from the referees, main results remain the sam

Inspecting Traditions

In this paper I examine my thesis body of work, Inspecting Traditions. This paper illuminates my process of making Jewish objects through the use of digital fabrication techniques. The work in Inspecting Traditions uses historically Jewish forms as a lens in which to speak about the history of ceramics and its relationship to 21st century technology. This work developed a dialogue between the historical sources and modern technology by using 3D printing to create vessels

The Use of Integrated Design to Deliver the Energy Efficiency in Buildings at Least Cost

This study gives us a concise overview to describe the different types of energy efficient buildings, focusing on the verification of design, interference check, prove feasibility, practicability, attitudes, and saving cost. Energy efficiency in buildings may require specific solutions and evaluation. The aim of this study is to investigate the impacts of using the integrated design to deliver energy efficiency in buildings at least cost. Also, this research seeks to mitigate the barriers that impede achievable cost reductions. The literature review and based discussions lead to generate of propositions and questions. In chapters about the methodology and analysis, the two associated approaches have been employed, the quantitative and qualitative, qualitative and quantitative approaches, examined by research, offering rich expressive analyses and viewed as harmonizing. In this research, the both qualitative and quantitative approaches utilized the research practice that face the problem of construct the gathering data; and are subject to avoid potential bias; in order to examine the impacts of the integrated design on the energy efficiency in buildings and the cost. This study undertakes a number of recommendations, and identifies lessons to be learned; also, promote improving the design of the energy efficiency in buildings. With these contributions, the research helps prospective users to utilize the integrated design as a potential method offered to energy efficiency in buildings at least cost. To improve the future work, this study will research further trends to cover the subject areas deeper, in the present questions as below: - • To investigate the role of public to mitigate the barriers. • Examine new ways of improving communications to achieve the aim of study

Field methods beyond the classroom: For every door closed, a Zoom window opens

This poster presents a methodology for teaching field methods remotely and explores its potential future applications