We consider a family U of finite universes. The second order quantifier QR, means for each U ∈ U quantifying over a set of n(R)-place relations isomorphic esto a given relation. We define a natural partial order on such quantifiers called interpretability. We show that for every QR, ever QR is interpretable by quantifying over subsets of U and one to one functions on U both of bounded order, or...

Aggressive early deflation is a QR algorithm deflation strategy that takes advantage of matrix perturbations outside of the subdiagonal entries of the Hessenberg QR iterate. It identifies and deflates converged eigenvalues long before the classic small-subdiagonal strategy would. The new deflation strategy enhances the performance of conventional large-bulge multishift QR algorithms, but it is ...

The popularity of QR codes for encoding information such as URIs has increased exponentially in step with the technological advances and availability of smartphones, digital tablets, and other electronic devices. We propose using QR codes on specimens in biological collections to facilitate linking vouchers' electronic information with their associated collections. QR codes can efficiently prov...

A quasi-regular cell complex is defined and shown to have a reasonable barycentric subdivision. In this setting, Whitney's theorem that the ^-skeleton of the barycentric subdivision of a triangulated n-manifold is dual to the (n /c)th Stiefel-Whitney cohomology class is proven, and applied to projective spaces, lens spaces and surfaces. 1. QR complexes. A (finite) cell structure on a space X is...

The QR algorithm is still one of the most important methods for computing eigenvalues and eigenvectors of matrices. Most discussions of the QR algorithm begin with a very basic version and move by steps toward the versions of the algorithm that are actually used. This paper outlines a pedagogical path that leads directly to the implicit multishift QR algorithms that are used in practice, bypass...

QR code is the type of matrix barcode, which was first designed for the automotive industry by Denso Wave in Japan. The QR Code system has become admired outside the automotive industry due to its fast readability and greater storage capacity compared to standard UPC barcodes. This paper take account of QR codes basics, its real time application in day to day life and research areas associated....

With the continued proliferation of smart mobile devices, Quick Response (QR) code has become one of the mostused types of two-dimensional code in the world. Aiming at beautifying the appearance of QR codes, existing works have developed a series of techniques to make the QR code more visual-pleasant. However, these works still leave much to be desired, such as visual diversity, aesthetic quali...