We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if Λ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of Λ in a non-principal direction has Hausdorff dimension min(γ, 1), where γ is the Hausdorff dimension of Λ. This gener...

This study was undertaken to investigate whether certain hazardous chemicals were present as components in new carpets, and if so, in what quantities. The study included analysis of eight new carpet samples that were available for retail in the UK. Some of the carpet samples contained high levels of organotins, in particular TBT (up to 47,500 ppb). One sample contained high levels (1600 ppb) of...

Quality assessment in carpet manufacturing is performed by humans who evaluate the appearance retention (AR) grade on carpet samples. To quantify the AR grades objectively, different research based on computer vision have been developed. Among them Local Binary Pattern (LBP) and its variations has shown promising results. Nevertheless, the requirements of quality assessment on a wide range of c...

We consider the use of task pool teams in implementation of the master equation on random Sierpinski carpets. Though the basic idea of dynamic storage of the probability density reported earlier applies straightforward to random carpets, the randomized construction breaks up most of the simplifications possible for regular carpets. In addition, parallel implementations show highly irregular com...

In 1984 Bedford and McMullen independently introduced a family of self-affine sets now known as Bedford-McMullen carpets. Their work stimulated lot research in the areas fractal geometry non-conformal dynamics. this survey article we discuss some aspects carpets, focusing mostly on dimension theory.

Old carpets may be reservoirs of dust, lead (Pb), and dust mite allergen. The purpose of this study was to determine if the dust, Pb, dust mite allergen, bacteria, and fungi on the surface of carpets could be reduced by 90% in 1 week with the use of a Hoover Self Propelled Vacuum with Embedded Dirt Finder (HSPF). A high-volume surface sampler (HVS3) was used to measure surface dust and pollutan...

For the development of polymer carpets as active devices for micro- and nanotechnology, a control of the polymer carpet morphology and especially control of the stimulus responsive polymer brush is needed. Here, we report on the first example for the fabrication of patterned polymer carpets. On a two-dimensional framework of fully crosslinked and chemically patterned nanosheets, polymer brushes...

We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on the Sierpinski gaskets and the Sierpinski carpets to their boundaries, where boundaries mean the triangles and rectangles which confine gaskets and carpets. As an application, we construct diffusion processes on ...