Carpeting can be found throughout various buildings, whether residential or commercial. This carpeting can be very useful to forensic scientists, especially when biological samples are present on it. However, obtaining high quality DNA profiles from this potential piece of evidence can be challenging due to the presences of Polymerase Chain Reaction (PCR) inhibitors that will interfere with the...

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...

In 1836 Henry Fox Talbot, an inventor of photography, published the results of some experiments in optics that he had previously demonstrated at a British Association meeting in Bristol. "It was very curious to observe that though the grating was greatly out of the focus of the lens...the appearance of the bands was perfectly distinct and well defined...the experiments are communicated in the h...

It is shown that the homeomorphism groups of the (generalized) Sierpiński carpet and the universal Menger continua are not zero-dimensional. These results were corollaries to a 1966 theorem of Brechner. New proofs were needed because we also show that Brechner’s proof is inadequate. The method by which we obtain our results, the construction of closed imbeddings of complete Erdős space in the h...

We construct a Sierpinski carpet E ⊂ R of area zero and a K0 > 1 with the property that every K0-quasiconformal image of E contains rectifiable curves, but such that E has some quasiconformal image containing no non-constant rectifiable curves. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary:

One of the sources inspiration used to increase aesthetic value a design product is traditional arts owned by that culture. When Turkish art examined, it seen oldest carpet. For this reason, carpet was as means in urban landscape designs. The aim research emphasize importance using local and cultural values designs provide proposals for preservation transfer these future generations. In context...