@book {11859, title = {Linear Algebra 1\&2 Course Notes}, year = {2016}, edition = {4.0}, author = {Dan Wolczuk} } @book {11858, title = {Introduction to Linear Algebra for Science and Engineering, 2/E}, year = {2012}, publisher = {Pearson }, organization = {Pearson }, url = {http://catalogue.pearsoned.ca/educator/product/Introduction-to-Linear-Algebra-for-Science-and-Engineering/9780321748966.page}, author = {Dan Wolczuk and Daniel Norman} } @article {11861, title = {On the Inhomogeneous Hall\&$\#$39;s Ray of Period-One Quadratics}, journal = {Experimental Mathematics}, volume = {10}, year = {2001}, pages = {487-496}, abstract = {

For quadratics with period-one negative continued fraction expansions,

X\theta =\frac{1}{ a-{\dfrac{\mathstrut 1}{a-{\dfrac{\mathstrut 1}{a- \cdots }}}}},

we show that the inhomogeneous Lagrange spectrum,

\bL (\theta) :=\bigl\{ \liminf\nolimits_{|n|\rightarrow \infty} |n|@\|n\theta -\gamma\| : \gamma \in \funnyR,\; \gamma \not\in \funnyZ+\theta \funnyZ\bigr\},

contains an inhomogeneous Hall{\textquoteright}s ray

with $$c(\theta)=\tfrac{1}{4}\bigl(1-O(a^{-1/2})\bigr)\hbox{.}

We describe gaps in the spectrum showing that this is essentially best possible. Pictures of computed spectra are included. Investigating such pictures led us to these results.

}, url = {https://projecteuclid.org/euclid.em/1069855248}, author = {Christopher G. Pinner and Dan Wolczuk} }