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We develop the classical theory of Diophantine approximation without assuming monotonicity or convexity. A complete ‘multiplicative’ zero-one law is established akin to the ‘simultaneous’ zero-one law...
It is known that the number of di erent classical messages which can be communicated with a single use of a classical channel with zero probability of decoding error can sometimes be increased by us...
We characterize the zero-temperature limits of minimal free energy states for interacting corpora – that is, for objects with finitely many degrees of freedom, such as articulated rods. These li...
A mapping $f:Z^n\rightarrow R^n$ is said to possess the direction preserving property if $f_i(x)>0$ implies $f_i(y)\geq 0$ for any integer points $x$ and $y$ with $\|x-y\|_{\infty}\leq 1$. In this ...

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