for all . One can explicitly construct such a system as follows. One can take to be the Cantor space with the product -algebra and the shift with the function being the coordinate function at zero: (so in particular for any ). The only thing remaining is to construct the invariant measur...
(In Heath-Brown’s original paper, the Selberg sieve is essentially replaced by the more combinatorial restriction for some large , where is the primorial of , but I found the computations to be slightly easier if one works with a Selberg sieve, particularly if the sieve is not squared to ...
Rank often describes something having a strong, unpleasant smell, typically because of decay or stagnation, while smelly is a broader term indicating any noticeable or strong odor, not necessarily unpleasant.
For example, she has the opinion that every sequence of digits is a number. Although this might seem a bit careless, it turns out to be the initial spark and a driving force of the whole investigation. In the history of mathematics, the “naive” approach of putting difficulties with ...
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal r
you can (arguably) think of likelihood in terms ofpossibility theory,rather than probability theory, and that possibility theory is naturally formulated in terms of the (somewhat obscure) mathematical languages ofmaxitive measure theory, idempotent probability theory and tropical algebra/tropical geometry...
Requiring that a floating-point representation be normalized makes the representation unique. Unfortunately, this restriction makes it impossible to represent zero! A natural way to represent 0 is with 1.0 × , since this preserves the fact that the numerical ordering of nonnegative real numbers ...
A tangent line is one for which the order of contact is >= 2, and an infllectional tangent one for which it is >= 3, etc. Then (I believe this is Descartes' method), we can do differential calculus for all polynomials this way just by algebra. So what we teach in college about...
A little algebra, leading to equation 5, will maybe make things just a little easier to see. F = H - TS Equation 5The significance of this equation is that it is the value of F which tells you whether any give chemical reaction will go forward spontaneously, or whether it needs to b...
The caveat is that we have to work with periodic subsets of , rather than all of ; we believe this is largely a technical restriction of our method, and it is likely that can be removed with additional effort and creativity. We also remark that when , the periodic tiling conjecture was ...