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The key to the success of the circle method lies in the converse of the above statement: the only way that the trivial upper bound (2) comes close to being sharp is when all correlate with the same character , or in other words are simultaneously large. This converse is largely captured...
For general , it was easy to see that bounded rank implied bounded analytic rank; Theorem 2 is the converse statement. We tried a number of ways to show that bounded analytic rank implied bounded rank, in particular spending a lot of time on ergodic-theoretic approaches, but eventually we...
The converse (math) statement: "If we won’t be able to drive to school, then it snows." Though it seems like this statement does not make sense, rest assured that you have done the operation correctly. The use of words in place of numbers and functions in logic is just a demonstrati...
This of course does require a pretty good sized vocabulary and good listening comprehension skills. I would put fluency at C1 personally. I suppose I kind of take it literally, fluency is reached when I can have a fluent conversation. I also don’t think that fluency is necessarily what ...
Make a Statement Personalized maternity t-shirts are also a great way for the mom-to-be to get a message across to inquisitive friends and strangers. “We’re Not Finding Out!” or “Don’t Touch the Belly!” are pretty clear. And let’s face it, after about the fifth month, the ...
How does canvas fabric impact the environment? Since canvas primarily contains natural materials, the production of this material has a relatively low negative impact on the environment. Gesso, the finishing material that is applied to painting canvas, commonly consists of a mix of natural and synth...
Interviews: Students converse with an interviewer or a group of interviewers that explores their interests, experiences, goals, and opinions. ?♂️Pro Tip: If you plan to conduct an oral examination or interview for your student assessment, you can do so in a highly flexible way by askin...
But I’ve always thought that the converse of Vonnegut’s admonition is also true: Pretending to be better than we are can be a way of setting the bar higher, not just for ourselves but for those around us.People have a deep hunger for idealism. The best entrepreneurs have the co...
This should be compared with the paper of Vu, Wood, and Wood, which introduces a converse principle that embeds finite subsets of (or more generally, a characteristic zero integral domain) in a Freiman field-isomorphic fashion into finite subsets of for arbitrarily large primes , allowing one ...