The proofs behind an approximate root
For a uniformly continuous function whose endpoint values bracket zero, can we establish a point where the function's value is within any requested error of zero?
Applications
Problems studied with Axeyum
Each page describes a concrete use of Axeyum and links to its artifact records. Inclusion records an application; it does not claim that the mathematical result is new or that a publication exists.
Problem list
10 problem studies
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01
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02
The proofs behind an approximate maximum
For a uniformly continuous function on a closed interval, can we establish a point whose value is within a requested error of every value on the interval?
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03
An exact Mean Value Theorem witness
For p(x) = x^3 on [0,3], find an interior point where the derivative equals the secant slope.
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04
Certified polynomial integration
Compute an antiderivative of 3x^2 + 2x and check the result without trusting the integration procedure.
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05
Primality of 2^89 - 1
Can an independently checked certificate establish that the Mersenne number 2^89 - 1 is prime?
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06
Two four-color Rado numbers
What are the four-color Rado numbers for 5(x-y) = 3z and 5(x-y) = 4z?
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07
Optimal sorting networks on three to six channels
What is the minimum number of comparators needed to sort every Boolean input on three, four, five, or six channels?
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08
A BCNF decomposition counterexample
Can a BCNF decomposition preserve a lossless join while failing to preserve a functional dependency?
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09
The cause of an infeasible ICU roster
Which constraints make a 102-row ICU night roster infeasible?
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10
The cause of an impossible project deadline
Which constraints make a 60-row project schedule incompatible with its delivery deadline?
Related collections
Research describes active programs and open questions.
Publications contains bibliographic records.
Artifacts exposes individual fact and evidence records.