K-theory doesn't exist

Unsatisfiable Linear k-CNFs Exist, for every k

We call a CNF formula linear if any two clauses have at most one variable in common. Let Linear k-SAT be the problem of deciding whether a given linear k-CNF formula is satisfiable. Here, a k-CNF formula is a CNF formula in which every clause has size exactly k. It was known that for k ≥ 3, Linear k-SAT is NP-complete if and only if an unsatisfiable linear k-CNF formula exists, and that they do...

All Directed BIBDs with k = 3 Exist

A directed BIBD with parameters (v,b,r,k,λ*) is a BIBD with parameters (v, b, r, k, 2λ*) in which each ordered pair of varieties occurs together in exactly λ* blocks. It is shown that λ*v(v 1) = 0 (mod 3) is a necessary and sufficient condition for the existence of a directed (v, b, r, k, λ*) BIBD with k = 3. Disciplines Physical Sciences and Mathematics Publication Details Seberry, J and Skill...

Multiple Vitamin K Forms Exist in Dairy Foods

Background: The plant-based form of vitamin K (phylloquinone, vitamin K-1) has been well quantified in the US diet. Menaquinones (vitamin K-2) are another class of vitamin K compounds that differ from phylloquinone in the length and saturation of their side chain, but they have not been well characterized in foods. Objectives: The objectives of this study were to 1) quantify phylloquinone and t...

K - Theory

K-Theory and Intersection Theory

2.1 Dimension and codimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Dimension relative to a base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Cartier divisors . . . . . . . . . . . . . . . . . . . . . . . . . . . ...