What polynomial satisfies a given endomorphism?

On graphs with a given endomorphism monoid

9.1 Elliptic Curves with a given Endomorphism Ring

and we know that this ring is isomorphic to Z or an order O in an imaginary quadratic field K; in fact, the ring on the right is equal to Z or O (viewed as a subring of C).1 To simplify the discussion, we shall treat the isomorphism in (1) as an equality and view elements of End(EL) as elements of Z or O. How might we construct an elliptic curve with endomorphism ring O? An obvious way is to us...

Testing Whether a Set of Code Words Satisfies a Given Set of Constraints

This paper investigates the problem of testing whether a set of code words satisfies certain biologically motivated Hamming distance constraints. The paper provides three efficient techniques to verify the code words, namely, the Enumeration, Table Lookup, and Encoding methods, with applications to the design of DNA words. The Enumeration method enumerates all combinations of positions in a wor...

When a C * -algebra Is a Coefficient Algebra for a given Endomorphism

The paper presents a criterion for a C *-algebra to be a coefficient algebra associated with a given endomorphism.

Given a Problem, What Is the X?

We are interested in the strategy exhibited by problem solvers when working on comparison algebra problems, particularly, what affects the choice of X (the independent variable of the function) in each of twelve similar problems. Our findings demonstrate that both natural and formal language comprise factors affecting the choice of the variable. THEORETICAL BACKGROUND The piling papers and book...