MathOverflow

I have three explicit elliptic curves over $\mathbb{Q}$ arising as Jacobians of genus-one quartics$$Y^2 = c^2(1-u^2)^2 + 4b^2u^2,$$with rational basepoint $(u,Y)=(0,c)$. I need Mordell-Weil rank/generator information. Sage 10.9, PARI/GP, and mwrank have...

Malo's theorem (1895). Consider the polynomials
$$f(x) = a_0 + a_1 x + \cdots + a_m x^m, \qquad g(x) = b_0 + b_1 x + \cdots + b_n x^n,$$
such that the roots of $f$ are all real, and the roots of $g$ are all real and of the same sign. Then the Hadamard product...

In the proof of Theorem 3.1 of the paper Inequalities for M-matrices, Ando evaluates a matrix function (see equation boxed in orange below) via an integral representation of a Pick function (see Lemma 3.1):
Transcription
3. FUNCTIONS OF $M$-MATRICES

Is there an example of a finite lattice (order) with the coatoms being the only meet-irreducible elements, such that the average size of the principal ideals generated by the coatoms is strictly greater than half the number of its elements?
I think that proving that it doesn't exist must be difficult because it would basically prove the union-closed sets conjecture, but maybe it is possible to build an example....