For the elliptic curve E overQ(t) found by Kihara, with torsion group Z/4Z and rank ≥ 5, which is the current record for the rank of such curves, by using a suitable injective specialization, we determine exactly the rank and generators of E(Q(t)).

Now assume |G : H| is infinite and that H is definable in G (but H need no longer be infinite or G-normal). Let Z = Z◦(G), and note that (a) implies that Z is infinite. If |Z : H ∩Z| is infinite, then |HZ : H| is infinite as well. In this case we are done since H ≤ HZ ≤ NG(H). Otherwise, |Z : H ∩Z| is finite, so the connectedness of Z implies that Z ≤ H. We can now proceed by induction on the r...

BACKGROUND Identifying key variables such as disorders within the clinical narratives in electronic health records has wide-ranging applications within clinical practice and biomedical research. Previous research has demonstrated reduced performance of disorder named entity recognition (NER) and normalization (or grounding) in clinical narratives than in biomedical publications. In this work, w...

The properties of singular graphs obtained in a previous paper "On the construction of graphs of nullity one", lead to the characterization of graphs of small rank. The minimal configurations that are contained in singular graphs were identified as "grown" from certain cores. A core of a singular graph G is a subgraph induced by the vertices corresponding to the non-zero components of an eigenv...

We introduce the growth rank of a C∗-algebra — a (N∪ {∞})-valued invariant whose minimal instance is equivalent to the condition that an algebra absorbs the Jiang-Su algebra Z tensorially — and prove that its range is exhausted by simple, nuclear C∗-algebras. As consequences we obtain a well developed theory of dimension growth for approximately homogeneous (AH) C∗-algebras, establish the exist...

In this paper, we first construct a Lie algebra L from rank 3 quantum torus, and show that it is isomorphic to the core of EALAs of type A1 with coordinates in rank 2 quantum torus. Then we construct two classes of irreducible Z-graded highest weight representations, and give the necessary and sufficient conditions for these representations to be quasifinite. Next, we prove that they exhaust al...

One of the purposes of this paper is to prove that if G is a noncompact connected semisimple Lie group of real rank one with finite center, then L(G) ∗ L(G) ⊆ L(G). Let K be a maximal compact subgroup of G and X = G/K a symmetric space of real rank one. We will also prove that the noncentered maximal operator M2f(z) = sup z∈B 1 |B| ∫ B |f(z)| dz is bounded from L2,1(X) to L2,∞(X) and from Lp(X)...

We discuss the determination of the Z” mass and width from the total hadronic cross section with emphasis on radiative corrections and normalization errors. We find that a combined fit of the mass and width, which takes the absolute normalization of the cross section into account, significantly reduces the errors in these parameters in comparison to the standard procedure of fitting only the sh...