Cultured fibroblasts from a patient with gyrate atrophy of the retina do not convert L-ornithine, uniformly labeled with carbon-14, to proline. This metabolic block is caused by deficient L-ornithine:2-oxoacid aminotransferase activity in the patient. Her heterozygote father has intermediate activity of this enzyme.

Abstract It is proved that the normalized $$L^2$$ L 2 metric on moduli space of n -vortices a two-sphere, endowed with any Riemannian metric, converges uniformly in Bradlow limit to Fubini–Study metric. This establishes, rigorous setting, longstanding informal conjectur...

Let G be a locally compact topological group. We prove that if G is not a SIN-group, then the quotient Banach space U L (G)=U(G) contains an isometric linear copy of l 1. To get this result, we rst establish an extension theorem for (bilaterally) uniformly continuous functions on G.

Among all restricted integer compositions with at most m parts, each of which has size at most l, choose one uniformly at random. Which integer does this composition represent? In the current note, we show that underlying distribution is, for large m and l, approximately normal with mean value ml 2 .

Consider the Erdős-Rényi random graph G(n, M) built with n vertices and M edges uniformly randomly chosen from the set of ( n 2 ) edges. Let L be a set of positive integers. For any number of edges M 6 n/2 + O(n), we compute – via analytic combinatorics – the number of isolated cycles of G(n, M) whose length is in L.

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that E [L] /n converges to a constant γk. We prove a conjecture of Sankoff and Mainville from the early 80’s claiming that γk √ k → 2 as k → ∞.

We consider the system of N (≥ 2) elastically colliding hard balls with masses m1, . . . , mN , radius r, moving uniformly in the flat torus TL = R/L · Z , ν ≥ 2. It is proved here that the relevant Lyapunov exponents of the flow do not vanish for almost every (N + 1)-tuple (m1, . . . ,mN ;L) of the outer geometric parameters.

It is proved in this paper that an irreducible module over the non-graded Virasoro-like algebra L, which satisfies a natural condition, is a GHW module or uniformly bounded. Furthermore, we give the complete classification of indecomposable L-modules V = ⊕ m,n∈Z Cvm,n which satisfy Lr,svm,n ⊆ Cvr+m,s+n+1 + Cvr+m,s+n.

We show that if L is a second-order uniformly elliptic operator in divergence form on R, then C1(1+ |α|) ≤ ‖L‖L1→L1,∞ ≤ C2(1+ |α|). We also prove that the upper bounds remain true for any operator with the finite speed propagation property.