Given an infinite-dimensional Banach space X, we introduce the daugavetian index of X , daug (X), as the greatest constant m > 0 such that kId+ Tk > 1 +mkTk for all T ∈ K(X). We givetwo characterizations of this index and we estimate it in some examples. We show that the daugavetian index of a c0-, l1or l∞-sum of Banach spaces is the infimum index of the summands. Finally, we calculate the daug...

This paper reports on variation in leaf area index (L) in five Eucalyptus globulus Labill. plantations in response to application of nitrogen, thinning at age 2 years and variation in climate wetness index (the ratio of rainfall to potential evaporation). Observed L is compared with: (i) L predicted to optimize net primary productivity for a given average annual temperature, annual water use an...

This is essentially a note on Section 7 of Perelman’s first paper on Ricci flow. We list some basic properties of the index form for Perelman’s L-length, which are analogous to the ones in Riemannian case (with fixed metric), and observe that Morse’s index theorem for Perelman’s L-length holds. As a corollary we get the finiteness of the number of the L-conjugate points along a finite L-geodesi...

Duality is the operation that interchanges hypervertices and hyperfaces on oriented hypermaps. The duality index measures how far a hypermap is from being self-dual. We say that an oriented regular hypermap has duality-type {l, n} if l is the valency of its vertices and n is the valency of its faces. Here, we study some properties of this duality index in oriented regular hypermaps and we prove...

The problem of finding the eigenvalues and eigenvectors of a matrix referring to an N-sector ring can be reduced to a number of smaller eigenvalue problems in which the dimensions of the vector space are reduced by a factor N. Suppose we need to solve an eigenvalue problem for a matrix A associated with a storage ring, for example in analyzing orbit errors as in Ref.(l}. We number the N superpe...

We prove a variant of the well-known Reidemeister-Schreier Theorem for finitely L-presented groups. More precisely, we prove that each finite index subgroup of a finitely L-presented group is itself finitely L-presented. Our proof is constructive and it yields a finite L-presentation for the subgroup. We further study conditions on a finite index subgroup of an invariantly finitely L-presented ...

Theorem 1. Let L be a locally compact, nondiscrete topological field. a) Then L is a finite extension of one of the following fields: (i) K = R. (ii) K = Qp. (iii) K = Fp((t)). b) In case (i) L = R or L = C. c) In case (ii) the ramification index e(L/Qp) and residual degree f(L/Qp) are uniquely determined by the abstract field L, and for any given e, f ∈ Z, the number of finite extensions L/Qp ...