Incorporating spectral data into logistic regression model to classify land cover: a case study in Mt. Qomolangma (Everest) National Nature Preserve Jungang Gao a b & Yili Zhang a a Department of Land-Use/Land-Cover Change and Land Resources Research, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, PR China b Department of Resources and Env...

where k is the first Betti number b^M), T is a flat riemannian λ -torus, M~ is a compact connected Ricci-flat (n — λ;)-manifold, and Ψ is a finite group of fixed point free isometries of T x M' of a certain sort (Theorem 4.1). This extends Calabi's result on the structure of compact euclidean space forms ([7] see [20, p. 125]) from flat manifolds to Ricci-flat manifolds. We use it to essentiall...

1.1. We denote by V a connected ^-dimensional complete Riemannian manifold, by d = d(V) the diameter of V, and by c = c(V) and c~ = c~(V), respectively, the upper and lower bounds of the sectional curvature of V. We set c = c(V) = max (| c1, | c~ |). We say that F i s ε-flat, ε > 0, if cd < ε. 1.2. Examples. a. Every compact flat manifold is ε-flat for any ε > 0. b. Every compact nil-manifold p...

Let {Pn} be a sequence of covers of a space X such that {st(x,Pn)} is a network at x inX for each x ∈ X. For each n ∈ N, let Pn = {Pβ : β ∈ Λn} and Λn be endowed the discrete topology. Put M = {b = (βn) ∈ Πn∈NΛn : {Pβn} forms a network at some point xb in X} and f : M −→ X by choosing f(b) = xb for each b ∈ M . In this paper, we prove that f is a sequentiallyquotient (resp. sequence-covering, c...

Abstract Motivated by the problem of finding algebraic constructions finite coverings in commutative algebra, Steinitz realization number theory and study Hurwitz spaces geometry, we investigate vector bundles underlying structure sheaf a flat branched covering. We prove that, up to twist, every bundle on smooth projective curve arises from direct image smooth, connected cover.

Let D = (V,A) be a directed graph. For U ⊆ V , δin(U) and δout(U) denote the sets of arcs entering U and leaving U , respectively. Moreover, δ(U) := δin(U) ∪ δout(U), din(U) := |δin(U)| (the indegree), dout(U) := |δout(U)| (the outdegree), and d(U) := |δ(U)| (the degree or total degree). If U = {u} is a singleton, we replace the argument {u} by u. We attach subscript D or A if useful. For B ⊆ A...

It is proved that if $\varphi\colon A\to B$ a local homomorphism of commutative noetherian rings, nonzero finitely generated $B$-module $N$ whose flat dimension over $A$ at most $\mathrm{edim}\, A - \mathrm{edim}\, B$, free $B$, and $\varphi$ special type complete intersection. This result motivated by "patching method" developed Taylor Wiles, conjecture de Smit, the first author, dealing with ...