Grassland degradation due to overgrazing is common in many areas of the world. This study analyzed the potential of the stable carbon isotope (δ(13)C) value as a structural microcosmic index to monitor processes of grassland degradation. The δ(13)C values of plant leaves, roots and soils in non-grazed (NG) and over-grazed (OG) grassland were measured from samples collected from the seven types ...

The classical Dirac theorem asserts that every graph G on n vertices with minimum degree δ(G) ≥ dn/2e is Hamiltonian. The lower bound of dn/2e on the minimum degree of a graph is tight. In this paper, we extend the classical Dirac theorem to the case where δ(G) ≥ bn/2c by identifying the only non-Hamiltonian graph families in this case. We first present a short and simple proof. We then provide...

If a pure simplicial complex is partitionable, then its h-vector has combinatorial interpretation in terms of any partitioning the complex. Given non-partitionable Δ, we construct Γ⊇Δ same dimension such that both Γ and relative (Γ,Δ) are partitionable. This allows us to rewrite as difference two h-vectors partitionable complexes, giving an analogous By contrast, for given Δ it not always possi...

Abstract The order of integration is valid to characterize linear processes; but it is not appropriate for non-linear worlds. We propose the concept of summability (a re-scaled partial sum of the process being Op(1)) to handle non-linearities. The paper shows that this new concept, S (δ): (i) generalizes I (δ); (ii) measures the degree of persistence as well as of the evolution of the variance;...

We study the surface quasi-geostrophic equation with an irregular spatial perturbation∂tθ+u⋅∇θ=−ν(−Δ)γ/2θ+ζ,u=∇⊥(−Δ)−1θ, on [0,∞)×T2, ν⩾0, γ∈[0,3/2) and ζ∈B∞,∞−2+κ(T2) for some κ>0. This covers case of ζ=(−Δ)α/2ξ α<1 ξ a white noise T2. Depending relation between γ α, our setting is subcritical, critical or supercritical in language Hairer's regularity structures [38]. Based purely analytical t...

A (γ, δ)-elastic channel is a binary symmetric channel between a sender and a receiver where the error rate of an honest receiver is δ while the error rate of a dishonest receiver lies within the interval [γ, δ]. In this paper, we show that from any non-trivial elastic channel (i.e., 0 < γ < δ < 12 ) we can implement oblivious transfer with information theoretic security. This was previously (K...

Guruswami and Sinop [11] give a O(1/δ) approximation guarantee for the non-uniform Sparsest Cut problem by solving O(r)-level Lasserre semidefinite constraints, provided that the generalized eigenvalues of the Laplacians of the cost and demand graphs satisfy a certain spectral condition, namely, λr+1 ≥ Φ∗/(1 − δ). Their key idea is a rounding technique that first maps a vector-valued solution t...

— Given a closed (not necessarly compact) semi-algebraic set X in Rn, we construct a non-negative semi-algebraic C2 function f such that X=f−1(0) and such that for δ > 0 sufficiently small, the inclusion of X in f−1([0, δ]) is a retraction. As a corollary, we obtain several formulas for the Euler characteristic of X. Résumé. — Étant donné un ensemble semi-algébrique fermé (non nécessairement co...

We show that the number of rational points of height ≤ H on a non-rational plane curve of degree d is Od(H 2/d−δ), for some δ > 0 depending only on d. The implicit constant depends only on d. This improves a result of Heath-Brown, who proved the bound O (H2/d+ ). We also show that one can take δ = 1/450 in the case d = 3.

We present a proof that the number of breakpoints in the arrival function between two terminals in graphs of treewidth $w$ is $n^{O(\log^2 w)}$ when the edge arrival functions are piecewise linear. This is an improvement on the bound of $n^{\Theta(\log n)}$ by Foschini, Hershberger, and Suri for graphs without any bound on treewidth. We provide an algorithm for calculating this arrival function...