If δ is an ordinal, we denote by C(δ) the class of all cardinal sequences of length δ of locally compact scattered (in short: LCS) spaces. If λ is an infinite cardinal, we write Cλ(δ) = {s ∈ C(δ) : s(0) = λ = min[s(ζ) : ζ < δ]}. An LCS space X is called Cλ(δ)-universal if SEQ(X) ∈ Cλ(δ), and for each sequence s ∈ Cλ(δ) there is an open subspace Y of X with SEQ(Y ) = s. We show that • there is a...

Following cultivation, substantial loss of soil organic matter occurs in surface layers. No-till is an agronomic practice to reverse or slow the matter. We reviewed 95 research papers that used 13C natural abundance soils quantify impact tillage on C dynamics cropping systems. New (from current systems) accumulated under no-till, whereas most extreme cultivation (mouldboard ploughing) mixed new...

Let G be a connected graph with vertex set V (G), order n = |V (G)|, minimum degree δ and edge-connectivity λ. Define the inverse degree of G as R(G) = ∑ v∈V (G) 1 d(v) , where d(v) denotes the degree of the vertex v. We show that if R(G) < 2 + 2 δ(δ + 1) + n− 2δ (n− δ − 2)(n− δ − 1) , then λ = δ. We also give an analogous result for triangle-free graphs.

A consistent learner is required to correctly and completely reflect in its actual hypothesis all data received so far. Though this demand sounds quite plausible, it may lead to the unsolvability of the learning problem. Therefore, in the present paper several variations of consistent learning are introduced and studied. These variations allow a so-called δ –delay relaxing the consistency deman...

This paper considers estimation of the regression function and its derivatives in nonparametric regression with fractional time series errors. We focus on investigating the properties of a kernel dependent function V (δ) in the asymptotic variance and finding closed form formula of it, where δ is the long-memory parameter. It is shown that V (δ) has a unified form for δ ∈ (−0.5, 0.5)\0 with V (...