Bichain graphs form a bipartite analog of split permutation graphs, also known as split graphs of Dilworth number 2. Unlike graphs of Dilworth number 1 that enjoy many nice properties, split permutation graphs are substantially more complex. To better understand the global structure of split permutation graphs, in the present paper we study their bipartite analog. We show that bichain graphs ad...

While the concept of similarity is well grounded in psychology, text similarity is less well-defined. Thus, we analyze text similarity with respect to its definition and the datasets used for evaluation. We formalize text similarity based on the geometric model of conceptual spaces along three dimensions inherent to texts: structure, style, and content. We empirically ground these dimensions in...

Most procedures currently used for the structural and geometric design of pavements fail to treat adequately the effects of mixed traffic on pavement life. The effects of the magpitude$ the configuration, and the number of repetitions of various wheel loads should be included as variables in any good pavement design procedure. An analysis of the axle loads observed on Texas highways is used wit...

In this paper, the off-diagonal geometric phase of thermal state in hydrogen atom under the effects of external magnetic field is considered. Increasing temperature tends to suppress the off-diagonal geometric phase, including 1-order and 2-order cases. On the other hand, the relationship between the geometric phase and external magnetic field is discussed.

The objective of this paper is to present a significant improvement to the approach of Duncan et al. [1, 8] to analyze the deformations of curves in sequences of 2D images. This approach is based on the paradigm that high curvature points usually possess an anatomical meaning, and are therefore good landmarks to guide the matching process, especially in the absence of a reliable physical or def...

The approach to spot speed prediction in two-lane highways followed in this study aims to evaluate the effects of a comprehensive set of speed factors, with a special focus on the geometric characteristics of the road segment to which the element belongs. Two flexible models were developed for different types of roads based on a stochastic frontier formulation in which the maximum operating spe...

Building on the scaffolding constructed in the first two articles in this series, we now proceed to the geometric phase of our sheaf -complex theoretic quasidualization of Kubota’s formalism for n-Hilbert reciprocity. Employing recent work by Bridgeland on stability conditions, we extend our yoga of t-structures situated above diagrams of specifically designed derived categories to arrangements...

Proof. If E ≡ +∞ onX, then there is nothing to prove. So, assume E 6≡ +∞. Denote α = infu∈X E(u) ≥ −∞ and choose a strictly decreasing sequence (αm) such that αm ↘ α as m → ∞. Let Kαm = {u ∈ X : E(u) ≤ αm}, then by assumption Kαm is compact. Moreover, it’s clear that Kαm+1 ⊂ Kαm for all m ∈ N, i.e. we have a decreasing nesting of compact sets. By Cantor’s Intersection Theorem, we know that K = ∞ ⋂

‎we obtain the asymptotic expansion of the sequence with general term $frac{a_n}{g_n}$‎, ‎where $a_n$ and $g_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎also‎, ‎we obtain some explicit bounds concerning $g_n$ and $frac{a_n}{g_n}$.

We are interested in constructing concrete independent events in purely atomic probability spaces with geometric distribution. Among other facts we prove that there are uncountable many sequences of independent events.