The representation theory of the unitary groups is of fundamental significance in many areas of physics and chemistry. In order to label states in a physical system with unitary symmetry, it is necessary to have explicit bases for the irreducible representations. One systematic way of obtaining bases is to generalize the ladder operator approach to the representations of SU(2) by using the form...

We consider the chain ladder reserving method in a Bayesian set up, which allows for combining individual claims development data with portfolio information as for instance development patterns from industry-wide data. We derive the Bayes estimators and the credibility estimators within this Bayesian framework. We show that the credibility estimators are exact Bayesian in the case of the expone...

Locomotor impairments after spinal cord injury (SCI) are often assessed using open-field rating scales. These tasks have the advantage of spanning the range from complete paralysis to normal walking; however, they lack sensitivity at specific levels of recovery. Additionally, most supplemental assessments were developed in rats, not mice. For example, the horizontal ladder beam has been used to...

A constrained system is presented by a finite-state labeled graph. For such systems, we focus on block-type-decodable encoders, comprising three classes known as block, block-decodable, and deterministic encoders. Franaszek gives a sufficient condition which guarantees the equality of the optimal rates of block-decodable and deterministic encoders for the same block length. In this paper, we in...

A topological index is a numerical measure that characterises the whole structure of graph. Based on vertex degrees, idea an atom-bond connectivity A B C was introduced in chemical graph theory. Later, different versions ABC were crea...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

We investigated the relationship between LiDAR and ladder fuels in the northern Sierra Nevada, California USA. Ladder fuels are often targeted in hazardous fuel reduction treatments due to their role in propagating fire from the forest floor to tree crowns. Despite their importance, ladder fuels are difficult to quantify. One common approach is to calculate canopy base height, but this has many...

A ladder lottery, known as the “Amidakuji” in Japan, is a common way to choose a permutation randomly. A ladder lottery L corresponding to a given permutation π is optimal if L has the minimum number of horizontal-lines among ladder lotteries corresponding to π. In this paper we show that for any two optimal ladder lotteries L1 and L2 of a permutation, there exists a sequence of local modificat...

Cohen, Lewin and Zagier found four ladders that entail the polylogarithms Lin( k 1 ) := P r>0 kr 1 =r n at order n = 16, with indices k 360, and 1 being the smallest known Salem number, i.e. the larger real root of Lehmer's celebrated polynomial 10 + 9 7 6 5 4 3 + + 1, with the smallest known non-trivial Mahler measure. By adjoining the index k = 630, we generate a fth ladder at order 16 and a ...

Cohen, Lewin and Zagier found four ladders that entail the polylogarithms Lin(α −k 1 ) := ∑ r>0 α −kr 1 /r n at order n = 16, with indices k ≤ 360, and α1 being the smallest known Salem number, i.e. the larger real root of Lehmer’s celebrated polynomial α + α − α − α − α − α − α + α + 1, with the smallest known non-trivial Mahler measure. By adjoining the index k = 630, we generate a fifth ladd...