In this paper we introduce a new graph composition, called 2-amalgam, and we prove that the 2-amalgam of perfect graphs is perfect. This composition generalizes many of the operations known to preserve perfection, such as the clique identification, substitution, join and amalgam operations. We give polynominal-time algorithms to determined whether a general graph is decomposable with respect to...

In this paper we consider the absolute variation statistics of a composition σ = σ1 · · ·σm of n which is a measure of the sum of absolute differences between each consecutive pair of parts in a composition. This and some related statistics which we discuss, can also be interpreted within the context of bargraph polygons and bargraph walks of area n. In this context, absolute variation correspo...

A (1, k)-composition of a positive integer n consists of an ordered sequence of the integers 1 and k whose sum is n. A palindromic (1, k)-composition is one for which the sequence is the same from left to right as from right to left. We give recursive equations and generating functions for the total number of such compositions and palindromes, and for the number of 1’s, k’s, “+”signs and summan...

A composition is a sequence of positive integers, called parts, having a fixed sum. By an m-congruence succession, we will mean a pair of adjacent parts x and y within a composition such that x ≡ y (mod m). Here, we consider the problem of counting the compositions of size n according to the number of m-congruence successions, extending recent results concerning successions on subsets and permu...

This paper deals with Carlitz compositions of natural numbers (adjacent parts have to be different). The following parameters are analysed: number of parts, number of equal adjacent parts in ordinary compositions, largest part, Carlitz compositions with zeros allowed (correcting an erroneous formula from Carlitz). It is also briefly demonstrated that so-called 1-compositions of a natural number...

Let Y = (y1, y2, . . . ), y1 ≥ y2 ≥ · · · , be the list of sizes of the cycles in the composition of c n transpositions on the set {1, 2, . . . , n}. We prove that if c > 1/2 is constant and n → ∞, the distribution of f(c)Y/n converges to PD(1), the Poisson-Dirichlet distribution with paramenter 1, where the function f is known explicitly. A new proof is presented of the theorem by Diaconis, Ma...

We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and the theory of species. We prove that the composition of two cofree coalgebras is cofree and give conditions which imply that the composition is a one-sided Hopf algebra. These conditions hold when one coalgebra is a graded Hopf operad D and the other is a connected graded coalgebra w...

China has vast reserves of shale gas. Currently, shale gas is one of the focuses of the unconventional reservoir. Well logs play an import role in shale gas production, and it is the bridge connecting geology, geophysics and petroleum engineering. In the exploration stage, well logs are used to identify lithology, evaluate the parameters of mineral types and compositions, total organic carbon (...

Microalgae have been receiving worldwide attention as promising feedstock for production of carbon neutral biodiesel. As an alternative fuel, biodiesel is very imperative for the sustainable development of mankind. Biodiesel production process is generally carried out through upstream and downstream processing to generate cellular biomass, extracted oil and finally transesterification reaction....

Our understanding of biology has been greatly improved through recent developments in mass spectrometry, which is providing detailed information on protein and metabolite composition as well as protein-metabolite interactions. The high sensitivity and resolution of mass spectrometry achieved with liquid or gas chromatography allows for detection and quantification of hundreds to thousands of mo...