In this paper, we introduce a new operation on the species, the exponential composition of species, which is constructed based on the arithmetic product and the quotient species, and get a functional equation expressing the species of connected graphs as the exponential composition of the species of prime graphs with respect to the Cartesian multiplication.

We enumerate prime graphs with respect to the Cartesian multiplication of graphs by expressing the species of connected graphs as the exponential composition of the species of prime graphs, where the exponential composition of species is constructed based on the arithmetic product of species of Maia and Méndez and the quotient species.

Thermochemical conversion of non-edible biomass offers an efficient and economically process to provide valuable fuels and prepare chemicals derived from biomass in the context of developing countries. Pyrolysis has advantages over other thermochemical conversion techniques because it can convert biomass directly into solid, liquid and gaseous products by thermal decomposition of biomass in the...

In the attempt to discover a new polymorph of rofecoxib (Vioxx®), an unexpected product resulted. The product was characterised by chemical composition, thermal behaviour and structure and found to be 6-methylsulphonylphenanthro-[9,10-C] furan-1(3H)-one, a photo-cyclization degradation product of rofecoxib. This is a significant finding because it indicates that without appropriate control of t...

We describe an algebraic approach for computing with vector based semantics. The tensor product has been proposed as a method of composition, but has the undesirable property that strings of different length are incomparable. We consider how a quotient algebra of the tensor algebra can allow such comparisons to be made, offering the possibility of data-driven models of semantic composition.

Bridging problem domain and solution in product line engineering is a time-consuming and error-prone process. Since both domains are structured differently (features vs. artifacts), there is no natural way to map one to the other. Using an explicit and formal mapping creates opportunities for consistency checking and automation. This way both the configuration and the composition of product ins...

The multiplicative sum Zagreb index is defined for a simple graph G as the product of the terms dG(u)+dG(v) over all edges uv∈E(G) , where dG(u) denotes the degree of the vertex u of G . In this paper, we present some lower bounds for the multiplicative sum Zagreb index of several graph operations such as union, join, corona product, composition, direct product, Cartesian product and strong pro...

In the present work a novel inferential control strategy cascaded with a nonlinear profile position controller is employed to control the top and bottom product compositions of a simulated depropanizer column. The inferential model for estimating product compositions is developed using the wave propagation model, and the composition profile position of both rectifying and stripping section is c...

A steady increase of product titers and the corresponding change in impurity composition represent a challenge for development and optimization of antibody production processes. Additionally, increasing demands on product quality result in higher complexity of processes and analytics, thereby increasing the costs for product work-up. Concentration and composition of impurities are critical for ...

Most Lie group integrators can be expanded in series indexed by the set of ordered rooted trees. To each tree one can associate two distinct higher order derivation operators, which we call frozen and unfrozen operators. Composition of frozen operators induces a concatenation product on the trees, whereas composition of unfrozen operators induces a somewhat more complicated product known as the...