On Linear Differential Equations Involving a Para-Grassmann Variable

As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to n-generalized Fibonacci numbers is established. Several other classes of differential equations (systems of first order, equations with variable coefficients, nonlinear equations) are also considered and the analogies or differences to the usual (''bosonic'') differential equations discussed

Motzkin numbers of higher rank: Generating function and explicit expression

The generating function and an explicit expression is derived for the (colored) Motzkin numbers of higher rank introduced recently. Considering the special case of rank one yields the corresponding results for the conventional colored Motzkin numbers for which in addition a recursion relation is given

A generalization of boson normal ordering

In this paper we define generalizations of boson normal ordering. These are based on the number of contractions whose vertices are next to each other in the linear representation of the boson operator function. Our main motivation is to shed further light onto the combinatorics arising from algebraic and Fock space properties of boson operators.Comment: 10 pages, 1 (LaTeX) figur

Single Impurity Anderson Model with Coulomb Repulsion between Conduction Electrons on the Nearest-Neighbour Ligand Orbital

We study how the Kondo effect is affected by the Coulomb interaction between conduction electrons on the basis of a simplified model. The single impurity Anderson model is extended to include the Coulomb interaction on the nearest-neighbour ligand orbital. The excitation spectra are calculated using the numerical renormalization group method. The effective bandwidth on the ligand orbital, $D^{eff}$, is defined to classify the state. This quantity decreases as the Coulomb interaction increases. In the $D^{eff} > \Delta$ region, the low energy properties are described by the Kondo state, where $\Delta$ is the hybridization width. As $D^{eff}$ decreases in this region, the Kondo temperature $T_{K}$ is enhanced, and its magnitude becomes comparable to $\Delta$ for $D^{eff} \sim \Delta$. In the $D^{eff} < \Delta$ region, the local singlet state between the electrons on the $f$ and ligand orbitals is formed.Comment: 5 pages, 3 figures, LaTeX, to be published in J. Phys. Soc. Jpn Vol. 67 No.

Wick's theorem for q-deformed boson operators

In this paper combinatorial aspects of normal ordering arbitrary words in the creation and annihilation operators of the q-deformed boson are discussed. In particular, it is shown how by introducing appropriate q-weights for the associated ``Feynman diagrams'' the normally ordered form of a general expression in the creation and annihilation operators can be written as a sum over all q-weighted Feynman diagrams, representing Wick's theorem in the present context.Comment: 9 page

Monomer transport limitations in emulsion polymerization

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Building A Solar Farm On A Rolling Landscape: A Case Study

The well-being of the environment in the United States is becoming dependent on a change from unreliable and scarce resources such as coal as a means to generate electricity to a more eco-friendly and abundant source. Solar farms provide the opportunity to generate electricity with no effect on global warming, no environmentally hazardous emissions, and are not affected by the fluctuating costs of fuel. One construction company in particular has noticed this as not only a terrific opportunity to improve the nations’ environmental footprint, but also as a tremendous business opportunity; Swinerton. Swinerton recently developed a renewable energy division that focuses on the creation and maintenance of solar farms. The division, now known as Swinerton Renewable Energy, was created in 2010 and has since then built themselves into the number 1 solar energy contractor in the entire world. This case study will examine one of their first solar farm projects, a 9.4MW site in Sacramento County, CA. Furthermore, this paper will examine the current industry trends, the project specifics, the challenges encountered, the benefits of this project, and the lessons learned to be applied to the industry

Opening Plenary Talk - Polymer reaction engineering in the origins of life: How to get from synthetic rubber to chemical evolution

How does a chemical engineer go from synthetic rubber production to origins of life research and still be in polymer reaction engineering? The answer is simple: There are significant problems in chemical evolution (and likely in many other fields of research) where the tools of polymer reaction materials can be applied very effectively. This talk documents two of them. Please download the file below for full content