A contribution to the connections between Fibonacci Numbers and Matrix Theory

We present a lovely connection between the Fibonacci numbers and the sums of inverses of $(0,1)-$ triangular matrices, namely, a number $S$ is the sum of the entries of the inverse of an $n \times n$ $(n \geq 3)$ $(0,1)-$ triangular matrix iff $S$ is an integer between $2-F_{n-1}$ and $2+F_{n-1}$. Corollaries include Fibonacci identities and a Fibonacci type result on determinants of family of (1,2)-matrices.Comment: 7 pages, 2 figure

New constructions of non-regular cospectral graphs

We consider two types of joins of graphs $G_{1}$ and $G_{2}$, $G_{1}\veebar G_{2}$ - the Neighbors Splitting Join and $G_{1}\underset{=}{\lor}G_{2}$ - the Non Neighbors Splitting Join, and compute the adjacency characteristic polynomial, the Laplacian characteristic polynomial and the signless Laplacian characteristic polynomial of these joins. When $G_{1}$ and $G_{2}$ are regular, we compute the adjacency spectrum, the Laplacian spectrum, the signless Laplacian spectrum of $G_{1}\underset{=}{\lor}G_{2}$ and the normalized Laplacian spectrum of $G_{1}\veebar G_{2}$ and $G_{1}\underset{=}{\lor}G_{2}$. We use these results to construct non regular, non isomorphic graphs that are cospectral with respect to the four matrices: adjacency, Laplacian , signless Laplacian and normalized Laplacian

Designing a System for Upgrading of Heavy Crude Oils Through Electron Beam Treatment

Low-quality crude oil reserves require prohibitively high energy costs to extract and transport. The extreme viscosity and impurities of these oils prevents them from being transported via pipeline, requiring the use of more expensive trucks or trains. Light crude oil has a viscosity ranging up to 100 cP at 40°C. In contrast, Crude Oil #1 under investigation measures 33,855 cP, and Crude Oil #2 is 4,570,000 cP at the same temperature as measured in the laboratory. Sulfur content of both exceeds 5% by mass. Effects of the exposure of these oils to an electron beam discharge are being researched to reduce viscosity with higher conversion factors, using less energy at low temperatures. To facilitate this investigation, a flow loop was created with controls to adjust oil initial temperature with line heaters, radiation dose rate with height adjustment, flow shear rate through flow channel angle, and flow residence time through a gear pump.The flow loop uses stainless steel lines with a gear pump built to handle viscous oil at 230°C, and makes extensive use of aluminum versus steel in a modular frame to prevent overheating from the e-beam. To support the flow test cart, a remote control station cart was created, along with a fire safety cart and mobile test cell for safe sample extraction and shakedown testing. In designing the system and writing safety documentation, the test vehicles were further refined as new concerns were addressed and potential hazards mitigated. Preliminary testing of the various system components yielded a successful design. The end result is a set of systems that allows for ease of variability in operating parameters such as dose rate, gas environment, and added hydrogenation