Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagon...

Magnetic Resonance Imaging (MRI) is a noninvasive imaging method widely used in medical diagnosis. Data in MRI are obtained line-by-line within the K-space, where there are usually a great number of such lines. For this reason, magnetic resonance imaging is slow. MRI can be accelerated through several methods such as parallel imaging and compressed sensing, where a fraction of the K-space lines...

BACKGROUND Automated calculations by laboratory information system (LIS) are efficient and accurate ways of providing calculated laboratory test results. Due to the lack of established advanced mathematical functions and equation logic in LIS software, calculations beyond simple arithmetic functions require a tedious workaround. Free and bioavailable testosterone (BT) calculations require a qua...

1.1 Our motivation for the work presented below comes from the realisation of the rather paradoxical situation with the mathematics used by physicists in the last 70 or so years. Physicists have always been ahead of mathematicians in introducing and testing new methods of calculations, leaving to mathematicians the task of putting the new methods and ideas on a solid and rigorous foundation. Bu...

-Dynamic Voltage Restorer (DVR) is a device used to mitigate voltage sags which are a significant power quality issue. This paper involves mathematical calculation for leading series voltage injection for mitigation of sags thereby achieving utility power factor improvement as well as power sharing between DVR and utility as per requirement and available distributed generation. Mathematical der...

introduction: ordered subset expectation maximization (osem), is an effective iterative method for spect image reconstruction. the aim of this study is the evaluation of the role of system matrix in osem image reconstruction method using four different physical beam radiation models with three detection configurations. methods: spect was done with an arc of 180 degree in 32 projections after i...

In this paper I try to describe both the role of mathematics in shaping our understanding of how neural networks operate, and the curious new mathematical concepts generated by our attempts to capture neural networks in equations. My target reader being the non-expert, I will present a biased selection of relatively simple examples of neural network tasks, models and calculations, rather than t...

saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. because of heterogeneous nature of cell populations, the cell population balance equation (pbe) can be used to capture the dynamic behavior of such cultures. in this work, an unstructured-segregated model is used for d...