Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the invariant formalism of quantum mechanics. I first describe the essential mathematical features of the Hilbert-space invariant formalism. This is followed by a...

Photogrammetric Computer Vision algorithms often deal with complex numerical calculations and complex data structures. For modelling the numerical calculations usually a mathematical model is used. For the data structures an Object-Oriented model is appropriate. But there is still a lack in modelling the combination of both kinds of notation. In this paper we present a new modelling technique f...

background: the monte carlo (mc) method is not only used for dose calculations around brachytherapy sources but also for benchmarking treatment planning systems (tps) calculations. materials and methods: three 60co sources of gzp6 brachytherapy unit were simulated using mcnp4c mc code. the radial dose functions were calculated by mc method and gzp6 tps and were compared. results: there was a go...

the scarcity of water resources and supply resources limitation, have caused an increasing gap between water supply and demand specially in recent decades in almost all regions of the globe. one of the best known solutions proposed by the economists is using the different water pricing approaches thereby obtaining the optimal allocation and social justice. to this purpose, this paper uses the p...

original article     the aim of this study was to design and build a software for noise propagation prediction (indoor and from indoor to outdoor spaces) which is being commonly used in industry.  in this regard, firstly a mathematical complex model was created based on existing relationships about noise propagation in indoor spaces and transmission through the walls and propagation in outdoor ...

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...

i n the past decades, the effect of different tax amendments on various economic issues has been studied. the majority of these studies have avoided considering shadow economy as part of the calculation and analysis, and an issue, which has received little attention, is the relationship between green tax reforms and shadow economy, as for informal labor, which is well-connected to unemployment ...

We describe the concept of quantum crystallography (QCr) and present examples of its potential as a technique for facilitating computational chemistry, particularly, applications of quantum mechanics. Structural information has been used to facilitate quantum-mechanical calculations for several decades. Recent advances in theory and computational facilities have led to research opportunities th...

Most methods of creating plots in METAPOST work by doing all of their calculations in METAPOST, or by doing all of their calculations in a preprocessing program. There are advantages to dividing the work more equitably, by doing the mathematical and data-visualization calculations in a preprocessing program and doing the graphical and layout calculations in METAPOST. The MetaPlot package provid...

Most methods of creating plots in MetaPost work by doing all of their calculations in MetaPost, or by doing all of their calculations in a preprocessing program. There are advantages to dividing the work more equitably by doing the mathematical and data-visualization calculations in a preprocessing program and doing the graphical and layout calculations in MetaPost. The MetaPlot package provide...