The Discrete Ordinates with Time Stepping (DOTS) numerical solution method for the general discrete ordinates approximation of the radiative transport equation is presented. A pseudo-time iteration is employed, with simultaneous updating of all ordinates in each sweep. This may be beneficial for ...
The relative QY was calculated using the following equation. where Φf, is the fluorescence QY, FL is the total fluorescence intensity (the integrated area of the emission spectrum in wavelength scale) with excitation at λex normalized by the intensity of the excitation light, Af is the ...
(see [ 6 ]). it depends on an arbitrary function. it is obvious that every solution of this equation satisfies the system $$\begin{aligned} \phi (h^n(t))=\alpha ^n\phi (t)+\beta _n, \end{aligned}$$ where \(\beta _n= \beta \frac{\alpha ^{n}-1}{\alpha ^{n}-1}\)...
7 How can I construct three vertical dots similar to \vdots but which span the same height as a colon :? \vdots is usually intended for use in matrices or a set of equations to indicate that there are many elements. I am intending its use within an in-line equation for purposes of...
The authors obtain sufficient conditions which guarantee that all bounded solutions of the difference equation x n+1 =f(x n ,...,x n-k )+g(n,x n ,x n-1 ,...,x n-k ) are slowly varying in the sense that lim(x n+1 -x n )=0.doi:10.1080/10236190310001625271...
It is also possible for teachers to make an equation to complete the puzzle within some specific numbers. While seeking the patterns, kids will be able to master the mechanics of completing figures from an abstract form. Therefore, math teachers and tutors are able to make use of thepuzzle ...
Thus, the bandgap for the FL emission before and after protonation are 2.26 eV (550 nm), and 2.0 eV (620 nm) according to equation Eg = hν. Thus, the detailed internal energy level structure of the carbon dots before and after protonation and the changes in the ...
\documentclass{svmult} \usepackage{amssymb,amsmath,amsfonts} \usepackage{mathtools} \usepackage{bm} \usepackage{tikz} \usetikzlibrary{arrows,trees,decorations,external,positioning,backgrounds} \sloppy \begin{document} \begin{equation*} Y = \begin{pmatrix} 1 & 0 & \hdots & \hdots & 0 \...
Below is an equation related to the PLQY, which is expressed as [75], [76]:(1)Φχ=Φst(Kχ/Kst)(ηχ/ηst)where Φ is QY, K is the slope determined by the curves, η is the refractive index of the solvent, st refers to a standard with known quantum yield and χ indicates ...
Considering the effect of the magnetic field and the electrostatic potential, the equation thus reads: $$[{v}_{F}{{{\mathbf{\sigma}}} \cdot (-i\hslash {{{\mathbf{\nabla}}} +e{\bf A})+{V}_{\beta }({\bf r})]\psi ({\bf r})=E\psi ({\bf r})$$ (1) where \({{...