Outgoing

The Problem A backyard swimming pool is being filled by two different hoses. One hose can fill the pool in 10 hours, and it takes the other hose 14 hours to fill the pool. How long will it take for the two hoses to fill the pool if they re turned on at the same time  

Let x represent the amount of time it ll take the two hoses, working together, to fill the pool. Then write two fractions, one with x divided by 10 and the other with x divided by 14 to represent how much of the whole job each hose can accomplish. Add the two fractions together, set the sum equal to 1, and solve for x. 

It ll take 5 hours and 50 minutes to fill the pool with the two hoses. 

The Problem A pool takes six hours to fill and eight hours to drain. The drain was accidentally left open for the first three hours while the pool was filling and then closed. How long did it take for the pool to be filled  

In the first three hours, the intake was g- = tj-, which is obtained by dividing 

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The oil and gas industry produces much waste material, such as scrap metal, human waste, unspent chemicals, oily sludges and radiation. All of the incoming streams to a facility such as a production platform end up somewhere, and only few of the outgoing streams are useful product. It is one of the responsibilities of the engineer to try to limit the amount of incoming material which will finally become waste material. 

There is an aspect of nonlinear spectroscopy which we have so far neglected, namely the spatial dependence of the signal. In general, tln-ee incident beams, described by /c-vectors k, k2 and will produce an outgoing beam at each of the directions ... 

For the reflected wave associated with equation (A3.11.13a). the total outgoing flux is ss /i -[ [,so the reflection probability is... 

For X —> +CO, it is possible to make look like equation (A3,11.20i by setting (p (JT) = e. This shows that the plus Green fiinction is associated with scattering solutions in which outgoing waves move to the right in the V —> CO limit. For v —> -oo, equation (A3.11.39) becomes... 

Electron-impact energy-loss spectroscopy (EELS) differs from other electron spectroscopies in that it is possible to observe transitions to states below the first ionization edge electronic transitions to excited states of the neutral, vibrational and even rotational transitions can be observed. This is a consequence of the detected electrons not originating in the sample. Conversely, there is a problem when electron impact induces an ionizing transition. For each such event there are two outgoing electrons. To precisely account for the energy deposited in the target, the two electrons must be measured in coincidence. 

Figure Bl.6.12 Ionization-energy spectrum of carbonyl sulphide obtained by dipole (e, 2e) spectroscopy [18], The incident-electron energy was 3.5 keV, the scattered incident electron was detected in the forward direction and the ejected (ionized) electron detected in coincidence at 54.7° (angular anisotropies cancel at this magic angle ). The energy of the two outgoing electrons was scaimed keeping the net energy loss fixed at 40 eV so that the spectrum is essentially identical to the 40 eV photoabsorption spectrum. Peaks are identified with ionization of valence electrons from the indicated molecular orbitals.

In this approximation, the wave fiinction is identical to the incident wave (first tenn) plus an outgoing spherical wave multiplied by a complex scattering factor... 

For accurate ion trajectory calculation in the solid, it is necessary to evaluate the exact positions of the intersections of the asymptotes (A A2) of the incoming trajectory and that of the outgoing trajectories of both the scattered and recoiled particles in a collision. The evaluation of these values requires time integrals and the following transfonnation equations ... 

Forward recoil spectrometry (FRS) [33], also known as elastic recoil detection analysis (ERDA), is fiindamentally the same as RBS with the incident ion hitting the nucleus of one of the atoms in the sample in an elastic collision. In this case, however, the recoiling nucleus is detected, not the scattered incident ion. RBS and FRS are near-perfect complementary teclmiques, with RBS sensitive to high-Z elements, especially in the presence of low-Z elements. In contrast, FRS is sensitive to light elements and is used routinely in the detection of Ft at sensitivities not attainable with other techniques [M]- As the teclmique is also based on an incoming ion that is slowed down on its inward path and an outgoing nucleus that is slowed down in a similar fashion, depth infonuation is obtained for the elements detected. 

Nikitin [20, 21] for more elaborate models which include interference effects arising from the phases or eikonals associated with the incoming and outgoing legs of the trajectory. 

The transition probability at a particular total energy (E ) from vibrational level i to / may be expressed as the ratio between the coiresponding outgoing and incoming quantities [71]... 

One can obtain the explicit expressions for and as defined in Eq. (13) considering the following outgoing fluxes in the nonieactive and reactive channels... 

The energy and state resolved tiansition probabilities are the ratio of two quantities obtained by projecting the initial wave function on incoming plane waves (/) and the scattered wave function on outgoing plane waves [F)... 

The equation of restriction can embody causality, lower boundedness of energies in the spectrum, positive wavenumber in the outgoing wave (all these in nonrelativistic physics) and interactions inside the light cone only, conditions of mass speciality, and so on in relativistic physics. In the case of interest in this... 

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