Insider term

The inside terms of the determinant represent the characteristic polynomial P(A) of A ... 

Step 1 Write down both matrices, and note if inside terms are equal. 

Integral terms extending on R are reduced to iJc using Boundary Integral Elements on the boundaries of the FEM domain (especially the influence of the source field hs). Inside the FEM domain, edge elements are used to compute the reaction field. 

Figure 8. The representation of an open contour T in terms of an open contour Fi2 in the vicinity of the conical intersection at C12 and a closed contour F23 at the vicinity of a conical intersection at C23 F = F12 + F23, It is assumed that the intensity of Xu is strong along F12 (full line) and weak along F23 (dashed line), ia) The situation when C23 is outside the closed contour F23, (6) The situation when C23 is inside the closed contour F23.

An undesirable side-effect of an expansion that includes just a quadratic and a cubic term (as is employed in MM2) is that, far from the reference value, the cubic fimction passes through a maximum. This can lead to a catastrophic lengthening of bonds (Figure 4.6). One way to nci iimmodate this problem is to use the cubic contribution only when the structure is ,utficiently close to its equilibrium geometry and is well inside the true potential well. MM3 also includes a quartic term this eliminates the inversion problem and leads to an t". . 11 better description of the Morse curve. 

In the Couette flow inside a cone-and-plate viscometer the circumferential velocity at any given radial position is approximately a linear function of the vertical coordinate. Therefore the shear rate corresponding to this component is almost constant. The heat generation term in Equation (5.25) is hence nearly constant. Furthermore, in uniform Couette regime the convection term is also zero and all of the heat transfer is due to conduction. For very large conductivity coefficients the heat conduction will be very fast and the temperature profile will... 

As the number of elements in the mesh increases the sparse banded nature of the global set of equations becomes increasingly more apparent. However, as Equation (6,4) shows, unlike the one-dimensional examples given in Chapter 2, the bandwidth in the coefficient matrix in multi-dimensional problems is not constant and the main band may include zeros in its interior terms. It is of course desirable to minimize the bandwidth and, as far as possible, prevent the appearance of zeros inside the band. The order of node numbering during... 

Optically pure (Section 7 4) Descnbing a chiral substance in which only a single enantiomer is present Orbital (Section 1 1) Strictly speaking a wave function i i It is convenient however to think of an orbital in terms of the probability i i of finding an electron at some point relative to the nucleus as the volume inside the boundary surface of an atom or the region in space where the probability of finding an electron is high... 

Inside the point of inflection of equation (31) equation (32) is identical to MM2 with the cubic stretch term turned on. At very long bond distances, it is identical to MM2 with the cubic stretch term turned off. 

The nonconvective energy flux across the boundary is composed of two terms a heat flux and a work term. The work term in turn is composed of two terms useful work deflvered outside the fluid, and work done by the fluid inside the control volume B on fluid outside the control volume B, the so-called flow work. The latter may be evaluated by imagining a differential surface moving with the fluid which at time 2ero coincides with a differential element of the surface, S. During the time dt the differential surface sweeps out a volume V cosdSdt and does work on the fluid outside at a rate of PV cos dS. The total flow work done on the fluid outside B by the fluid inside B is... 

For pressure drop inside tubes, d is 0.046 and F is the fluid-flow path length. Across tubes banks, a is 0.75 and F is the product of the number of tube rows and the number of fluid passes across the tube bank. The physical property term is again tabulated after being normalised so that the lowest value is approximately unity. 

Informed opinion is a nonmathematical technique which is often called blue-sky estimating. The two terms are not necessarily synonymous. Informed opinion may be the consensus of people inside the company, along with or without outside opinions. Such a consensus can be broadened into the Delphi technique, which uses a sequential series of questioimaires submitted to a panel of experts who have Httie or no contact with each other. Blue-sky answers are akin to the informed opinion except that they usually consist of subjective speculation by experts in a confined one-day meeting in which each participant knows the views of the others. 

Placement of vascular access ports is similar to that of a long-term indwelling arterial catheter. A small incision is made over the selected vein and a second incision is made lower in the anterior chest to create a pocket to house the port. The catheter is tuimeled subcutaneously from its entry point into the vein with the tip inside the right atrium. The final position of the catheter is verified by fluoroscopy, secured with sutures, and the subcutaneous pocket is closed. The port septum is easily palpable transcutaneously, and the system may be used immediately. A surgeon typically inserts the vascular access port in an outpatient setting. 

Coils For flow inside helical coils, Reynolds number above 10,000, multiply the value of the film coefficient obtained from the apphcable equation for straight tubes by the term (1 + 3..5 D /DJ. 

Fin efficiencies and fin dimensions are available from manufacturers. Ratios of finned to inside surface are usually available so that the terms Aj, A, and A may be obtained from these ratios rather than from the total surface areas of the heat exchangers. 

When it is known that Hqg varies appreciably within the tower, this term must be placed inside the integr in Eqs. (5-277) and (5-278) for accurate calculations of hf. For example, the packed-tower design equation in terms of the overall gas-phase mass-transfer coefficient for absorption would be expressed as follows ... 

In situations in which one cannot assume that Hl and Hql I e constant, these terms must be incorporated inside the integrals in Eqs. (14-24) and (14-25). and the integrals must be evaluated graphically or numerically (by using Simpsons nile, for example). In the normal case involving stripping without chemical reactions, the hquid-phase resistance will dominate, making it preferable to use Eq. (14-25) in conjunction with the relation Hl — Hql. 

Pore Diffusion When flmd transport through a network of fluid-filled pores inside the particles provides access for solute adsorption sites, the diffusion fliix can be expressed in terms of a pore diffusion coefficient D as ... 

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