Right-left axes

For the case of a double-D coil we multiply each matrix element with an element shifted by a constant distance of the same line. This is done in x- and y-direction. The distance between the two elements is the correlation length X for filtering in x-direction and a second correlation length for the movement in y-direction. Thus one gets two new matrices Ax and Ax for the filtering from the left to the right (positiv x-direction) and vice versa (negativ x-direction). 

In order to perform this procedure on all elements of matrix A a margin with constant values aj and a ,j and a length of X (left/right) or % (top/bottom) is added on each side of matrix A. The two new matrices A and Ai are combined to form a resulting matrix Ax for the filtering in x-direction ... 

Figure 9.7 The NMR spectrum of an AX spin system (shown schematically). Left NMR transitions. Right Resulting NMR spectrum.

Fig. 20. Energy level diagrams for square pyramidal chromophores of cobalt(II). Left, Dq(ax) =Dg (base) a= 100°. Middle, the effect of the variation of the ratio Dj(ax)/D (base) for Dq hase) = 1 kK. Right, the effect of the variation of a angle on the energy levels Dq(ax) = X)j(base) = 1 kK...

Figure 2.56. Experimental (left) and computed (right) decomposed XES spectra of NH3/Cu(l 10). The upper panels contain states of mainly ax symmetry and the lower ones mainly e-symmetry. To find agreement with experiment the molecules must be tilted ( 40°) in the calculations. From Ref. [112].

Fig. 8.10. Computer-simulated NOESY cross peaks between signals with different T2 values. Conditions p[ — p =40 s 1 p[ - 50 s-1 p( = 200 s I o/j = 5 s l. (A) f[" = t2m = 0.01 s (B) t["ax = T , r2max = T2J (C) t["ax = T, r2max = T. Note that the upper left cross peak has maximal intensity in case (B), the lower right cross peak has maximal intensity in case (C), whereas in case A the two intensities are equal and intermediate between the larger and the smaller of cases (B) and (C). For simplicity, fra = T[ = T( has been taken. A cos2 weighting function has been applied.

In order to solve such systems of linear equations on a computer, it helps to realize that only the coefficients of the system (1.1) play a role. For efficient computer use, such systems should be rewritten in matrix form Ax = b by extracting the coefficient matrix A on the left hand side of (1.1) and the vector b on the right hand side of (1.1). Here... 

We assume a racemic mixture of equal concentrations of dextro- (Ad) and levo-enantiomers (AL) of the complex, together with partly dissociated achiral complexes (Ax)- The incident unpolarized light beam is described as equal intensities of left- and right-circularly polarized light, l and /r, respectively, propagating along the z direction. Because of optical absorption, molecular diffusion, and chemical reactions, Ih IT, AD, and AL will depend on the spatial coordinate z and time t. This can be expressed by the following differential equations ... 

Fig. 5. Optical images of the bulges which appeared when printing Xi02 ink on OTS-treated glass (contact angle = 98.3°) at 25°C, for Ax = 0.05 mm (left-hand side), 0.08 mm (centre) and 0.1 mm (right-hand side). (From Ref. 26, 2007 The Royal Society of Chemistry.)...

The accuracy of this difference scheme is 0 Ar -F Ax ), provided the integrals entering (5.1.7) and (5.1.8) are calculated with accuracy of O(Ax ). The difference equations are solved first from the left to the right with the boundary condition g = 0 (no correlations at r ). Similar to the discussed scheme (5.1.18), non-line u effects are taken here into account iteratively. 

The abscissa interval containing the intersection point is scanned from left to right in 500 steps and the two CL(T) distributions at each point (resolution y-range/100) are multiplied to obtain the volume jj PDyi(x,y) PDY2(x,y) 5x 5y (approximated by SE PDyi(x,y) PD)/2(x, y) Ax Ay), which is equated with 100% the points at which the cumulative overlap function reaches 2.5, respectively 97.5% are the results. 

Boundary conditions most commonly encountered in practice are the specified temperature, specified heat flux, convection, and radiation boundary conditions, and here we develop the finite difference fonnulations for them for the case of steady one-dimensional heat conduction in a plane wall of thickness L as an example. The node number at the left surface at. r = 0 is 0, and at the right surface at x = L it is M. Note that the width of Ihe volume element for either boundary node is Ax/2. 

Considep two-dimensional transient heat transfer in an L-shaped solid body that is initially at a uniform temperalure of 90°C and whose cross section is given in Fig. 5-51. The thermal conductivity and diffusivity of the body are k = 15 W/m C and a - 3.2 x 10 rriVs, respectively, and heat is generated in Ihe body at a rate of e = 2 x 10 W/m. The left sutface of the body is insulated, and the bottom surface is maintained at a uniform temperalure of 90°C at all times. A1 time f = 0, the entire top surface is subjected to convection to ambient air at = 25°C with a convection coefficient of h = 80 W/m C, and the right surface is subjected to heat flux at a uniform rate of r/p -5000 W/m. The nodal network of the problem consists of 15 equally spaced nodes vrith Ax = Ay = 1.2 cm, as shown in the figure, Five of the nodes are at the bottom surface, and thus their temperatures are known. Using the explicit method, determine the temperature at the top corner (node 3) of the body after 1,3, 5, 10, and 60 min. 

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