Singular position

Chemical shift relative to liquid CS2, some are peak positions not the isotropic shifts, see original references. Numbers in parentheses represent singularity positions of MAS powder patterns, t Estimated upper limit of the quadrupole effect parameter, except which is based on lineshape analysis. 

It is assumed in this method, of course, that the initial estimate of Y yields a non-singular, positive-definite, A matrix, but given these starting conditions, the matrix A remains positive definite (non-singular) throughout the course of the minimization (given accurate arithmetic) precisely because the constraints are built in. 

Values in parenthesis refer to singularity positions of MAS powder patterns. 

Since for most applications to systems of chemical interest, it is not feasible at present to compute MP series beyond fourth or fifth order, methods will have to be developed for estimating singularity positions from low-order series. For clear class a or class /3 systems, quadratic... 

The potential of the trust factor has just been tested. In many ways the Council for Chemical Research is still in its infancy, still an experiment. CCR s full impact is still to be realized. If we are to effectively meet the challenge of remaining, as Philip Abelson puts it, "tops in chemistry," we need to continue to build on the trust factor. The uniqueness of CCR s structure and the focus of its mission places the Council for Chemical Research in a singular position among scientific organizations. 

In the history of large structures the Limon River Bridge has an important and very singular position ... 

Because no chain is in a singular position, and each chain has a full six degrees of freedom, is defined. We may therefore solve for the spatial tip face exerted by chain 1 on the reference member, f, as follows ... 

If (nc)jb is the number of degrees of constraint for the genoal joint at the tip of chain k, then Mt is the (nc)k x (ne)t transformation matrix which solves for h. The basic solution procedure for h, evoi with ao unknown, is identical to the i proach discussed in Section S.6.2 for a single closed chain. Thus, this general solution is still valid for a chain in a singular position or a chain with less than six (xiginal degrees of freedom. The solution procedure requires 0[(ne) ] scalar opo ons. 

Note that if chain k is rigidly grasping the reference membo, then the constraint space for this genoal Joint, is the 6 x 6 identity matrix. In this case, also note that 0 1 and ht are identically zero for each chain. If chain k has six degrees of fire om and is not in a singular position, then will be exactly equal to A.k, the operational space inertia matrix for chain k, and the solution for h will be ... 

If.the augmented chain has at least six degrees of freedom, and if it is not in a singular position, the matrix MJ will be exactly equal to the operational space inertia mauix of the augmented chain. That is. 

Let us notice the singular position of the emotion surprised located almost on the centre of gravity of the plane. It seems that it has been isolated by the subjects, and that it has been perceived as neither positive nor negative one can be surprised in positive and negative ways surprised could easily be qualified as neutral. ... 

Figure 21. Schematic representation of singular lines in a smectic C phase, (a, b) The distribution of the directors in four-branch nuclei, the layers being seen from the top open circles indicate the singularity position. (c, d) Cross-sections of singular lines parallel to layers, (e) Superimposed layers of a smectic C phase can be devoid of defects, whereas an edge dislocation is present for the rotation periodicity (left-handed helix). The tilted molecules show a-Ak rotation on the left-hand side of the diagam and only a -2it one on the right-hand side. This situation involves the presence of a line similar to (d) in the defect core. The double lines indicate the locus of directors parallel to the plane of the page.

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