Projection coordinate

Figure 8 A joint principal coordinate projection of the occupied regions in the conformational spaces of linear (Ala) (triangles) and its conformational constraint counterpart, cyclic-CAla) (squares), onto the optimal 3D principal axes. The symbols indicate the projected conformations, and the ellipsoids engulf the volume occupied by the projected points. This projection shows that the conformational volume accessible to the cyclic analog is only a small subset of the conformational volume accessible to the linear peptide, (Adapted from Ref. 41.)...

Assign dedicated refinery personnel to be stationed in the engineering contractor s office to coordinate project activities and act as a liaison between the refinery and the contractor... 

The competent authorities of the Netherlands, the task force member responsible for coordinating Project Prism activities in Europe, have launched a specific time-bound operation focusing on backtracking investigations. The operation is aimed at identifying companies and individuals responsible for the manufacture and diversion of precursors of amphetamine-type stimulants, specifically P-2-P, in the region. If successful, the operation may be expanded to include areas beyond Europe. 

A.E. acknowledges the Turkish Academy of Sciences in the framework of the Young Scientist Award Program (KAE/TUBA-GEBIP/2001-2-8) and Ege University, Faculty of Pharmacy, project coordination (Project No. 04/ECZ/003) for their financial support. 

As already discussed in Section 2.4, in 3-D any point (denoted by the vector r) can be described by its three coordinate projections x, y, z (in emits such as m, nm, A, or pm) using an orthogonal coordinate system with emit vectors eX/ ex, ex hence r = xex + yeY + zez- In noncrystallographic textbooks, the position vector r is usually given in a Cartesian (orthogonal) system. 

Financial support from a coordinated project between the National Research Council of Canada (NRC) and the Spanish National Research Council (CSIC) is gratefully acknowledged. 

To understand this, take the matrix group G — GL2, with H the upper triangular group. Here G acts on k1 = kei ke2, and H is the stabilizer of ev In fact G acts transitively on the set of one-dimensional subspaces and since H is the stabilizer of one of them, the coset space is the collection of those subspaces. But they form the projective line over k, which is basically different from the kind of subsets of fc" that we have considered. In the complex case, for instance, it is the Riemann sphere, and all analytic functions on it are constant whereas on subsets of n-space we always have the coordinate projection functions. 

Proof. By the lemma it is enough to construct all the finite-dimensional V in Am. Such a V is a subcomodule of the direct sum of its coordinate projections to A, so we may deal just with V in A. The original representation gives us a Hopf algebra surjection of B = k[X11, Xm, 1/det] onto A, and V is contained in the image of some subspace (l/detj j/(Xy) deg(/) < s. These subspaces are B-subcomodules of B, and hence also are /I-subcomodules it will be enough to construct them. 

SMHI/FBS has, through the years, also participated in a number of ICES and HELCOM coordinated projects such as Joint Skagerrak Expedition (1966), lYES/IBTS (1971— ), IBY (1969-1970), BOSEX (1977), PEX 86 (1986), SKAGEX (1990-1991). 

An equation similar to the Eq. (4) holds true for general quantum amplitudes E) and general hamiltonian operators. Eq. (4) is a model constructed from a coordinate projection procedure. The wave function F(x, p) is the projection on coordinate space of the general probability amplitude (x, p) = (x, p ) [14], Since E(x, p) are eigenfunctions of the molecular hamiltonian, the only way to change the state of a system prepared in a given stationary state is via the coupling operator U. 

FIGURE 45- Projection of the 2-dimens1 onaL pattern space onto axis or 2 destroys the structure of the clusters. An appropriate rotation of the axes defines new coordinates and y which are Linear combinations of the original coordinates- Projection onto the y -axis preserves the structure of the clusters. 

Hoegl, M., Weinkauf, K., and Gemuenden, H. G. (2004), "Interteam coordination, project commitment, and teamwork in multiteam R D projects A longitudinal study," Organization Science, 15 (1), 38-55. 

For more than one decade now, a large number of EC coordinated projects have been performed imder the umbrella of the international coordinated project MIRAGE (Migration of RAdionuclides through the GEosphere), and a recently performed review study on the project MIRAGE aimed to come to a critical evaluation of the state-of-the-art in the different research areas of the project and to evaluate how the results obtained contribute to rqKjsitory perfonnance/safety assessment. The study focused on the three main research areas of that project such as ... 

The PAC was responsible for coordinated projects for new-product development and supply chain improvement. Figure 23.5 reflects MJN s solution to the problem of organizing for supply chain improvement broached in Chapters 10 and 11. To aid growth objectives, supply chain and product-development initiatives were under common leadership. This structure makes SCM a company-wide raffier than a fimctional effort. 

The task to solve an underdetermined linear system of equations occurs frequently in multibody dynamics, e.g. when using coordinate projection methods to stabilize the numerical integration of the index reduced system of equations of motion, see Sec. 5.3.1. 

Coordinate projection is applied after an integration step is completed. Considering a multibody system in its index-1 form (5.1.3a),(5.1.3b),(5.1.4b), a typical integration step results in values Pn,Vn, and An being the solution of the nonlinear system... 

We pointed out earlier that for equations of motion of constrained mechanical systems written in index-1 form the position and velocity constraints form integral invariants, see (5.1.16). Thus the coordinate projection and the implicit state space method introduced in the previous section can be viewed as numerical methods for ensuring that the numerical solution satisfies these invariants. 

Both projection methods differ by the quantities which are projected. The coordinate projection method projects the solution of the discretized equation orthogonally onto the manifold M = x ip x) — (p xo) = 0 while the derivative projection determines Xn in such a way that the residual Sh xn) — fn is orthogonal to the tangent on M in xq. 

Figure 5.9 Projection methods coordinate projection (left) and derivative projection (right)...

For performing the Gaufi-Newton iteration we have to integrate Eq. (7.3.2) and to compute the sensitivity matrix with respect to the initial values. In both subtasks we make use of the solution properties by applying coordinate projection. 

Eich93] Eich E. (1993) Convergence results for a coordinate projection method applied to constrained mechanical systems. SIAM J. Numer. Anal, 30(5) 1467-1482. 

---