Cone, defined

Aiming at a network-based pathway analysis, the elementary flux modes provide a handle on the set of possible pathways through a metabolic network. In particular, each feasible steady-state flux distribution can be represented by a nonnegative combination of generating vectors that span the flux cone defined... 

Illustration 2.1.6 Consider the cases shown in Figure 2.5(a,b). Let us denote the columns of A4 as flj, aa, and a3. System 1 has a solution if the closed convex cone defined by Ax < 0 and the open half-space defined by c x > 0 have a nonempty intersection. System 2 has a solution if c lies within the convex cone generated by alra3, and a3. 

Since v = (2E /fi )l/2, the in-plane scattering of AB at various values of E can be represented by the concentric circles with radius u AB, which are shown in Figure 1.5. If uAB > C, then the complete lab distribution of AB ranges over 4n steradians and is easy to resolve. On the other hand, if ab < C, the scattering is confined to a cone defined by a small angle about C. This may occur either because E is small, or because mAB mc-If the reaction is appreciably exothermic, then v and therefore u AB and u c, can have a wide distribution of values, even when v and C are precisely defined. A detector at a laboratory angle 0 observes products with a spread of lab velocities each corresponding to a different pair of values for u and 0. Consequently, the lab-c.m. transformation of the differential cross sections, which is now represented [50] by the expression... 

The interpretation of Equation (2) is that if a solar collector is to be able to capture all of the radiation incident within the acceptance cone defined by 0max (Figure 4), at most it can have a concentration ratio given by Cmax- This rule comes from the fundamental principles of thermodynamics (Rabl, 1985) and is obeyed by all optical systems. 

The cones defined by the t-angles can be regarded as an indication of the steric shielding of the metal center with respect to the virtual apical positions of the coordination polyhedron. The e-values are practically identical for 4a,b (Fig. 2.7 127.0°, 125.6°, respectively). Interestingly, e is significantly increased to 138.6° in 4 c. This effect is again attributed to the strong repulsive interaction between the... 

The same eigenfunctions in spherical coordinates used in the previous subsection and introduced in 3.1 are the basis for the analysis of the hydrogen atom confined by a circular cone defined by a fixed value of the polar angle 9 = 9q. The boundary condition requiring the vanishing of the wave function at such an angle must be satisfied by the hypergeometric function in Equation (36),... 

We formulate the confinement of the hydrogen atom by an elliptical cone defined by xi = Xio- The boundary condition on the complete wave function of Equation (48), with its factors from Equations (39) and (57), is... 

Consider the point isotropic source of strength Sg particles per second located a distance d away from the detector, as shown in Fig. 8.6. If one draws a sphere centered at the source position and having a radius greater than d, the number of particles/(m s) on the surface of the sphere is Sq/AvR. The particles that will hit the detector are those emitted within a cone defined by the location of the source and the detector aperture. If the lines that define this cone are extended up to the surface of the sphere, an area is defined there. 

Figure 8.7 (a) The detector is at distance d from the source. (6) The source is assumed to be at the center of the sphere. The cone defined by the angle determines the area (differential area i4) on the surface of the sphere. 

The condition for constructive interference in all dimensions is a set of the common intersection of these cones, defined by the simultaneous solution of the respective equations. Thus, the equations represent one form of the scattering conditions required for diffraction to occur in three dimensions... 

Taper n. (1) In a conical transition section of an extruder screw, the vertex angle of the axial cone defined by the increasing root diameter of the screw. Compare with helical transition. (2) Often used. Syn draft in molds. 

Figure 3.18 (a) The numerical aperture of an objective is defined in terms of the half angle of the cone of rays (/ii).The effect of using an immersion oil is shown in (b) and (c)—peripheral rays which are refracted out of the cone defined by the numerical aperture when the space between the coverglass and objective is filled with air, propagate into the front lens of the objective when refraction is eliminated by filling the space with index matching oil. 

In Fig. 5(b), we consider another possible situation. Here the rod element OA is at a fixed angle tp to OB, although distributed uniformly around the cone defined by that angle. In this case the coefficients to describe OA about OB are simply the amplitudes of the harmonic function at xjr, hence... 

In this expression Vq is the inner potential which is equal to the sum of the Fermi energy and the work function, i.e., the energy of the bottom of the conduction band of a metal measured from the vacuum level (see fig. 3). This leads to an escape cone defined by the largest value of d satisfying eq. (6) for an electron energy of j inside the crystal, only those electrons travelling within a cone of half-angle 0 oriented normal to the surface will escape, with... 

Figure 2.11 Illustration of the alignment and movement of a molecule around a cone (defined by the tilt angle 0) of a molecule in the SJ phase.

The set of all metric spaces satisfying the distance limits, being the intersection of the box defined by the limits and the convex cone defined by the triangle inequalities, is itself a convex set. Thus every value of every distance between its lower and upper limits is attained in some metric space consistent with all the limits. 

To easily visualize these zones, the nebulization of a solution of yttrium (about 1 mg/L concentration) can be used as an indicator. The bright red color of the central cone defines the IRZ. The red color originates from the atomic emission of Y atoms excited by the plasma. Above the IRZ is a bright blue bullet, which defines the NAZ. This color is due to excited Y ions, which emit blue visible radiation. If the plasma and sample introduction system are performing satisfactorily, these colored zones should be well defined and reproducible. The use of this... 

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