Symmetric applications

This latter explanation was verified by Webster and Schrank 187 who demonstrated that a transverse polarization of freshly decaptitated avena coleoptiles (containing no auxin ) could be electrically induced symmetrical application of exogenous auxin to the stump after electrical stimulation produced curvature A consistent behavior was exhibited if decapitated stumps, with auxin containing agar blocks on top, were electrically stimulated bending again occurred towards the positive side, similar to the case in which auxin was applied to only one side of freshly decapitated stumps without electrical stimulation (Fig. 12). 

Fig. 12. Curvature responses of decapitated avena coleoptiles as a function of auxin concentration. (A) curvature obtained in 90min, auxin applied asymmetrically (standard auxin test). (B) curvature produced in 60 min by symmetrical application of auxin upon succeeding transverse electrical stimulation. Bending occurs towards the positive pole, as sketched187 ...

The best column design for GPC as well as for affinity chromatography is a column with adaptors at both ends (Fig. 3.3C). This column type guarantees even surfaces of the gel bed, symmetrical application of sample, and regular flow of the eluent. 

Symmetrical application of magnetic field gradients around the refocusing pulse in a spin echo will refocus the signal from static molecules. However, microscopic molecular motion (Brownian motion) will cause dephasing of individual magnetic moments to a degree which is dependent on the freedom of the molecular motion of the water in cells. Freedom of the molecular motion... 

It is easy to calculate tire value of e as an application of the MAXWELL S equations in the case of a symmetric tube without defect. 

Gershinsky G and Poliak E 1995 Variational transition state theory application to a symmetric exchange in water J. Chem. Phys. 103 8501... 

The implicit-midpoint (IM) scheme differs from IE above in that it is symmetric and symplectic. It is also special in the sense that the transformation matrix for the model linear problem is unitary, partitioning kinetic and potential-energy components identically. Like IE, IM is also A-stable. IM is (herefore a more reasonable candidate for integration of conservative systems, and several researchers have explored such applications [58, 59, 60, 61]. 

Note that in equation system (2.64) the coefficients matrix is symmetric, sparse (i.e. a significant number of its members are zero) and banded. The symmetry of the coefficients matrix in the global finite element equations is not guaranteed for all applications (in particular, in most fluid flow problems this matrix will not be symmetric). However, the finite element method always yields sparse and banded sets of equations. This property should be utilized to minimize computing costs in complex problems. 

The resulting alkyl 3 5-dinitrobenzoate may be employed for the characterisation of the ether. The method is only applicable to symmetrical or simple ethers a mixed aliphatic ether ROR would yield a mixture of inseparable solid esters. 

This procedure is applicable to the preparation of both symmetrical anhydrides (R and R the same) and mixed anhydrides (R and R different)... 

The view factor F may often be evaluated from that for simpler configurations by the application of three principles that of reciprocity, AjFij = AjFp that of conservation, XF = 1 and that due to Yamauti [Res. Electrotech. Lab. (Tokyo), 148, 1924 194, 1927 250, 1929], showing that the exchange areas AF between two pairs of surfaces are equal when there is a one-to-one correspondence for all sets of symmetrically placed pairs of elements in the two surface combinations. 

The peak value of a fault current will depend upon the content of the d.c. component. The d.c. component will depend upon the p.f. of the faulty circuit and the instant at which the short-circuit commences on the current wave. (Refer to Figure 13.27, illustrating the variation in asymmetry with the p.f. of the faulty circuit. For ease of application, it is represented as a certain multiple of the r.m.s. value of the symmetrical fault current /sc )... 

Various techniques exist that make possible a normal mode analysis of all but the largest molecules. These techniques include methods that are based on perturbation methods, reduced basis representations, and the application of group theory for symmetrical oligomeric molecular assemblies. Approximate methods that can reduce the computational load by an order of magnitude also hold the promise of producing reasonable approximations to the methods using conventional force fields. 

Compressors built to the API standard are required to have equal thrust capability in both directions that is, the bearing is to be symmetrically constructed. However, the thrust bearings can be combined using various numbers of pads on each side, or a tapered land can be combined with the multiple-segment design. Other combinations of the four thrust bear ings discussed are found in certain isolated applications. 

Antithetic conversion of a TGT by molecular rearrangement into a symmetrical precursor with the possibility for disconnection into two identical molecules. This case can be illustrated by the application of the Wittig rearrangement transform which converts 139 to 140 or the pinacol rearrangement transform which changes spiro ketone 141 into diol 142. 

B. Application of the singlet-level and pair-level theories for fluids with spherically symmetric associative interactions... 

The present chapter is organized as follows. We focus first on a simple model of a nonuniform associating fluid with spherically symmetric associative forces between species. This model serves us to demonstrate the application of so-called first-order (singlet) and second-order (pair) integral equations for the density profile. Some examples of the solution of these equations for associating fluids in contact with structureless and crystalline solid surfaces are presented. Then we discuss one version of the density functional theory for a model of associating hard spheres. All aforementioned issues are discussed in Sec. II. 

B. Application of the Singlet-level and Pair-level Theories for Fluids with Spherically Symmetric Associative Interactions in Contact with Surfaces... 

The above procedure produces blast parameters applicable to a completely symmetrical blast wave, such as would result from the explosion of a hemispherical vessel placed directly on the ground. In practice, vessels are either spherical or cylindrical, and placed at some height above the ground. This influences blast parameters. To adjust for these geometry effects, and 7 are multiplied by some adjustment factors derived from experiments with high-explosive charges of various shapes. 

Detailed balance is a chemical application of the more general principle of microscopic reversibility, which has its basis in the mathematical conclusion that the equations of motion are symmetric under time reversal. Thus, any particle trajectory in the time period t = 0 to / = ti undergoes a reversal in the time period t = —ti to t = 0, and the particle retraces its trajectoiy. In the field of chemical kinetics, this principle is sometimes stated in these equivalent forms ... 

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