Curve multimodal

It can be shown that for the single-mode case AEa represents the crossing point energy of the two potential curves belonging to the initial and final electronic states. For the multimode case, there are numerous crossing points and AEa in this case represents the minimal crossing-point energy of these two potential surfaces (see Appendix I). In other words, for the multimode case of... 

Distribution functions for very short n-alkane chains are calculated. The results obtained implicate the discrete nature of the RIS approximation as the origin of the multimodal nature of the short-chain distribution, and suggest that the best representation of such results would be a simple unimodal curve averaging out all of the minima and retaining only the most prominent maximum. 

Another limitation of this method is that it tends to present the most compact distribution. That is, the structure of a multimodal curve is suppressed unless one is willing to invest the time to tediously parametrize for a better fit to the experimental data. The eventual limiting factor will be the experimental error itself. 

I2 transitions excited within the gain curve of a doubled Nd YAG laser at 532 nm. Frequencies of I2 transitions are given in vacuum wavenumber (cm ) units for the major peaks, along with assignments. A multimode laser will excite primarily the three strong central lines. 

Our picture of the transitions between centres is very incomplete so far, based on studies of distribution curve shapes in the products. When a monomer is polymerized by a living mechanism on two or more centres of widely differing reactivity, chains of characteristic legth are produced on each centre type. In a strictly living medium where centres of one type are not transformed to another, a product with a bi- or multimodal distribution curve of degrees of polymerization is formed. When the various centre types are in a dynamic equilibrium where the centre type changes in the course of propagation, the distribution curve of the product will be broader than the width of either of the peaks in the previous case, but narrower than the overall... 

Average Particle Size A powder has many average sizes hence it is essential that they be well specified. The median is the 50 percent size half the distribution is coarser and half finer. The mode is a high-density region if there is more than one peak in the frequency curve, the distribution is said to be multimodal. The mean is the center of gravity of the distribution. The center of gravity of a mass (volume) distribution is defined by Xyu = 2) XdV/ Z dV where dV = X dN dV is the volume of dN particles of size X This is defined as the volume-moment mean diameter and differs from the mean for a number or surface distribution. 

Figure 7 is a plot of the [lyJ-MW relationship for a multimodal PMMA (Mn 3080, Mw 19,120) superimposed onto the MWD of the sample. The smooth bold curve in this figure represents the literature intrinsic viscosity molecular weight relationship... 

To better visualize the situation, we present in Fig. 2 representative cuts through the PES of the benzene cation (Fig. 2a) as well as the monofluoro derivative (Fig. 2b). A linear combination of the normal coordinates of the JT active modes vg — vg is chosen for the benzene cation and one of the totally symmetric modes for the monofluoro benzene cation. Both are defined to minimize the energy of the conical intersection between the A and C states of the monofluoro derivative, and between the X and B states of the parent cation (within the subspace of JT active coordinates). For the parent cation one identifies a low-energy inter-state curve crossing which is mediated by the multimode JT effect in the two degenerate electronic states. The latter is reflected by the symmetric crossing between the two lowest potential energy curves in Fig. 2a which acmally represents a cut... 

In practice the computerized data reduction procedure consists of the series of steps listed in Table I. For both multimodal resonant frequency data and constant frequency dynamic taken at several different frequencies, the correct value of the reference temperature (Tq) is that which reduces the scatter of the modulus and loss tangent data to fit a smooth curve. The initially assumed value of T0 is taken as the temperature corresponding to the loss tangent maximum or Tg. If this value of T0 does not give satisfactory superposition, the assumed value of T0 is adjusted to a slightly higher value and the procedure is repeated until a satisfactory superposition is achieved. Previous... 

FIGURE 2.5 The mixture of macromolecules of chains with different degrees of polymerization results in a distribution curve. These can be monomodal (broad or narrow), multimodal, or bimodal. 

Atomic Force Microscopy (ATM). A Nanoscope IIIA Multimode (Digital Instruments, Santa Barbara, CA) was used for atomic force microscopy measurements. The AFM was operated in force mode, with a scan rate of 1 Hz, and a 2 -piezo total displacement of 500 nm, without calibrating the scanner before each measurement (routine calibration only). Both ap-proach/extension and retraction force curves of the cantilever were recorded. 

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