Hermans function

The values of the amorphous orientation index in the form of Hermans function of orientation if a), determined by the authors for PET fibers are listed in Table 6. The differences in the values of fa quoted in Table 6 and referring to particular investigation methods can result from the fact that in some methods the orientation of the amorphous and mesophase are considered jointly. Consequently, in such a case the values of fa will be overrated. 

The quantitative assessment of the overall orientation of PET fibers is generally made on the basis of fiber optical anisotropy measurements, i.e., measurements of the optical birefringence of the fiber. The determination of the value of optical birefringence makes it possible to determine the value of Hermans function of orientation based on the equation ... 

The factor having the strongest effect is the elongation imparted in the process of production stretching. Second, the overall orientation is affected by the stretching rate. For the same draw ratio, the overall orientation grows with an increase in the stretching rate. The effect of the draw ratio on the value of Hermans function of orientation is illustrated by the values of/o, established by the authors and depicted in Table 7. 

AG Davies, CA Spike, JE Shaw, RK Herman. Functional overlap between the mec-8 gene and five sym genes in Caenorhabditis elegans. Genetics 153 117-134,1999. 

This expression is called the Hermans function it is a nice example of unification in physics, in this case between optics and X-ray diffraction. This relation has a broad theoretical validity. 

If Eq. (13.165) is substituted in the Hermans function Eq. (13.151) we obtain a general relationship between the birefringence and the compliance of well-oriented fibres ... 

The Herman function is equal to 1 when the chain axis is parallel to the film orientation, 0 when the system is randomly oriented, and 1/2 when the chain axis is perpendicular to the film orientation direction. This function can be calculated from measurements of the dichroic ratio by using [20]... 

Herman M F, Kluk E and Davis H L 1986 Comparison of the propagation of semiclassical frozen Gaussian wave functions with quantum propagation for a highly excited enharmonic oscillator J. Chem. Phys. 84 326... 

Bumendtein BA, James KE, Lind BK, Herman EM. Functions and organization of coordinating centers for multicenter studies. Controlled Clin Trials 1995 16 4S-29S. 

Without loss of generality y = y can be assumed. If the dipole moment can be assumed to be a linear function of coordinate within the spread of the frozen Gaussian wave packet, the matrix element (gy,q,p, Pjt(r) Y,q, p ) can be evaluated analytically. Since the integrand in Eq. (201) has distinct maxima usually, we can introduce the linearization approximation around these maxima. Namely, the Taylor expansion with respect to bqp = Qq — Qo and 8po = Po — Po is made, where qj, and pj, represent the maximum positions. The classical action >5qj, p , ( is expanded up to the second order, the final phase-space point (q, p,) to the first order, and the Herman-Kluk preexponential factor Cy pj to the zeroth order. This approximation is the same as the ceUularization procedure used in Ref. [18]. Under the above assumptions, various integrations in U/i(y, q, p ) can be carried out analytically and we have... 

To explore this issue, Monte Carlo computer simulations were run using the protocol outlined in the previous section. In these simulations, however, a peptide of sequence Ac-Ala-Xaa-Ala-Ala-NMe was employed (Xaa = Gin or Asn), the backbone was not constrained to the PPII conformation, and a side chain-to-backbone hydrogen bond was constrained using a potential function previously used to constrain a-helical backbone-to-backbone hydrogen bonds (Tun and Hermans, 1991 Creamer and Rose, 1994). 

Uniaxial orientation parameter (Hermans orientation function) Scattering data evaluation program by A. Hammersley (ESRF) Free Electron Laser Hamburg Full width at half-maximum... 

This observation is expected from theory, as the observed thickness distributions are exactly the functions by which one-dimensional short-range order is theoretically described in early literature models (Zernike and Prins [116] J. J. Hermans [128]). From the transformed experimental data we can determine, whether the principal thickness distributions are symmetrical or asymmetrical, whether they should be modeled by Gaussians, gamma distributions, truncated exponentials, or other analytical functions. Finally only a model that describes the arrangement of domains is missing - i.e., how the higher thickness distributions are computed from two principal thickness distributions (cf. Sect. 8.7). Experimental data are fitted by means of such models. Unsuitable models are sorted out by insufficient quality of the fit. Fit quality is assessed by means of the tools of nonlinear regression (Chap. 11). 

History. Starting from the ID point statistics of Zernike and Prins [116] J. J. Hermans [128] designs various ID statistics of black and white rods. He applies these models to the SAXS curves of cellulose. Polydispersity of rod lengths is introduced by distribution functions, / , (,r)108. Hermans describes the loss of correlation along the series of rods by a convolution polynomial . One of Hermans lattice statistics is namedparacrystalby Hosemann [5,117]. Hosemann shows that the field of distorted structure is concisely treated by the methods of complex analysis. A controversial subject is Hosemann s extension of ID statistics to 3D [63,131,227,228],... 

Figure 9.4. The orientation of structural entities (rods) in space with respect to the (vertical) principal axis and the values of for, the uniaxial orientation parameter (Hermans orientation function) for (a) fiber orientation, (b) isotropy, (c) film orientation...

Herman-Kluk method, direct molecular dynamics, Gaussian wavepacket propagation, 380—381 Hermite basis functions ... 

Herman and Skillman [79] used an HFS algorithm to calculate radial atomic wave functions and energy eigenvalues for all atoms, tabulating all results and the computer software at the same time. They treated all single electronic... 

Turbulent flow chromatography uses large particle packing materials and high flow rates to separate small molecules from proteins and other matrix components in plasma. In one example, Herman et al.109 reported that turbulent flow chromatography was useful for a series of discovery compounds as the online extraction step in LC/MS/MS analysis. As an alternative, Hsieh et al.89-104 107 described the use of a single mixed function column as a simpler process for direct plasma injection applications. 

Coen, P. G., McDonald, E. R., 3rd, Herman, J. G., and El-Deiey, W. S. Tat-binding protein-1, a component of the 26 S proteasome, contributes to the E3 ubiquitin ligase function of the von Hippel-Lindau protein. Nat Genet... 

Lewkowich IP, Herman NS, Schleifer KW, Dance MP, Chen BL, Dienger KM, Sproles A A, Shah JS, Kohl J, Belkaid Y, Wills-Karp M CD4+CD25+ T cells protect against experimentally induced asthma and alter pulmonary dendritic cell phenotype and function. J Exp Med 2005 202 1549-1561. 

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