Order multiplication

Rehr J J, Albers R C and Zabinski S I 1992 High order multiple scattering calculation of x-ray absorption fine structure Phys. Rev. Lett. 69 3397-400... 

We have derived time-reversible, symplectic, and second-order multiple-time-stepping methods for the finite-dimensional QCMD model. Theoretical results for general symplectic methods imply that the methods conserve energy over exponentially long periods of time up to small fluctuations. Furthermore, in the limit m —> 0, the adiabatic invariants corresponding to the underlying Born-Oppenheimer approximation will be preserved as well. Finally, the phase shift observed for symmetric methods with a single update of the classical momenta p per macro-time-step At should be avoided by... 

Kinetic models proposed for sorption/desorption mechanisms including first-order, multiple first-order, Langmuir-type second-order, and various diffusion rate laws are shown in Sects. 3.2 and 3.4. All except the diffusion models conceptualize specific sites to or from which molecules may sorb or desorb in a first-order fashion. The following points should be taken into consideration [ 181,198] ... 

Elliott JP, Radin TG. The effect of corticosteroid administration on uterine activity and preterm labor in high-order multiple gestations. Obstet Gynecol 1995 85(2) 250 1. 

Tur R, Barri PN, Coroleu B, Buxaderas R, Parera N, Balasch J. Use of a prediction model for high-order multiple implantation after ovarian stimulation with gonadotropins. Fert Steril 2005 83 116-21. 

A convenient procedure for determining the point group of a non-linear of non-cubic molecule is designed. The system requires finding out the axis of highest order, multiple axis of this order and additional twofold axis as prime step. 

Calculation of the multiple scattering by means of a real-space cluster approach is considerably more flexible than band-structure methods. Since this technique does not rely on crystal periodicity, it can readily be applied to interpret data for materials of arbitrary atomic arrangements. The sensitivity to higher order correlations has been shown. Fujikawa et al. (94,96) favor short-range-order multiple-scattering XANES theory, in which atoms are not divided into shells but the scattered waves are classified into a direct term and a fully multiple-scattering term. 

The recommended procedure for the design and the safe operation of a cooled tubular reactor for first order/ multiple reactions is given in Table II. Once the reactor has been designed and installed, the tube diameter cannot be changed anymore. Moreover, with the requirement U should be kept constant at... 

M. Eden, A. Brinkmann, H. Luthman, L. Eriksson, and M. H. Levitt, Determination of molecular geometry by high-order multiple-quantum evolution in solid-state NMR, J. Magn. Reson., 144 (2000) 266-279. 

The nature of the metal-alkynyl bond has long been a matter of debate, especially with regard to the metal-C(sp) bond order. Multiple bonding could in principle arise from interactions between occupied alkynyl k levels and empty d-orbitals at the metal or from backbonding between filled metal d-orbitals and unoccupied 71 levels on the alkynyl ligand. Early photoelectron spectroscopy work on... 

Spectra of higher order multiplicity occur for systems where the coupling constant is of similar magnitude to the chemical shift difference between the coupled nuclei. Such a case is referred to as an system, where nucleus A has the smaller and nucleus B the larger chemical shift. 

Field et al.62 developed a general procedure to estimate the Saupe order parameters for spin systems aligned in liquid crystal media by iteratively fitting the experimental and simulated spectral widths of the high-order multiple quantum spectra. 

Grasso, C., M. Quist, K. Ke, and C. Lee. 2003. POAVIZ A partial order multiple sequence alignment visualizer. Bioinformatics 19 1446-8. 

Managers may also be interested in the comparative differences between perspectives provided by rank summary statistics such as median rank, mean rank, and midrange of ranks. The rank range approach can also provide an interesting alternative for conducting such comparative analysis. The statistics of interest can be treated as second-order multiple indicators for the units instead of using the indicator data from which the statistics were derived. Poset Cl level and rank range analyses are then conducted in a parallel manner to the procedures described above. It would not be informative, however, to consider the end-member elimination effects in this... 

On the contrary, when applying the GEMANOVA model the interactions are modelled as one higher-order multiplicative effect, resulting in the eqn 9.5... 

Rehr JJ, Zabinsky Zl, Albers RC (1992) Higher-order multiple seattering calculations of X-ray-absorption fine stmeture. Phys Rev Lett 69 3397-4000 Riekwood PC (1981) The largest crystals. Am Mineral 66 885-907... 

Y. Wang, G.M. Stocks, W.A. Shelton, D.M.C. Nicholson, Z. Szotek, and W. M. Tern-merman, Order-multiple scattering approach to electronic structure calculations, Phys. Rev. Lett. 75 2867 (1995). 

When applied to longitudinal magnetization, the C7 sequence in general excites even-order multiple (double)-quantiun coherences. Applying C7 to transverse magnetization, in general leads to excitation of odd-order multiple-quantum coherences. Using POST-C7, triple-quantum coherence in fully C-labelled L-alanine has been excited in this way, with a triple-quantum filter efficiency of 8% for the central and 4% for the two peripheral spins. ... 

In correspondence ivith the guidelines given above, the catalyst effectiveness is mostly only a weak function of p, and y. Therefore p >= //( ). The latter function is available in analytical form for first-order reactions [38]. In the general case, it has to be determined from the numerical solution of the catalyst particle balances, as done for instance in [35, 39-42]. In the case of negative reaction orders, multiple effectiveness factors can be obtained [32]. This is illustrated in Fig. 5.27 for the MTBE synthesis where the rate has a negative order with respect to the educt methanol. 

First order multiplicative intuitionistic linear logic... 

For a vapour layer in contact with a wall, the fluid density is below than pj. A complete interface is obtained in a particular case equ. (13) has an even order multiple root. In this case, the first simple root of equ. (13) below than p is Pp. It follows that ... 

A distinct advantage of the coaxial capillary approach is in the surface treatment of the device both W/O/W and O/W/0 emulsions can be formed without any surface modification ofthe capillaries, because neither the middle nor the inner fluid touches the capillary wall surface. This is clearly different from the other techniques mentioned above in this section. An additional advantage is the flexibility of the system. For example, the structure ofthe device can be easily modified to make higher order multiple emulsions, such as triple emulsions [100, 101]. 

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