Six number

Consider a quantity of some liquid, say, a drop of water, that is composed of N individual molecules. To describe the geometry of this system if we assume the molecules are rigid, each molecule must be described by six numbers three to give its position and three to describe its rotational orientation. This 6N-dimensional space is called phase space. Dynamical calculations must additionally maintain a list of velocities. 

HT motors must have a minimum six numbers of resistance temperature detectors (RTDs) (See section 12.8). 

The si2e of the opening will depend upon the width and height required by the current-carrying conductors. Say, for six numbers 152.4 mm x 6.35 mm busbars, as shown in Figure 28.27, an opening of 170 mm x 250 mm will be adequate. 

The Problem The probability of winning a lottery, where you have to pick six numbers from the numbers 1 through 54, is 0.00000387 percent. How many tickets do you have to buy (and combinations of numbers do you have to choose) to be sure that you have a ticket with all the winning numbers on it ... 

This results in a mixing time characteristics incorporating six numbers ... 

With respect to unsaturated hydrocarbons we should note that compounds exhibiting one or several double bonds are often called alkenes or olefins. Finally, we need to add a brief note concerning the nomenclature in aromatic systems, particularly, in six-numbered rings such as benzene. Here the terms ortho-, meta-, and ara-substi-tution are often used to express the relative position of two substituents in a given ring system. Identically, we could refer to those isomers as 1,2-(ortho), 1,3-(meta), 1,4-(para) disubstituted compounds (see margin). 

Suppose that we consider a gas like nitrogen that can form a diatomic molecule. There are still three degrees of freedom for each atom, so each nitrogen molecule would have six degrees of freedom, and it would take six numbers to specify the positions of the atoms composing the molecule. There are 3 at degrees of freedom per molecule, where nat is the number of atoms per molecule. 

Suppose a lottery ticket costs 1 per play. The game is played by drawing 6 numbers without replacement from the numbers 1 to 48. If you guess all six numbers, you win the prize. Now, suppose that N = the number of tickets sold and P = the size of the prize. N and P are related by... 

Many spectroscopic phenomena depend to first order on symmetric second-rank tensors, that is, on six independent numbers [9]. The information contained in these six numbers, and its experimental accessibility in different media are illustrated in Figure 3. In fluids, five of these numbers are usually inaccessible to experiment, and the surviving isotropic value of... 

If it expands too slowly, the Universe recollapses before stars form. [After Martin Rees, Just Six Numbers (New York Basic Books, 2000), 87, fig. 6.1.]... 

Martin Rees, Just Six Numbers (New York Basic Books, 2000). 

Figure 5.14 Gradient elution chromatogram of a mixture of phenolic solutes. The six numbered peaks refer to the sample. The remaining signals to the blank. Linear gradient 0 — 100% methanol in water. /0=125 s. Figure taken from ref. [536]. Reprinted with permission.

Determine the sum of squares replicate error as follows (i) calculate tire mean response for the six replicates (ii) calculate the difference between the true and average response, square these and sum tire six numbers. 

The lottery has taken on multiple forms with the advent of the computer. In the first form, the lottery (Lotto) may be a ticket with a series of six numbers of one through forty. The numbers can be drawn at random by the computer, or the numbers can be chosen by hand in a televised event. Each 1 lottery ticket contains two sets of six numbers, for example,... 

The six numbered ring di-substituted complex, Cp2Zr (g-H)2BC5H10 27 was prepared... 

Butanol longer-chain primary alcohols often suffer double elimination. That is, they lose one molecule of water and one of ethylene simultaneously through a six-numbered cyclic mechanism, thus displaying an M-46 peak... 

The six number for a peptide bond formed by residues A and B, is obtained by adding the number of atoms in A and B. Thus, in alanylglycine, the six number is zero since the atoms in the side chains of alanine and glycine do not occupy position 6, whereas the six number for valylglycine is 6 since atoms in the side chain of valine occupy position 6 of the dipeptide. Peptides with a six number of 6, such as valylglycine or leucylleucine, are hydrolyzed slowly, whereas those with numbers of 3 are hydrolyzed at intermediate rates and those with numbers of zero, are hydrolyzed most rapidly. The six numbers of the dipeptides examined by Synge (1945) as well as those for some synthetic polyamino acids (Heyns et al., 1958) correlate fairly well with the experimentally determined relative... 

Both programs work by adding up numbers. MLX, used for entering machine language programs, adds six numbers (plus the memory location). So you could type 000, 000, 000, 000, 013, 015 to get a total of 28. But 000, 000, 000, 000, 015, 013 also add up to 28. MLX wouldn t know the difference. 

Subsequent prompts will ask you to type in subsequent lines from the MLX listing. Each line is six numbers plus a checksum. If you enter any of the six numbers wrong or the checksum wrong, the computer will sound a buzzer and prompt you to reenter the entire line. If you enter the line correctly, a pleasant bell tone will sound and you may go on to enter the next line. 

This paper will discuss the state of the art in 3D structure refinement using empirical, semi-empirical and ab initio methods. We believe that the success story of liquid state NMR in protein structure elucidation is going to continue within the solid state (or membrane environment) if chemical shifts can be successfully exploited. Neutron and X-ray diffraction methods owe their success to a simple formula that connects the measured reflex intensities with the nuclear positions or the electron density, respectively. The better we understand how chemical shifts change with the three-dimensional arrangement of atoms, the more reliably we can construct molecular models from our NMR experiments. As we can in principle determine up to six numbers per nucleus if we perform a full chemical shift tensor analysis, we need to address the question whether whole CS tensor or at least its principal values can be used in structure calculations. 

Rees, M. (2000). Just Six Numbers The Deep Forces That Shape the. Universe. New York, NY Basic Books. 

From the standpoint of a stress-strain curve, the constitutive behavior discussed in the previous section corresponds to a limited range of loads and strains. In particular, as seen in fig. 2.10, for stresses beyond a certain level, the solid suffers permanent deformation and if the load is increased too far, the solid eventually fails via fracture. From a constitutive viewpoint, more challenges are posed by the existence of permanent deformation in the form of plasticity and fracture. Phenomenologically, the onset of plastic deformation is often treated in terms of a yield surface. The yield surface is the locus of all points in stress space at which the material begins to undergo plastic deformation. The fundamental idea is that until a certain critical load is reached, the deformation is entirely elastic. Upon reaching a critical state of stress (the yield stress), the material then undergoes plastic deformation. Because the state of stress at a point can be parameterized in terms of six numbers, the tensorial character of the stress state must be reflected in the determination of the yield surface. 

The Idoux steric constant A6 is defined as the change in the six number, that is, the difference of the six number of the X substituent of the ester XCOOX minus the six position number of the same substituent X in the part X of the ester ]Idoux, Hwang etal., 1973 Idoux, Scandrett etal., 1977]. 

The logarithms of the second-order rate constants for hydrolysis of 1-methyl-5,5-disubstituted barbiturates correlated well with Newman s six numbers for both C-5 substituents.329 Linear relationships between enthalpy and entropy of activation for hydrolysis of barbiturates have been described,325-337-566-567 and multiparameter correlations of hydrolysis rate... 

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