How the Method Works

This method assumes that the moment of inertia is constant throughout the piping configuration, that the flattening of pipe bends during expansion or contraction will be negligible and that all anchor points are 100% fixed. 

Ft = 750 lbs. (This figure may be any one the designer may choose, but preferably one that conforms to his standard anchoring system). 

Draw an assumed piping configuration and calculate the neutral axis position  

Note that new components were made wherever the neutral axis crossed any section, with the exception of bends. 

The difference in moment by considering a bend as two components is in general negligible. 

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Binsch [6] provided the standard way of calculating these lineshapes in the frequency domain, and implemented it in the program DNMR3 [7], Fonnally, it is the same as the matrix description given in section (B2.4.2.3). The calculation of the matrices L, R and K is more complex for a coupled spin system, but that should not interfere witii the understanding of how the method works. This work will be discussed later, but first the time-domain approach will be developed. 

Outline the principle by which the analytical technique operates. A flow-chart may help. This section should be written so as to allow an at-a-glance summary of how the method works. Include an explanation of the principle of the... 

An alternative to the oxidation-number method for balancing redox reactions is the half-reaction method. The key to this method is to realize that the overall reaction can be broken into two parts, or half-reactions. One half-reaction describes the oxidation part of the process, and the other half-reaction describes the reduction part. Each half is balanced separately, and the two halves are then added to obtain the final equation. Let s look at the reaction of aqueous potassium dichromate (K2Cr2C>7) with aqueous NaCl to see how the method works. The reaction occurs in acidic solution according to the unbalanced net ionic equation... 

As we learned after the anthrax attacks in 2001, the ability to rapidly detect and to identify a bioterrorism agent is critical. A variety of methods are used for this purpose, including DNA fingerprinting, DNA sequencing, PCR, and ELISA immunoassays. As students read about how these methods are utilized in fighting terrorism, they learn how the methods work. It is even better if they can actually apply at least some of the methods in the laboratory. A number of suppliers provide kits designed for educational use,25 and in most cases, it is possible to use these activities in a way that simulates a bioterrorism scenario. 

Marti (1967) introduced the Kr/Kr method for determining CRE ages. The Al/ Ne method sketched above rests only on analyses of meteorites in contrast, the Kr/Kr method also demands knowledge of the relative cross-sections for certain nuclear reactions. To see how the method works, we write Equation (1) for Kr, a stable isotope produced mainly by spallation, and Equation (2) for Kr, which has a half-life of 0.229 Myr, and then divide one by the other, obtaining... 

Figure 5 shows how the method works. The individual points show average annual global CO2/ O2 concentrations over the years 1990-2000. 

The techniques of determining molecular structure by X-ray diffraction analyses have been initiated, developed, and expanded during the twentieth century, and in this book we have tried to show how the method works and what type of results can be expected. 

The Frasch method is based on the low melting point of sulfur. The element melts at a temperature slightly higher than that of boiling water (212°F/1(X)°Q. Here is how the method works ... 

To simulate bulk systems, one will often apply periodic boundary conditions in all spatial directions. For this kind of boundary conditions, a wide variety of algorithms exists, which we will shortly present here. A special focus will be on the classical Ewald method and its most efficient ancestor, the P M method of Hockney and Eastwood [2]. We explain how the method works and how one can automatically determine the optimal parameters for this method. 

There is no guarantee that a given group of molecules nor any derivatives of them will provide conglomerates but there are some well known cases, thus with a-amino acids, certain known derivatives, such as the A-acetyl amides, generally crystallise as conglomerates. We shall give some examples to show how the method works. 

Now that we understand how the method works, at least in principle, we will take a sine wave, add Gaussian noise, and explore the result of least-squares smoothing. 

Let us go back to the general problem of dynamics. The goal is to perform a near the identity canonical transformation that gives the Hamiltonian a suitable form, that we shall generically call a normal form. We shall use the method based on composition of Lie series. Let us briefly recall how the method works. A near the identity transformation is produced by the canonical flow at time e of a generating function %(p, q), and takes the form... 

Here is how the method works. High-energy neutrons resulting from cosmic ray collisions reach Earth continually from outer space. They enter the atmosphere and cause the slow formation of by bombarding ordinary atoms ... 

In addition to UV/IR-MALDI, there is another possibility for bringing protein ions into the gas phase electrospray ionization (ESI). Figure 7.7 illustrates how the method works. The proteins are not gasified via incorporation into an evaporable matrix but by spraying the protein solution as finest droplets. Weak acids serve as ionization helpers, and organic solvents as spraying helpers. Acetonitrile/water 50 50 with 0.1% acetic acid is a typical carrier solution. Salts and detergents disrupt ESI and have to be removed. For this, Troxler et al. (1999) use small return-phase columns (Cg, elution with TFA, acetonitrile). 

The formulation of the GPRG method that has been presented here differs from earlier presentations of the old renormalization group method [3-5], not only by virtue of the manner in which the effective coupling function is introduced [see the derivation of Eq. (5.65)] but by the role this function plays in enforcing the validity of the self-similarity assumption [see the derivation of Eq. (5.57)]. The intimate relationship between the effective coupling function and the object function, as illustrated by Eqs. (5.75) and (5.89), is an essential part of the theory that is unique to our approach. The remainder of this section is devoted to two examples that are illustrative of how the method works in practice. 

What has been said previously about the Hartree-Fock method is only a sort of general theory. The time has now arrived to show how the method works in practice. We have to solve the Haitree-Fock-Roothaan equation (ef. Chapter 8, pp. 431 and 531). 

For simple cases, the approach is no more streamlined than the others, but the example shows how the method works. The first-order Markovian character is built into the approach on the implicit assumption that it is only the immediately previous group along the chain which affects the likelihood of a given unit being present on the next step. This will become clearer in subsequent sections. It accounts for the fact that the averages calculated by this method reflect a geometric quality of the distributions as... 

If in need of any of these plates, it is also possible to dip or spray these chemicals onto a plain silica gel plate (use the W-type mentioned above), dry, activate, and use. This could be done initially to see how the method works before purchasing a box of them. Often, most manufacturers of TLC plates can be called for sample plates. 

The method of weighted residuals is a way of reducing the number of independent variables or the problem domain dimension. The basic idea of the method is to approximate the solution of the problem over a domain by a functional form called a trial function. The trial function s form is specified but it has adjustable constants. The trial function is chosen so as to give a good solution to the original differential equation. An excellent treatment of the method is given in the book by Finlayson (1972). As an example of how the method works, let us consider the heat conduction equation... 

Draw the apparatus you would use, and explain how the method works. 

Natural gas transmission pipes are sometimes protected against corrosion by the maintenance of a small potential difference between the pipe and an inert electrode buried in the ground. Describe how the method works. 

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