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Addition mathematical operation

The major focus of this chapter will be on macros that extend the already considerable power of the spreadsheet, by incorporating external program instructions. Starting with Excel 5, the macro language (i.e., the computer language used to encode the macro) of Excel is VBA, which is sufficiently flexible and powerful to allow the spreadsheet user to introduce additional mathematical operations of his or her own choice, operations that are not already part of the usual spreadsheet repertoire. Earlier versions of Excel used a less transparent and certainly much less powerful macro language, calledXLM, which will not be discussedhere. [Pg.375]

It can be shown that the detector D, which measures the intensity of interference as a function of M3 mirrors position (so depending on the optical path difference 5 between the two routes) records an interferogram which depends on inverse Fourier transform of emission spectrum of the source LS and on inverse Fourier transform of transparency (transmission) spectrum of the sample S (sample). After Fourier transform of detector D signal and some additional mathematical operations on detector signal the transmission (or optional absorption spectrum) spectrum of the sample S in known form is obtained. [Pg.158]

To extract infomiation from the wavefimction about properties other than the probability density, additional postulates are needed. All of these rely upon the mathematical concepts of operators, eigenvalues and eigenfiinctions. An extensive discussion of these important elements of the fomialism of quantum mechanics is precluded by space limitations. For fiirther details, the reader is referred to the reading list supplied at the end of this chapter. In quantum mechanics, the classical notions of position, momentum, energy etc are replaced by mathematical operators that act upon the wavefunction to provide infomiation about the system. The third postulate relates to certain properties of these operators ... [Pg.7]

As a general rule, mathematical operations involving addition and subtraction are carried out to the last digit that is significant for all numbers included in the calculation. Thus, the sum of 135.621, 0.33, and 21.2163 is 157.17 since the last digit that is significant for all three numbers is in the hundredth s place. [Pg.14]

In addition to the measured values and the analytical values (e.g. content, concentration), latent variables are included in the scheme. Latent variables can be obtained from measured values or from analytical values by means of mathematical operations (e.g. addition, subtraction, eigenanal-ysis). By means of latent variables and their typical pattern (represented in chemometric displays) special information can be obtained, e.g. on quality, genuineness, authenticity, homogeneity, origin of products, and health of patients. [Pg.41]

The BET approach is essentially an extension of the Langmuir approach. Van der Waals forces are regarded as the dominant forces, and the adsorption of all layers is regarded as physical, not chemical. One sets the rates of adsorption and desorption equal to one another, as in the Langmuir case in addition, one requires that the rates of adsorption and desorption be identical for each and every molecular layer. That is, the rate of condensation on the bare surface is equal to the rate of evaporation of molecules in the first layer. The rate of evaporation from the second layer is equal to the rate of condensation on top of the first layer, etc. One then sums over the layers to determine the total amount of adsorbed material. The derivation also assumes that the heat of adsorption of each layer other than the first is equal to the heat of condensation of the bulk adsorbate material (i.e., van der Waals forces of the adsorbent are transmitted only to the first layer). If it is assumed that a very large or effectively infinite number of layers can be adsorbed, the following result is arrived at after a number of relatively elementary mathematical operations... [Pg.177]

Although blocks are used to identify many types of mathematical operations, operations of addition and subtraction are represented by a circle, called a summing point. As shown in Figure 6, a summing point may have one or several inputs. Each input has its own appropriate plus or minus sign. A summing point has only one output and is equal to the algebraic sum of the inputs. [Pg.116]

Additionally, with the inclusion of computers as part of an instrument, mathematical manipulation of data was possible. Not only could retention times be recorded automatically in chromatograms but areas under curves could also be calculated and data deconvoluted. In addition, computers made the development of Fourier transform instrumentation, of all kinds, practical. This type of instrument acquires data in one pass of the sample beam. The data are in what is termed the time domain, and application of the Fourier transform mathematical operation converts this data into the frequency domain, producing a frequency spectrum. The value of this methodology is that because it is rapid, multiple scans can be added together to reduce noise and interference, and the data are in a form that can easily be added to reports. [Pg.31]

In Matlab the standard mathematical operators for addition (+) and subtraction (-) can be used directly with matrices. As with transposition, Matlab automatically calls the appropriate functions to perform the operations. ... [Pg.13]

In Excel, mathematical operations of one or more cells can be dragged to other cells. Since a cell represents one element of an array or matrix, the effect will be an element-wise matrix calculation. Thus, addition and subtraction of matrices are straightforward. An example ... [Pg.13]

In Subheading 2.3. the important class of vectors with continuous-valued components is described. A number of issues arise in this case. Importantly, since the objects of concern here are vectors, the mathematical operations employed are those applied to vectors such as addition, multiplication by a scalar, and formation of inner products. While distances between vectors are used in similarity studies, inner products are the most prevalent type of terms found in MSA. Such similarities, usually associated with the names Carbo and Hodgkin, are computed as ratios, where the inner product term in the numerator is normalized by a term in the denominator that is some form of mean (e.g., geometric or arithmetic) of the norms of the two vectors. [Pg.41]

Probability bounds analysis combines p-boxes together in mathematical operations such as addition, subtraction, multiplication, and division. This is an alternative to what is usually done with Monte Carlo simulations, which usually evaluate a risk expression in one fell swoop in each iteration. In probability bounds analysis, a complex calculation is decomposed into its constituent arithmetic operations, which are computed separately to build up the final answer. The actual calculations needed to effect these operations with p-boxes are straightforward and elementary. This is not to say, however, that they are the kinds of calculations one would want to do by hand. In aggregate, they will often be cumbersome and should generally be done on computer. But it may be helpful to the reader to step through a numerical example just to see the nature of the calculation. [Pg.100]

The p in pH is a mathematical operator. We have been dealing with several operators, including addition, subtraction, and square roots. The p-function... [Pg.232]

In addition to providing probability density functions, the wavefunction may also be used to calculate the value of a physical observable for that state. In quantum mechanics, a physical observable A has a corresponding mathematical operator A. When A satisfies the relation... [Pg.9]

For the respective quantum mechanical description of a molecule in a stationary state, a few additional aspects need to be addressed. First, the system state is characterized by a wavefunction VP, and system properties, such as the total energy or dipole moment, are calculated through integration of VP with the relevant operator in a distinct way. Note that an operator is simply an instruction to do some mathematical operation such as multiplication or differentiation, and generally (but not always) the order in which such calculations are performed affects the final result. Second, the wavefunctions V obey the Schrodinger equation ... [Pg.98]

For many mathematical operations, including addition, subtraction, multiplication, division, logarithms, exponentials and power relations, there are exact analytical expressions for explicitly propagating input variance and covariance to model predictions of output variance (Bevington, 1969). In analytical variance propagation methods, the mean, variance and covariance matrix of the input distributions are used to determine the mean and variance of the outcome. The following is an example of the exact analytical variance propagation approach. If w is the product of x times y times z, then the equation for the mean or expected value of w, E(w), is ... [Pg.122]

Of course, random measurement error is unavoidable when real data are used. If we now suppose A is a 50 x 50 data matrix (50 spectra digitized at 50 points) with some random error, the exact solution for Equation 4.2 would require 50 pairs or dyads of basis vectors, one row basis vector and one column basis vector for each pair. The additional 48 pairs of row and column vectors would be required to account for the random variation in A. Usually, we are not interested in building a model that includes the random errors. Fortunately, by using the appropriate mathematical operations, we can use our original two basis vectors to reduce the rank or dimensionality of A from 50 to 2 without any significant loss of information. This allows us to ignore the basis vectors that explain random error. This data compression capability of the PCA model is exploited frequently and is one of its most important features. [Pg.73]

Matrix algebra provides a powerful method for the manipulation of sets of numbers. Many mathematical operations — addition, subtraction, multiplication, division, etc. — have their counterparts in matrix algebra. Our discussion will be Umited to the manipulations of square matrices. For purposes of illustration, two 3x3 matrices will be defined, namely... [Pg.187]

Let us now examine briefly the approach provided by the structural analysis. An examination of Eq. (5) shows that the rate of change of the amount a< of each species depends not only on at but on the amounts a, of other species as well. Thus, changes in the amount of A, during the reaction affect the amounts of species there is strong coupling between the variables in the set of Eqs. (5). It is this coupling between the variables a,-and aj that is the source of the difficulties outlined above. We shall show that a monomolecular reaction system with n species A, can be transformed, by means of appropriate mathematical operations (which involve only addition and multiplication), into a more convenient equivalent monomolecular reaction system, with n hypothetical new species Bi, which has the property that changes in the amount 6, of any species B, does not affect the amount of any other species Bj. This means that there is a set of species Bi equivalent to the set of species Ai such that the variables b, in the rate equations for the B species are completely uncoupled. [Pg.211]

Spreadsheets are very powerful and convenient computational tools to illustrate mathematical relationships, and to solve numerical problems, as demonstrated in this book within the context of analytical chemistry. The original spreadsheets were poorly suited to perform some types of mathematical operations, such as iterations. Fortunately, the open structure of modern Excel allows the user to introduce extra features, by incorporating additional programs that accommodate particular needs. Macros are the most convenient and user-friendly way to give the spreadsheet such... [Pg.481]

The elementary mathematical operations are addition, subtraction, multiplication, and division. Some rules for operating on numbers with sign can be simply stated ... [Pg.5]

In addition to the four elementary arithmetic operations, there are some other important mathematical operations, many of which involve only one number. The magnitude, or absolute value, of a scalar quantity is a number that gives the size of the number irrespective of its sign. It is denoted by placing vertical bars before and after the symbol for the quantity. This operation means... [Pg.6]

Compare and contrast the multiplication/division significant figure rule to the significant figure rule applied for addition/subtraction mathematical operations. Explain how density can be used as a conversion factor to convert the volume of an object to the mass of the object, and vice versa. [Pg.30]

This very special operating point has an additional mathematical property. The gradient of the curve for possible steady state solutions in this point is equal to the gradient of the dynamic stability limit curve this way, both gradients are equal to the sensitivity in this point of operation. The best way to make use of this characteristic is by setting equal the steady state mass balance and the dynamic stability relationship in a suitable parameter presentation (c.f. Equ. 4-120). In a second step the term in the middle and the very right hand term are partially differentiated with respect to the steady state conversion Xs (c.f. Equ. 4-121). This represents the equality of both gradients, as the term dXs/dTo, which would have to be calculated to form the total derivative, cancels out. [Pg.128]

Modern software s controlled spectrophotometers allow not only acquisition and storage of registered spectra They are equipped in modules enable mathematical operation like addition, subtraction, multiplication as well as derivatisation. [Pg.255]


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Operators addition

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