Row, defined

If we let columns in the design matrix define the constituents as follows 1, 2 define the substrate, columns 3, 4 define the amine co-substrate, and columns 5, 6 define the solvent, the first row in the design matrix in Table 11 would thus correspond to a selection of a substrate projected in the [( — ),( — )] quadrant, an amine from the [(—),( + )] quadrant, and a solvent from the [( + ),( + )] quadrant. The other rows define other combinations. The test items selected accordingly are shown in Table 13. To permit fair comparisons as to the performance of the reaction, it is necessary to adjust the experimental conditions for each system to yield an optimum result. The danger of using standardized conditions has been emphasized [1] and the arguments against such a technique are not repeated here. The conditions which afforded a maximum yield were determined by response surface techniques and these results are also shown in Table 13. 

Vc Reference crossflow velocity in gaps in a tube row (defined in Table 17.36), m/s, ft/s... 

For all OD polytypes (both subfamilies A and B) of Series 0, the PID has also a translational symmetry reminiscent of that relation between pairs of translationally equivalent rows defining a minimal rhombus ... 

The lateral interaction between the ID rows is definitely much weaker than along the ID rows. Does it mean that these patterns of alkylated molecules are not periodic in 2D Not necessarily, some of these ID systems will assemble into highly ordered 2D structures, while others will not. For instance, in the case of alkylated bis-ureaderivatives (with or without oligothiophenes), the molecular orientation in adjacent rows, defined by the orientation of the carbonyl groups, is not correlated [26]. 

There are many definitions for risk. Rowe defines risk as the potential for realization of unwanted, negative consequences of an event. Risk aversion is action taken to control or reduce risk. 

As regards the transition elements, the first row in particular show some common characteristics which define a substantial part of their chemistry the elements of the lanthanide and actinide series show an even closer resemblance to each other. 

The incidence matrix is an n A m matrix where the nodes (atoms) define the columns (n) and the edges (bonds) correspond to the rows [m). An entry obtains the value of 1 if the corresponding edge ends in this particular node (Figure 2-16),... 

Both tables, the atom and the bond lists, are linked through the atom indices. An alternative coimection table in the form of a redundant CT is shown in Figure 2-21. There, the first two columns give the index of an atom and the corresponding element symbol. The bond list is integrated into a tabular form in which the atoms are defined. Thus, the bond list extends the table behind the first two columns of the atom list. An atom can be bonded to several other atoms the atom with index 1 is connected to the atoms 2, 4, 5, and 6. These can also be written on one line. Then, a given row contains a focused atom in the atom list, followed by the indices of all the atoms to which this atom is bonded. Additionally, the bond orders are inserted directly following the atom in-... 

Similarly the stereobonds" can be defined and added to the bond list in the fourth column of the CT. A single bond acquires the value of 0 if it is not a "stereobond, 1 for np (a wedged bond). 4 for either up or down, and 6 for down (a basbed bond), The cisjtrans or E[Z configuration of a double bond is determined by the x,y.2 coordinates of the atom block if the value is 0, Tf it is 3, the double bond is either cis or tmns. In the bond block of our example (Figure 2-76), the stereocenter is set to 1 (up) at atom 6 (row 6, column 4 in the bond block), whereas the configurations of the double bonds are determined by the x,y coordinates of the atom block. 

The characteristic of a relational database model is the organization of data in different tables that have relationships with each other. A table is a two-dimensional consti uction of rows and columns. All the entries in one column have an equivalent meaning (c.g., name, molecular weight, etc. and represent a particular attribute of the objects (records) of the table (file) (Figure 5-9). The sequence of rows and columns in the tabic is irrelevant. Different tables (e.g., different objects with different attributes) in the same database can be related through at least one common attribute. Thus, it is possible to relate objects within tables indirectly by using a key. The range of values of an attribute is called the domain, which is defined by constraints. Schemas define and store the metadata of the database and the tables. 

Before we start to calculate the Laplacian matrix we define the diagonal matrix DEG of a graph G. The non-diagonal elements are equal to zero. The matrix element in row i and column i is equal to the degree of vertex v/. 

A matrix can be defined as a two-dimensional arrangement of elements (numbers, variables, vectors, etc.) set up in rows and columns. The elements a are indexed as follows ... 

If M is an n X n matrix with elements Mij, (the first subscript specifies the row number and the second subscript specifies the column number), then the product M x = y is a vector whose components (when subscripts i,j,k, etc. appear, they can take any value 1,2,...n unless otherwise specified) are defined as follows ... 

The ordered set of measurements made on each sample is called a data vector. The group of data vectors, identically ordered, for all of the samples is called the data matrix. If the data matrix is arranged such that successive rows of the matrix correspond to the different samples, then the columns correspond to the variables as in Figure 1. Each variable, or aspect of the sample that is measured, defines an axis in space the samples thus possess a data stmcture when plotted as points in that / -dimensional vector space, where n is the number of variables. 

The Rowe-Claxton empirical equation has been found to conform to many experimental studies of heat transfer in a packed bed, such as the reactor typically used in the catalytic processes described earlier. It is first necessary in this situation to define die voidage of the system, AV, where... 

Boundary conditions are special treatments used for internal and external boundaries. For example, the center line in cylindrical geometry is an internal boundary that is modeled as a plane of symmetry. External boundaries model the world outside the mesh. The outermost row of elements is often used to implement the boundary condition as shown in Fig. 9.13. The mass, stress, velocity, etc., of the boundary elements are defined by the boundary conditions rather than the governing equations. External boundary conditions are typically prescribed through user input. 

The most reliable recycle reactors are those with a centrifugal pump, a fixed bed of catalyst, and a well-defined and forced flow path through the catalyst bed. Some of those shown on the two bottom rows in Jankowski s papers are of this type. From these, large diameter and/or high speed blowers are needed to generate high pressure increase and only small gaps can be tolerated between catalyst basket and blower, to minimize internal back flow. 

The flow in an axial-flow eompressor is defined by the eontinuity, momentum, and energy equations. A eomplete solution to these equations is not possible beeause of the eomplexity of the flow in an axial-flow eompressor. Considerable work has been done on the effeets of radial flow in an axial-flow eompressor. The first simplifieation used eonsiders the flow axisym-metrie. This simplifieation implies that the flow at eaeh radial and axial station within the blade row ean be represented by an average eireumferen-tial eondition. Another simplifieation eonsiders the radial eomponent of the veloeity as mueh smaller than the axial eomponent veloeity, so it ean be negleeted. 

The arrangement of lattice points in a 2D lattice can be visualized as sets of parallel rows. The orientation of these rows can be defined by 2D Miller indices (hksee Figure lb). Inter-row distances can be expressed in terms of 2D Miller indices, analogous to the notation for 3D crystals. 

---