Row equivalent

Yet it is generally accepted today that the elements following actinium involve 5/ energy levels, identifying them as the seventh-row equivalents of the lanthanides. 

We can use elementary row operations, also known as elementary matrix operations to obtain matrix [g p] from [A c]. By the way, if we can achieve [g p] from [A c] using these operations, the matrices are termed row equivalent denoted by X X2. To begin with an illustration of the use of elementary matrix operations let us use the following example. Our original A matrix above can be manipulated to yield zeros in rows II and III of column I by a series of row operations. The example below illustrates this ... 

These two matrices (original and final) are row equivalent because by using simple row operations the right matrix was formed from the left matrix. The final matrix is equivalent to a set of equations as shown below ... 

In general, the nucleophilicity pattern is in accord with the soft or Class b requirements of platinum(II). Ligands with light element donors, N, O and F, are considerably less effective than their second-row equivalents. Thus, F" < Cl- < Br < I- R20 < R2S < R2Se and R3N R3P > R3As. Carbon donors, e.g. CNR and CN , are good nucleophiles towards Ptn. The extent to which the nucleophilicity is modified by the substituents attached to the donor has not yet been evaluated thoroughly. Probably the most extensive set of data refers to sulfur donors, the values... 

A set of reactions is linearly independent if no reaction in the set can be written as a linear combination of the other reactions in the set. linear independence of reactions is equivalent to.linear independence of the rows of v. The rank of a matrix is the number of linearly independent rows (equivalently co.lumns) of the matrix., so the rank of v is the number of. linearly Independent reactions in the network. 

Non-Double-Couple Earthquakes, Fig. 1 Three source types commonly used in decomposing moment tensors (from left to righi) isotropic, double couple (DC), and compensated linear-vector dipole (CLVD). Top row equivalent force systems, in principal-axis... 

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. 

For any sizeable system the Slater determinant can be tedious to write out, let alone the equivalent full orbital expansion, and so it is common to use a shorthand notation. Various notation systems have been devised. In one system the terms along the diagonal of the matrix are written as a single-row determinant. For the 3x3 determinant we therefore have ... 

For each M , Ml combination for which one can write down only one product function (i.e., in the non-equivalent angular momentum situation, for each case where only one product function sits at a given box row and column point), that product function itself is one of the desired states. For the p2 example, the piapoot and piap.ia (as well as their four other Ml and Ms "mirror images") are members of the 3p level (since they have Ms = 1) and IpiapiPI and its Ml mirror image are members of the level (since they have Ml... 

The cofactor A , of the element is the signed minor of determined by the rule A = (—The value of Al is obtained by forming any of the equivalent expressions 2- =i OijAij, Z =i /A , where the elements must be taken from a single row or a single column of A. 

Figure 6-5(b) is a case for a reaction of unity, that is, all the pressure rise is in the rotor, with the stator blades acting only as guide vanes to deflect the gas. A reaction of unity is aerodynamically the equivalent of R = 0 or impulse, as shown at Figure 6-5(f) since it corresponds to an interchange of the moving and fixed blade row. 

The.se two approaches may be shown to be thermodynamically equivalent and, given the same assumptions, will lead to identical results for the state downstream of a cooled row (if the input conditions are the same—see the published discussion of Ref. 7 ). But the Young and Wilcock method gives a fuller understanding of the details of the cooling process. 

The actual load on the derrick is the sum of the bottom row in Table 4-4. The equivalent load is four times the force in leg A, which is the largest load of all four legs. 

The structure of the group 0[H] implies that two configurations of the form (1.38) are equivalent or nonequivalent with respect to G [ft] depending on whether the superfigures determined by the r rows form equivalent or nonequivalent configurations with respect... 

Moving down in a column is equivalent in many respects to moving to the left in the periodic table. Since we find basic properties predominant at the left of the periodic table in a row, we can expect to find basic properties increasing toward the bottom of a column. Thus the base strength of the alkaline earth hydroxides is expected to be largest for barium and strontium. The greatest acid strength is expected for beryllium hydroxide. 

It will be seen that this is antisymmetric, for interchanging any two electrons is equivalent to interchanging two rows of the determinant, and hence to changing its sign. 

The number of singular vectors r is at most equal to the smallest of the number of rows n or the number of columns p of the data table X. For the sake of simplicity we will assume here that p is smaller than n, which is most often the case with measurement tables. Hence, we can state here that r is at most equal to p or equivalently that rindependent measurements in X. Independent measurements are those that cannot be expressed as a linear combination or weighted sum of the other variables. 

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