Pivot elements

Pellerin, L. Lactate as a pivotal element in neuron-glia metabolic cooperation. Neurochem. Int. 43 331-338, 2003. 

The vector coordinates (1.13) occupy the array A(N,M). The nodule will replace the IP-th basis vector by the JP-th vector of the system. The pivot element is A(IP,JP). Since the module does not check whether A(IP,JP) is nonzero, you should do this when selecting the pivot. The information on the current basis is stored in the entries A(0,J) and A(I,0) as follows ... 

In this example we perform a transformatian, and hence enter "t". Then the row index and the column index of the pivot element are required. We enter "1,1" and the program returns the new coordinates ... 

Use back-substitution to determine the solution whose leading coefficient corresponds to the rightmost undetermined pivot element. Set this coefficient to unity. 

Append this solution vector to the set of equations and remove elements to the right of the new pivot element by Gauss elimination. 

While early work emphasized high symmetry of this ligand, the current trends may take advantage of asymmetric substitution to adapt the basic poly(l-pyrazolyl)borate framework to various enzyme-like tasks. This could be done by placing appropriate functionalities in such a manner that they will interact, as needed, with a transition metal (or metals). Achievement of these refinements of the ligand stem is likely to result from advances in boron chemistry, boron being here the pivotal element,... 

Pawlewski s rule, 46 periodic system, 25 perpendicular axes, theorem of, 436 phlegmatic liquids, 281 phosphorus pentoxide, purity of, 281 physico-chemical constants, xli piezometer, 58 pivotal element, 387... 

A multireaction version of Eq. (2.2-2) is obtainable by continuing the elimination above as well as below the pivotal elements this is the Gauss-Jordan algorithm of Section A.3. The final nonzero rows form a matrix a, here given by... 

The use of the largest available pivot element, Upk, in column k limits the growth of rounding error by ensuring that the multipliers ouk/ocpk) in Eq. (A.3-2) all have magnitude 1 or less. 

Carry out the following elementary operations to make the pivot element a%2 equal to 1 and the other elements in the second column equal to zero ... 

Editors, inviting important papers and directing the pivotal elements of their editorial life. 

Affinity determines the detectability (increases with affinity) and the specificity (increases with greater differences in affinity of antibodies for specific and non-specific antigen). This pivotal element of EIA must be understood for meaningful assay designs. Affinity can be expressed both in terms of reaction kinetics and thermodynamics. 

FIND THE ROW NUMBER OF THE PIVOT ROW AND THEN INTERCHANGE ROWS INORDER TO PLACE THE PIVOT ELEMENT ON THE DIAGONAL. 

C CHECK THAT THE PIVOT ELEMENT IS NOT TOO SMALL. OTHERWISE... 

A central issue in the attempt to establish a reliable database is the requirement of critically evaluated thermodynamic data for several key species. One such pivotal element is aluminum, which has an extensive literature of solubility and thermochemical data from which to choose, for each of the aqueous species or complexes. The aluminum species are fundamental to the calculation of solubility and reaction state with respect to many silicates and aluminum oxides and hydroxides and are principal components in numerous surface chemical reactions in the environment. Two key chapters in this volume address this fundamental problem Apps and Neil give a critical evaluation of the data for the aluminum system and Hem and Roberson present the kinetic mechanisms for hydrolysis of aluminum species. 

For example, in the first step of the triangularization of the jacobian matrix in Fig. 5-1, the submatrices 1, 2, 3, 4, 6, and 7 are considered. To initiate the elimination process, the largest element of column 1 of submatrices 1 and 2 of Fig. 5-1 is selected as the pivot element. If this element lies in submatrix 2, then submatrix 6 may be filled in the process of eliminating all elements above the pivot element. 

After the procedure has been applied to the last column of submatrix 2, the entire process is repeated for the next set of six submatrices namely, submatrices 4, 5, 7, 8, 10, and 11. If one or more of the pivot elements lie in submatrix 5, then submatrix 10 may be filled in the elimination process. 

We say that we have used the element aj i as the pivot element in this procedure. The left column is now as we want it to be. We now use the 22 element as the pivot element to clear the second column. We multiply the second row by j and replace the first row by the difference of the first row and the second to obtain... 

We now multiply the third row by j in order to use the 033 element as the pivot element. We subtract the third row from the second and replace the second row by the difference, obtaining... 

Rows and columns are rearranged that the absolutely largest element, the so-called Pivot element (-1.61), is placed in the left upper comer (Ab is omitted) ... 

The new first row obtained is divided by this Pivot element and new values of the elements in the first row are given as... 

Two types of C-pivot compounds were prominent during the past decades. These are shown in Fig. 1 as compounds 1-2 and 3-5. Both classes use glycerol as the pivot element, but in 1 and 2, the side arms are attached to the 1- and 2-positions, respectively. The former group was developed independently by Okahara and Gokel and their coworkers. The compounds represented by the 16-crown-5 structures 3-5 were studied extensively by Bartsch and his colleagues. The importance of the glycerol subunit for binding was recently demonstrated in the 16-crown-5... 

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