Ordered, consistently

Backward Analysis In this type of analysis, the discrete solution is regarded as an exact solution of a perturbed problem. In particular, backward analysis of symplectic discretizations of Hamiltonian systems (such as the popular Verlet scheme) has recently achieved a considerable amount of attention (see [17, 8, 3]). Such discretizations give rise to the following feature the discrete solution of a Hamiltonian system is exponentially close to the exact solution of a perturbed Hamiltonian system, in which, for consistency order p and stepsize r, the perturbed Hamiltonian has the form [11, 3]... 

Because their rates of substitution tue convenient for study, most work has been done with platinum complexes, and for lhe.se it is found that ligands can be airanged in a fairly consistent order indicating their relative abilities to labilize ligands irans to themselves ... 

Here the determination of the column of eigenvalues for the ith class, from eqs. (21) and (22) provides a consistent ordering of the rows without the need to appeal to normalization and orthogonality conditions. 

Numerical solution for resulting function fok is presented on Fig. 7. Being able to find numerical solutions for functions fik and f k for a given order parameter configuration A(t) one can find self-consistent order parameter configuration satisfying to Eq. (41) which is presented on Fig. 6. 

Are the points of comparison/contrast presented in a logical, consistent order that the reader can follow easily ... 

The book is divided into three sections consisting of chapters arranged in a consistent order, though some chapters could be put in the second or third section. On the other hand, a uniform treatment and style cannot be anticipated in the book that represents the efforts of many authors. Despite this, the presented works provide the comprehensive, high standard and modern study on the structure, investigations, preparation of inorganic sorbents, their numerous applications and deal with the adsorption on new and chemically modified inorganic solids. 

The consequence of a large Schmidt number, common in liquids, is that convection dominates over diffusion at moderate and even relatively low Reynolds numbers (assuming consistent order of magnitude in the terms). In gases these effects are of the same order. On the other hand, heat transfer in low-viscosity liquids by convection and conduction are the same order since the Prandtl number is approximately 1. In highly viscous fluids where the Prandtl number is large, heat transfer by convection predominates over conduction, provided the Reynolds number is not small. The opposite is true for liquid metals, where the Prandtl number is very small, so conduction heat transfer is dominant. 

Employing the solution for the ion concentration distribution and carrying out the quadratures in Eq. (6.2.19), we find, to consistent order, that... 

The quantity o> in (4.11) is called the relaxation factor. We observe that, for CO = 1, this iterative method reduces to the Gauss-Seidel iterative method of (4.8)-(4.8 ). For reasons of brevity, we shall say that a matrix G, which is cyclic of index 2, is consistently ordered [52] if it is the form of (4.10). With the concept of a consistent ordering. Young [52] established the following general relationship between the eigenvalues A of the successive overrelaxation matrix... 

Theorem 3. Let A he a symmetric and positive definite matrix, and let its corresponding Jacobi matrix M he cyclic of index 2 and consistently ordered. Then... 

We remark that, by using the fact that the Jacobi matrix M is cyclic of index 2 and consistently ordered, the inequality of (4.9) can be sharpened to... 

It is clear that no consistent order exists for the effectiveness of the groupings and careful consideration has to be given to all the possible influences on the force field in predicting the nature of a particular system ... 

The book is divided into two volumes, consisting of chapters arranged in a consistent order, though some chapters could be connected with the industrial (volume I) or environmental (volume II) fields. In order to highlight for potential readers all topics and considerations each volume of the monograph comprises the complete contents and the complete list of authors, but includes its own subject index only. It should be emphasized that all contributions were subjected to a rigorous review process, with almost all papers receiving two reviews from a panel of approximately fifty reviewers. 

Now, only the term linear in ti2 requires special attention in order to maintain a consistent order of 0(c ). For this purpose, we need to study the Taylor expansion of fi2 in Eq. (3.217), for which we first need to expand the distance... 

Table 3.2 presents a summary of our findings. Prom this table, it can be seen that the PRESS statistic selects a model order which is close to the best order obtained using the complete data set (M = 1000) starting with M — 400. However, the FPE criterion does not select a model order close to the best order until M = 800. In addition, it is interesting to note that with the smallest data set examined (M = 200), the PRESS statistic also manages to select the best low order model ni = 3), according to our earlier analysis, but this was not the case for the FPE criterion. These results show that, for this example, the PRESS statistic provides a consistent order estimate and is more robust than the FPE criterion in terms of sensitivity to data length effects. 

Delivety lead time and flexibility Delivety reliability and consistency Order fill... 

A tailored supply chain governed hy consistent order winning and qualifying criteria. 

The relative reactivities of the substrates follow a consistent order Acyl halides are most reactive, followed by anhydrides, then esters, and finally the amides, which are least reactive. 

Data will typically be represented in tabular form where we label columns by data nodes, D, and rows )y D x V pairs, i.e., joins. Entries in the table are represented as indexed lists of values. The order in which a dataset is tabulated does not actually provide any additional information, but in order to be processed by the instantiation algorithm, must be consistent with the pattern, in the following sense the order of columns must respect node order <, i.e., if A < B then the corresponding columns are in that order and for each row D, v), we require that v appears in column D m a. preceding row. In the following, we will assume that a consistent order has been chosen for a dataset, and refer to it as a P-table (see Table 1 for an example). 

The total energies for all the structures are AF-llb, AF-11 < AF-111 < AF-1 AF-IIb and AF-II have almost the same total energy. From carefiil analysis of structure, AF-IIb is obtained by rotating the second and the fourth layers of AF-llb by 90° around the z axis. AF-II and AF-IIb have alternate Ag-Se-Bi-Se-... chains in all periodic directions, but no Ag-Se-Bi-Se-... chains can be found in AF-I while it is only presented in the c direction in AF-III. The total energy is lower when more alternate Ag-Bi-Se chains existed. Furthermore, the AF-II stmcture has the consistent order of layer alternately stacking (Ag-Se-Bi-Se-...) with the intermediate-temperature phase of AgBiSe2 in the direction (111) (Fig. 7.3b, c). Since the lattice difference between AF-II and rhombohedral is less than 2 % (Table 7.1), the differences of energy and electron stmcture between them are also small, AE 7.4 meV/f.u. (f.u. = formula unit), where the electron stmcture is... 

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