# Poles

Where Ui denotes input number i and there is an implied summation over all the inputs in the expression above A, Bj, C, D, and F are polynomials in the shift operator (z or q). The general structure is defined by giving the time delays nk and the orders of the polynomials (i.e., the number of poles and zeros of the dynamic models trom u to y, as well as of the noise model from e to y). Note that A(q) corresponds to poles that are common between the dynamic model and the noise model (useful if noise enters system close to the input). Likewise Fj(q) determines the poles that are unique for the dynamics from input number i and D(q) the poles that are unique for the noise N(t). [c.189]

Calculations of mutual locations of poles and zeros for these TF models allow to trace dynamics of moving of the parameters (poles and zeros) under increasing loads. Their location regarding to the unit circle could be used for prediction of stability of the system (material behavior) or the process stationary state (absence of AE burst ) [7]. [c.192]

The radial distance between poles. [c.635]

Distance between poles. [c.637]

To be easily attracted by the poles created perpendicularly to the defect, particles must satisfy precise conditions concerning dimensions, shape, density and magnetic property. [c.637]

The preceding upper limit to particle size can be exceeded if more than one bubble is attached to the particle, t A matter relating to this and to the barrier that exists for a bubble to attach itself to a particle is discussed by Leja and Poling [63] see also Refs. 64 and 65. The attachment of a bubble to a surface may be divided into steps, as illustrated in Figs. XIII-8a-c, in which the bubble is first distorted, then allowed to adhere to the surface. Step 1, the distortion step, is not actually unrealistic, as a bubble impacting a surface does distort, and only after the liquid film between it and the surface has sufficiently thinned does [c.474]

If the contact angle is zero, as in Fig. XIII-8e, there should be no tendency to adhere to a flat surface. Leja and Poling [63] point out, however, that, as shown in Fig. XIII-8/, if the surface is formed in a hemispherical cup of the same radius as the bubble, then for step la, the free energy change of attachment is [c.476]

J. Leja and G. W. Poling, Preprint, International Mineral Processing Congress, London, April 1960. [c.493]

The —(/i /2p)W (Rx) matrix does not have poles at conical intersection geometries [as opposed to W (R )] and furthermore it only appears as an additive term to the diabatic energy matrix (q ) and does not increase the computational effort for the solution of Eq. (55). Since the neglected gradient term is expected to be small, it can be reintroduced as a first-order perturbation afterward, if desired. [c.196]

A few substances such as iron and cobalt-nickel alloys irt ferromagnetic i.e. are strongly attracted to the poles of a magnet. Most other substances are diamagnetic, i.e. are very weakly repelled from the field of a magnet. Some ions and molecules are. however, paramagnetic, i.e. are very weakly attracted by a magnet. Thus if we hang a tube containing liquid oxygen (i.e. highly concentrated oxygen) just above the poles of a powerful electromagnet. the tube is pulled towards the magnet as shown thus [c.229]

Covering Conformational Space Poling [c.515]

Modification of the energy surface using poling. (Figure adapted from Smellie A S, S L Teig and P Towbin 5b. Poling Promoting Conformational Variation. Journal of Computational Chemistry 16 171-187.) [c.516]

Hie poling function typically adopts the following general functional form [c.517]

These results reveal the positive poles as having rather different characters from those previously attributed to them according to the older view they were very strongly jw-directing, a characteristic which is now seen to be much weaker than was thought. Lack of knowledge of partial rate factors led to earlier overestimates of the effect. Further consideration of the effects of these substituents by examining the way in which they influence the Gibbs functions of activation at m- and [c.169]

Further light on the substituent effects of nitrogen poles comes from [c.172]

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. [c.173]

That is why mutual location of poles and zeroes in the model is an important factor for consideration of fracture process and could serve for prediction of other mechanical properties. Investigation of material properties (stress, strength, strain, fetigue, and others) using square pulse load P is one of the important practical applications of AE testing. In the practical testing loads are created during period of time close to static loads and continue for several minutes. Registration of AE responses starts almost immediately after application of loads and is carried out for a fixed period of time (2-5 minutes). As IN as OUT are low frequency processes and are in time equilibrium state. That is why it is possible to use them for identification of materials. As an example, building up a dynamic model of the material is proposed using P and AE responses [6]. Experiments were carried out on two types of materials, which were presented by concrete specimens with different brittle and plastic properties. Cement - sand (cement stone) mixture was used for modeling of brittle material specimens. Hard concrete with plasticizing admixture was used for modeling of plastic material specimens. [c.191]

Figure 6. Location of poles and zeros for visco-elasto-plastic material (left) and brittle material (right) under loading close to fiacture. |

The quantum dynamies of bound and seattered systems is elosely eorrelated tlirough the eoneept of resonanees whieh are, heuristieally, quasi-bound states in whieh the system ean spend time [6, ], 8 and 9, 91, 92, 93 and 94]. More fonnally, resonanees are poles of the. S -matrix. (See seetion A3.11.) In a seattering proeess, the eross seetion typieally exhibits peaks as a fiinetion of the seattering energy, exaetly at (or near) the energy of the resonanees. For example, in a one-dimensional seattering off a double weh, the seattering probabilities exliibit sharp peaks when the eollision energy matehes the energy of the quasi-bound states in the well (figure B3.4.10). (See figure B3.4.11 for a realistie example.) [c.2306]

In Figure 2a several important stages in the circling are labeled with Arabic numerals. In the adjacent Figure 2b the values of 0(<1), ) are plotted as tj) increases continuously. The labeled points in the two Figures correspond to each other. (The notation is that points that represent zeros of tan 0 are marked with numbers surrounded by small circles, those that represent poles are marked by numbers placed inside squares, other points of interest that are neither zero nor poles are labeled by free numbers.) The zero value of the topological phase (0/2) arises from the fact that at the point 3 (at which ()> = it/2), 0 retiaces its values, rather than goes on to decrease. [c.132]

In this equation, the gradient term U(qx)Wtta (Rx)U(qx) Vr,z (Rx) = W > (R x) Vr x (Rx) still appears and, as mentioned before, introduces numerical inefficiencies in its solution. Even though a truncated Bom-Huang expansion was used to obtain Eq. (53), wJja (Rx), although no longer zero, has no poles at conical intersection geometries [as opposed to the full W (Rx) matrix]. [c.195]

The combined inductive and field effects of these poles do not produce strong discrimination between the m- and /i-positions in nitration m p for. NMe3+, and smaller for the protonated poles). This situation is in marked contrast to that produced by, say, the nitro group ( 9.1.3), and suggests that the —M effect is more discriminating between m- and -positions than is the — I effect. [c.169]

With the cations the closely similar reactivities of p- and wr-positions reveal a substituent effect which causes deactivation of the ring without much discrimination between/- and rw-positions such a substituent effect is seen as arising from the field effect, which on a simple picture of the transition state, and depending on the distribution of the charge in the transition state, could slightly favour either position. Support for this view is seen in the fact that the deactivating power of a positive pole falls off far less rapidly with distance from the ring than is the case with a neutral substituent (the case of PhCHjNOg and PhNOg (see below) should be compared with a corresponding pair of cations). Also, for a given degree of overall deactivation the poles produce more /-substitution than do neutral substituents nitrobenzene and phenyl trimethyl ammonium are of similar gross reactivity, but the latter produces considerably more of the /-isomer in nitration than does the former. [c.172]

See pages that mention the term

**Poles**:

**[c.338] [c.88] [c.637] [c.494] [c.2564] [c.110] [c.133] [c.133] [c.197] [c.20] [c.356] [c.516] [c.516] [c.517] [c.517] [c.524] [c.673] [c.167] [c.169] [c.172] [c.173] [c.173] [c.174] [c.174]**

Power supply cookbook (2001) -- [ c.0 ]

Introduction to computational chemistry (2001) -- [ c.258 ]