Dyadic numbers

C.T. Tai. Dyadic Green functions in electromagnetic theory. IEEE Press Series on Electromagnetic Waves, Second Edition, ISBN 0-7803-0449-7, IEEE Order Number PC0348-3, 1993. 

Having completed the decomposition and reconstruction of a function at a finite number of discrete values of scale, let us turn our attention to the discretization of the translation parameter, u, dictated by the discrete-time character of all measured process variables. The classical approach, suggested by Meyer (1985-1986), is to discretize time over dyadic intervals, using the sampling interval, t, as the base. Thus, the translation parameter, u, can be expressed as... 

Besides the intake interview, which can help gather information, there are a number of assessment measures for determining the quality of an important interpersonal relationship. The questions on these measures generally ask about things like communication styles, satisfaction in the relationship, joint decision making, and in some cases, abusive behavior. Two of the most well-known measures are the Dyadic Adjustment Scale (Spanier, 1976) and the Marital Satisfaction Inventory (Snyder, 1979). Therapists and counselors also may choose to interview couples together (with the consent of client and partner), and some therapists may recommend couples therapy (see Chapter 5) as part of the overall approach to treatment if deemed appropriate to help the client. Relationship assessments can yield important information that may be useful when working with couples. 

Likewise, the Tm values of aromatic polyamides (aramids) arc higher than those of the corresponding aliphatic polyamides (nylons). The Tm of monadic and dyadic nylons decreases as the number of methylene groups in the chain increases. Thus the Tm values decrease stepwise as the number of... 

The fundamental quantities in elasticity are second-order tensors, or dyadicx the deformation is represented by the strain thudte. and the internal forces are represented by Ihe stress dyadic. The physical constitution of the defurmuble body determines ihe relation between the strain dyadic and the stress dyadic, which relation is. in the infinitesimal theory, assumed lo be linear and homogeneous. While for anisotropic bodies this relation may involve as much as 21 independent constants, in the euse of isotropic bodies, the number of elastic constants is reduced lo two. 

The basic properties of the aromatic amines decrease with the number of radicles introduced the primary aromatic amines are stable the secondary aromatic amines are decomposed by water and the tertiary aromatic amines are unstable. In organic chemistry, compounds containing the monadic group NH2 are called amines or amides and compounds with the dyadic group NH are called imides. The existence of compounds like... 

This principle as originally stated by Curie in 1908, is quantities whose tensorial characters differ by an odd number of ranks cannot interact (couple) in an isotropic medium. Consider a flow J, with tensorial rank m. The value of m is zero for a scalar, it is unity for a vector, and it is two for a dyadic. If a conjugate force A) also has a tensorial rank m, than the coefficient Ltj is a scalar, and is consistent with the isotropic character of the system. The coefficients Lij are determined by the isotropic medium they need not vanish, and hence the flow J, and the force A) can interact or couple. If a force A) has a tensorial rank different from m by an even integer k, then Ltj has a tensor at rank k. In this case, Lfj Xj is a tensor product. Since a tensor coefficient Lt] of even rank is also consistent with the isotropic character of the... 

The dyadic fractions are those which have a finite representation as binary numbers. Rationals which are not dyadic have a binary fraction representation which after a while repeats some pattern to infinity. Irrationals do not have any such pattern in their infinite binary representation nThis is not quite true, because some schemes have special rules at the ends which allow for definition of new vertices which don t have old vertices on both sides. Others do not, and then each new polygon covers a slightly shorter parametric range than the previous one. This distinction can be ignored until we come to the chapter on end-conditions at page 175. 

The Hadamard transform is an example of a generalized class of a DFT that performs an orthogonal, symmetric, involuntary linear operation on dyadic (i.e., power of two) numbers. The transform uses a special square matrix the Hadamard matrix, named after French mathematician Jacques Hadamard. Similarly to the DFT, we can express the discrete Hadamard transform (DHT) as... 

Only six coefficients are required to characterize the coupling dyadic at the center of reaction. But then an additional three scalars are required to specify the location of this point, so that the total number of independent scalars required for a complete characterization is still nine. Similarly, three scalars suffice for the translation dyadic if we refer them to the principal axes of translation [see Eq. (44)], but then three additional scalars (e.g., an appropriate set of Eulerian angles) are required to specify the orientations of these axes. So it comes down to the same thing—namely, that six scalars are required. The same is true of the rotation dyadic at any point, and of the coupling dyadic at the center of reaction. 

A systematic investigation of the number and nature of the nonzero coefficients of the symbolic force dyadic and torque pseudodyadic operators may be made for bodies possessing various types of geometric symmetry. 

From the full WPT we can generate a large number of possible redundant subtrees, or arbitrary WP trees (called wavelet bases). In fact, the total number of two-way (dyadic) bases is at least (2-)" for a tree depth equal to niev. For example, a dyadic WPT with tree depth niev = 12 has a library of at least 4.2 xlO bases The WPT has an important advantage compared with the WT because fast algorithms exist for the efficient search of the best wavelet basis, based on the minimisation of a cost function such as an entropy criterion. 

For the dyadic case (m = 2), Npar = Nf/2 - 1. For short compact wavelets (i.e. small Nf), the number of parameters is not a large number and, consequently, the search space has a low dimensionality. Furthermore we shall show that, experimentally, the hyper-surface in the search space is smooth. 

Likewise, the T is lower when an odd number of methylene groups are present in dyadic nylon. The of nylon 66 is 538 K, while the of nylon 56 is 496 K (Table 7.2). 

NH(CH2)5C0 4 with regular sequences of six carbon atoms between the nitrogen atoms. A nylon with two numbers is termed dyadic indicating that it contains both dibasic acid (or acid chloride) and diamine moieties, in which the first number represents the diamine and the second the diacid used in the synthesis. The monadic nylons have one number, indicating that synthesis involved only one type of monomer. This terminology means that a poly (a-amino acid) would be nylon-2. 

Monadic (or AB) polyamides are based upon a single repeating lactam with, on the one end an amine reactive group, and on the other end a carboxylic acid group. The lactam thus reacts with itself and the number describes the lactam involved. Dyadic (or AABB) polyamides are based on the reaction of a diamine and a diacid. The diamine and the diacid react alternatively with each other in a salt solution. In regards to the nomenclature, the first number describes... 

Because of the generic nature of Fig. 1, no details of the interconnection between the VPU and the memory are shown. Still, these details are very important for the effective speed of a vector operation when the bandwidth between the memory and the VPU is too small, it is not possible to take full advantage of the VPU because it has to wait for operands and/or has to wait before it can store results. When the ratio of arithmetic-to-load/store operations is not high enough to compensate for such situations, severe performance losses may be incurred. The influence of the number of load/store paths for the dyadic vector operation c = a- -b (a, b, and c vectors) is depicted in Fig. 2. 

---