Black model

Kenneth J. Arrow, "On Mathematical Models in the Social Sciences," 1951, cited and discussed in Max Black, Models and Metaphors. Studies in Language and Philosophy (Ithaca Cornell University Press, 1962) 223225. 

Though not by Cloitre and Shinn. Black, Models andMetaphors, 37 quoted by Richard Boyd, "Metaphor and Theory Change What Is Metaphor a Metaphor For " 356408, in Ortony, Metaphor and Thought, 357. 

The Black model uses equation (7.20) to derive the price of an interest rate option. 

In 1976 Fisher Black presented a slightly modified version of the B-S model, using similar assumptions, for pricing forward contracts and interest rate options. Banks today employ this modified version, the Black model, to price swaptions and similar instruments in addition to bond and interest rate options, such as caps and floors. The bond options described in this section are options on bond futures contracts, just as the interest rate options are options on interest rate futures. 

The Black model refers to the underlying assets or commodity s spot price, S t). This is defined as the price at time t payable for immediate delivery, which, in practice, means delivery up to two days forward. The spot price is assumed to follow a geometric Brownian motion. The theoretical price, F t,T), of a futures contract on the underlying asset is the price agreed at time t for delivery of the asset at time T and payable on delivery. When t= T, the futures price equals the spot price. As explained in chapter 12, futures contracts are cash settled every day through a clearing mechanism, while forward contracts involve neither daily marking to market nor daily cash settlement. 

Each caplet can be priced individually and the results summed to give the total cap premium. The Black model assumes constant volatility, so banks use later models to price products for which this assumption is considered materially unrealistic. 

For microsurgery, a plastic disposable 60-mm Petri dish is used. Grafts between embryos are most easily made in a dish containing black modeling clay (Pastalina, Certified Nontoxic, Van Aken International, Rancho Cucamonga, CA 91730). The clay, available from many toy and art stores, is pressed into the bottom of the dish to a depth of 2-3 mm. To sterilize the clay, the dish is flooded for 20-30 s with 70% alcohol and rinsed in five changes of sterile saline. 

Figure 2.21. Nyquist impedance in the Randles model (model with C in black model with CPE in gray)...

The authors have made detailed investigations of the effect of coexisting gas on reaction (2.2) and found that the presence of H2O (water vapor) and small concentrations of SO2 substantially promote this reaction. Figure 2.8 shows the results of TPR of a carbon black (model soot) in loose contact with Pt/Si02 under different... 

The Black model refers to the underlying asset s or commodity s spot price, S t). This is defined as the price at time r payable for immediate delivery, which, in practice, means delivery up to two days forward. The spot price... 

The picture just painted is much too black. Models to be discussed in Section 3.1 do give very accurate accounts of the cohesive energies of most of the alkali halides, a good result obtained by allowing the ions to be less than rigid. The main feature of Figure 2— that most of the alkali halides have the sixfold-coordinated NaCl structure—comes out of those deformable-ion calculations as well. (Actually, the calculations predict that all alkali halides have the NaCl... 

Identification of the material properties as an estimation of transfer function (TF) for the black box model. In this case the problem of identification is solving according to the results of the input (IN) and output (OUT) actions. There is a transfer of notion of mathematical description of TF on characterization of the material. This logical substitution gives us an opportunity to formalize testing procedure and describe the material as a set of formulae, which can be used for quantitative and qualitative characterization of the materials. 

Figure 1. Dynamic model of testing of the material as a black box , where IN - loads and actions OUT - response of the material as measuring characteristics N - noise (combination of uncertain factors) ...

As a point of interest, it is possible to form very thin films or membranes in water, that is, to have the water-film-water system. Thus a solution of lipid can be stretched on an underwater wire frame and, on thinning, the film goes through a succession of interference colors and may end up as a black film of 60-90 A thickness [109]. The situation is reminiscent of soap films in air (see Section XIV-9) it also represents a potentially important modeling of biological membranes. A theoretical model has been discussed by Good [110]. 

The model of non-mteracting hannonic oscillators has a broad range of applicability. Besides vibrational motion of molecules, it is appropriate for phonons in hannonic crystals and photons in a cavity (black-body radiation). 

Increased trust in pattern recognition The active user involvement in the data mining process can lead to a deeper understanding of the data and increases the trust in the resulting patterns. In contrast, "black box" systems often lead to a higher uncertainty, because the user usually does not know, in detail, what happened during the data analysis process. This may lead to a more difficult data interpretation and/or model prediction. 

Fig. 1. Atomic stmctuial models of (a), graphite, and (b), carbon black.

Figure 3 The mimmum energy conformation of the off-lattice 46-mer P-baiTel model. Hydrophobic residues are in gray, hydrophilic residues in black, and neutral residues are white. (Adapted from Ref. 44.)...

Figure 1 Chemical structure and space-filling representation of a phosphatidylcholine, DPPC. Different parts of the molecule are referred to by the labels at the left together the choline and phosphate are referred to as the headgroup, which is zwitteriomc. In the space-filling model, H atoms are white, O and P gray, and C black. (From Ref. 55.)...

Tsai et al. have also used RAIR to investigate reactions occurring between rubber compounds and plasma polymerized acetylene primers deposited onto steel substrates [12J. Because of the complexities involved in using actual rubber formulations, RAIR was used to examine primed steel substrates after reaction with a model rubber compound consisting of squalene (100 parts per hundred or phr), zinc oxide (10 phr), carbon black (10 phr), sulfur (5 phr), stearic acid (2 phr). 

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