Factors returns

Both the time of analysis and experimental design may affect the results. An explanation for the increase in adenylates under the conditions of our experiment is still needed. Since both ATP alone and total adenylate concentrations have increased, it does not appear that a shift in phosphorylation can account for the increases. The decrease in photosynthesis and increase in adenylates occur during the same time period and both factors return to normal after 21 hr. From previous research we know that the photosynthetic levels of ozonated pinto bean foliage decrease immediately after ozone exposure even when symptoms do not develop ( ). This does not hold true for the adenylate or respiration responses. Therefore, it appears that the ozone-initiated increase in adenylates is not correlated directly to the photosynthetic response. The increase in respiration persists when adenylate content and photosynthetic rates have returned to normal. Impaired mitochondrial function appears to be a secondary response more closely related to symptom development. 

The total-cost method does not in general provide a satisfactory means for making most insulation investment decisions, since an economic return on investment is required by investors and the method does not properly consider this factor. Return on investment is considered by Rubin ( Piping Insulation—Economics and Profits, in Practical Considerations in Piping Analysis, ASME Symposium, vol. 69,1982, pp. 27-A6). The incremental method used in this reference requires that each incremental in of insulation provide the predetermined return on investment. The minimum thickness of installed insulation is used as a base for calculations. The incremental installed capital cost for each additional V2 in of insulation is determined. The energy saved for each increment is then determined. The value of this energy varies directly with the temperature level [e.g., steam at 538°C (1000°E) has a greater value than condensate at 100°C (212°F)]. The final increment selected for use is required either to provide a satisfactory return on investment or to have a suitable payback period. 

The data that can go into computing factor returns will of course depend on what the factors are. It can include bond and index level data as well as currency exchange rates. Assume that we have the factor return series. To construct covariances, we could postulate that the underlying random processes are time stationary and compute covariances using equally weighted factor returns. We actually know that mar-... 

Specific returns are residual returns not explained by common factors. Common factors returns are typically larger than specific returns for higher quality investment-grade instruments this is no longer the case in the lower portion of the investment grade segment and for high-yield instruments. 

Common factors, returns, exposures, and a specific risk model—everything is there except for one last critical ingredient the covariance matrix. Building a sensible covariance matrix for more than a few factors is a complicated task that involves solving several problems. 

Factor return series often have different lengths, some series starting earlier than others. Return series can also have holes. As a result, what works well for two factors is here useless. That is, filling the factor covariance matrix row i and column j using the usual formula produces a non-positive definite matrix. A statistical approach known as the EM algorithm is the conventional workaround. Details on the algorithm can be found in Dempster, Laird, and Rubin, and for the purpose of this discussion, we only need to know that there exists a tool that can use incomplete series to produce an optimal estimate of the true covariance matrix. 

With a model that has on the order of 180 factors, we need to solve for over 16,000 covariances. Factor returns series include, in many cases, less than 30 to 40 periods. With such a small sample size compared to the number of factors, we have a severely underdetermined problem and are virtually assured that the covariance forecasts will show a large degree of spurious linear dependence among the factors. One consequence is that it becomes possible to create portfolios with artificially low risk forecasts. The structure of these portfolios would be pecu-... 

Factor returns, hereafter called STB returns, are computed by regressing government bond s returns or LIBOR/swap key rate returns onto the shift, twist, and butterfly principal components. STB returns and other factor returns then go into the computation of the covariance matrix of all common factors. The shift, twist, and butterfly shapes are stable over time and only need to be reestimated periodically. 

An m -factor returns model takes the following form ... 

If we multiply both sides of a thermochemical equation by a factor n, then AH Note that H is an extensive quantity, must also change by the same factor. Returning to the melting of ice... 

Add the Boltzmann factor to the accumulated sum of Boltzmann factors and the potent energy contribution to its accumulated sum and return to step 1. 

Cyclic conjugation although necessary for aromaticity is not sufficient for it Some other factor or factors must contribute to the special stability of benzene and compounds based on the benzene ring To understand these factors let s return to the molecular orbital description of benzene... 

Cholesterol is biosynthesized in the liver trans ported throughout the body to be used in a va riety of ways and returned to the liver where it serves as the biosynthetic precursor to other steroids But cholesterol is a lipid and isn t soluble in water How can it move through the blood if it doesn t dis solve in if The answer is that it doesn t dissolve but IS instead carried through the blood and tissues as part of a lipoprotein (lipid + protein = lipoprotein) The proteins that carry cholesterol from the liver are called low density lipoproteins or LDLs those that return it to the liver are the high-density lipoproteins or HDLs If too much cholesterol is being transported by LDL or too little by HDL the extra cholesterol builds up on the walls of the arteries caus mg atherosclerosis A thorough physical examination nowadays measures not only total cholesterol con centration but also the distribution between LDL and HDL cholesterol An elevated level of LDL cholesterol IS a risk factor for heart disease LDL cholesterol is bad cholesterol HDLs on the other hand remove excess cholesterol and are protective HDL cholesterol IS good cholesterol... 

Returning to the data of Table 7.1, it is apparent that there is a good deal of variability among the r values displayed by various systems. We have already seen the effect this produces on the overall copolymer composition we shall return to the matter of microstructure in Sec. 7.6. First, however, let us consider the obvious question. What factors in the molecular structure of two monomers govern the kinetics of the different addition steps This question is considered in the few next sections for now we look for a way to systematize the data as the first step toward an answer. 

Figure 2.1 served as the basis for our initial analysis of viscosity, and we return to this representation now with the stipulation that the volume of fluid sandwiched between the two plates is a unit of volume. This unit is defined by a unit of contact area with the walls and a unit of separation between the two walls. Next we consider a shearing force acting on this cube of fluid to induce a unit velocity gradient. According to Eq. (2.6), the rate of energy dissipation per unit volume from viscous forces dW/dt is proportional to the square of the velocity gradient, with t]q (pure liquid, subscript 0) the factor of proportionality ... 

The elasticity of a fiber describes its abiUty to return to original dimensions upon release of a deforming stress, and is quantitatively described by the stress or tenacity at the yield point. The final fiber quaUty factor is its toughness, which describes its abiUty to absorb work. Toughness may be quantitatively designated by the work required to mpture the fiber, which may be evaluated from the area under the total stress-strain curve. The usual textile unit for this property is mass pet unit linear density. The toughness index, defined as one-half the product of the stress and strain at break also in units of mass pet unit linear density, is frequentiy used as an approximation of the work required to mpture a fiber. The stress-strain curves of some typical textile fibers ate shown in Figure 5. 

In air, PTFE has a damage threshold of 200—700 Gy (2 x 10 — 7 x 10 rad) and retains 50% of initial tensile strength after a dose of 10" Gy (1 Mrad), 40% of initial tensile strength after a dose of 10 Gy (10 lad), and ultimate elongation of 100% or more for doses up to 2—5 kGy (2 X 10 — 5 X 10 rad). During irradiation, resistivity decreases, whereas the dielectric constant and the dissipation factor increase. After irradiation, these properties tend to return to their preexposure values. Dielectric properties at high frequency are less sensitive to radiation than are properties at low frequency. Radiation has veryHtde effect on dielectric strength (86). 

For most purposes only the Stokes-shifted Raman spectmm, which results from molecules in the ground electronic and vibrational states being excited, is measured and reported. Anti-Stokes spectra arise from molecules in vibrational excited states returning to the ground state. The relative intensities of the Stokes and anti-Stokes bands are proportional to the relative populations of the ground and excited vibrational states. These proportions are temperature-dependent and foUow a Boltzmann distribution. At room temperature, the anti-Stokes Stokes intensity ratio decreases by a factor of 10 with each 480 cm from the exciting frequency. Because of the weakness of the anti-Stokes spectmm (except at low frequency shift), the most important use of this spectmm is for optical temperature measurement (qv) using the Boltzmann distribution function. 

Compared to the expression of equation 5, having no axial current flow, power output is reduced by the factor 1/(1 + /5 ). This is because part of the kinetic and thermal energy of the gas generates the axial current j which flows upstream in the gas and returns through the electrode wads. This current does not flow through the external load and so represents a loss. 

Contraction of muscle follows an increase of Ca " in the muscle cell as a result of nerve stimulation. This initiates processes which cause the proteins myosin and actin to be drawn together making the cell shorter and thicker. The return of the Ca " to its storage site, the sarcoplasmic reticulum, by an active pump mechanism allows the contracted muscle to relax (27). Calcium ion, also a factor in the release of acetylcholine on stimulation of nerve cells, influences the permeabiUty of cell membranes activates enzymes, such as adenosine triphosphatase (ATPase), Hpase, and some proteolytic enzymes and facihtates intestinal absorption of vitamin B 2 [68-19-9] (28). 

As can be seen from this analysis, the natural gas feedstock and capital charges amount to over 93% of the total production cost before return on investment. Therefore, energy consumption and capital investment are the key factors in determining ammonia production profitabiUty. 

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