Envision

An illustrative example generates a 2 x 2 calibration matrix from which we can determine the concentrations xi and X2 of dichromate and permanganate ions simultaneously by making spectrophotometric measurements yi and j2 at different wavelengths on an aqueous mixture of the unknowns. The advantage of this simple two-component analytical problem in 3-space is that one can envision the plane representing absorbance A as a linear function of two concentration variables A =f xuX2). 

We envision a potential energy surface with minima near the equilibrium positions of the atoms comprising the molecule. The MM model is intended to mimic the many-dimensional potential energy surface of real polyatomic molecules. (MM is little used for very small molecules like diatomies.) Once the potential energy surface iias been established for an MM model by specifying the force constants for all forces operative within the molecule, the calculation can proceed. 

After diagonalization of the EHT matrix, the lowest 4 orbitals have an energy sum of about —70 eV. The electronic energy for these doubly occupied orbitals is 2(—70) = — 140 eV. The energy gain of the molecule relative to its atoms is —140 — ( — 110) = —30eV = —690 kcal mol (1 eV = 23 kcal mol ) therefore, the molecule is stable relative to its atoms. We can envision an energy cycle with three steps (Eig. 7-5) ... 

Most of the envisioned practical applications for nonlinear optical materials would require solid materials. Unfortunately, only gas-phase calculations have been developed to a reliable level. Most often, the relationship between gas-phase and condensed-phase behavior for a particular class of compounds is determined experimentally. Theoretical calculations for the gas phase are then scaled accordingly. 

These ZEV vehicles are envisioned to be electric battery vehicles (see Batteries, secondary cells-other). The California fleet average standards are to be met by spiling combinations of various classes of vehicles. Manufacturers must certify their new cars in one of the categories shown. The sales weighted average for a given year must then be at or below the standard shown in Table 8. 

Biomedical Applications. In the area of biomedical polymers and materials, two types of appHcations have been envisioned and explored. The first is the use of polyphosphazenes as bioinert materials for implantation in the body either as housing for medical devices or as stmctural materials for heart valves, artificial blood vessels, and catheters. A number of fluoroalkoxy-, aryloxy-, and arylamino-substituted polyphosphazenes have been tested by actual implantation ia rats and found to generate Httle tissue response (18). 

Many classes of second-order material appHcations can be envisioned by noting the sinusoidal nature of electromagnetic radiation and rewriting equation 2... 

Air- or dry-laid pulp machinery can be envisioned as a series of forming-unit modules. Each module consists of two to four perforated dmms through which airborne fibers are circulated and further agitated by mechanical beaters placed in close proximity to the inner dmm surfaces. As the fibers... 

Because of the advent of improved analytical techniques, together with the tools of biotechnology, a new generation of products is envisioned with silk. 

Computers. It is difficult to envision how technical service in the chemical industry could be carried out without computer technology (qv). 

Euleria.n Models. Of the Eulerian models, the box model is the easiest to conceptualize. The atmosphere over the modeling region is envisioned as a well-mixed box, and the evolution of pollutants in the box is calculated following conservation-of-mass principles including emissions, deposition, chemical reactions, and atmospheric mixing. 

As shown in equation 12, the chemistry of this developer s oxidation and decomposition has been found to be less simple than first envisioned. One oxidation product, tetramethyl succinic acid (18), is not found under normal circumstances. Instead, the products are the a-hydroxyacid (20) and the a-ketoacid (22). When silver bromide is the oxidant, only the two-electron oxidation and hydrolysis occur to give (20). When silver chloride is the oxidant, a four-electron oxidation can occur to give (22). In model experiments the hydroxyacid was not converted to the keto acid. Therefore, it seemed that the two-electron intermediate triketone hydrate (19) in the presence of a stronger oxidant would reduce more silver, possibly involving a species such as (21) as a likely reactive intermediate. This mechanism was verified experimentally, using a controlled, constant electrochemical potential. At potentials like that of silver chloride, four electrons were used at lower potentials only two were used (104). 

A pipelined floating-point multiply unit might accomplish a floating-point multiply by performing four independent suboperations, labeled a, b, c, and d, on the operands. The suboperations can be envisioned as the four workers on a four-person assembly line. The floating-point multiply pipeline could accept a new set of operands every clock cycle. The pipeline occupancy of this code fragment would look like... 

Iodide and thiocyanate ion are effective catalysts for inducing a related rearrangement (62AG(E)S28). This reaction can be envisioned as proceeding by nucleophilic attack on the lesser substituted aziridinyl carbon atom by iodide ion to give an iodoethyl intermediate such as (132) which is subsequently converted to the final product. 

A similar term of number of transfer units per actual stage could also be envisioned. 

From the perspective of ecological integrity called for in the Clean Water Act, any adjustment to the implementation of toxic metals criteria needs to be integrated with both sediment criteria and biological criteria to provide ecosystem protection envisioned by the Act. 

To achieve these objectives, RCRA authorized EPA to regulate the generation, treatment, storage, transportation, and dispos of hazardous wastes. The structure of the national hazardous waste regula-toiy program envisioned by Congress is laid out in Subtitle C of RCRA (Sections 3001 through 3019), vdiich authorized EPA to ... 

The key element of life-cycle design is Life-Cycle Assessment (LCA). LCA is generally envisioned as a process to evaluate the environmental burdens associated with the cradle-to-grave life cycle of a produc t, process, or ac tivity. A produc t s life cycle can be roughly described in terms of the following stages ... 

Assuming = 0 will potentially add bias to the interpretation of plant measurements. Further, the plant bias may to some extent mask the error in the measurements. While the designer may have envisioned a constant set of conditions or a specified time dependence, it is likely that the actual operation changes due to external factors. 

In Fig. 8.18, we illustrate this just sufficient distribution in comparison to a hypothetical flaw distribution for an actual material. In this example, we envision a solid of finite extent, which will have a single critical flaw that activates at a minimum stress tensile stress, the population of flaws which activate should increase rapidly, perhaps as illustrated in Fig. 8.18. In contrast, a flaw distribution just sufficient to satisfy the energy balance criterion increases smoothly as JV [Pg.294]

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