Interdependent

Then, two things (that are actually interdependent) happen (1) The field intensity F = 0, (2) There exists a unique gauge g(R) and, since F = 0, any apparent field in the Hamiltonian can be transformed away by introducing a new gauge. If, however, condition (1) does not hold, that is, the electronic Hilbert space is truncated, then F is in general not zero within the tmncated set. In this event, the fields A and F cannot be nullified by a new gauge and the resulting YM field is true and irremovable. 

Since there is no conical intersection in the buffer zone, CTq, the second integral is zero and can be deleted so that we are left with the first and the third integrals. In general, the calculation of each integral is independent of the other however, the two calculations have to yield the same result, and therefore they have to be interdependent to some extent. Thus we do each calculation separately but for different (yet unknown) boundary conditions The first integral will be done for Gi2 as a boundary condition and the second for G23. Thus A will be calculated twice ... 

Taking into account the hydration shell of the NA and the possibility of the water content changing we are forced to consider the water -I- nucleic acid as an open system. In the present study a phenomenological model taking into account the interdependence of hydration and the NA conformation transition processes is offered. In accordance with the algorithm described above we consider two types of the basic processes in the system and thus two time intervals the water adsorption and the conformational transitions of the NA, times of the conformational transitions being much more greater... 

Correlation analysis reveals the interdependence between variables. The statistical measure for the interdependence is the correlation coefficient. 

Transferring torsional and nonbonded terms between force helds is much less reliable. These are lower-energy terms that are much more interdependent. It is quite common to hnd force helds with signihcantly different parameters for these contributions, even when the exact same equations are used. 

Try using obvious values for the parameters, such as bond lengths directly from crystal structures. This assumes that no interdependence exists between parameters, but it is a starting point. 

Four features of food are recognized to determine acceptance, ie, flavor, nutritive value, appearance, and mouthfeel. When all four aspects are in proper quantitative proportions, a food finds general acceptance. When all four are interdependent, appearance takes precedence over the others. However, a report by the Food Marketing Institute has shown that consumers placed nutrition second to flavor in importance (6). 

The American Society of Mechanical Engineers (ASME) United Engineering Center 345 East 47th Street New York, NY 10017 The ASME Boiler and Pressure Vessel Code, under the cognisance of the ASME PoHcy Board, Codes, and Standards, considers the interdependence of design procedures, material selection, fabrication procedures, inspection, and test methods that affect the safety of boilers, pressure vessels, and nuclear-plant components, whose failures could endanger the operators or the pubHc (see Nuclearreactors). It does not cover other aspects of these topics that affect operation, maintenance, or nonha2ardous deterioration. 

The preparation, reduction, and refining operations are very much interdependent, and for a given metal must be considered as parts of a single flow sheet. To illustrate the principles of extractive metallurgy, however, it is convenient to discuss the various operations separately. 

Early ia the development of chemical reaction engineering, reactants and products were treated as existing ia single homogeneous phases or several discrete phases. The technology has evolved iato viewing reactants and products as residing ia interdependent environments, a most important factor for multiphase reactors which are the most common types encountered. 

GE Improving the quaUty of life through technology and innovation interdependent balance between responsibiUty to customers, employees, society, and shareholders (no clear hierarchy) individual responsibiUty and opportunity honesty and integrity. 

Kelvin showed the interdependence of these phenomena by thermodynamic analysis, assuming that the irreversible processes were independent of the reversible ones. This approach was later proved theoretically sound using Onsager s concepts of irreversible thermodynamics (9). 

The rate and extent of deterioration ate governed by the interdependent factors of temperature, time, and moisture. In locations not conducive to decay or insect attack, wood is extremely stable at ordinary temperatures. However, with increasing temperature, the degradation of surface layers progresses into the interior layers. Prolonged heating at temperatures as low as 90°C may cause charring. 

Two variables of primary importance, which are interdependent, are reaction temperature and ch1orine propy1ene ratio. Propylene is typically used ia excess to act as a diluent and heat sink, thus minimising by-products (eqs.2 and 3). Since higher temperatures favor the desired reaction, standard practice generally involves preheat of the reactor feeds to at least 200°C prior to combination. The heat of reaction is then responsible for further increases in the reaction temperature toward 510°C. The chlorine propylene ratio is adjusted so that, for given preheat temperatures, the desired ultimate reaction temperature is maintained. For example, at a chlorine propylene molar ratio of 0.315, feed temperatures of 200°C (propylene) and 50°C (chlorine) produce an ultimate reaction temperature of approximately 500°C (10). Increases in preheat temperature toward the ultimate reactor temperature, eg, in attempts to decrease yield of equation 1, must be compensated for in reduced chlorine propylene ratio, which reduces the fraction of propylene converted and, thus aHyl chloride quantity produced. A suitable economic optimum combination of preheat temperature and chlorine propylene ratio can be readily deterrnined for individual cases. 

Joint Authorship. When more than one author has created a work, the work is said to be a joint work. Under the law, such a joint work is one prepared by two or more authors with the intention that their contributions be merged into inseparable or interdependent parts of a unitary whole. Thus joint authorship can occur when a composer and a lyricist collaborate on a song. Even though their contributions can exist independendy of each other, ie, the music as an instmmental, the lyrics as a poem, they were created as interdependent parts of a unitary whole, ie, the song. Two scientists collaborating on an article for a scientific journal are similarly joint authors. Their contributions caimot be teased out of the article they have written and so are inseparable parts of a unitary whole. The test of joint authorship is intention. The creation must be made with the intention that the contributions be merged into one work, and that intention caimot be imputed after the fact of creation if it was not there to begin with. 

From this information it is possible to prepare bar charts by using a 4-week month and noting on the chart the interdependence of the various functions. The starting time for each class of work is fixed on the chart, and the duration is calciilated from the labor-hours allocated to that work from the control estimate. Work should progress smoothly as time elapses, but the operations must be linked by the order of necessaiy precedence. Starting times for the various items of work will be staggered as drawings are released and also to smooth out labor requirements. 

Since and l ( are interdependent parameters the optimum design is achieved when /nr at is of the same magnitude as the relay operating current, i.e. I ( —... 

An important characteristic of biomolecular motion is that the different types of motion are interdependent and coupled to one another. For example, a large-scale dynamic transition cannot occur without involving several medium-scale motions, such as helix rearrangements. Medium-scale motions cannot occur without involving small-scale motions, such as side-chain movement. Finally, even side-chain motions cannot occur without the presence of the very fast atomic fluctuations, which can be viewed as the lubricant that enables the whole molecular construction to move. From the point of view of dynamic... 

Develop (e.g., write) the hyperbolic equation in terms of the dimensionless variables. This breaks the interdependence of exponential and pre-exponential terms. 

Assuming that a relationship exists among corrosion, population, and sulfur dioxide, why might one expect this interdependence ... 

The most common method of displaying the interdependence of stress, strain and time is by means of creep curves. However, it should be realised that these... 

I FIGURE I (.49 In thermal models, the ventilation airflow rates are input parameters in airflow models, on the other hand, room air tmiperatures must be defined In the output. Since natural ventilation airflows and room air temperatures are interdependent, both parameters must be intcgratly considered in the solution process. This is possible only by an integration of the natural airflow model into the thermal model. 

However, in thermally driven naturally ventilated enclosures, airflow rates and room air temperatures are interdependent and can be determined only simultaneously by using an integrated airflow and thermal model. 

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