Most-general term

Besides, condition (5) is necessary for S to be an upper bound to the corresponding eigenvalue E. The question how to control the behavior of the variational energy by using rather weakly constrained variational trial functions, motivated the formulation of a number of minimax principles [4-6]. A detailed discussion and classification of these approaches has been given in ref. [7]. In most general terms, they are based on the following condition ... 

Ah, the crux of the problem, is it not Up until now, we ve just assumed we have some set of molecular orbitals i or Vu which we can manipulate at will. But how does one come up with even approximate solutions to the many body Schrodinger equation without having to solve it Start with the celebrated linear combination of atomic orbitals to get molecular orbitals (LCAO-MO) approximation. This allows us to use some set of (approximate) atomic orbitals, the basis functions which we know and love, to expand the MOs in. In the most general terms,... 

The question of possible limits on the production of work from heat engines was taken up brilliantly by a young French military engineer, Sadi Carnot (Sidebar 4.1). Carnot s monograph of 1824, Reflections on the Motive Power of Fire, pointed to the answers to these questions in a remarkably bold and incisive (if abstract) way. Carnot introduces the question of the motive power (ability to cause movement) of fire (heat) in its most general terms ... 

From Griffith s theory, it follows in most general terms that the destructive stress concentration corresponds to a material s cohesive strength. 

The proposed framework for risk-based classification of all radioactive and hazardous chemical wastes developed in Section 6.2.2 represents waste classification in its broadest, most general terms. Thus, this classification system can be viewed as the highest level of a possible hierarchy of hazardous waste classifications (e.g., see Figure 4.2). Further subclassification of these broadly defined waste classes may be desirable for such purposes as protection of workers during waste operations, protection of public health and the environment following waste disposal, and development of efficient methods of waste management taking into account the characteristics of actual wastes. 

In most general terms, the species identified in metal solutions are best described as "matrix-bound, in that the system comprises a solute (metal) species in a host (solvent) matrix. Before discussing details of the experimental data, we first attempt a general rationalization (61, 108) of the spectrum of possible matrix-bound states found in metal solutions. 

In its most general terms, the overall question to be addressed is How does one go about developing a selective agent in the absence of information... 

The preceding introduction might lead one to believe that this chapter could simply be divided into two basic parts—thermochemical considerations and kinetic considerations—which would cover all the relevant subject matter. However, in the last decade, first-principles (ab initio) computations have become commonplace and their results have often confirmed predictions based on thermochemical approaches, sometimes even surpassing them in accuracy. Hence, there is a need to encompass both thermochemical and ab initio treatments. We group the latter under the heading structural energetics and explore this topic further in Section 2.2. We also talk about the relevant thermodynamic and kinetic factors for specific systems in their respective chapters. For now, we discuss thermodynamics and kinetics in the most general terms. 

Besides a range of possible device applications, the science of these materials is truly fascinating.1-6 In the most general terms, multiferroics are materials in which ferromagnetism, ferroelectricity and feiToelasticity occur in the same... 

The most general term computational chemistry appears in the greatest number of advertisements. However, this term (or computational chemist) is not used in all advertisements. In fact, these terms appear in only about 40% of them. 

In most general terms, physical chemistry has as its task the compact, quantitative description of the properties and behavior of matter. Within this framework we can make a useful, if sometimes arbitrary, distinction between systems whose properties do not change with time and those systems whose properties are time-dependent. Chemical kinetics is that branch of physical chemistry concerned with the study of the latter systems, and in particular with the subgroup of those systems whose chemical composition is changing with time, i.e., systems in which chemical reactions are occurring. 

The aiming/firing system for the 60mm Mortar is based on the mil. This system, described in detail in the field manual,is too lengthy to cover here except in the most general terms. 

The terms unsteady and transient are often used interchangeably, but these terms are not synonyms. In fluid mechanics, unsteady is the most general term that applies to any flow that is not steady, but transient is typically used for developing flows. When a rocket engine Is fired up, for example, there are transient effects (the pressure builds up inside the rocket engine, the flow accelerates, etc.) until the engine settles down and operates steadily. I he term periodic refers to the kind of unsteady flow in which the flow oscillates about a steady mean. 

The development of a suitable strategy to prevent droplet flocculation in an emulsion, therefore, depends on identification of the physicochemical origin of flocculation in this particular system. In the most general terms, flocculation can be prevented by ensuring that the repulsive forces dominate the attractive forces. 

This unfortunately generates a glaring inconsistency the functional dependence of A, on V3 is absent from the function 3 = 0 also, it makes no sense to have to refer to system 3 when combining systems 1 and 2. To resolve this difficulty we introduce a new requirement namely, we demand that V3 occur in the functions difference between 0i and 02 is constructed. This is achieved in most general terms by requiring that the functions 0 assume the forms 0 = f2 P2, - - qiV )... 

In most general terms, one starts with the overall criterion for chemical equilibrium, (Y,i T//x/)eq = 0, developed in Section 2.9. Here again the v/ indicate stoichiometry coefficients for the generalized chemical reaction = 0 where... 

The temptation of remaining satisfied with the generalization must be avoided- This monograph has been written in the most general terms, mainly to provide a simple account of the basic ideas on defect solids. The detail of even the simplest problem is still controversial, and herein is the problem for the future. 

Chemical partitioning also occurs between water and solid phases and between air and solid phases, in a process most generally termed sorption. Types of sorption include adsorption, in which a chemical sticks to the two-dimensional surface of a solid, and absorption, in which a chemical diffuses into a three-dimensional solid. Chemical sorption in the environment is much more difficult to predict than is chemical partitioning between air and water, partly because the types of sorptive solid phases (sorbents) vary enormously, and partly because there are many different mechanisms by which sorption can occur. In this section, only partitioning between water and solid phases is considered. 

As mentioned above, CVD, the most general term describing the deposition process, implies nothing about the crystallinity of the grown layer. Epitaxy is directed at single crystal layers on single crystal substrates. Vapor phase epitaxy (VPE) was coined to parallel liquid phase epitaxy (LPE). 

In the most general terms, an infrared spectrometer consists of a light source, a dispersing element, a sample compartment and a detector. Of course, there is tremendous variability depending on the application. 

In the most general terms, the atmosphere is divided into lower and upper regions. The lower atmosphere is generally considered to extend to the top of the stratosphere, an altitude of about 50 kilometers (km). Study of the lower atmosphere is known as meteorology, study of the upper atmosphere is called aeronomy. 

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