Main Definitions

An ordinary graph is a special case of a hypergraph with degrees of all the edges equal to two. 

A hypergraph H = (V,E) is labeled if there exists labeling functions defined on the set of vertices V and on the set of edges E, which establish a correspondence between each vertex and each edge and some label. Let A V) = a(ui).a(up) and A E) = a Ei). a Eq) be the sets of possible labels called vertex and edge alphabets. The sets A V) and A E) may be represented by symbolic, numerical and structural labels. 

Structural labels are permutations. A permutation of a finite set of elements X = 1. n is the injective mapping of the set X. The permutation is recorded as 

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Maintaining cleanliness and sterility is involved in everyday practice but, for the most part, is not under the direct control of anaesthetists. Nevertheless, a familiarity will be expected with the main definitions and methods of achieving adequate cleanliness. 

Implied definitions, occurring in Notes to the main definitions, are indicated by using bold type for the terms so defined. 

The subject of acids and bases is very extensive. The discussion in this book is restricted to the definitions of acids and bases in aqueous solutions and their applications to the nature of ions in aqueous solutions and their stabilities. The two main definitions are those accredited to... 

Let us present the main definitions of tensorial products and their matrix or reduced matrix (submatrix) elements, necessary to find the expressions for matrix elements of the operators, corresponding to physical quantities. The tensorial product of two irreducible tensors and is defined as follows ... 

Outside the QTAIM realm, the main definitions of atomic charges are Mulliken charge, electrostatic charge, and natural charge [3]. Values can differ considerably from one method to another, but the trend with a particular method can provide useful information. None of these three methods of assigning charge claims to be unique. 

There are numerous texts on basic statistics, some of them oriented towards chemists. It is not tire aim of this section to provide a comprehensive background, but simply to provide the main definitions and tables that are helpful for using this text. 

Two main definitions of bond order indices are reported below. Moreover, the term fractional bond order was suggested to refer to the inverse of any bond order index. Fractional bond order permits individual treatment of a and it molecular systems a bonds give simple graphs, while jt bonds introduce a weighted molecular framework with weights less than one [Randic et al, 1980]. 

While the Directive as reasonably expected covers all aspects of the clinical research process, it is underpinned by the principles of ICH GCP and as such, only main definitions, modifications, and additions of note are described in the following sections. 

Table 3.5 summarises the main definitions from percolation theory and their interpretation in terms of bubbles in the adherence region. The main idea is,... 

Table 3.5 Main Definitions of the Percolation Model and Their Interpretation as Bubbles in the Adherence Region [123]...

There are two main definitions of the angle of repose as follows. 

In this part of the book, fundamental chemical information of interest to petroleum chemists is given. The first chapter deals with the main definitions as well as the important properties of crude oil and petroleum products used by petroleum specialists. A short history is given as to how crude oil became the most important power source for our civilization for over thousands of years. 

The first six main definitions are related to dose terms ... 

Whatever procedure is used to calculate the molecular orbitals and their energies, a certain number of electron and energy indices can be defined from them, which are related to the essential chemical, physicochemical and biochemical properties of molecules. For a detailed discussion see ref. 2. Here we simply recall the main definitions ... 

This chapter overviews the background and main definitions and basic concepts, useful to the development of this investigation work. 

We describe in Chap. 2 the basic concepts, notation, and theory of nature-inspired optimization in general, and then of chemical optimization, in particular. This chapter overviews the background, main definitions, and basic concepts, useful for the development of this investigation work. 

OECD defines absorption capacity as the accumulation of adequate information dissemination, capacity building in local governance and civil society for the conception and implementation of development projects (OECD, 2006). Absorption capacity leads to a strong performance of the EU funds only if the economy, efficiency and effectiveness are taken fully into account (Sumpikova et.al, 2004). Sumpikova et.al. (2004), define absorption capacity as the extent to which a state is able to fully spend the allocated financial resources from the EU. The literature on absorption capacity of the EU fimds in the Candidate Countries uses the absorption classification of the EU providing three main definitions (Zerbirati 2004 Sumpikova et. al. 2004 Oprescu et.al. 2005, Georgescu, 2008). 

In this section the main definitions, properties of minerals are detailed and explained. 

We will see that the fundamental definitions of pressure, chemical potential, and temperature are based on the form U = U S,V,N). Unfortunately, while the main definitions of thermodynamics originate from the energy equation, the microscopic driving forces are better understood in terms of the entropy equation S = S U,V,W. So we need to switch back and forth betw-een S = S(U,V,N) and U = U(5, U,N). For example, in Chapter 2 we illustrated how S U) accounts for the tendency for heat to flow, but temperature is defined in terms of f/(S). This small inconvenience adds a few steps to our logic. 

In an effort at making this book self-contained 1 recapitulates the main definitions and results of I. and ll.,... 

With these remarks in hand let s list the main definitions of soft and hard acids and bases, connecting their hardness degree with electronegativity (Putz, 2008b, 2012b) ... 

Non dimensional numbers and equations. Table 2 summarizes the main definitions of the non-dimensional numbers and their order of magnitude. The non dimensional equations are then... 

In addition to the main definition of the terminology used in this standard according to JIS K 6900, the following are also used. 

Transport processes in electrochemical systems should be analyzed with vector analysis, a part of calculus. The main definitions of vector analysis are terms like scalar, vector, gradient, divergence, and curl values. The reader is encouraged to refresh his or her memory for definitions of these values. There are two key equations that are fundamental to transport processes in electrochemical systans. The first describes the flux vector, of the ith species [1] ... 

Since confusion in terminology and definitions still persists in the literature in spite of recommendations by the Commission on Biochemical Nomenclature, it is important to start this section by recalling the main definitions used to describe the conformation of the polypeptide chain. 

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