Chemical structure, discrete

Many ionic compounds can have water molecules incorporated into their solid structures. Such compounds are called hydrates. To emphasize the presence of discrete water molecules in the chemical structure, the formula of any hydrate shows the waters of hydration separated from the rest of the chemical formula by a dot. A coefficient before H2 O indicates the number of water molecules in the formula. Copper(II) sulfate pentahydrate is a good example. The formula of this beautiful deep blue solid is C11SO4 5 H2 O, indicating that five water molecules are associated with each CuSOq unit. Upon prolonged heating, CuSOq 5 H2 O loses its waters of hydration along with its color. Other examples of hydrates include aluminum nitrate nonahydrate, A1 (N03)3 9 H2 O,... 

For many synthetic copolymers, it becomes possible to calculate all desired statistical characteristics of their primary structure, provided the sequence is described by a Markov chain. Although stochastic process 31 in the case of proteinlike copolymers is not a Markov chain, an exhaustive statistic description of their chemical structure can be performed by means of an auxiliary stochastic process 3iib whose states correspond to labeled monomeric units. As a label for unit M , it was suggested [23] to use its distance r from the center of the globule. The state of this stationary stochastic process 31 is a pair of numbers, (a, r), the first of which belongs to a discrete set while the second one corresponds to a continuous set. Stochastic process ib is remarkable for being stationary and Markovian. The probability of the transition from state a, r ) to state (/i, r") for the process of conventional movement along a heteropolymer macromolecule is described by the matrix-function of transition intensities... 

Dendrimers are not really discrete chemical structures - they are non-descript materials,... 

Hint think back to the word puzzle in which you changed the word went into come . The same process of small discrete changes of chemical structure can be seen to apply here. 

Polymers, because of their long chemical structure cohere as solids even when discrete section of the chain are undergoing Brownian motions moving by diffusional jump processes from place to place. This is the main difference between elastic solids and polymers [1-7]. 

In most existing inventories, chemical identities are standardized through the use of CAS numbers, molecular formulas (chemicals with discrete structures), and IUPAC (International Union of Pure and Applied Chemistry) systematic nomenclature. Chemicals of unknown or variable composition, complex reaction products, and biological materials (UVCB), are usually listed alphabetically under subheadings or by definition.14 Some of the countries that have compiled various inventories include Australia, Canada, EU, Japan, Philippines, South Korea, and United States. 

The individual products of combinatorial chemistry are called members. The distinction between a member and a compound is important and is based on the respective level of characterization. A compound will meet the typical standards for reporting new chemical structures a member will fall short of that standard. In fact, a member may, in principle, simply be expected to be present in a library, especially for large libraries, and those that consist of mixtures rather than discrete samples of members. 

Mathematical chemistry, the new challenging discipline of chemistry has established itself in recent years. Its main goal is to develop formal (mathematical) methods for chemical theory and (to some extent) for data analysis. Its history may be traced back to Caley s attempt, more than 100 years ago, to use the graph theoretical representation and interpretation of the chemical constitution of molecules for the enumeration of acyclic chemical structures. Graph theory and related areas of discrete mathematics are the main tools of qualitative theoretical treatment of chemistry [1,2]. However, attempts to contemplate connections between mathematics and chemistry and to predict new chemical facts with the help of formal mathematics have been scarce throughout the entire history of chemistry. 

However, before mathematical methods could be employed in chemistry, the latter had to reach sufficient theoretical maturity. Thus, the graph theory and some other divisions of discrete mathematics could be applied to the solution of chemical problems only after the chemical structure theory had emerged. In the next section we shall briefly discuss some important landmarks in the development of ideas concerning the structure of chemical compounds. 

Liposomes are microscopic vesicles consisting of one or more phospholipid membranes surrounding a discrete water compartment. The lipid layer is composed of amphipathic phospholipids whose hydrophobic tails associate, while the polar hydrophihc heads align toward the bulk of the water phase. A variety of hposomes with unique physical and chemical structure can be manufactured by altering non-polar and polar groups. Excellent reviews have been recently pubhshed... 

Biological variability can be demonstrated quite readily by building a QSAR model, which discriminates between chemicals with different toxicological hazard classifications. Application of computer-based QSARs has resulted in developing novel predictive capabilities for representing chemical structures as a distribution of conformations and properties rather than discrete structures. 

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