Unique normal form

Crystal. Despite the sloppy use in modern vernacular, crystal is the normal form of the solid state of any matter. Crystals have repeated characteristic shapes unique to a substance—some being more exotic and functional than others. 

Similar to the potential utility of patterns generated from mass spectra analyses, patterns of protein expression observed by 2D-PAGE may also be used for diagnostic purposes [6, 46, 47]. 2D-PAGE resolves complex protein mixtures into numerous unique spots, forming a distinctive pattern. The pattern formed by the protein spots from normal and diseased tissue can then be visually compared. Proteins of interest can be excised from the gel, digested using trypsin, and analyzed by MS to reveal their identity. 

Considering the nature of the forces involved in the physical adsorption process (see Section 4.2.1), it is evident that the adsorption isotherm of a given adsorptive on a particular solid at a given temperature depends on the nature of both the gas and the solid, and therefore, each adsorbate-adsorbent system has a unique isotherm. In spite of this, a number of attempts have been made to express the adsorption isotherm data in a normalized form. It was seen that, for a large number of nonporous solids (type II isotherms), the plot of n/nm versus P/P° can be represented by a single curve, called the standard isotherm. Among these related attempts, the t- and as-methods are the most widely used. 

Mercury forms two series of compounds, mercurous and mercuric, but the former are not compounds of monovalent Hg in the sense that cuprous compounds, for example, are derivatives of monovalent Cu. A number of elements form compounds in which there are metal-metal bonds but mercury is unique in forming, in addition to Hg and the normal mercuric compounds, a series of compounds based on the grouping (-Hg-Hg-). (Evidence for the formation of the Cdf ion in molten Cd2(AlCl4)2 at 250°C is limited to the observation of one Raman line. )... 

The observed vibration frequencies of a molecule depend on two features of the molecular structure the masses and equilibrium geometry of the molecule and the potential eneigy surface, or force field, governing displacements from equilibrium. These are described as kinetic and potential effects, respectively for a polyatomic molecule the form and the frequency of each of the 3N—6 normal vibrations depend on the two effects in a complicated way. The object of a force field calculation is to separate these effects. More specifically, if the kinetic parameters are known and the vibration frequencies are observed spectroscopically, the object is to deduce the potential eneigy surface. A major difficulty in this calculation is that the observed frequencies are often insufficient to determine uniquely the form of the potential energy surface, and it is necessary to use data on the frequency shifts observed in isotopically substituted molecules or data on vibration/rotation interaction constants observed in high resolution spectra in order to obtain a unique solution. 

A table is said to be in first normal form if each row has the same number of columns, each column has a value, and there are no duplicate rows. Because an RDBMS uses a table defined with a fixed number of columns, it is always true that each row contains the same number of columns. If one allows that null is a value, then every column will have a value. It should be obvious that repeating a row in a table is wasteful, but also potentially confusing and prone to error. For example, if two rows in a table of logP contained the same name and logP, one row may have the logP changed at some point. Then which row would be the correct row This condition also illustrates the final aspect of first normal form There should be at least one column, or combination of columns, that could function as a key that uniquely identifies the row. This is the name column or compound id column in the above examples. The data in this column must be unique. 

It is not required that such a column actually be used as an SQL key, but it is wise to do so. In this way, the SQL uniqueness constraints can help to ensure that the table is in first normal form. While this one column must be unique, it is entirely possible and even likely that some other data values will not be unique. For example, there are expected to be many compounds that coincidentally have the same logP. This does not violate first normal form. 

Another way to think about first normal form is to simply consider what the table is intended to contain. If it contains data about structures, then there must be a unique way to identify those structures, for example, by name. For a table that contains information about structures, it must contain only information about structures. It must contain simple values that are associated with that structure, for example, molecular weight or logP. It must not contain complex information about its data values, such as the method used to determine logP. 

First normal form Each table should contain only data about a unique entity. Each row should have a unique identifier. If data tables violate first normal form, a careful reconsideration of which information belongs in which table should be undertaken. A structure table should be about structures, a logP table about logP values, and a method table about methods. 

In this class of binary compounds, a new tetragonal form of boron sulfide B2S3 prepared by high-pressure synthesis is noteworthy. Remarkably, instead of a simple structure related to that of normal ambient pressure form of B2 S3, it contains two kinds of supertetrahedra built up from 20 and 34 adamantane-type superclusters to form an elaborate three-dimensional framework (Figure 4) These supertetrahedra are linked to each other in a unique way forming an interpenetrating zinc-blende-type structure. This compound is a wide band-gap semiconductor with an energy gap of 3.7 eV. 

Turning now to the nanosecond time regime (lower half of Fig. 11), the emitted photons from a single molecule can provide still more useful information. On the time scale of the excited state lifetime, the statistics of photon emission from a single quantum system are expected [84] to show photon antibunching, which means that the photons space themselves out in time , that is, the probability for two photons to arrive at the detector at the same time is small. This is a uniquely quantvun-mechanical effect, which was first observed for Na atoms in a low-density beam [85]. Antibunching is fundamentally measured by computing the second-order correlation of the electric field (r) (whieh is simply the normalized form of the intensity-... 

The same as the compact form, the noncompact normal form is uniquely defined up to the automorphism of an enveloping complex algebra. For the interposition of the compact and noncompact forms in the algebra G, see Fig. 21. 

The A-H bond is a normal covalent bond, and the dominant view is that the H -B bond is dominantly electrostatic. The evidence is that it is only formed between atoms which are electronegative (O, N, F, S) and the strongest bonds are made with fluorine, which is the most electronegative of all. The reason why hydrogen is unique in forming such bonds is that it can approach other atoms closely on account of its small size and absence of iimer shell electrons. The bond does not have to be linear as the electrostatic force is not directional. 

Studies of the unique piezo- and pyro-electric properties of poled poly(vinylidene fluoride) have made a fundamental understanding of origin of the properties the subject of intense activity.Central to this study is the structure determination of the four phases, I, II, III, and IV, and their interconversion to test the correlation between orientation, crystal structure, and activity. The greatest piezoelectric activity is found with phase I, produced by subjecting phase II, the normal form produced on melt crystallizing, to intense electric fields up to 5 x 10 V cm, i.e. poling. The activity has been attributed to bulk polarization of the poly(vinylidene... 

Fatty acids normally occur naturally as esters fats oils phospholipids and waxes all are unique types of fatty acid esters There is however an important class of fatty acid derivatives that exists and carries out its biological role m the form of the free acid This class of fatty acid derivatives is described m the following section... 

In fine wool such as that obtained from merino sheep, the cuticle is normally one cell thick (20 x 30 x 0.5 mm, approximate dimensions) and usually constitutes about 10% by weight of the total fiber. Sections of cuticle cells show an internal series of laminations (Figs. 1 and 2) comprising outer sulfur-rich bands known as the exocuticle and inner regions of lower sulfur content called the endocuticle (13). On the exposed surface of cuticle cells, a membrane-like proteinaceous band (epicuticle) and a unique hpid component form a hydrophobic resistant barrier (14). These hpid and protein components are the functional moieties of the fiber surface and are important in fiber protection and textile processing (15). 

So far there have not been any restrictions on the MOs used to build the determinantal trial wave function. The Slater determinant has been written in terms of spinorbitals, eq. (3.20), being products of a spatial orbital times a spin function (a or /3). If there are no restrictions on the form of the spatial orbitals, the trial function is an Unrestricted Hartree-Fock (UHF) wave function. The term Different Orbitals for Different Spins (DODS) is also sometimes used. If the interest is in systems with an even number of electrons and a singlet type of wave function (a closed shell system), the restriction that each spatial orbital should have two electrons, one with a and one with /3 spin, is normally made. Such wave functions are known as Restricted Hartree-Fock (RHF). Open-shell systems may also be described by restricted type wave functions, where the spatial part of the doubly occupied orbitals is forced to be the same this is known as Restricted Open-shell Hartree-Fock (ROHF). For open-shell species a UHF treatment leads to well-defined orbital energies, which may be interpreted as ionization potentials. Section 3.4. For an ROHF wave function it is not possible to chose a unitary transformation which makes the matrix of Lagrange multipliers in eq. (3.40) diagonal, and orbital energies from an ROHF wave function are consequently not uniquely defined, and cannot be equated to ionization potentials by a Koopman type argument. 

A mixed T product can be decomposed into a unique sum of normal products according to the same rule as an ordinary T product, but with the omission of contractions between factors already in normal product form. 

In order that hot condenser water may be re-used in a plant, it is normally cooled by contact with an air stream. The equipment usually takes the form of a tower in which the hot water is run in at the top and allowed to flow downwards over a packing against a countercurrent flow of air which enters at the bottom of the cooling tower. The design of such towers forms an important part of the present chapter, though at the outset it is necessary to consider basic definitions of the various quantities involved in humidification, in particular wet-bulb and adiabatic saturation temperatures, and the way in which humidity data are presented on charts and graphs. While the present discussion is devoted to the very important air-water system, which is in some ways unique, the same principles may be applied to other liquids and gases, and this topic is covered in a final section. 

Chemical forces are normally irreversible in nature (at least in chromatography) and thus, the distribution coefficient of the solute with respect to the stationary phase is infinite or close to infinite. Affinity chromatography is an example of the use of chemical forces in a separation process. The stationary phase is formed in such a manner that it will chemically interact with one unique solute present in the sample and thus, exclusively extract it from the other materials... 

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