First Normal Form

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. 

In the above example, there were cases where multiple logP values for a single compound became important. If these were inserted into the table of structures, this would violate first normal form. So they were removed to a second table related to the first. When there are multiple values, there should be a separate table that contains information about those values. The table of structures must not be used to contain information about its data values but only information about structures. 

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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. 

We have designed and implemented an architecture for host-based access to diverse databases that meets some of the requirements and objectives described above. This architecture defines a consistent data model for chemical databases (structm es and reactions) and relational databases. The data model is hierarchical, and is formally related to the non-first normal form (NF2). This model has a well-developed theory, a long history, and is now being discussed as one approach to meeting modem requirements for object-oriented databases. 

In addition to modification of the catalyst, several variants of the Biginelli reaction have emerged as viable alternatives however, each method requires pre-formation of intermediates that are normally formed in the one-pot Biginelli reaction. First, Atwal and coworkers reported the reaction between aldol adducts 39 with urea 40a or thiourea 40b in the presence of sodium bicarbonate in dimethylformamide at 70°C to give 1,4-dihydropyrimidines 41. DHPM 42 was then produced by deprotection of 41. 

When enamines are treated with alkyl halides, an alkylation occurs that is analogous to the first step of 12-14. Hydrolysis of the imine salt gives a ketone. Since the enamine is normally formed from a ketone (16-12), the net result is alkylation of the ketone at the a position. The method, known as the Stork enamine reaction is an alternative to the ketone alkylation considered at 10-105. The Stork method has the advantage that it generally leads almost exclusively to monoalkylation of the ketone, while 10-105, when applied to ketones, is difficult to stop with the introduction of just one alkyl group. Alkylation usually takes place on the less substituted side of the original ketone. The most commonly used amines are the cyclic amines piperidine, morpholine, and pyrrolidine. 

To achieve the desired separation of the reactive degree of freedom from the bath modes, we use time-dependent normal form theory [40,99]. As a first step, the phase space is extended through the addition of two auxiliary variables a canonical coordinate x, which takes the same value as time t, and its conjugate momentum PT. The dynamics on the extended phase space is described by the Hamiltonian... 

Figure 8 displays the escape actions thus obtained for trajectories that react into channel A or B. It confirms, first of all, that all escape actions are positive. Furthermore, they take a maximum in the interior of each reactive island and decrease to zero as the boundaries of the islands are approached. These boundaries therefore coincide with the invariant manifolds that are characterized by 1 = 0. A more detailed study of the island structure [40] reveals in addition that the time-dependent normal form approach is necessary to describe the islands correctly. Neither the harmonic approximation of Section IVB1 nor the earlier autonomous TST described in Section II yield the correct island boundaries. 

A. Jorba, A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems, Exp. Math. 8, 155 (1999). 

This representation is also called normal form and it is graphically depicted in Figure 3. It can be seen that the normal form is composed of three parts respectively given by the subsystems (4a), (4b) and (4c). The first part presents a linear structure and it is given by a chain of r — 1 integrators, whereas the second part has a nonlinear structure, where the input-output relationship explicitly appears. Finally, the last part is conformed by the dynamics of the n — r complementary functions. This part is called internal dynamics because it cannot be seen from the input-output relationship (see Figure 3) and whose structure can be linear or nonlinear. 

After completing the first phase we have a feasible basic solution. The second phase is nothing else but the simplex method applied to the normal form. The following module strictly follows the algorithmic steps described. 

CNDO/2 Cl calculations performed by Bertran et al.150 to evaluate the variation of the tautomeric constant Kf,e upon excitation do predict a shift toward the rare imine forms 6 in the first excited singlet state, and a shift toward the normal form 2 in the first triplet state. 

The (generally complex) quantity p plays a role analogous to the order parameter familiar from phase transitions. The fact that only one such parameter survives in the final equations illustrates the enormous reduction of degrees of freedom associated with the first bifurcation. Note also the similarity between equations (8) and (9) and the normal forms at which one arrives in the qualitative theory of differential equations in the vicinity of resonance points.3... 

Scale Prevention. The scale normally formed on heat transfer surfaces of sea water evaporators consists of calcium carbonate, magnesium hydroxide, and/or calcium sulfate. The first two form as a result of the breakdown of bicarbonate in sea water, which is initially saturated with calcium carbonate. Calcium sulfate scale forms purely as a result of its inverted solubility curve. Sea water is not saturated with calcium sulfate and an economically reasonable amount of fresh water can be recovered from sea water without exceeding saturation with calcium sulfate. However, at the start of this investigation, the solubility of calcium sulfate in sea water was not accurately enough known to tell whether 30, 50, or 80% of the water content could be removed at various temperatures without encountering calcium sulfate scale. 

Follow the steps outlined in the text. First, count the total number of valence electrons. Phosphorus has 5, and each chlorine has 7, for a total of 40. Next, decide on the connections between atoms, and draw a line to indicate each bond. Because chlorine normally forms only one bond, it s likely in the case of PC15 that all five chlorines are bonded to a central phosphorus atom, which expands its valence shell ... 

However, photo-activation puts so much energy into the molecule, that many pathways become available to the first electronically excited state in addition to the relatively simple pericyclic change. For this reason, none of the photochemical reactions above can be guaranteed to be pericyclic, and all that one should take from these results is the very strong and suggestive contrast with the rules for thermal cycloadditions. This contrast is accentuated by the observation that photochemical Diels-Alder reactions are very rare, in spite of the ease with which 6-membered rings are normally formed. 

For example, Figs. 2.43 and 2.44 present the measured [55] viscosity and first normal stress difference data, respectively, for three blow molding grade high density polyethylenes along with a fit obtained from the Papanastasiou-Scriven-Macosko [59] form of the K-BKZ equation. A memory function with a relaxation spectrum of 8 relaxation times was used. 

The coefficients used to fit the data are summarized in Table 2.11 [43], The viscosity and first normal stress coefficient data presented in Figs. 2.30 and 2.31 where fitted with the Wagner form of the K-BKZ equation [41],... 

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