Strong formulation

Particularly for freeze-dried products, formulation and process are interrelated. Properties of the formulation, in particular the collapse temperature, will have a significant impact on the ease of processing. An efficient process is one that runs a high product temperature. However, the temperature cannot be too high or product quality will be compromised. As the glass transition temperature depends on chemical composition of the amorphous phase, Tg and collapse temperature are strongly formulation dependent. Collapse temperatures for common excipient systems vary from less than —50°C to around —10°C (Table 2). 

The potential for hydrodynamic artefacts (e.g., floating, clogging of material to screens, adhesion to equipment of the formulation or variable flow conditions in the vicinity of the formulation due to other reasons) is strongly formulation dependent and thus has to be evaluated for each type of formulation. In order to detect artefacts, careful visual inspection of the dissolution test equipment is crucial. Video recordings can be used to aid such investigations. 

A weak formulation is an equation derived from the original (strong) formulation of a physical problem by alleviating the strict differentiability requirements for the unknown function. This is often achieved by lowering the order of partial derivatives appearing in the equation, for instance, using integration by parts. 

Besides the basis set nature of the FE approach, the essential difference between the FE and FD methods is manifested in Eq. [17] and the nature of the boundary conditions. For the FE case, the general boundary condition (j)(0) = c is required on one side of the domain, while a second boundary condition = C2 is automatically implied by satisfaction of the variational condition. (These two constants were assumed to be 0 for some of the discussion above.) The first boundary condition is termed essential, while the second is called natural. The FE method is called a weak formulation, in contrast to the FD method, which is labeled a strong formulation (requiring both boundary conditions from the start and twice differentiable functions). A clear statement of these issues is given in the first chapter of Ref. 103, and the equivalence of the strong and weak formulations is proven there. Most electronic structure applications of FE methods have utilized zero or periodic boundary conditions. 

The least-Squares Method Based on Variational Principles (Strong Formulation)... 

Considering the strong formulation of the boundary conditions, the following norm-equivalent least-squares function is defined for the generalized problem formulation... 

In the following, the general implementation issues of the generalized problem formulation (12.402) are presented. Based on variational or weighted residual principles (strong formulation), the algebraic equation system (12.401) in which A and F are defined by (12.492)-(12.493) or alternatively (12.496)-(12.497) as obtained by the strong formulation of the least-squares technique ... 

Table 5.21 gives the characteristics of stocks used today to formulate heavy fuels. A few of these are strongly downgraded compared with their homologs of 1970s. 

The increase in the oil-change interval has already been a strong incentive for improving lubricant formulations. The increase in engine operating temperatures and the development of catalytic converters are without doubt two orientations that will have consequences on lubricant additives. 

The merits of (enantioselective) Lewis-acid catalysis of Diels-Alder reactions in aqueous solution have been highlighted in Chapters 2 and 3. Both chapters focused on the Diels-Alder reaction of substituted 3-phenyl-1-(2-pyr idyl)-2-prop ene-1-one dienophiles. In this chapter the scope of Lewis-acid catalysis of Diels-Alder reactions in water is investigated. Some literature claims in this area are critically examined and requirements for ejfective Lewis-acid catalysis are formulated. Finally an attempt is made to extend the scope of Lewis-acid catalysis in water by making use of a strongly coordinating auxiliary. 

Since the principal hazard of contamination of acrolein is base-catalyzed polymerization, a "buffer" solution to shortstop such a polymerization is often employed for emergency addition to a reacting tank. A typical composition of this solution is 78% acetic acid, 15% water, and 7% hydroquinone. The acetic acid is the primary active ingredient. Water is added to depress the freezing point and to increase the solubiUty of hydroquinone. Hydroquinone (HQ) prevents free-radical polymerization. Such polymerization is not expected to be a safety hazard, but there is no reason to exclude HQ from the formulation. Sodium acetate may be included as well to stop polymerization by very strong acids. There is, however, a temperature rise when it is added to acrolein due to catalysis of the acetic acid-acrolein addition reaction. 

Due to the strong ionic nature of lithium trifluoromethanesulfonate, it can increase the conductivity of coating formulations, and thereby enhance the dissipation of static electricity in nonconducting substrates (see Antistatic agents) (25). 

Water-based flexo inks can be formulated with either a soluble toner or with the Day-Glo EPX Series which is a tme pigment and can be formulated like a conventional pigment dispersion. The Radiant Aquabest or the Day-Glo WST can be formulated in an alkaline water-soluble system to yield strong inks. They have limited shelf life and inferior fade, but do not necessarily requite additional binder. Day-Glo EPX must be formulated with a binder such as a hard resin or can be used with one of the soluble toners such as WST. The EPX Series has several advantages over soluble toners such as much superior fade, exceUent ink stabiHty, and some hiding power over kraft-type papers. A disadvantage of the EPX is its lower tinctorial strength than other fluorescent toners. 

Trisodium phosphate is strongly alkaline many of its appHcations depend on this property. For example, many heavy-duty cleaning compositions contain trisodium phosphate as a primary alkalinity source. The crystalline dodecahydrate itself is marketed as a cleaning compound and paint remover. Traditionally, trisodium phosphate has been used in water softening to remove polyvalent metal ions by precipitation as insoluble phosphates. Because the hypochlorite complex of trisodium phosphate provides solutions that are strongly alkaline and contain active chlorine, it is used in disinfectant cleaners, scouring powders, and automatic dishwashing formulations. 

On curing, amino resins not only react with the nucleophilic sites (hydroxyl, carboxyl, amide) on the other film formers in the formulation, but also self-condense to some extent. Highly alkylated amino resins have less tendency to self-condense (33,34) and are therefore effective cross-linking agents, but may require the addition of a strong acid catalyst to obtain acceptable cure even at bake temperatures of 120—177°C. 

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