Lump, lumps

Now one may want to impose another constraint, namely, that each of the original N species appears in only one of the N" species hence, every column of L has to be a unit vector of the type 0, 0,.. ., 1,.. ., 0. This is called proper lumping. Lumping that is not proper, however, is possible see Section II,C. 

The phosphorous pentoxide is added portionwise to the alcohol at a rate such that the pentoxide dissolves and reacts without lumping. Lumping makes complete dissolution difficult and the P2O5 unreactive. The reaction between the alcohol and the P2O5 is carried out in the liquid phase and is basically exothermic. No catalyst is required. The addition of a small amount of hypophosphorous acid or its salt gives a colorless, color-stable product. 

The dissolution behaviour and rate are typical for a polymer. It is recommended to add the powder slowly and in small portions to the solvent, which should be vigorously stirred. This ensures that copovidone dissolves rapidly without forming lumps. Lumps are relatively slow to dissolve. 

Lump Sum contract contractor manages and executes specified work to an agreed delivery date for a fixed price. Penalties may be due for late completion of the work, and this provides an incentive for timely completion. Payment may be staged when agreed milestones are reached. 

Lump sum contracts tend to be favoured by companies awarding work (if the scope of work can be well defined) as they provide a clear incentive for the contractor to complete a project on time and within an agreed price. 

If the reference date is set at the beginning of the year (e.g. 1.1.98) then full year discount factors imply that t is a whole number and that cashflows occur in lump sums at the end of each year. If the cashflow occurs uniformly throughout the year and the reference date is the beginning of the year then mid-year discount factors are more appropriate, in which case the discounting equation would be ... 

The total number of bits set on A is a + c. and the total number of bits set on B is b + c. These totals form the basis of an alternative notation that uses a instead of a + c, and b instead oib + c [16]. This notation, however, lumps together similarity and dissimilarity components" - a disadvantage when interpreting a similarity measure. 

Carry out this preparation precisely as described for the a-compound, but instead of zinc chloride add 2 5 g. of anhydrous powdered sodium acetate (preparation, p. 116) to the acetic anhydride. When this mixture has been heated on the water-bath for 5 minutes, and the greater part of the acetate has dissolved, add the 5 g. of powdered glucose. After heating for I hour, pour into cold water as before. The viscous oil crystallises more readily than that obtained in the preparation of the a-compound. Filter the solid material at the pump, breaking up any lumps as before, wash thoroughly with water and drain. (Yield of crude product, io o-io 5 g.). Recrystallise from rectified spirit until the pure -pentacetylglucose is obtained as colourless crystals, m.p- 130-131° again two recrystallisations are usually sufficient for this purpose. 

CAUTION. The vapour of selenium dioxide is poisonous, and all operations involving the hot material, alone or in solution, should be performed in a fume-cupboard. If lumps of selenium dioxide have to be powdered in a mortar, the latter should also be in a fume-cupboard, with the window lowered as far as possible, to avoid inhaling the fine dust. (cf. p. 191)... 

In order to prepare the free base, place the remaining half of the crude hydrochloride in a 200 ml. beaker, add 20 ml. of water, and then stir the mixture with a glass rod until a thin paste of uniform consistency (quite free from lumps) is obtained. Now... 

Required Ethyl acetoacetate, 32 g. (32 ml.) acetaldehyde-ammonia, lO g. Note. The aldehyde-ammonia should preferably be fresh material the quantity should be increased to 15 g. if an old sample, which has formed brown sticky lumps, is employed.)... 

This matrix is usually diagonalized using a simple mass lumping technique (Pittman and Nakazawa, 1984) to minimize the computational cost of pressure calculations in this method. 

STRESS. Applies the variational recovery method to calculate nodal values of pressure and, components of the stress. A mass lumping routine is called by STRESS to diagonalize the coefficient matrix in the equations to eliminate the... 

A force field that can produce vibrational spectra has a second advantage in that the Ay// calculations can be put on a much more satisfactory theoretical base by calculating an enthalpy of formation at 0 K as in ab initio procedures and then adding various thermal energies by more r igorous means than simply lumping them in with empirical bond enthalpy contributions to Ay//-. The stronger the theoretical base, the less likely is an unwelcome surprise in the output. 

By adding a few lumps of solid carbon dioxide this produces a number of cold spots here and there, and assists the formation of crystals. 

Hydrogen chloride. Method 1 from concentrated sulphuric acid and fused ammonium chloride). The most convenient procedure is to allow concentrated sulphuric acid to react with lumps of fused ammonium chloride in a Kipp s apparatus. The gas may be dried by passage through a wash bottle containing concentrated sulphuric acid the latter should be followed by an empty wash bottle or flask as a precaution against sucking back of the contents of the reaction vessel. 

The hard lump of sulphur remaining in the flask is best removed by boiling with concentrated nitric acid in the fume cupboard. 

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