Prism volume

Prism Volume = (area of base) X (altitude) lateral surface area = (perimeter of right section) X (lateral edge). 

Tidal prism volume of water that flows in and out of an area between higher high tide and lower low tide. 

By comparison of the ratio of prism volume to the ellipsoid volume, a maximal volume filling factor/ ax follows from the area filling factor using/ ax =yFfl. This upper bound of the volume filling factor is valid if all particles have an identical size of D. In this case, the minimum composite film thickness corresponds with the mean vertical diameter of the particles dc = Ffe if all particles lie exactly in one plane. Because there is a statistical particle size distribution, the composite film thickness must be defined from the maximal vertical diameter of the largest particle dc = Db can be obtained from the image analysis data. It is better to calculate Db with Db = Dmax(l - Vl - inax ) The filling factor/is decreased further by the ratio between the mean particle... 

Another example can be given for derivation first order partial differential equation without mathematics, first linguistically and then translation of the linguistic sentences into mathematical notation. The same notation can be expanded to n dimensional space by considerations of physical meanings, unit homogeneity, initial and boundary conditions. Let us imagine that there is a parallelized prism volume, V, made of incompressible material as in Fig. 4.9a. Herein, incompressibility is the main assumption. 

Fig. 15 Way of assessing the volume of a cell using constant current SICM method. The illustration of the measuring process (b). Approaching the cell volume with the sum of 13 X 13 rectangular prisms volumes of Zxy height. Figure is taken from [152]...

For each combination of atoms i.j, k, and I, c is defined by Eq. (29), where X , y,. and Zj are the coordinates of atom j in Cartesian space defined in such a way that atom i is at position (0, 0, 0), atomj lies on the positive side of the x-axis, and atom k lies on the xy-plaiic and has a positive y-coordinate. On the right-hand side of Eq. (29), the numerator represents the volume of a rectangular prism with edges % , y ., and Zi, while the denominator is proportional to the surface of the same solid. If X . y ., or 2 has a very small absolute value, the set of four atoms is deviating only slightly from an achiral situation. This is reflected in c, which would then take a small absolute value the value of c is conformation-dependent because it is a function of the 3D atomic coordinates. 

Benzo[e]pyrene (1,2-benzpyrene) [192-97-2] M 252.3, m 178-179 , 178-180 . Purified by passage through an AI2O3 column (Woelm, basic, activity I) and eluted with CgHg and recrystd from 2 volumes of EtOH- CeHe (4 1). Forms colourless or light yellow prisms or needles. [J Chem Soc 3659 1954 Justus Liebigs Ann Chem 705 190 1967.] 1,3,5-Trinitrobenzene complex m 253-254° (orange needles from... 

Benzaldehyde-2-sulfonic acid sodium salt [1008-72-6] M 208.2, m dec on heating. Forms prisms or plates by extracting with boiling EtOH, filtering, evaporate to dryness and recrystallise the Na salt from a small volume of H2O. The N-phenylhydrazone sodium salt recrysts from H2O, m 174.5°. [Gnehm and Schiile Justus Liebigs Ann Chem 299 363 1898.]... 

To a stirred suspension of 10 grams (35 mmol) of 7-chloro-5-phenyl-3H-1,4-benzodiazepin-2(1H) one 4-oxide in approximately 150 ml of methanol was added in portions an excess of a solution of diazomethane in ether. After about one hour, almost complete solution had occurred and the reaction mixture was filtered. The filtrate was concentrated in vacuo to a small volume and diluted with ether and petroleum ether. The reaction product, 7-chloro-1-methyl-5-phenyl-3H-1,4-benzodiazepin-2(1 H)-one 4-oxide, crystallized in colorless prisms. The product was filtered off and recrystallized from acetone, MP 188°-189°C. 

Figure 2.1 Hyper-prism built on the column-vectors (alf a2, a3) of a non-singular matrix A3 x 3. The determinant is equal to the volume of the hyper-prism. When one of the vectors can be expressed as a linear combination of the others, both the volume and the determinant vanish and the matrix A is singular.

If det A =0, the column-vectors A are not linearly independent (nor are the column-rows) and the matrix is singular. At least one edge-vector of the hyper-prism made of the column-vectors is in the subspace of the remaining edge-vectors the volume of the hyper-prism vanishes and det A = 0. 

Let us dwell on Figure 6.4 for a moment. The standards and sample solutions are introduced to the instrument in a variety of ways. In the case of a pH meter and other electroanalytical instruments, the tips of one or two probes are immersed in the solution. In the case of an automatic digital Abbe refractometer (Chapter 15), a small quantity of the solution is placed on a prism at the bottom of a sample well inside the instrument. In an ordinary spectrophotometer (Chapters 7 and 8), the solution is held in a round (like a test tube) or square container called a cuvette, which fits in a holder inside the instrument. In an atomic absorption spectrophotometer (Chapter 9), or in instruments utilizing an autosampler, the solution is sucked or aspirated into the instrument from an external container. In a chromatograph (Chapters 12 and 13), the solution is injected into the instrument with the use of a small-volume syringe. Once inside, or otherwise in contact with the instrument, the instrument is designed to act on the solution. We now address the processes that occur inside the instrument in order to produce the electrical signal that is seen at the readout. 

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