Semi-open formula

Semi-open formulas are used when the problem exists at only one limit. At the closed end of the integration, the weights from the standard closed-type formulas are used and at the open end, the weights from open formulas are used. (Weights for closed and open formulas of various orders of error may be found in standard numerical methods texts.) Given a closed extended trapezoidal rule of one order higher than the preceding formula, i.e.. 

Such early designs involved the construction of one or two structures built perpendicular to the shore on one or both sides of the inlet s opening to the sea. The designs were based on experience at first and later on some nebulous semi-empirical formulae. The structures were usually built of rocks or wooden cribs filled... 

Chezy formula A semi-empirical formula that relates the rate of discharge of liquid in an open channel to its dimensions, slope, and surface roughness as Q = CA-JrM where C is the Ch zy coefficient, A is the cross-sectional area of the channel, m is the mean hydraulic diameter, and i is the slope of the channel. The formula was devised by French engineer Antoine Ch zy (1718-98) who was responsible for designing a canal system to supply water to Paris. The Ch zy coefficient was developed further in 1890 by Irish engineer Robert Manning (1816-97). See manning formula. 

Semi-Theoretical and Empirical Velocity Fields Since the use of formulas to calculate the velocities outside an arbitrary opening could be very tedious, only some examples of these formulae are given. These calculations are best done on computers and there are some dedicated programs to calculate and visualize the flow fields outside exhaust openings. There could sometimes be problems when calculating the velocity field outside an opening close to... 

Constitutional formulae were designed "on paper", primarily to be "in harmony" with known chemical properties and without pretension to "represent the symmetrical or spatial arrangement of the atom in a compound" [22], Not only was this stipulation gradually relaxed to represent three-dimensional structures, but the connecting lines were also soon after assumed to represent definite electronic links between atoms. This assumption opened the door for the introduction of semi-empirical quantum-mechanical characterization of chemical bonds. It is important to realize that chemical bonds have never been observed in any experiment and that they only exist as conjectures to interpret primitive molecular graphs. Their value as heuristic aids in the study of chemical change and composition is beyond dispute, but as a basis for the theoretical understanding of chemical cohesion they are of little value. 

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