Curve classes

CLASS( ELEMENTARY CURVE(d), TRIMMED CURVE(d), COMPOSITE CURVE(d), INSTANCE(CURVE(d)), CASE d OF 

This is the class of elementary, trimmed, and composite curves. 

CLASS( LINE(d), LINE SEGMENT(d), POLYGON(d), CIRCLE(d), ELLIPSE(d), PARABOLA(d), HYPERBOLA(d), POLY.CURVE(d), B SPLINE CURVE(d), 

This entity type represents all bounded curves. It consists of the trimmed curves and those conics that are bounded by their geometric definition. The purpose of introducing this entity type is to guarantee that the result of a wireframe model is always bounded. 

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ENTITY EDGE CURVE = CLASS ( LINE(D3), CIRCLE(D3), ELLIPSE(D3),... 

Given experimental measurements with p= 123.4 and a = 12.9, draw the entire probability distribution curve for the population of all experimental measurements in the class studied. 

It should be noted that the modern view is that all partially miscible liquids should have both a lower and upper critical solution temperature so that all such systems really belong to one class. A closed solubility curve is not obtain in all cases because the physical conditions under normal pressure prevent this. Thus with liquids possessing a lower C.S.T., the critical temperature (the critical point for the liquid vapour system for each component, the maximum temperature at which liquefaction is possible) may be reached before the consolute temperature. Similarly for liquids with an upper C.S.T., one or both of the liquids may freeze before the lower C.S.T. is attained. 

The technique most often used (i.e., for an atom transfer) is to hrst plot the energy curve due to stretching a bond that is to be broken (without the new bond present) and then plot the energy curve due to stretching a bond that is to be formed (without the old bond present). The transition structure is next dehned as the point at which these two curves cross. Since most molecular mechanics methods were not designed to describe bond breaking and other reaction mechanisms, these methods are most reliable when a class of reactions has been tested against experimental data to determine its applicability and perhaps a suitable correction factor. 

The distribution curves may be regarded as histograms in which the class intervals (see p. 26) are indefinitely narrow and in which the size distribution follows the normal or log-normal law exactly. The distribution curves constructed from experimental data will deviate more or less widely from the ideal form, partly because the number of particles in the sample is necessarily severely limited, and partly because the postulated distribution... 

Column 9. Aj/Aj j gives that fraction of the area under the entire curve which has accumulated up to the Nth class. Since the curve is a weight distribution, this is equal to the weight fraction of material in the sample having M < Mj. 

Plotnikov P.I. (1995) On a class of curves arising in a free boundary problem for Stokes flow. Siberian Math. J. 36 (3), 619-627. 

Table 1 is condensed from Handbook 44. It Hsts the number of divisions allowed for each class, eg, a Class III scale must have between 100 and 1,200 divisions. Also, for each class it Hsts the acceptance tolerances appHcable to test load ranges expressed in divisions (d) for example, for test loads from 0 to 5,000 d, a Class II scale has an acceptance tolerance of 0.5 d. The least ambiguous way to specify the accuracy for an industrial or retail scale is to specify an accuracy class and the number of divisions, eg. Class III, 5,000 divisions. It must be noted that this is not the same as 1 part in 5,000, which is another method commonly used to specify accuracy eg, a Class III 5,000 d scale is allowed a tolerance which varies from 0.5 d at zero to 2.5 d at 5,000 divisions. CaHbration curves are typically plotted as in Figure 12, which shows a typical 5,000-division Class III scale. The error tunnel (stepped lines, top and bottom) is defined by the acceptance tolerances Hsted in Table 1. The three caHbration curves belong to the same scale tested at three different temperatures. Performance must remain within the error tunnel under the combined effect of nonlinearity, hysteresis, and temperature effect on span. Other specifications, including those for temperature effect on zero, nonrepeatabiHty, shift error, and creep may be found in Handbook 44 (5). The acceptance tolerances in Table 1 apply to new or reconditioned equipment tested within 30 days of being put into service. After that, maintenance tolerances apply they ate twice the values Hsted in Table 1.

Fig. 12. Calibiation curves for a Handbook 44 Class III 5,000 d scale. See text.

Fig. 4. Typical STC rating curves. Numbers on curves designate sound-transmission class (STC).

Glassification of Phase Boundaries for Binary Systems. Six classes of binary diagrams have been identified. These are shown schematically in Figure 6. Classifications are typically based on pressure—temperature (P T) projections of mixture critical curves and three-phase equiHbria lines (1,5,22,23). Experimental data are usually obtained by a simple synthetic method in which the pressure and temperature of a homogeneous solution of known concentration are manipulated to precipitate a visually observed phase. 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (soHd line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, C , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are CO2—/ -hexane and CO2—benzene. More compHcated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (Hquid—Hquid) immiscihility lines, and even three-phase (Hquid—Hquid—gas) immiscihility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include CO2—hexadecane and CO2—H2O Class IV, CO2—nitrobenzene Class V, ethane—/ -propanol and Class VI, H2O—/ -butanol. 

Fig. 6. Qualitative piessuie—tempeiatuie diagiams depicting ctitical curves for the six types of phase behaviors for binary systems, where C or Cp corresponds to pure component critical point G, vapor 1, Hquid U, upper critical end point and U, lower critical end point. Dashed curves are critical lines or phase boundaries (5). (a) Class I, the Ar—Kr system (b) Class 11, the CO2—CgH g system (c) Class 111, where the dashed lines A, B, C, and D correspond to the H2—CO, CH —H2S, He—H2, and He—CH system, respectively (d) Class IV, the CH —C H system (e) Class V, the C2H -C2H OH...

External-pressure failure of shells can result from overstress at one extreme or n om elastic instability at the other or at some intermediate loading. The code provides the solution for most shells by using a number of charts. One chart is used for cylinders where the shell diameter-to-thickness ratio and the length-to-diameter ratio are the variables. The rest of the charts depic t curves relating the geometry of cyhnders and spheres to allowable stress by cui ves which are determined from the modulus of elasticity, tangent modulus, and yield strength at temperatures for various materials or classes of materials. The text of this subsection explains how the allowable stress is determined from the charts for cylinders, spheres, and hemispherical, ellipsoidal, torispherical, and conical heads. 

Figure 1.11 Derating curve for higher ambient temperatures for insulation class E or B...

Figure 1.12 Derating curve for temperature rise restriction (drawn for class E insulation)...

Each repeat forms a right-handed P-loop-a structure similar to those found in the two other classes of a/p structures described earlier. Sequential p-loop-a repeats are joined together in a similar way to those in the a/P-bar-rel stmctures. The P strands form a parallel p sheet, and all the a helices are on one side of the P sheet. However, the P strands do not form a closed barrel instead they form a curved open stmcture that resembles a horseshoe with a helices on the outside and a p sheet forming the inside wall of the horseshoe (Figure 4.11). One side of the P sheet faces the a helices and participates in a hydrophobic core between the a helices and the P sheet the other side of the P sheet is exposed to solvent, a characteristic other a/p structures do not have. 

Upha/beta (a/p) structures are the most frequent and most regular of the pro-kein structures. They fall into three classes the first class comprises a central core of usually eight parallel p strands arranged close together like the staves pf a barrel, surrounded by a helices the second class comprises an open twisted parallel or mixed p sheet with a helices on both sides of the p sheet and Ihe third class is formed by leucine-rich motifs in which a large number of parallel p strands form a curved p sheet with all the a helices on the outside bfthis sheet. 

Tackifying resins enhance the adhesion of non-polar elastomers by improving wettability, increasing polarity and altering the viscoelastic properties. Dahlquist [31 ] established the first evidence of the modification of the viscoelastic properties of an elastomer by adding resins, and demonstrated that the performance of pressure-sensitive adhesives was related to the creep compliance. Later, Aubrey and Sherriff [32] demonstrated that a relationship between peel strength and viscoelasticity in natural rubber-low molecular resins blends existed. Class and Chu [33] used the dynamic mechanical measurements to demonstrate that compatible resins with an elastomer produced a decrease in the elastic modulus at room temperature and an increase in the tan <5 peak (which indicated the glass transition temperature of the resin-elastomer blend). Resins which are incompatible with an elastomer caused an increase in the elastic modulus at room temperature and showed two distinct maxima in the tan <5 curve. 

The procedure must be carried out in this manner the noise spectrum is superimposed on NC or NR diagrams, and the highest intercepted NC or NR curve represents the noise. For example, when a noise is represented by an NC 50 curve, it means that its spectrum does not exceed the NC curve, in correspondence of which at 1000 Hz the pressure level is equal to 50 dB(A). If the intercepted point is placed between 250 and 1000 Hz, the noise is classified as neutral under 250 Hz is called rumbly, while over 1000 Hz is classed as hissy. 

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