Interval closed

Refs. 34 and 35 for a more up-to-date discussion.) This they verified experimentally by determining drop weights for water and for benzene, using tips of various radii. Knowing the values of 7 from capillary rise measurements, and thence the respective values of a, / could be determined in each case. The resulting variation of / with r/V / has been fitted to a smoothing function to allow tabulation at close intervals [36]. 

Continuous-type buckets (Fig. 21-5/) are generally back-mounted to chain or belt at close intervals. They are usually fabricated of steel. Style 5 is standard for normal materi s, with style 6 a low-front type for better discharge of difficult materials. Style 7 buckets are used for additional capacity or large lumps, and style 8 for inclined crusher-type elevators. Style 9 bu( ets are designed for extremely high capacities and are usually side-mounted and hinged together. 

The absolute maximum (or minimum) of f(x) at x = a exists if f(x) < f(a) (or f(x) > f(a)) for all x in the domain of the function and need not be a relative maximum or minimum. If a function is defined and continuous on a closed interval, it tvill altvays have an absolute minimum and an absolute maximum, and they tvill be found either at a relative minimum and a relative maximum or at the endpoints of the interval. 

Potential data loggers are now available to undertake close interval pipeline surveys. These increasingly popular surveys, determine a pipeline s pipe-to-soil potential at nominal intervals, of as little as 1 m. Additional information is gained by the recording at each point, of both the pipe-to-soil potential with the cathodic protection system ON , together with the potential some 100-300 ms after the cathodic protection system is switched OFF . This instantaneous OFF potential being devoid of any IR drop component present in the ON potential measurement. 

Figure 4. Concentration-dependent ion channel blockade by (R)-JV-methylanatoxinol. The patterns identified as bursts and separated by long (>8 msec) closed intervals are indicated with a bar, the figure was designed to show approximately 2 bursts per trace. The dose-related decrease in mean channel open time resulted from the blockade of the open channel by the (R)-A -methylanatoxinol. The channel amplitude is related to membrane voltage (as was given in Figure 3) by the slope conductance such that 1 pA is equivalent to 30 mV. Continued on next page.

The Legendre polynomials are one example of a family of polynomials, said to be orthogonal on the closed interval [a, b] with respect to a weight function w(x) if... 

Dempster-Shafer structure A kind of nncertain number representing indistinguish-ability within bodies of evidence. In this book, a Dempster-Shafer structure is a hnite set of closed intervals of the real line, each of which is associated with a nonnegative value m, such that the sum of all such m s is 1. 

Wo can verify without difficulty that the condition (4. 5 is satisfied provided the coefficients p, q0, qt, p0, pt arc appropriately differentiable in the closed interval... 

Now we keep our eyes on a fixed, isolated eigenvalue X0 of II0 with finite multiplicity m. Then we can take two real numbers a, ft such that aother point of the spectrum of II0. It means that the projection... 

Remark 1 A convex combination of two points is in the closed interval of these two points. 

The Watkins number is a dimensionless measure of appropriateness in the closed interval 0 < Wa < 1. It was introduced... 

In fact, the complete electronic density of a molecule can be represented by an infinite family of such MIDCOs, a family that contains one set G(a) of continuous surfaces for every threshold value a from the open-closed interval... 

The hypotheses of Theorem 4.4 are stable to perturbation, in the sense that if they hold for particular values of the parameters and uptake functions then they continue to hold for all nearby values of the parameters and for nearby uptake functions. By a nearby uptake function we mean an uptake function with the properties that (a) it satisfies requirements (i) and (ii) of Section 1, and (b) it and its derivative are uniformly close to the given uptake function and its derivative on the closed interval [0,1]. The reason for this stability is that simple eigenvalues depend continuously on the entries of a matrix. 

Given that flowstone and stalagmites may provide relatively continuously time lines that can be accurately calibrated by U/Th dating, it is possible to extract paleoclimatic signals beyond the bulk deposition of the calcite itself. This has been accomplished by tracking various isotope and trace element profiles. Samples can be drilled at sufficiently close intervals along a sawed slab of stalagmite or flowstone to provide profiles with a time resolution of a few tens to a few hundred years. 

The introduced concepts are illustrated by the trapezoidal membership function A in Fig. 2. This function is defined on the closed interval [a,b] of real numbers (i.e., X = [a,b]), which may represent the range of values of a physical variable. 

Fuzzy sets on [R that satisfy these requirements capture various linguistic expressions, describing approximate numbers or intervals, such as numbers that are close to a given real number or numbers that are around a given interval of real numbers. Moreover, we can define meaningful arithmetical operations on these fuzzy sets via the a-cut representation. At each a-cut, these operations are the standard arithmetical operations on closed intervals ... 

A base variable with its range of values (a closed interval of real numbers)... 

We assume that the a-cuts G (a), Gg(a), and G(-(a) of three fuzzy sets A, B, and C, respectively, depend at least piecewise continuously on the a parameter from the unit interval [0,1], where continuity is understood within the metric topology of the underlying space X. On the closed interval [0,1], the scaled Hausdorff distance ah GJ a),Ggia)) is an at least piecewise continuous function of the level set value a. This function either attains its maximum ft(G ( a ), Gg a )) at some value a within [0,1] or it converges to its supremum value... 

The generalization of ordinary arithmetic to closed intervals is known as interval arithmetic. An interval is defined as a closed bounded set of real numbers (Moore, 1979) ... 

In Figure 3 the relationship between analyses by the neutral and alkaline reagents I, II, and III is shown for corresponding samples collected simultaneously or at very close intervals over a wide range of ozone concentrations. Because of the extreme range of concentrations a log-log plot is used. Concentrations above 100 p.p.m. (v./v.) were determined titrimetrically below this, photometrically. 

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