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Many classes will need to implement either the IComparable or IComparable<T> interface because it enables one object to be compared to another by various methods defined by the NET Framework 18 introduced the IComparable and IComparable<T> interfaces, where they were used to enable two objects of a generic type parameter to be compared They were also mentioned in the discussion of Array, earlier in this chapter However, because of their importance and applicability to many situations, they are formally examined here IComparable is especially easy to implement because it consists of just this one method: int CompareTo(object v) This method compares the invoking object against the value in v It returns greater than zero if the invoking object is greater than v, zero if the two objects are equal, and less than zero if the invoking object is less than v

If x = 0 then d 1 (ln |x|) = dx x In other words, 1 dx = ln |x| + C x More generally, we have d 1 du ln |u| = dx u dx and 1 du dx = ln |u| + C u dx EXAMPLE 64

Method public virtual bool Equals(object ob)

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where Wj is a weight sequence with positive values Equation (513) shows that a rational B-spline of order k can be obtained by modifying B-splines of order k (Versprille, 1975) Eq (513) yields values of the Rj,k(x) for a speci ed order, knot sequence, and weight sequence in the domain of interest by repeatedly forming linear combinations of positive quantities Rational B-splines have a number of interesting properties, some of which are pertinent to the numerical procedures used in evaluating them and in applying them The non-zero values of Rj,k(x) occur only on the interval [Tj, Tj+k] in the knot sequence In other words, a rational B-spline of order k is non-zero only over k of the adjacent intervals between knots A further characteristic of rational B-splines of order k is that for any given point, x, all but k adjacent Rj,k(x) are zero These non-zero values of rational B-splines sum to 1 and can be written as

Purpose Returns true if the invoking object is the same as the one referred to by object Returns false otherwise Returns true if ob1 is the same as ob2 Returns false otherwise Performs shutdown actions prior to garbage collection In C#, Finalize( ) is accessed through a destructor Returns the hash code associated with the invoking object Obtains the type of an object at runtime Makes a shallow copy of the object This is one in which the members are copied, but objects referred to by members are not Returns true if ob1 and ob2 refer to the same object Returns false otherwise Returns a string that describes the object

public static bool Equals(object ob1, object ob2) protected Finalize( )

Calculate 4 x+1 dx, 1

public virtual int GetHashCode( ) public Type GetType( ) protected object MemberwiseClone( )

Barkan, P, The Calculation of High-Speed Motion of a Flexible Cam Actuated System, PhD disse, Pennsylvania State University, 1953 Grewal, PS, and Newcombe, WR, Dynamic Performance of High-Speed Semi-Rigid Follower Cam Systems Effects of Cam Pro le Errors, Mech Mach Theory, 23 (2): 121, 1988 Harris, TA, Rolling Bearing Analysis, John Wiley and Sons, New York, 1991 Johnson, RC, Method of Finite Differences in Cam Design, Machine Design, 27: 195, 1955 Kim, HE, and Newcombe, WR, Stochastic Error Analysis in Cam Mechanisms, Mech Mach Theory, 13, 1978 Kim, HE, and Newcombe, WR, The Effect of Cam Pro le Errors and System Flexibility on Cam Mechanism Output, Trans ASME, Mechanism and Machine Theory, 17 (1): 57, 1982 Newcombe, HR, and Kim, HE, Some Results of the Effect of Waviness in Cam Pro les on the Output Motion, Trans 8th OSU Applied Mechanisms Conference St Louis, Mo, 1983 Norton, RL, Effect of Manufacturing Method on Dynamic Performance of Cams, Mechanism and Machine Theory, Parts 1 and 2, 23 (3): 291 208, 1988 Older eld, J, On Application of Finite-Difference Method for Kinematics of Mechanisms, Zastosowania Matematyki IV (in Polish), p 176, 1958 Wiederrich, JL, Design of Cam Pro les for Systems with High Inertial Loadings, PhD thesis, Stanford University, Palo Alto, Calif 1973

public static bool ReferenceEquals(object ob1, object ob2) public virtual string ToString( )

Part II:

Assistant Professor of Mechanical Engineering, Design Division Stanford University Palo Alto, California

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