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A common choice of branch cut is the negative real axis, although the choice is largely a matter of convenience. The logarithm has a jump discontinuity of 2 π i when crossing the branch cut. The logarithm can be made continuous by gluing together countably many copies, called sheets, of the complex plane along the branch cut. On each sheet ...
Any number log z defined by such criteria has the property that e log z = z. In this manner log function is a multi-valued function (often referred to as a "multifunction" in the context of complex analysis). A branch cut, usually along the negative real axis, can limit the imaginary part so it lies between −π and π. These are the chosen ...
Industrial applications of cutting-stock problems for high production volumes arise especially when basic material is produced in large rolls that are further cut into smaller units (see roll slitting). This is done e.g. in paper and plastic film industries but also in production of flat metals like steel or brass.
Rebar detailing is the discipline of preparing 'shop/placing' or 'fabrication' drawings or shop drawings of steel reinforcement for construction.. Engineers prepare 'design drawings' that develop required strengths by applying rebar size, spacing, location, and lap of steel.
A single branch of the complex logarithm. The hue of the color is used to show the argument of the complex logarithm. The brightness of the color is used to show the modulus of the complex logarithm. The real part of log(z) is the natural logarithm of | z |. Its graph is thus obtained by rotating the graph of ln(x) around the z-axis.
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A single-cut file has one set of parallel teeth while a cross-cut or double-cut file has a second set of cuts forming diamond shaped cutting surfaces. [1] In Swiss-pattern files the teeth are cut at a shallower angle, and are graded by number, with a number 1 file being coarser than a number 2, etc.
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