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Page "Cauchy–Riemann equations" ¶ 78
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More and complicated
More complicated grammars can be used to parse, and other languages with even more letters.
More complicated techniques permit large fields of color ( intarsia, for example ), busy small-scale patterns of color ( such as Fair Isle ), or both ( double knitting and slip-stitch color, for example ).
More complicated systems have more degrees of freedom, for example two masses and three springs ( each mass being attached to fixed points and to each other ).
More recently, many security experts such as Bruce Schneier recommend that people use passwords that are too complicated to memorize, write them down on paper, and keep them in a wallet.
More advanced implementations may support more complicated operations, such as pull_lowest_priority_element, inspecting the first few highest-or lowest-priority elements ( peeking at the highest priority element can be made O ( 1 ) time in nearly all implementations ), clearing the queue, clearing subsets of the queue, performing a batch insert, merging two or more queues into one, incrementing priority of any element, etc.
More complicated mechanisms have been discovered that lead to ozone destruction in the lower stratosphere as well.
More complicated monomers are also used.
More complicated conditions on the derivative lead to less precise but still highly useful information about the original function.
More generally, vector fields are defined on differentiable manifolds, which are spaces that look like Euclidean space on small scales, but may have more complicated structure on larger scales.
More complicated interactions which slow grain boundary motion include interactions of the surface energies of the two grains and the inclusion and are discussed in detail by C. S.
More complicated switch systems, such as double slips are restricted to low-speed operation.
More complicated trajectories are sometimes used.
More accurate calculations can be made without these simplifying assumptions, but they are more complicated.
More complicated in design than other water closets, reliability is lower and maintenance more difficult.
More complicated counter rhythms are created with sticks beaten on any resonant surface.
More complicated systems may use other input devices such as voice or a computer interface.
More complicated equations can sometimes be expressed as the sum of functions of the three variables.
More complicated configurations are also possible.
More complicated master-key lock systems are also made, with two or more levels of master keying, so there can be subordinate master keys which open only certain subsets of the locks, and a top-level master key which opens all the locks.
More complicated cases may apply special routing rules in addition such as Time of Day routing.
More complicated objects are represented by simpler stand-ins ( a sheep, for instance, appears as a rectangular place-holder marked " Insert Sheep ") or not represented at all.
More complicated coupled-cluster methods such as CCSDT and CCSDTQ are used only for high-accuracy calculations of small molecules.
More complicated algorithms include the Luhn algorithm ( 1954 ), which captures 98 % of single digit transposition errors ( it does not detect 90 ↔ 09 ), while more sophisticated is the Verhoeff algorithm ( 1969 ), which catches all single digit substitution and transposition errors, and many ( but not all ) more complex errors.
More generally, it can be applied to any classical system in thermal equilibrium, no matter how complicated.

More and generally
More generally, suppose that an experiment consists of a number of independent trials, that each trial results in either a `` success '' or a `` non-success '' ( `` failure '' ), and that the probability of success remains constant from trial to trial.
More generally, in a k-dimensional array, the address of an element with indices i < sub > 1 </ sub >, i < sub > 2 </ sub >, …, i < sub > k </ sub > is
More recently, an abettor is generally known as an accomplice.
More expensive pigments are generally replicated by hues.
More generally, one curve is a curvilinear asymptote of another ( as opposed to a linear asymptote ) if the distance between the two curves tends to zero as they tend to infinity, although usually the term asymptote by itself is reserved for linear asymptotes.
More generally, as noted by A. W.
More generally, a binary relation between two sets A and B is a subset of.
More generally, a new component is said to be backward compatible if it provides all of the functionality of the old component.
More generally, an n-piece cubic Bézier curve can approximate a circle, when each inner control point is the distance from an outer control point on a unit circle, where t is 360 / n degrees, and n > 2.
More generally, every C *- algebra is a Banach algebra.
More generally, a series
More generally, if ƒ has a branch-point near the origin of such a nature that then
More generally, calculus ( plural calculi ) refers to any method or system of calculation guided by the symbolic manipulation of expressions.
More generally, many philosophers and scientists have been unhappy about the difficulty of producing a definition that does not involve circularity or fuzziness.
More broadly, philosophers who do not accept the possibility of zombies generally believe that consciousness is reflected in behavior ( including verbal behavior ), and that we attribute consciousness on the basis of behavior.
Among the teachings of Jesus Christ in the Gospel of Luke and the Gospel of Matthew, the message to his followers that one should " Turn the other cheek " and his example in the story Pericope Adulterae, in which Jesus intervenes in the stoning of an adulteress, are generally accepted as his condemnation of physical retaliation ( though most scholars agree that the latter passage was " certainly not part of the original text of St John's Gospel ") More militant Christians consider Romans 13: 3 – 4 to support the death penalty.
* More generally, compact groups such as an orthogonal group are compact, while groups such as a general linear group are not.
More generally, compact sets can be separated by open sets: if K < sub > 1 </ sub > and K < sub > 2 </ sub > are compact and disjoint, there exist disjoint open sets U < sub > 1 </ sub > and U < sub > 2 </ sub > such that and.
More generally, electric current can be represented as the rate at which charge flows through a given surface as:
More generally, the idea of a contractive mapping can be defined for maps between metric spaces.
More generally, unspecific coercion may be the form taken by disciplinary coercion, and this appears to be in fact the case within the most effective command systems of the modern world.
More generally, judges look at the difficulty and execution of jumps, stunts and tumbling, synchronization, creativity, the sharpness of the motions, showmanship, and overall routine execution.
More generally among Baptists, a variety of parachurch agencies and evangelical educational institutions may be supported generously or not at all, depending entirely upon the local congregation's customs and predilections.
More generally, one can consider finite direct sums of matrix algebras.
More generally, inheritance now is quite different than those in the past.

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