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esign patterns, or patterns, are solutions to recurring problems in a given context amid competing concerns. They try to bring together and document the core solution to a given problem. They are identified and documented in a form that s easy to share, discuss, and understand. They are useful problem-solving documentation for software designers and are used repeatedly to help solve common problems that arise in the course of software engineering. Documentation for the design pattern should provide a discussion on the difficulties and interests surrounding the problem and arguments as to why the given solution balances these competing interests or constraints that are inherent in the issue being solved. The value of the pattern is not just the solution to the problem; value can also be found in the documentation that explains the underlying motivation, the essential workings of the solution, and why the design pattern is advantageous. The pattern student will be able to experience all or at least some of the experience and insight that went into providing the solution. This will undoubtedly help the designer to use the pattern and possibly adapt it or adjust it further to address needs accordingly. Patterns can be combined and used in concert to solve larger problems that cannot be solved with just one pattern. Once the pattern student has become more familiar with these patterns, their combined applicability to a new set of problems will become much easier to identify.

(5.36)

Design patterns are beneficial because they describe a problem that occurs repeatedly, and then they explain the solution to the problem in a way that can be used many times over. Design patterns are helpful for the following reasons:

The cijk ( z w ) are analytic functions in R and the Ak (w ) are operator-valued elds. Now, de ne a conformal transformation z w( z ). A conformal eld or primary eld is one that transforms as w w ( z, z ) = (w, w ) z z

n They provide a common language for design discussions. n They provide solutions to real-world problems. n Their format captures knowledge and documents best practices for a domain. n They document decisions and the rationale that lead to the solution.

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This command says we need a cell that has the Apple code required to insert text into a label. Furthermore, we want the words Hello World! to populate the cell. Here is the full code:

(5.37)

n They reuse the experience of predecessors. n They communicate the insight already gained previously. n They describe the circumstances (when and where), the influences (who and

what), and the resolution (how and why it balances the influences) of a solution. Nevertheless, patterns are not the be-all and end-all, they are by no means a silver bullet or panacea, and they cannot be universally applied to all situations. You can t always find the solution to every problem by consulting the pattern playbook. Patterns have been excessively hyped and have been used by designers to make them appear knowledgeable.

We say that (h, h ) are the conformal weights or conformal dimension of the eld. In particular, h + h is the dimension which describes how the eld behaves under scaling, while h h is the spin of , which describes how the eld is transformed under a rotation. If Eq. (5.37) is satis ed, then it follows that ( z , z )(dz )h (d z )h = ( w, w)(dw)h (dw)h (5.38)

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Design Patterns by Gamma et al., Also Known as the Gang of Four (GoF)

That is, ( z , z )(dz )h (d z )h is invariant under a conformal transformation. Working in the complex plane, time ordering is transformed into radial ordering because as we mentioned above, the radial direction encodes the ow of time in the z plane. Consider two operators de ned in the complex plane A( z ) and B(w ) . The radial-ordering operator R xes the order of the operators based on which one has the larger radius in the complex plane. That is, A( z ) B( w), z > w R[ A( z ) B( w)] = f ( 1) B( w) A( z ), w > z If the operators are fermionic, then f = 1. One operator product expansion of particular interest involves the energymomentum tensor. In the complex plane Tzz ( z ) = : z X z X : (5.39)

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