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We conclude that the Fresnel and Fraunhofer approximations can be considerably improved with the NFFA, especially for wide-angle computations while still utilizing the FFT for computation by more accurately sampling the output points. The major difference between the Fresnel/Fraunhofer approximations and the NFFA is indeed the different sampling points. The different phase factors outside the integrals in Eqs. (7.2-11) and (7.3-11) are comparable except for very wide angles of diffraction and do not affect the diffraction intensity pattern at the output plane. Hence, when the Fresnel approximation is used as it has always been, the results are still suf ciently accurate at the new sampling points determined by Eqs. (7.3-8) and (7.3-9), but now these results are really the NFFA results at the new sampling points. The new permissible z-distance in the NFFA is smaller than the permissible z-distance with the Fresnel approximation by a considerable factor such as 18. As long as semi-irregular output point is acceptable, the NFFA can be considered to be as accurate as the angular spectrum method, but also with wide angles of diffraction, at most geometries considered in practice.

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6: Interacting with Relational Databases All of the keywords in SQL are case insensitive. Column and table names are case insensitive. Strings are quoted with the single quote character ('). The asterisk character (* ) acts as a wildcard when specifying the subject of a command. (String literal matches use % although many databases seem to support both.) Collections of items are delimited by round brackets (( and )). The language itself defines primitive data types and also the operators you use to work with those types. Most of the time the data type is implied by the way the data is used and combined with the operators. Once you've defined the table definitions, the operators know what sort of data you are using and how to do the appropriate comparisons. These operators are similar to the ones you are familiar with from Java >, <, <=, and == all have the same meanings. Some operators are also in text form. Logical actions may use word forms such as AND, OR, and NOT to describe actions, or the Java/C style of &&, ||, and ! respectively. Note SQL does not define a character that terminates a statement: The character depends on the database software. These terminators are only used when entering a text file to the database command line or in a console window. The two most common forms of terminators are the semicolon (; ), used in DB2, PostgreSQL, and MySQL, and the backslash g (\g ), used in Oracle, MiniSQL, and SQLServer. Check your database documentation to find out which character you need to use. Interfaces like JDBC and ODBC do not require the use of terminators for a command.

1 (t2 )E[Y 1,t2 (t2 ) 1A(Y 1,t2 ) ]pY 1 (t2 ),(Y 1 ) (t2 ) (0, 0) dt2 I I t1 (t1 )E[ 1A(Y t1 ) ] + t1 (0) E[Y t1 ,0 (t )1 t ,0 ]p t (0) 1 IA(Y 1 ) Y 1 (0) t1 t1 ,1 I + (1)E[Y (t1 ) 1A(Y t1 ,1 ) ]pY t1 (1) (0) (0, 0) dt . (t1 ) 1 1 t1 (t2 )E[Y t1 ,t2 (t1 )Y t1 ,t2 (t2 ) 0 1 t ,t ]p t t (0, 0) dt I

The evidence suggests that DI improves cross-wave continuity: both reactive and proactive DI reduce misclassification and under-reporting of events; in addition, reactive DI reduces keying error and proactive DI with routing reduces coding variability and consequent spurious change Returning to Figure 61, DI reduces spurious changes at the seam and constant wave responses caused by under-reporting of events or statuses, especially for respondents who experienced a change during the reference period.

These results showed very accurate reconstructions of the desired images. Compared to the results from the Lohmann method discussed in Section 15.8, there was consequently a signi cant increase in the reconstruction quality for high resolution gray-scale images. Like the DOEs designed with the Lohmann method, the transmittance function designed with ODIFIIT can also be coded as ( 1,1) to make binary phase holograms. This can be further extended to code holograms with multiple levels of phase quantization. This corresponds to multilevel phase elements. For example, four levels of phase quantization can be implemented when encoding the hologram.

2. When a patient has missing teeth in which the soft thermoplastic appliance will not be able to provide occlusal contacts for the opposing teeth. 3. When a patient has moderately severe or severe tooth attrition from nocturnal parafunctional habits. Soft appliances appear to wear more rapidly than acrylic appliances, so patients with excessively heavy parafunctional habits may wear through the soft appliance in a relatively short time.

where m 1 is the (m 1)-dimensional area measure of S m 1 . The integral on the right-hand side is bounded by 2 r2 1 + r2