Non-canonical PoS and SoP Forms

Non-canonical PoS and SoP forms

It is often the case that the canonical minterm form can be simplified to an equivalent SoP form. This simplified form would still consist of a sum of product terms. However, in the simplified form, it is possible to have fewer product terms and/or product terms that contain fewer variables. For example, the following 3-variable function: has the canonical minterm representation: f = a ′ b c a b c displaystyle f=a'bcabc , but it has an equivalent simplified form: f = b c displaystyle f=bc . In this trivial example, it is obvious that b c = a ′ b c a b c displaystyle bc=a'bcabc , but the simplified form has both fewer product terms, and the term has fewer variables. The most simplified SoP representation of a function is referred to as a minimal SoP form. In a similar manner, a canonical maxterm form can have a simplified PoS form. While this example was easily simplified by applying normal algebraic methods [ f = ( a ′ a ) b c displaystyle f=(a'a)bc ], in less obvious cases a convenient method for finding the minimal PoS/SoP form of a function with up to four variables is using a Karnaugh map. The minimal PoS and SoP forms are very important for finding optimal implementations of boolean functions and minimizing logic circuits.

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Approved forms of identification

Section 1 of Act 23 specifies that only the following forms of photo identification are acceptable: A Wisconsin driver's license An nondriver identification card issued by the Wisconsin Department of Transportation Photo identification issued by the United States military A United States passport or passport card A United States naturalization certificate, issued not more than two years prior to the election An unexpired receipt for a Wisconsin driver's license or nondriver identification card (this is given at the Department of Motor Vehicles, as Wisconsin's licenses and identification cards are printed and mailed from an outstate provider in California) A tribal identification card issued by a recognized Wisconsin Native American tribe An unexpired identification card issued by an accredited Wisconsin college or university with a date of issuance, a date of expiration not later than two years after the date of issuance, the voter's signature, and further provided that the student also present proof of enrollment in said college or university

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Related art forms

Many tribes throughout North America, besides those on the Plains, also painted hides, following different aesthetic traditions. Subarctic tribes are known for their painted caribou hides. On the Plains, when buffalo herds were being slaughtered in the late 19th century, other painting surfaces became available, such as muslin, paper, and canvas, giving birth to Ledger art. Contemporary Plains beadwork and jewelry used designs from hide painting.

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Forms

CD-RISC2An abbreviated, two-item version of the CD-RISC, the CD-RISC2, was created in 2005 to reduce administration time. It assessed resilience in members of the general population as well as patients with Post-traumatic Stress Disorder, depression, and anxiety. The two items used for this scale are item 1 ("Able to adapt to change") and item 8 ("Tend to bounce back after illness or hardship"). These items were chosen because Connor and Davidson deemed them capable of "etymologically capturing the essence of resilience." After analysis of test-retest reliability, convergent validity, and divergent validity, the CD-RISC2 demonstrated "significant correlation" with both the CD-RISC as a whole and with the individual items of the CD-RISC. The authors argue that since the CD-RISC2 sufficiently represents the original measure, the 2-item CD-RISC2 can be utilized in place of the 25-item CD-RISC. 10-item CD-RISCCampbell-Sills and Stein (2007) refined the original 25-item CD-RISC and validated a 10-item version of the measure, called the CD-RISC-10. The authors recognized the 25-item version's acceptable demonstration of reliability and validity but were concerned about the measure's 5-factor structure. They were confused about the conceptual relationships between items that appeared in the same factors (e.g., positive acceptance and secure relationships) and questioned the statistical analyses used to reach the conclusions. In light of these concerns, the authors worked to establish the factor structure of the CD-RISC using a more systematic approach. Additionally, they hoped to analyze the measure's construct validity to further validate it. Using factor analysis and three independent samples, the authors concluded that modifying the original scale to only include 10-items would improve the validity of the scale. They deleted items that, theoretically, would make sense to include in a measure of resilience but that did not carry enough statistical weight to still be included (e.g. measures of social support). They used exploratory factor analysis and confirmatory factor analysis to justify these deletions. The 10 items included in this abridged scale assess one's ability to endure difficult experiences, including "change, personal problems, illness, pressure, failure, and painful feelings." The authors found that scores on the 10-item CD-RISC correlated highly with score on the original 25-item CD-RISC. There were limitations to this analysis. For example, the samples used in this study to evaluate the psychometric properties of the 10-item CD-RISC did not include a clinical sample or a sample of individuals who had experienced high levels of trauma. Because of this, the conclusions drawn cannot be applied to these populations. The authors recognize that this could be considered an issue since the concept of resilience is often only considered relevant when related to the experience of trauma. However, the authors explain that resilience can be applied to more moderate levels of stress. Therefore, the concept of resilience and the 10-item CD-RISC measure can be applied to the general population, not just those who have experienced trauma. The authors also cite problems with using retrospective self-report to collect data (which, in this case, was unavoidable) and suggest that a resilience measure that does not rely on self-report should be created.