Question: In abstract algebra, more general structures are defined by relaxing some of the axioms defining a group. For example, if the requirement that every element has an inverse is eliminated, the resulting algebraic structure is called a monoid. The natural numbers N (including 0) under addition form a monoid, as do the nonzero integers under multiplication (Z {0}, ), see above. There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q {0}, ) is derived from (Z {0}, ), known as the Grothendieck group. Groupoids are similar to groups except that the composition a b need not be defined for all a and b. They arise in the study of more complicated forms of symmetry, often in topological and analytical structures, such as the fundamental groupoid or stacks. Finally, it is possible to generalize any of these concepts by replacing the binary operation with an arbitrary n-ary one (i.e. an operation taking n arguments). With the proper generalization of the group axioms this gives rise to an n-ary group. The table gives a list of several structures generalizing groups.
Try to answer this question if possible: Axioms are defined by relaxing what?
Answer: unanswerable
Question: In the semiconductor industry, infrared light can be used to characterize materials such as thin films and periodic trench structures. By measuring the reflectance of light from the surface of a semiconductor wafer, the index of refraction (n) and the extinction Coefficient (k) can be determined via the Forouhi-Bloomer dispersion equations. The reflectance from the infrared light can also be used to determine the critical dimension, depth, and sidewall angle of high aspect ratio trench structures.
Try to answer this question if possible: What equations are used to figure out the index of refraction and extinction Coefficient?
Answer: Forouhi-Bloomer dispersion
Question: The modern pharmaceutical industry traces its roots to two sources. The first of these were local apothecaries that expanded from their traditional role distributing botanical drugs such as morphine and quinine to wholesale manufacture in the mid 1800s. Rational drug discovery from plants started particularly with the isolation of morphine, analgesic and sleep-inducing agent from opium, by the German apothecary assistant Friedrich Serturner, who named the compound after the Greek god of dreams, Morpheus. Multinational corporations including Merck, Hoffman-La Roche, Burroughs-Wellcome (now part of Glaxo Smith Kline), Abbott Laboratories, Eli Lilly and Upjohn (now part of Pfizer) began as local apothecary shops in the mid-1800s. By the late 1880s, German dye manufacturers had perfected the purification of individual organic compounds from coal tar and other mineral sources and had also established rudimentary methods in organic chemical synthesis. The development of synthetic chemical methods allowed scientists to systematically vary the structure of chemical substances, and growth in the emerging science of pharmacology expanded their ability to evaluate the biological effects of these structural changes.
Try to answer this question if possible: Morphine was named after what Greek god?
Answer: Morpheus
Question: Countrywide, sued by California Attorney General Jerry Brown for "unfair business practices" and "false advertising" was making high cost mortgages "to homeowners with weak credit, adjustable rate mortgages (ARMs) that allowed homeowners to make interest-only payments". When housing prices decreased, homeowners in ARMs then had little incentive to pay their monthly payments, since their home equity had disappeared. This caused Countrywide's financial condition to deteriorate, ultimately resulting in a decision by the Office of Thrift Supervision to seize the lender.
Try to answer this question if possible: What happened to home equity when housing prices decreased?
Answer:
disappeared