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SAFETY NOTE It is crucial that reactions not be conducted in closed systems without using extreme precautions. The concept of not heating a closed system, as a practical illustration of the gas laws (PV = nRT), is impressed on chemistry students at an early stage. However, even without heating, conducting a reaction in a closed system can be hazardous, speci cally any reaction that does (or could) produce a gaseous product or by-product. Some common examples include decarboxylation reactions and those involving highly nitrogenous molecules like azides (RN3) and diazo compounds (R 2C N2). Application of the gas laws makes this problem readily understood. Recall that a mole of a gas occupies the relatively large volume of 22.4 L. Any reaction that produces a gaseous product in a closed system must substantially increase the pressure because the volume is xed. Such pressure increases can easily be large enough to separate ground glass joints, even those that are held together with rubberbands, springs, clamps, or even wire. The possibility of spilling reaction mixtures that have their own intrinsic hazards is reason enough not to conduct reactions in closed systems. In a worst-case scenario, the pressure jump may be suf cient to explode the apparatus. This can occur even without ammable reactants, but the consequence is no different shards of glass and reaction mixture shot around the lab. To attempt to address the possibility of reaction explosion for any cause, safety shields made from a variety of tough, clear plastics are available (Fig. 4.10). These are no substitute for a carefully planned and executed reaction, however.

A LNA is a block that is typically placed as the first active component of a receive chain. As the name suggests, the primary purpose of an LNA is to provide some gain to the signal while adding minimal amount of noise. By doing so, it provides a larger signal at its output than its input, while the SNR at the output is only slightly worse than that at the input. The noise added by the circuit can be quantified by using the concept of NF as described earlier. Recall that NF can be described as 10 log(output SNR)/ (input SNR). Equivalently, NF can be described as the total input-referred noise of the circuit as compared to the noise from the source resistance: NF = 10 log 1 + Ni 4kTRs

During the 1990s, the Federal Housing Administration (FHA) participated in several new programs offering no down payment loans to rst-time home purchasers through gifts from nonpro t organizations These programs were analyzed by FHA s Inspector General, who found that the default rate in 2001 was almost 20 percent on a large sample of such no-down-payment loans38 Nevertheless, the FHA continued until the middle of 2008 to allow the purchaser to meet its normal requirement for a 3 percent down payment by a gift from a nonpro t group, which, in practice, was often af liated with the developer or builder of the home In 2005 and 2006, for example, 40 percent of all rst-time buyers took out mortgages with no down payments, according to the National Association of Realtors.