In this lecture, we will revisit the application of Newton's second law to a system of particles and derive some useful relationships expressing the conservation of angular momentum. Center of Mass Consider a system made up of n particles. A typical particle, i, has mass mi, and, at the instant considered, occupies the position Ti relative to a frame xyz. We can then define the center of mass, G, as the point
Iterating Block ciphers Definition A product cipher combines two or more transformations in a manner intending that the resulting cipher is more secure than the individual components. Definition An iterated block cipher is a block cipher involving the sequential repetition of an internal function called a round function. Parameters include the number of rounds Nr, the block bitsize n, and the bitsize k of the input key K from which Nr subkeys Ki (round keys) are derived. For invertibility (allowing unique decryption), for each value Ki the round function is a bijection on the round input
n contrast to alcohols with their rich chemical reactivity, ethers (compounds contain- ing a C-0-C unit) undergo relatively few chemical reactions. As you saw wher we discussed Grignard reagents in Chapter 14 and lithium aluminum hydride reduc- tions in Chapter 15, this lack of reactivity of ethers makes them valuable as solvents in a number of synthetically important transformatio. In the present chapter you will learn
H ydrocarbons that contain carbon-carbon triple bond are called alkynes. Non- cyclic alkynes have the molecular formula C, H2n-2. Acetylene (HCCH) is th simplest alkyne. We call compounds that have their triple bond at the end of a carbon chain(RC=CH) monosubstituted, or terminal, alkynes. Disubstituted alkynes (RCCR') are said to have internal triple bonds. You will see in this chapter that a car- bon-carbon triple bond is a functional group, reacting with many of the same reagents
Shock Capturing vs. Shock Fitting hocks when the shocks or di n the solution as regions of large gradients without having to give them any special treatment. If we use conservative schemes, the Lax-Wendroff theorem 's. will be to a weak solution We know tha reak solutions satisfy the jump conditions and therefore give the correct shock
