Explain the microscopic mechanisms for the relation of macroscopic variables for an isothermal process, an isobaric process, and an isochoric process occurring in an ideal gas.

(a) Use the Quine-McCluskey procedure to find all prime implicants of the function $G(A, B, C, D, E, F)=\Sigma m(1,7,11,12,15,33,35,43,47,59,60)+\Sigma d(30,50,54,58)$. Identify all essential prime implicants and find all minimum sum-of-products expressions. (b) Repeat part (a) for G′.

(a) Use the Quine-McCluskey method to find all prime implicants of $f(a, b, c, d, e)=\Sigma m(1,2,4,5,6,7,9,12,13,15,17,20,22,25,28,30)$. Find all essential prime implicants, and find all minimum sum-of-products expressions. (b) Repeat part (a) for f'.

A Prolog database contains the following, where boss(X, Y ) means “X is Y’s boss” and supervisor(X, Y) means “X is Y’s supervisor”:

$$\begin{array}{l} \text{boss(mike, joan)}\\ \text{boss(judith, mike)}\\ \text{boss(anita, judith)}\\ \text{boss(judith, kim)}\\ \text{boss(kim, enrique)}\\ \text{boss(anita, sam)}\\ \text{boss(enrique, jefferson)}\\ \text{boss(mike, hamal)}\\ \text{supervisor(X, Y) <= boss(X, Y)}\\ \text{supervisor(X, Y) <= boss(X, Z) and supervisor (Z, Y)}\\ \end{array}$$

Find the results of the following queries: a. ?boss(X, sam) b. ?boss(judith, X) c. ?supervisor(anita, X)

Show how to make the 8-to-3 priority encoder of Figure 9-20 using two 4-to-2 priority encoders and any additional necessary gates.

Toe Computer Security Institute (CSI) conducts an annual survey of computer crin1e at U.S. businesses. CSI sends survey questionnaires to computer security personnel at all U.S. corporations and government agencies. Toe latest CSI survey was sent by post or email to 5,412 firms, and 351 organizations responded. Forty-one percent of the respondents admitted unauthorized use of computer systems at their firms during the year. (CSI Computer Crime and Security Survey, 2010/2011.) a. Identify the population of interest to CSI. b. Identify the data collection method used by CSI. Are there any potential biases in the method used? c. Describe the variable measured in the CSI survey. Is it quantitative or qualitative? d. What inference can be made from the study result?

A and B are subsets of a set S. Prove the following set identities by showing set inclusion in each direction.

$$\left.\begin{array}{l} \text { a. }(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime} \\ \text { b. }(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime} \end{array}\right\} \text { De Morgan's laws }$$

c. $A \cup(B \cap A)=A$ d. $\left(A \cap B^{\prime}\right)^{\prime} \cup B=A^{\prime} \cup B$ e. $(A \cap B) \cup\left(A \cap B^{\prime}\right)=A$ f. $[A \cap(B \cup C)]^{\prime}=A^{\prime} \cup\left(B^{\prime} \cap C^{\prime}\right)$

Find the inverse Laplace transform of the function. $\frac{Z^{2}}{(z-2)^{3}}$

Write the d’Alembert solution for the problem $u_{t t}=c^{2} u_{x x}$ for $-\infty<x<\infty, t>0$ and $u(x, 0)=f(x), u_{t}(x, 0)=g(x)$ for $-\infty<x<\infty$. $c=1, f(x)=x^{2}, g(x)=-x$

Use > or < to compare the whole numbers. $74,328 \square 74,238$

Perform the elementary row operation or sequence of row operations on A and then produce a matrix $\Omega$ so that $\Omega A$ is the end result.

$$A=\left(\begin{array}{ccc} -4 & 6 & -3 \\ 12 & 4 & -4 \\ 1 & 3 & 0 \end{array}\right)$$

; interchange rows 2 and 3, then add the negative of row 1 to row 2.

Maximize Z=14x+21y subject to

$$\begin{aligned} 2 x+3 y & \leq 12 \\ x+5 y & \leq 8 \\ x, y & \geq 0 \end{aligned}$$

Find the present value of the given perpetuity. $60,000 per year at the rate of 8% yearly

Find a fundamental matrix for the system and write the general solution as a matrix. If initial values are given, solve the initial value problem. $x_{1}^{\prime}=2 x_{1}+x_{2}-x_{3}, x_{2}^{\prime}=3 x_{1}-2 x_{2}, \ x_{3}^{\prime}=3 x_{1}+x_{2}-3 x_{3} ; x_{1}(0)=1, x_{2}(0)=7, x_{3}(0)=3$