Name two different uses for the C++ operator *.

When a program is finished with a chunk of dynamically allocated memory, it should free it with the __________ operator.

Write a program that dynamically allocates an array large enough to hold a user-defined number of test scores. Once all the scores are entered, the array should be passed to a function that sorts them in ascending order. Another function should be called that calculates the average score. The program should display the sorted list of scores and averages with appropriate headings. Use pointer notation rather than array notation whenever possible.

Input Validation: Do not accept negative numbers for test scores.

Each byte in memory is assigned a unique __________.

Form the operator $\hat{A}^2$ if $\hat{A}=d^2 / d y^2+3 y(d / d y)-5$. Be sure to include an arbitrary function on which the operator acts.

Briefly describe how the or operator works.

Let $G$ be a graph. The line graph of $G$ is a new graph $L(G)$ whose vertices are the edges of $G$; two vertices of $L(G)$ are adjacent if, as edges of $G$, they share a common end point. In symbols:

$$V[L(G)]=E(G)\text{ and }E[L(G)]=\{e_1e_2:|e_1\cap e_2|=2\}$$

Prove or disprove the following statements about the relationship between a graph and its line graph : a. If $G$ is Eulerian, then $L(G)$ is also Eulerian. b. If $G$ has a Hamiltonian cycle, then $L(G)$ is Eulerian. (See Exercise 50.16 for the definition of a Hamiltonian cycle.) c. If $L(G)$ is Eulerian, then $G$ is also Eulerian. d. If $L(G)$ is Eulerian, then $G$ has a Hamiltonian cycle.

(a) Confirm that the kinetic energy operator, $- \left( \hbar ^ { 2 } / 2 m \right) \mathrm { d } ^ { 2 } / \mathrm { d } x ^ { 2 }$, is hermitian. (b) The operator corresponding to the angular momentum of a particle is $( \hbar / \mathrm { i } ) \mathrm { d } / \mathrm { d } \phi ,$ where $\phi$ is an angle. Is this operator hermitian?

$$\begin{array} { l } { \text { Find a Hamiltonian circuit in } } \\ { \text { Cay } \left( \{ ( a , 0 ) , ( b , 0 ) , ( e , 1 ) \} : Q _ { 4 } \oplus Z _ { m } \right) } \\ { \text { where } m \text { is even. } } \end{array}$$

Write the Hamiltonian function and find Hamilton's canonical equations for the three-dimensional motion of a projectile in a uniform gravitational field with no air resistance. Show that these equations lead to the same equations of motion as found.

An expression using the conditional operator is called a(n) _________ expression.

Briefly describe how the || operator works.

Consider a mass m constrained to move in a vertical line under the influence of gravity. Using the coordinate x measured vertically down from a convenient origin O, write down the Lagrangian L and find the generalized momentum p = ∂xL/∂ẋ. Find the Hamiltonian H as a function of x and p, and write down Hamilton's equations of motion. It is too much to hope with a system this simple that you would learn anything new by using the Hamiltonian approach, but do check that the equations of motion make sense.)

A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) = 35x - 0.25x². Using this model, what is the maximum profit the tour operator can expect?