The __________ operator is used to dynamically allocate memory.

Briefly describe how the or operator works

This determines whether two different String objects contain the same string.

a. the == operator

b. the = operator

c. the equals method

d. the stringCompare method

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

Discuss the concept of polymorphism/operator overloading.

Briefly describe how the | | operator works.

The _______ operator is used to dynamically allocate memory.

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.

Is $\cos x$ an eigenfunction of the operator $\hat{A}$ if $\hat{A} f(x)=x f(x)$ ?

Show that the operator $\hat{p}^{\prime}$ obtained by applying a translation to the operator $\hat{p}$ is $\hat{p}^{\prime}=\hat{T}^{\dagger} \hat{p} \hat{T}=\hat{p}$.

Prove that the digraph obtained from $\operatorname{Cay}\left(\{(1,0),(0,1)\} : Z_{4} \oplus Z_{7}\right)$ by deleting the vertex $(0,0)$ has a Hamiltonian circuit.

$$\begin{aligned} \text { Show that there is no Hamiltonian path in } \\ & \operatorname { Cay } \left( \{ ( 1,0 ) , ( 0,1 ) \} : Z _ { 3 } \oplus Z _ { 2 } \right) \\ \text { from } ( 0,0 ) \text { to } ( 2,0 ) \end{aligned}$$

(a) If ||A|| is an operator norm, prove that

$$\| I \| = 1,$$

where I is an identity matrix. (b) Is there a vector norm that induces the Frobenius norm as an operator norm? Why or why not?

$$\begin{array} { c } { \text { Find a Hamiltonian circuit in } } \\ { \quad \operatorname { Cay } \left( \{ ( a , 0 ) , ( b , 0 ) , ( e , 1 ) \} : Q _ { 4 } \oplus Z _ { 3 } \right) } \end{array}$$