Consider a one-dimensional lattice with a basis of two non-equivalent atoms of masses M_1and M_2.

1. Find the dispersion relations (ω versus k).

2. Sketch the normal modes in the first Brillouin zone.

3. Show that the ratio of the displacements of the two atoms u/v for the k = 0 optical mode is given by:u/v=-M_2/M_1

Derive the Sackur-Tetrode equation starting from the multiplicity givenin Ch. 2:

Ω =(1/N!)(V^{N}/h^{3N})(pi^{3N/2}/3N^{2}!)(2mU)^{3N/2}

The Sackur-Tetrode equation is:

S=Nk[ln((V/N)((4pi*m*U)/(3Nh^{2}))^{3/2})+(5/2)]

There is a solid, spherical dielectric (radius = 3 m) with a total charge of 30 μC and with uniform charge density. What is the electric field strength and the electric potential at

-the center? (answer is 0 N/C and 135,000 V just show the work)

-a distance 2 m from the center? (answer is 20,000 N/C and 115,000 V just show the work)

Explain the following briefly:

i) Potential ordinary share ii) Ordinary share iii) Financial instrument iv) Equity instrument v) Options, warrant and their equivalents

State the double entry for the following:

i) Pre-acquisition dividend ii) Post-acquisition dividend iii) Impairment in associate iv) Provision for unrealized profit v) Depreciation of plant

When transforming word u[1 : i] to v[1 : j], in addition to adding, removing, or changing a letter, suppose we also allow for the swapping of adjacent letters. For example, transforming u = tera to v = tear requires a single edit that swaps the ‘r’ with the ‘a’. Provide the recurrence for d(i, j) that occurs when one performs this edit.

1. How many milliliters of a 1:20 w/v solution of copper sulfate should be used to prepare 1 L of a 0.50% w/v solution?

2. How many grams of lidocaine should be added to a 2 % lidocaine ointment to prepare 1000 g of 5% of lidocaine ointment? (Mixing pure lidocaine and 2% lidocaine ointment)

Endotracheal and Tracheostomy Suctioning

1.Make a table and indicate ‘When To Perform Suction and in Whom’, then the other column would include ‘When NOT To Perform Suction.’

2. Watch the following videos:

a.https://www.youtube.com/watch?v=jOkO2lfny5A

b.https://www.youtube.com/watch?v=ern1Z77DUVo

Make a reflection about these two procedures by writing a minimum of 200-300 words essay.

1. Vector u =< 0,−1,3 > is given. Find a non zero vector v which is perpendicular to u. Then find a vector w which is perpendicular to both u and v. Explain the reason for your selection clearly.

2. Find the slope of the tangent line to the parametric curve x = 5 + sin(3θ) and y = −3 + 2tanθ at θ = π.

1.) Find the sum V in cartesian and polar coordinates of V1=1000 m/s, V2=1800 m/s 2.) Find the difference of V in polar and cartesian coordinates for V3= 800 m/s and V4= 1400 m/s. The angles are angle1= 35 deg, angle2= 60 deg, angle3= 130 deg, angle4= 340 deg.

A metric space X is said to be locally path-connected if for every x ∈ X and every open neighborhood V of x in X, there exists a path-connected open neighborhood U of x in X with x ∈ U ⊂ V.

(a) Show that connectedness + local path-connectedness ⇒ path-connectedness

(b) Determine whether path-connectedness ⇒ local path-connectedness.