1. Give an example of a 3rd order nonlinear ordinary differential equation.

Let A be a m × n matrix with entries in R. Recall that the row rank of A means the dimension of the subspace in R^N spanned by the rows of A (viewed as vectors in Rⁿ), and the column rank means that of the subspace in R^m spanned by the columns of A (viewed as vectors in R^m).

(a) Prove that

n = (column rank of A) + dim S,

where the set S is the solution space of the homogeneous equation AX = 0, that is, S = {column vectors X : AX = 0} .

(b) Show that

row rank of A = column rank of A.

Suppose you have been asked to develop a simple model for the movement of ants in the presence of a food source. Discuss how you could simulate this model. Your answer should include any simplifying assumptions, some parameters that you’d need, and the interaction rules you would set up.

i. Define Fourier Series and explain it usefulness. At what instance can a function ?(?) be developed as a Fourier series.
ii. If ?(?)=12(?−?), find the Fourier series of period 2? in the interval (0,2?)

Show theoretically that least-squares fitting and Lagrange polynomial fitting yields the same result when there are 2 data points and x₁= 0.

Air enters the compressor of a gas-turbine plant at ambient conditions of 100 kPa and 25°C with a low velocity and exits at 1 MPa and 347°C with a velocity of 90 m/s. The compressor is cooled at a rate of 1500 kJ/min, and the power input to the compressor is 235 kW. Determine the mass flow rate of air through the compressor. The inlet and exit enthalpies of air are 298.2 kJ/kg and 628.07 kJ/kg.

The mass flow rate of air is  kg/s.

Let a,b be an element in the integers with a greater or equal to 1. Then there exist unique q, r in the integers such that b=aq+r where z less than or equal r less than or equal a+(z-1). Prove the Theorem.

Draw ? on a torus (or the schematic representation where opposite

sides of a rectangle are identified.)

1. What is a differential?

2. What is a differential equation?

3. Besides the fact that you might need the course to graduate, how might differential equations be useful to you in real life?

Find the intervals of increase and decrease, find the local maximum and minimum values, find the intervals of concave up and concave down, find the inflection points and sketch the graph

f(deta) = 2cos(deta)+cos^2(deta), 0<=deta<=2pi

IS623 practice

Short Answer Questions

1. Suppose you have a secure system with three subjects and three objects, with levels as listed below. (10 points)

Here H dominates L. You wish to implement a Bell and LaPadula model of security for this system. Fill in the access rights (R and/or W) permitted by the model for each subject/object pair in the access matrix below:

2. Suppose a department has determined that some users have gained unauthorized access to the computing system. Managers fear the intruders might intercept or even modify sensitive data on the system. Cost to reconstruct correct data is expected to be $2,000,000 with 5% likelihood per year.

One approach to addressing this problem is to install a more secure data access control problem. The cost of access control software is is $50,000 with 80% effectiveness. Here is the summary of risk and control:

• Cost to reconstruct correct data = $2,000,000 with 5% likelihood per year
• Effectiveness of access control software: 80%
• Cost of access control software: $50,000

Determine the expected annual costs due to loss and controls. Also, determine whether the costs outweigh the benefits of preventing or mitigating the risks. (5 points)

3. Suppose your data’s binary stream is 1110101. What is the XOR result with the bit stream of 1111111? (2 points)

4. Suppose the following:
   • James’ public key = K_j, James’ private key = K_j^-1
   • Randy’s public key = K_r, Randy’s private key = K_r^-1
   • Each person’s public key is known to others; Each one’s private key is only known to the owner

1. Explain how Randy can send a plaintext P to James secretly (2 points)

2. Explain how James can verify if a plaintext P is sent from Randy (2 points)

3. Explain how Randy can verify if a plaintext P is sent from James and at the same time P is sent secretly from James to Randy. (2 points)

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 9y cos(x), 0 ≤ x ≤ 2π

local maximum?

local minimum?

saddle point(s)?

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = y² − 2y cos(x),    −1 ≤ x ≤ 7

local maximum?

local minimum?

saddle points?

You have studied different types and application of Data Warehousing (DWH). In this assignment you have to create dimensional model for DWH of any type and discuss it in detail. Identify the business objective and design Star and Snowflake schemas. Use erwin data modeling tool.