Problem 4. Let P be the orthogonal projection associated with a closed subspace S in a Hilbert space H, that is P is a linear operator such that

P(f) = f if f ∈ S and P(f) = 0 if f ∈ S^⊥.

(a) Show that P² = P and P^∗ = P.

(b) Conversely, if P is any bounded operator satisfying P² = P and P^∗ = P, prove that P is the orthogonal projection for some closed subspace of H.

(c) Using P prove that if S is a closed subspace of a separable Hilbert space, then S is also a separable Hilbert space.

Consider a Rankine cycle with an ideal intermediate steam pickup, one of which is open and the other is closed feed water heaters. The steam enters the turbine at 12.5 MPa pressure and 550 degrees Celsius temperature and expands to 10 kPa condenser pressure. The steam separated from the turbine at 0.8 MPa pressure is sent to the closed feed water heater and the steam separated at 0.3 MPa pressure is sent to the open feed water heater. The feed water is heated to the condensing temperature of the steam leaving the turbine in the closed heater. The steam comes out of the closed heater as a saturated liquid, then the pressure is lowered into a valve and sent to the open feed water heater. Show the cycle in a T-s diagram with saturated liquid and saturated vapor curves.

a)

Water flow that must pass through the boiler for the production of 250 MW net power,

b)

Calculate the thermal efficiency of the cycle.

q1:In an open economy, a reduction in domestic demand has:

Select one:

a. a larger effect on output than in a closed economy and a positive effect on the trade balance.

b. a smaller effect on output than in a closed economy and a positive effect on the trade balance.

c. a smaller effect on output than in a closed economy and a negative effect on the trade balance.

d. a smaller effect on output than in a closed economy and a no effect on the trade balance.

e. a larger effect on output than in a closed economy and a negative effect on the trade balance.

Q2:

Policy makers can become concerned if the unemployment rate is too low because:

Select one:

a. output will increase.

b. stock prices will fall.

c. an exchange rate crisis might occur.

d. output will decrease.

e. inflation might increase.

Q3:

When the unemployment rate rises:

Select one:

a. the number of discouraged workers tends to fall.

b. the number of employed workers tends to rise.

c. the number of discouraged workers tends to remain constant.

d. the number of employed workers tends to remain constant.

e. the labour force participation rate tends to fall.

You have been assigned to examine the financial statements of ABC corp. for the year ended December 31, 2019, as prepared following IFRS. You discover the following situations:

1. Physical inventory count on Dec31, 2018, improperly excluded merchandise costing $13,000 that had been temporarily stored in a public warehouse. ABC corp uses periodic inventory system
2. Physical inventory count on Dec31,2019, improperly included merchandise with a cost of $26,000 that had been recorded as a sale on Dec27, 2019, and was being held for the customer to pick up on Jan 4,2020
3. Depreciation of $6,700 for 2018 on delivery vehicles was not recorded
4. A collection of $4,600 on account from customer received on Dec 31,2019, was not recorded until Jan 2, 2020
5. A large piece of equipment was purchased on Jan 1, 2019 for $20,500 and was charged in error to repairs expense. The equipment estimated useful life 8 years and no residual value. ABC corp uses straight-line depreciation method for this type of equipment.
6. On Dec 31, 2018 accrued wages of $1,500 were not recognized and not recorded
7. A 3 years insurance premium paid on July 1,2018 for policy expires on June 30,2021, amount of $12,000 was charged to insurance expense
8. The Accountant recorded a purchase of supplies for $9,000 in 2019 that applied to 2020.
9. At the beginning of 2017, the company purchased equipment for $225,000(residual value $22,500) and had useful life 6 years. The accountant used straight line amortization, but failed to deduct the residual value in calculation the depreciation base for the past and current years.
10. A cheque for $44,000 was paid in January 1, 2019 to cover the rent for 2019 and 2020; the entire amount was debited to rental expense.

Instructions:

Prepare the required Journal entries (if any) to correct ABC corp's accounts, assuming each transaction is independent and assume 2019 books are not closed.

At the end of its first year of operations on December 31, 2020, Carla Vista Company’s accounts show the following.

The capital balance represents each partner’s initial capital investment. Therefore, net income or net loss for 2020 has not been closed to the partners’ capital accounts.

To record the division of net income for the year 2020 under each of the following independent assumptions.

(a)

Prepare a schedule showing the division of net income under assumption (3) above. (If an amount reduces the account balance then enter with a negative sign preceding the number e.g. -15,000 or parenthesis e.g. (15,000).)

1. This case suggests that a lack of continuous innovation contributed to American Express’s (AmEx) poor performance in 2014. Assuming this is true, what factors might prevent a firm the ?size and scope of AmEx from being able to innovate continuously?

Assume you are the VP Global Marketing of BMW. Explain how you could use the concept of backward innovation and another concept you have learned in this Global Marketing Management course to promote your company’s products in China.

Please, i need an analysis on the life of jeff bezoz founder and ceo of amazon, his background, career and key leadership characteristics. also how does a company cope with accelerating change. and how can a firm encourage innovation.

Marketing question

" Big Problems in Marketing Industry "

Balancing incremental and radical innovation

A. How do I successfully incorporate design principles into my organization?

B. How should we think about creating “platform” products?