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1. Give an example of a Banach space X , a closed convex set C in X, and a point u ∈ X which does not have a unique nearest point in C .Hint: Let X = R2 with the norm l(x, y)l := max(|x |, |y|).
2. Let (X, l·l) be a real normed space, E a linear subspace, and h ∈ E t. Give a proof that h can be extended to be a member of X t (the Hahn-Banach the- orem, 6.1.4) based on Theorem 6.2.11. Hint: Let U := {x ∈ X : lx l 1}. (Because of such relationships, separation theorems for convex sets are sometimes called "geometric forms" of the Hahn-Banach theorem.)
The American dream has always been a staple of American culture. When people speak of it, they often refer back to the first half of the 20th century. Despite this, the American Dream is just as relevant to American culture today as it was in the ..
a certain airplane has two independent alternators to provide electrical power. the probability that a given alternator
I need to find the maximum and minimum surface areas for 2 cubes with a total volume of 432 in^3. No other perameters are specified. I've been able to use common sense to find the max is 432 sq/inches
What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)?
By letting the period be one month, one has D = 100, Cu = 2.5, Ch= 0.50, Cr = 3.50, Cs= 0.20 and L = 0.75. What is the optimal inventory policy and the total cost of the system under the optimal policy?
write an application that simulates coin tossing. let the program toss the coin each time the user presses the toss
What is the significance level for the appropriate region of part (b)? How would you change the region to obtain a test with alpha=.001?
The largest value in a set of data is 160, and the smallest value is 70. If the resulting frequency distribution is to have six classes of equal width, what will be the class interval?
Identify the independent and dependent variable, and state the research hypothesis for your study. The variables must be categorical variables.
You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 95 percent confidence level and state that the estimated proportion must be within 2 percent of the population proportion.
For a random sample of 40 people, what is the 95% confidence interval of the proportion of people who feel that there is too much violence on TV?
According to Bienayme-Chebyshev rule, what percentages of these funds are likely to be within ±2 standard deviation of mean?
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