Simplify the following generalized functions then write out how they act on a suitable test function u( a) a ex Icirc acute (a) b a Icirc acute (a 1) c 3 Icirc acute ,(a) 3a Icirc acute 1(x) d e (cos x) Icirc acute (a) Icirc acute (a n) Icirc acute (a n) f 51(X) 82(x)...

Simplify the following generalized functions; then write out how they act on a suitable test function u(

Question:

Simplify the following generalized functions; then write out how they act on a suitable test function u( a):
a. ex Î´(a)
b. a Î´ (a - 1)
c. 3Î´,(a)-3aÎ´1(x)
d.

e. (cos x)[Î´(a) + Î´(a - n) + Î´(a + n) ]
f.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 18, 2016 09:04 AM

See More Questions

Use Exercise 11.2.20 to simplify the following generalized functions; then write out how they act on a suitable test function u(x): (a) p(x) = (x - 2)'(x) (b) (x) = (1 + sin x) [ (x) + ('(x)] (c)...
Write out the incidence matrix of the following digraphs. (a) (b) (c) (d) (e) (f)
Let x* be the solution of the equation h(x*) = 0. Show that the critical point of a generalized first-order polynomial is x* - 1 and the point of inflection is x* - 2. Polynomials form a useful set...
The following trial balance is taken from the General Fund of the City of Jennings for the year ending December 31, 2017. Prepare a condensed statement of revenues, expenditures, and other changes in...
What is the source of most franchisorfranchisee litigation? Which party does the standard franchise contract favor?
A barbershop has been using a level workforce of barbers five days per week, Tuesday through Saturday. The barbers have considerable idle time on Tuesday through Friday, with certain peak periods...
As discussed in Section 5.2, the lumped capacitance approximation may be applied if $B_{i} <0.1$, and, when implemented in a conservative fashion for a long cylinder, the characteristic length is...
On January 1, 2010, the Kelly Corporation acquired bonds with a face value of $500,000 for $483,841.79, a price that yields a 10% effective annual interest rate. The bonds carry a 9% stated rate of...
A proton accelerates from rest in a uniform electric field of 670 N/C. At one later moment, its speed is 1.30 Mm/s (nonrelativistic because v is much less than the speed of light). (a) Find the...
A transfer machine has six stations that function as follows: In addition, transfer time = 0.18 min. Average downtime per occurrence = 8.0 min. A total of 20,000 parts must be processed through the...
If f C1. should (f y)' = f ' or f + f '?
(a) Use duality to justify the formula f(x)'(x) = f(0)'(,x) - f'(0)8(x) when f C1. (b) Find a similar formula for f(x) (n) for the product of a sufficiently smooth function and the nth derivative...
Goliath plc is a food wholesaler. The most recent financial statements of the business are as follows: All sales and purchases are made on credit. The business is considering whether to grant...
An open loop transmittance is $G(s)=\frac{K(1-s)}{(1+s)}$. This is unity feedback configuration, will be stable for (a) $|\mathrm{K}|>1$ (b) $\mathrm{K}>1$ (c) \(\mathrm{K}
The Nyquist plot of a loop transfer function $\mathrm{G}(j \omega) \mathrm{H}(j \omega)$ of a system encloses the $(-1, j 0)$ point. The gain margin of the system is (a) less than zero (b) zero...
The open loop transfer function of a unity feedback control system is $\frac{10}{(s+5)^{3}}$. The gain margin of the system will be (a) $20 \mathrm{~dB}$ (b) $40 \mathrm{~dB}$ (c) \(60...
The Nyquist locus of a transfer function is given below: The locus is modified as shown below on addition of pole or poles to the original $\mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s})$. Then, the...
Non-minimum phase transfer function is defined as the transfer function 1. which has zeros in the right-half of $s$ plane. 2. which has zeros only in the left-half of $s$ plane. 3. which has...
Domestic Transfer and Storage is a large trucking company headquartered in the Midwest. Rapid expansion in recent years has been financed in large part by debt in a variety of forms. In preparing the...
Find the radius of convergence of? 1.2.3 1.3.5 (2n-1) r2n+1 -1
If f(x) = in (2x + x sin x), use the graphs of f, f, and f to estimate the intervals of increase and the inflection point of f on the interval (0, 15).
Investigate the family of functions f(x) = in (sin x + C). What features fo the members of this family have in common? How do they differ? For which values of C is f continuous on ( , )? For which...
Investigate the family of functions f(x) = cxecx2. What happens to the maximum and minimum points and the inflection points as c changes? Illustrate your conclusions by graphing several members of...
The Pew Internet and American Life Project reported on the widespread use of the Internet to search for information regarding experimental treatments or medicines. From telephone interviews of 1005...
write the differences between Microprocessors and Microcomputers. compare between them and draw the block diagram for each one. B) define the interface and mention it's types with brief description....
Write a program that prompts the user for the constitutive parameters (relative permittivity, relative permeability, and conductivity) in medium 1 and medium 2 separated by a planar surface. You are...

Simplify the following generalized functions; then write out how they act on a suitable test function u(

Question:

51(X)-82(x)

Step by Step Answer:

a b c d e ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions