Movatterモバイル変換

Question 1

0votes

1answer

52views

Computing Fourier transform for a real odd signal

Given a real and odd signal $x(t)$, such that $\vert X(\omega)\vert = e^{-\vert \omega\vert}$ is the magnitude of Fourier transform.Question: Find the Fourier Transform $X(w)$.My attempt:We know, $...

jayant

143

askedNov 21 at 21:48

Question 2

0votes

0answers

144views

The S.E-One Method for a particular class of functions

Into this textbook Book of Integrals: Exploring Species of Integrals and Their Techniquesof Miguel Santiago, I have read The S.E-One Method.Supposing to evaluate a definite integral over symmetric ...

Sebastiano

8,896

askedSep 16 at 15:55

Question 3

2votes

0answers

75views

Every odd function has a corresponding involution

Consider functions $f$ which are involutions, i.e.\begin{align}f(f(x))=x\quad \implies \quad f'(x)f'(f(x))=1.\end{align}Under the (Legendre-like) contact transformation\begin{align}f(x)=F'(X),\ ...

Eli Bartlett

2,506

askedJul 8 at 17:12

Question 4

3votes

2answers

203views

There exists at least one even function that is increasing

The following is an algebra exercise for public university applicants, where an increasing (or decreasing) function is understood in the strict sense:Determine if the following statements are True ...

bleaur

31

askedMay 25 at 4:45

Question 5

1vote

0answers

68views

Why can a rational function even in some argument be represented as a function of the square of that argument?

I am tackling some minor Analysis topic, which has nonetheless to do with rational functions and how they are integrated. My textbook says the following:If a rational function $R(u, v)$ is unaltered ...

Barbatulka

509

askedMay 8 at 11:19

Question 6

-2votes

1answer

162views

Odd functions like $\lfloor x \rfloor + 1/2$

Recently, it has come to my attention that $f(x)=\lfloor x \rfloor +\frac{1}{2}$ is an odd function.Verification:For $x\notin\Bbb{Z},$using $\lfloor x \rfloor + \lfloor -x \rfloor=-1$ we get that $$...

Aditya Teraiya

879

askedMar 20 at 2:10

Question 7

0votes

0answers

38views

Interpretation of boundary conditions

I am trying to interpret and visualize the effect that certain boundary conditions have on the future evolution of a wave. Assume $f(t,x)$ is solution to some wave equation in a box $x \in [-1,1]$ ...

Octavius

584

askedMar 1 at 14:43

Question 8

2votes

2answers

176views

How can the statements "$f(x) =x^3 - \frac4x$ is an odd function" and "if $f$ is an odd function, then $f(0)=0$" both be true?

In A Transition to Advanced Mathematics 8e pg. 52, there are two example proofs back to back that seem to contradict each other.One example proves "The function $f$ given by $f(x) = x^3 - \...

Eric

123

askedFeb 15 at 9:03

Question 9

4votes

3answers

192views

Find the minimum of $\sin (α-β-γ) \sin (α+β-γ) \sin (α-β+γ) \sin (α+β+γ)$

$α,β,γ\in\Bbb R,$$$f(α,β,γ):=\sin (α-β-γ) \sin (α+β-γ) \sin (α-β+γ) \sin (α+β+γ)$$Clearly, the maximum is $f(\frac{π}{2},\frac{π}{2},\frac{π}{2})=1$.I guessed the minimum is $-1$, but$$f(α,β,γ)=f(-...

hbghlyj

6,067

askedOct 25, 2024 at 8:33

Question 10

1vote

0answers

56views

How to prove that solutions of semilinear differential equations is even function?

My question comes from the book Stable Solutions of Elliptic Partial Differential Equations Louis Dupaigne, pages 30-32. Summary: Which uniqueness theorem to use for this differential equation ?I am ...

Richard

135

askedSep 19, 2024 at 11:22

Question 11

0votes

1answer

38views

In what sense is this column-sum=1, row-sum=2 matrix even, since the imaginary part of its Fourier vanishes?

Consider the following matrix$$M := \begin{pmatrix}1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 &...

Snared

1,058

askedAug 9, 2024 at 0:52

Question 12

2votes

1answer

130views

Puzzled by asymmetry of cosine integral

I used Mathematica to calculate the antiderivative of $\cos (\pi x)/x$. I obtained the cosine integral$$\int \frac {\cos (\pi x)}{x} dx = Ci(x)$$where$$\begin{aligned}Ci(x) &:= - \int_x^\...

Richard Burke

935

askedJul 4, 2024 at 14:35

Question 13

2votes

1answer

133views

Translation of odd and even functions

Let $\varphi: \mathbb{R} \to \mathbb{R}$ be a periodic function of period $L>0$, that is,\begin{equation}\label{periodicitycondition}\varphi(x+L)=\varphi(x),\; \forall\; x \in \mathbb{R}. \tag{1}...

pre-Hilbert

1,769

askedMay 25, 2024 at 21:55

Question 14

0votes

1answer

61views

Even/Odd with reference to the interval (domain)

As the definition goes, a function $f(x)$ is even if $f(-x)=f(x)$ and it is odd if $f(-x)=-f(x)$, in which the domain is not paid enough attention to.For example, $f(x)=x^2$ is even for any symmetric ...

Eureka

385

askedMay 15, 2024 at 22:57

Question 15

7votes

0answers

117views

Anything interesting known about this generalization of even and odd functions?

Let $n \in \mathbb N$. Let's say a complex function $f: U \rightarrow \mathbb C$ is "of type $k \pmod n$" if for one (and hence every) primitive $n$-th root of unity $\omega$,$$f(\omega z) =...

Torsten Schoeneberg

30.9k

askedMay 14, 2024 at 1:56

Movatterモバイル変換

Stack Exchange Network

Questions tagged [even-and-odd-functions]

Computing Fourier transform for a real odd signal

The S.E-One Method for a particular class of functions

Every odd function has a corresponding involution

There exists at least one even function that is increasing

Why can a rational function even in some argument be represented as a function of the square of that argument?

Odd functions like $\lfloor x \rfloor + 1/2$

Interpretation of boundary conditions

How can the statements "$f(x) =x^3 - \frac4x$ is an odd function" and "if $f$ is an odd function, then $f(0)=0$" both be true?

Find the minimum of $\sin (α-β-γ) \sin (α+β-γ) \sin (α-β+γ) \sin (α+β+γ)$

How to prove that solutions of semilinear differential equations is even function?

In what sense is this column-sum=1, row-sum=2 matrix even, since the imaginary part of its Fourier vanishes?

Puzzled by asymmetry of cosine integral

Translation of odd and even functions

Even/Odd with reference to the interval (domain)

Anything interesting known about this generalization of even and odd functions?

Hot Network Questions

Subscribe to RSS