Naturally occurring radioactive materials (NORM) and technologically enhanced naturally occurring radioactive materials (TENORM) consist of materials, usually industrial wastes or by-products enriched with radioactive elements found in the environment, such as uranium, thorium and potassium and any of their decay products, such as radium and radon. Produced water discharges and spills are a good example of entering NORMs into the surrounding environment. Natural radioactive elements are present in very low concentrations in Earth's crust, and are brought to the surface through human activities such as oil and gas exploration or mining, and through natural processes like leakage of radon gas to the atmosphere or through dissolution in ground water. Another example of TENORM is coal ash produced from coal burning in power plants. If radioactivity is much higher than background level, handling TENORM may cause problems in many industries and transportation.
Hi everyone,
I'm having problems with task c
In the task, the norm has already been defined, i.e. ##||\vec{c}||=\sqrt{\langle \vec{c}, \vec{c} \rangle }## I therefore first wanted to calculate the scalar product of the cross product, i.e. ##\langle \vec{a} \times \vec{b} , \vec{a} \times...
Let ##A(z)## be a matrix function with a simple pole at the origin; in other words, we can expand it into a Laurent series of the form ##\frac1{z}A_{-1}+A_0+zA_1+\ldots##, where ##A_i## are constant matrices and ##A_{-1}\neq 0##. Fix ##\theta_0\in[0,2\pi)## and ##c\in(0,1)## (here ##1## could...
Dear Everybody,
I am having trouble with last part of this question.
I believe the answer is no. But I have to proof the general case. Here is my work for the problem:
Suppose that we have two distinct norms on the same vector space ##X## over complex numbers. Then there exists no ##K## in...
TL;DR Summary: For every Complex matrix proove that: (Y^*) * X = complex conjugate of {(X^*) * Y}
Here (Y^*) and (X^*) is equal to complex conjugate of (Y^T) and complex conjugate of (X^T) where T presents transponse of matrix
I think we need to use (A*B)^T= (B^T) * (A^T) and
Can you help...
Let ##F:[0,2\pi] --> Complex##
##F## is integrable riemman.
show for all ##\epsilon>0## you can find a ##g##, continuous and periodic ##2\pi## s,t: ##||f-g||_2<\epsilon##
What I tried ( in short ), which is nothing almost, but all I know:
because g in continuous and periodic, according to...
Hi, a question regarding something I could not really understand
The question is:
Let V be a space with Norm $||*||$
Prove if $v_n$ converges to vector $v$.
and if $v_n$ converges to vector $w$
so $v=w$
and show it by defintion.
The question is simple, the thing I dont understand, what...
Hi,
I was reading through some notes on standard problems and their corresponding dual problems. I came across the L2 norm minimization for an equality constraint, and then I thought how one might formulate the dual problem if we had an L1-norm instead.
Question:
Consider the following...
(We are working in a real Euclidean space) So, we have to show two things: (1)the arrow goes from left to right, (2) the arrow comes from right to left.
(1) if we're given ##\langle x, y \rangle = 0 ##
$$
|| x+ cy||^2 = \langle x,x \rangle + 2c\langle x,y\rangle +c^2 \langle y,y \rangle $$
$$...
In https://mathworld.wolfram.com/InnerProduct.html, it states
"Every inner product space is a metric space. The metric is given by
g(v,w)= <v-w,v-w>."
In https://en.wikipedia.org/wiki/Inner_product_space , on the other hand,
"As for every normed vector space, an inner product space is a metric...
Now, i am extremelly confused about all this thing. More preciselly, i can't understand how 1.29 was obtained. It was used the A representation? How do he uses it? There is something to do with the canonical basis?
I have to perform a calculation on my data. Here is an example of data from just one time step (data from other time steps would appear as additional rows).
X
Y
Z
Total
2
2
1
3
Total = SQRT(X2 + Y2 + Z2).
The calculation I have to do is: (N • N), where "N" is an average.
I tried...
I don't know how to start to find the bounded condition nor the norm. I thought about finding a maximal norm to show that it is bounded but I don't know how to continue.
I am studying about power spectrum analysis in high energy astrophysics.
I cannot understand why the Poisson noise level is set to 2 after applying Leahy normalization.
$$P_{j}=2 /_{N \mathrm{ph}}\left|a_{j}\right|^{2}$$
The above is the equation for leahy norm, Can I expand the equation from...
Greetings,
suppose we have ##h(u)=\frac{1}{2} \left\|Au-b \right\|_{2}^2## with ##A## a complex matrix and ##b,u## complex vectors of suitable dimensions. Write ##u=u_1 + iu_2## with ##u_1## and ##u_2## as the real and imaginary part of ##u##, respectively.
Show that ##\frac {\partial h}...
Greetings,
suppose we have 3d vectors ##\mathbf{x}_k, \mathbf{y}_k, \mathbf{b}## for ##k=1,...,N## and a 3x3 matrix ##\mathbf{W}## with real elements ##w_{i,j}##.
Are the following two results correct?
$$
\frac{\partial}{\partial \mathbf{b}} \sum_k ||\mathbf{Wx}_k+\mathbf{b}-\mathbf{y}_k||² =...
This is what I have so far: $$ |\alpha\Psi_1 + \beta\Psi_2|^2 = |\alpha|^2|\Psi_1|^2 + |\beta|^2|\Psi_2|^2 + \alpha^*\beta\Psi_1^*\Psi_2 + \alpha\beta^*\Psi_1\Psi_2^* $$
$$=> |\alpha\Psi_1 + \beta\Psi_2|^2 = |\alpha|^2|\Psi_1|^2 + |\beta|^2|\Psi_2|^2 + 2Re(\alpha^*\beta\Psi_1^*\Psi_2) $$
I am...
I tried to find the element of best approximation
||t_0||≤||t||, ∀ y ∈ π
Then |x_0|+|y_0|+|z_0| ≤|x|+|y|+|z| and we have x_0+2y_0+z=1 and x+2y+z=1.
But I don't know hoe to continue...
I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra ...
I need yet further help in fully understanding the proof of Proposition 8.7 ...Proposition...
I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra ...
I need some further help in fully understanding the proof of Proposition 8.7 ...Proposition...
I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra ...
I need some help in fully understanding the proof of Proposition 8.7 ...Proposition 8.7 and...
I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra ...
I need some help in fully understanding the concepts in Proposition 8.6 ...Proposition 8.6...
I am reading Michael Field's book: "Essential Real Analysis" ... ...
I am currently reading Chapter 9: Differential Calculus in \mathbb{R}^m and am specifically focused on Section 9.2.1 Normed Vector Spaces of Linear Maps ...
I need some help in fully understanding Theorem 9.2.9 (3) ...
I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra ...
I need some help in fully understanding some remarks by Browder after Lemma 8.4 pertaining to...
I am reader Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra ...
I need some help in fully understanding the differences between Andrew Browder and Michael...
I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ...
I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ...
I need some help in order to understand some...
I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ...
I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ...
I need some help in order to understand some...
I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ...
I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ...
I need some help with some remarks by Garling concerning a...
I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ...
I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ...
I need some help with some remarks by Garling concerning a subset...
Are all complex integers that have the same norm associates of each other?
I have seen definitions saying that an associate of a complex number is a multiple of that number with a unit. And I understand that the conjugate of a complex number is also an associate. But I am looking for a...
Homework Statement
Let X = ##\mathbb{R^m}## and ||.|| be a Norm on X. The dual norm is defined as ##||y||_*:=sup({\langle\,x,y\rangle :||x|| \leq 1})##
a) Show that ##||.||_*## is also a norm
b) Construct two norms ##||.||^O## and ##||.||^C## so that:
{##x:||x||^O=1##} is a regular octahedron...
Hi, initially I would like to share this link: https://books.google.com.tr/books?id=gWeVPoBmBZ8C&pg=PA25&lpg=PA25&dq=matrix+measure+properties&source=bl&ots=N1unizFvG6&sig=kxijoOVlPAacZDEdyyCwam4RQnQ&hl=en&sa=X&ved=2ahUKEwjd7o-Ap53dAhWJGuwKHdRbAO04ChDoATABegQICBAB#v=onepage&q=matrix measure...
I am really confused about coordinate transformations right now, specifically, from cartesian to polar coordinates.
A vector in cartesian coordinates is given by ##x=x^i \partial_i## with ##\partial_x, \partial_y \in T_p \mathcal{M}## of some manifold ##\mathcal{M}## and and ##x^i## being some...
Hello
A simple question.
I have a linear integral operator (self-adjoint)
$$(Kx)(t)=\int_{a}^{b} \, k(t,s)\,x(s)\,ds$$
where $k$ is the kernel. Can I say that its norm (I believe in $L^2$) equals the spectral radius of $K?$
Thanks!
Sarah
I am exploring Gaussian integers in terms of roots, powers, primes, and composites. I understand that multiplying two integers with norm 5 result in an integer with norm 25. I get the impression that there are twelve unique integers with norm 25, and they come in two flavors:
(1) Four of them...
Hey! :o
Let $G$ be the iteration matrix of an iteration method. So that the iteration method converges is the only condition that the spectral radius id less than $1$, $\rho (G)<1$, no matter what holds for the norms of $G$ ?
I mean if it holds that $\|G\|_{\infty}=3$ and $\rho (G)=0.3<1$ or...
I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ...
I am currently focused on Chapter 9: "Differentiation on \mathbb{R}^n"
I need some help with the proof of Proposition 9.2.3 ...
Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows...
I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ...
I am currently focused on Chapter 9: "Differentiation on \mathbb{R}^n"
I need some help with the proof of Proposition 9.2.3 ...
Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows:
In the above...
I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ...
I am currently focused on Chapter 9: "Differentiation on ##\mathbb{R}^n##"
I need some help with the proof of Proposition 9.2.3 ...
Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows:
In the...
I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ...
I am currently focused on Chapter 9: "Differentiation on \mathbb{R}^n"
I need some help with the proof of Proposition 9.2.3 ...
Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows...
I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ...
I am currently focused on Chapter 9: "Differentiation on ##\mathbb{R}^n##"
I need some help with the proof of Proposition 9.2.3 ...
Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows:
In the...
I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ...
I am focused on Chapter 1: Continuity ... ...
I need help with an aspect of Example 1.3.5 ... ...
The start of Duistermaat and Kolk's Example 1.3.5 reads as...
This is rather basic, and may be a misconception of the notation, however, I can't make the following sum up:
The following is given:
x_n(t) = 1 -nt , (if 0 <= t <= 1/n) and 0, (if 1/n < t <= 1)
However, this part I can't grasp this part in the book:
\begin{equation}
||x_n||^2 = \int_0^1...
I have calculated that a matrix has a Frobenius norm of 1.45, however I cannot find any text on the web that states whether this is an ill-posed or well-posed indication. Is there a rule for Frobenius norms that directly relates to well- and ill-posed matrices?
Thanks
Hi, I am working on a home-task to analyse the properties of a ODE and its solution in a Hilbert space, and in this context I have:
1. Generated a matrix form of the ODE, and analysed its phase-portrait, eigenvalues and eigenvectors, the limits of the solution and the condition number of the...
The "Operator Norm" for Linear Transformations ... Browder, Lemma 8.4, Section 8.1, Ch. 8 ... ...
I am reader Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra...
The "Operator Norm" for Linear Transfomations ... Browder, page 179, Section 8.1, Ch. 8 ... ...
I am reader Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra...
Let ##(M,g)## a manifold with a Levi-Civita connection ## \nabla ## and ##X## is a vector field.
What is the formula of ## | \nabla X|^2 ## in coordinates-form?
I know that ##|X|^2= g(X,X)## is equivalent to ## X^2= g_{ij} X^iX^j## and ##\nabla X## to ##\nabla_i X^j = \partial_i X^j +...