Kernel Definition and 211 Threads

I have this remote server where I loaded the ISP-provided OS, namely Ubuntu 22.04. The lsb_release -d shows "Ubuntu 22.04.4 LTS" and uname -r shows "5.2.0". My problem arose when there seemed to be missing modules for kernel 5.2.0 in /lib/modules/5.2.0 for my needs. There is also no...

I started by converting the LSM from sum to integral form: $$f(x_c) = \sum_i[S(x_i)-F(x_i,;a,b,...)]^2 to f(x_c) = \int( S(x) - F(x-x_c)^2 dx$$ Since we are not interested in the other parameters (like offset), I assumed that they are fitted correctly and thus ignored them, turning...

I am not sure what the next step is: Linux kernel 4.18.0-425.3.1.el8.x86_64 work s fine. 4.18.0-425.10.1.el8_7.x86_64 works on two of my five machines. On the other two, I get the screen messages "CPU Stall" but nothing obvious in the log files. The troubled machines have older CPUs (Haswell)...

Does anyone know of a Kernel I can use to find a ring in a image ?

This is actually a solved exercise from a Brazilian book on Linear Algebra. The author presented the following solution: The kernel and image theorem tells us that dimension ##\dim V=n=\dim\ker\left(F\right)+\dim \text{im}\left(F\right)=\dim\ker\left(G\right)+\dim\text{im}\left(G\right)##. As...

This is a question from a mathematical statistics textbook, used at the first and most basic mathematical statistics course for undergraduate students. This exercise follows the chapter on nonparametric inference. An attempt at a solution is given. Any help is appreciated. Exercise: Suppose...

I hate to create a thread for a step in a calculation, by I don't know what else to do. I'm having a lot of trouble reproducing E. Weinberg's index calculation (found here https://inspirehep.net/literature/7539) that gives the dimension of the moduli space generated by BPS solutions in the...

I was reading the following webpage on Gaussian kernel but couldn't understand few details: https://www.imageeprocessing.com/2014/04/gaussian-filter-without-using-matlab.html . Would really appreciate it if you could guide me. Thanks in advance! Here you can find the high-res screenshot of the...

I did the first step, that is, show that f is a homomorphism. Now i need to find the kernel K of f. But i am a little confused how to find it. Seeing the image, can we say the kernel is {0,4}?

Let V = C[x] be the vector space of all polynomials in x with complex coefficients and let ##W = \{p(x) ∈ V: p (1) = p (−1) = 0\}##. Determine a basis for V/W The solution of this problem that i found did the following: Why do they choose the basis to be {1+W, x + W} at the end? I mean since...

Hey! :o Let $1\leq n,m\in \mathbb{N}$, $V:=\mathbb{R}^n$ and $(b_1, \ldots , b_n)$ a basis of $V$. Let $W:=\mathbb{R}^m$ and let $\phi:V\rightarrow W$ be a linear map. Show that $$\ker \phi =\left \{\sum_{i=1}^n\lambda_ib_i\mid \begin{pmatrix}\lambda_1\\ \vdots \\ \lambda_n\end{pmatrix}\in...

Hello, I'm currently studying the Fejér kernel, which has the form of . I want to know whether there are some methods to approximate this function into polynomials. Thanks a lot for the help!

I have been reading a lot about Reproducing Kernel Hilbert Spaces mainly because of their application in machine learning. I do not have a formal background in topology, took linear algebra as an undergrad but mainly have encountered things such as, inner product, norm, vector space...

ok I am new to this basis of kernel and tried to understand some other posts on this but they were not 101 enough Find the basis for kernel of the differential operator $D:C^\infty\rightarrow C^\infty$, $D^4-2D^3-3D^2$ this can be factored into $D^2(D-3)(D+1)$

I'm in my second year in college and I've taken an Operating Systems course that has a project component. I've been assigned Memory Forensics as my project topic. On approaching the professor I was told that I need to attempt to attack the Linux Kernel ( I'm guessing that means I need to write...

Hey! :o Let $K/F$ be a finite Galois extension and let $G= \operatorname{Gal}(K/F)$. For each $\sigma\in G$ we define $V_{\sigma}=\{\sigma (b)-b:b\in K\}$. Show that $V_{\sigma}$ is $F$-subspace of $\ker \operatorname{Tr}_{K/F}$. Show that $K/\mathcal{F} (\langle \sigma \rangle) \cong...

Hey! :o Let $q$ be a power of a prime and $n\in \mathbb{N}$. We symbolize with $Tr$ the map of the trace from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, i.e. $Tr:\mathbb{F}_{q^n}\rightarrow \mathbb{F}_q$, $\displaystyle{Tr(a)=\sum_{j=0}^{n-1}a^{q^j}}$. I want to calculate the dimension of the image...

We know that kernel of a homomorphism consists of all the elements that map to the additive identity, 0. Here is my naive question: Why don't we define the kernel as all of the elements that map to the multiplicative identity, 1? Why isn't there a name for the set of all elements that map to the...

Homework Statement I am translating so bear with me. We have two group homomorphisms: α : G → G' β : G' → G Let β(α(x)) = x ∀x ∈ G Show that 1)β is a surjection 2)α an injection 3) ker(β) = ker(α ο β) (Here ο is the composition of functions.) Homework Equations This is from a...

Suppose that we have, for purposes of example, the homomorphism ##\pi : \mathbb{R}^2 \to \mathbb{R}## such that ##\pi((x,y)) = x+y##. We see that ##\ker(\pi) = \{(x,y)\in \mathbb{R}^2 \mid x+y=0\}##. How can we enumerate all of the cosets of the kernel? My thought was that of course as we range...

Homework Statement Let ##\mathbb{F}_3## denote the field with 3 elements and let ##V = \mathbb{F}_3^2##. Let ##\alpha, \beta, \gamma, \delta## be the four one-dimensional subspaces of ##V## spanned by ##(1,0), (0,1), (1,1)## and ##(1,-1)## respectively. Let ##\operatorname{GL}_2...

Hey! :o Let $A\in \mathbb{C}^{2\times 2}$ and $L_A:\mathbb{C}^{2\times 2}\rightarrow \mathbb{C}^{2\times 2}, \ X\mapsto A\cdot X$. We consider the matrix \begin{equation*}A=\begin{pmatrix}-1 & 2 \\ 2 & -4\end{pmatrix}\end{equation*} and the basis \begin{equation*}B=\left \{\begin{pmatrix}1...

Homework Statement Are these functions homomorphisms, determine the kernel and image, and identify the quotient group up to isomorphism? C^∗ is the group of non-zero complex numbers under multiplication, and C is the group of all complex numbers under addition. Homework Equations φ1 : C−→C...

I was wondering about "writing a module to a linux kernel." This question haven't asked yet. Would you please explain why linuxers write such modules to a linux kernel? What is the reason? Thank you.

Before I begin learning what System Calls, Kernel, and Operating System is, I want to confirm that Operating System concepts like Multi-threading, Concurrency, Parallelism, Scheduling, Memory Management, Process Management, Network Management, Device Drivers can be implemented by using Linux...

Homework Statement Show that k(x,0)=δ(x). Where k(x,t) is the heat kernel and δ(x) is the Dirac Delta at x=0. Homework Equations k(x,t) = (1/Sqrt[4*π*D*t])*Exp[-x^2/(4*D*t)] The Attempt at a Solution I am just clueless from the beginning. I am guessing this is got to do with convolution...

Hi All, I am trying to see if there is a "nice" ( relatively straightforward) way of finding the solution/kernel of the map : ##f(A)=A^n -Id ## , where A is an ## k \times k ## matrix and ##n## is a positive integer. Question: what is the kernel of this map? Cranking out matrix coefficients...

[mentor note: thread moved from Linear Algebra to here hence no homework template] So, i was doing a Linear Algebra exercise on my book, and thought about this. We have a linear map A:E→E, where E=C°(ℝ), the vector space of all continuous functions. Let's suppose that Aƒ= x∫0 ƒ(t)dt. By the...

Hi at all On my math methods book, i came across the following Fredholm integ eq with separable ker: 1) φ(x)-4∫sin^2xφ(t)dt = 2x-pi With integral ends(0,pi/2) I do not know how to proceed, for the solution...

Homework Statement Show that if T is normal, then T and T* have the same kernel and the same image. Homework Equations N/A The Attempt at a Solution At first I tried proving that Ker T ⊆ Ker T* and Ker T* ⊆ Ker, thus proving Ker T = Ker T* and doing the same thing with I am T, but could not...

Homework Statement Let ##T:M_2 \to M_2## a linear transformation defined by ##T \begin{bmatrix} a&b\\ c&d \end{bmatrix} = \begin{bmatrix} a&0\\ 0&d \end{bmatrix}## Describe ##ker(T)## and ##range(T)##, and find their basis. Homework Equations For a linear transformation ##T:V\to W##...

I'm reading a book on vortex methods and I came across the above mentioned terms, however, I don't understand what they mean in mathematical terms. The book seems to be quite valuable with its content and therefore I would like to understand what the author is trying to say using the above...

Homework Statement Suppose T:V→U is linear and V has finite dimension. Prove that I am Tt = (Ker T)0 Homework Equations dim(W)+dim(W0)=dim(V) where W is a subspace of V and V has finite dimension. The Attempt at a Solution I first proved I am Tt ⊆ (Ker T)0. Let u be an arbitrary element of...

I have encountered this theorem in Serge Lang's linear algebra: Theorem 3.1. Let F: V --> W be a linear map whose kernel is {O}, then If v1 , ... ,vn are linearly independent elements of V, then F(v1), ... ,F(vn) are linearly independent elements of W. In the proof he starts with C1F(v1) +...

Hi, (This is more of a math question but I thought Astronomy people would be more familiar with the equation and how it's used) So in Monaghan 1992 (http://adsabs.harvard.edu/abs/1992ARA&A..30..543M, bottom of pg 554) a cubic spline in three dimensions is defined. I tried to integrate it (using...

Homework Statement Let ##n>1\in\, \mathbb{N}##. A map ##A:\mathbb{R}_{n}[x]\to\mathbb{R}_{n}[x]## is given with the rule ##(Ap)(x)=(x^n+1)p(1)+p^{'''}(x)## a)Proof that this map is linear b)Find some basis of the kernel b)Find the dimension of the image Homework Equations ##\mathbb{R}_{n}[x]##...

Hi! Everyone. I encounter some trouble in deriving the kernel of Laplace equation with prescribed boundary conditions. Given the following preposition: $$T(x, y) = \int_{-\infty}^{\infty}dx'\frac{y/\pi}{(x-x')^{2}+y^2}F(x')...[1]$$ satisfies the Laplace equation for ##x\in(-\infty, \infty)##...

I am working on a problem that goes like this: Show that $Ker (F) \cap I am (F) = \{0\}$ if $F: W \rightarrow W$ is linear and if $F^4 = F.$ I have the solution but there is one step which I need help: (the delineation is mine) (1) Suppose that there exists $x$, such that $x \in Ker(F) \cap...

Homework Statement Let P2 be the vector space of all polynomials of a degree at most 2 with real coefficients. Let T: P2→ℝ be the functioned defined by: ##T(p(t)) = p(2) - p(1)## a) Find a non-zero element of the Kernel of T. (I think I figured this one out, but I'm not too sure). b) Find a...

Homework Statement Let T: P4--->P3 be a linear transformation given by T(p)=p'. What is the kernel of T? Homework EquationsThe Attempt at a Solution T(a0+a1+a2x2+a3x3+a4x4)=a1+2a2x+3a3x2+4a4x3 Ker(T)= { T(p)=0} so, a1+2a2x+3a3x2+4a4x3=0 then a1=2a2x+3a3x2+4a4x3 Ker(T)= { (-2,1,0,0)...

Homework Statement φ is a homomorphism of groups. φ: ℝ^x -> ℝ^x, where φ(α) = α^4, for all α ∈ ℝ^x. Note that ℝ^x is a group under multiplication. Describe ker(φ) and Im(φ). Homework EquationsThe Attempt at a Solution This is another one of those problems that has me scratching my head due...

Mod note: Moved from Precalc section 1. Homework Statement Given l : IR3 → IR3 , l(x1, x2, x3) = (x1 + 2x2 + 3x3, 4x1 + 5x2 + 6x3, x1 + x2 + x3), find Ker(l), Im(l), their bases and dimensions. My language in explaining my steps is a little sloppy, but I'm trying to understand the process and...

Homework Statement Given the linear transformation l : R2 → R2 , l(x, y) = (2x − 2y, −x + y), write the matrix associated to l with respect to the standard basis of R2 , find Kerl, I am l, its bases and dimensions. Find all vectors of R2 that are mapped to (4, −2). Homework Equations Ax=0...

I am preparing myself for maths exam and I am really struggling with kernels. I have following six kernels and I need to prove that each of them is valid and derive feature map. 1) K(x,y) = g(x)g(y), g:R^d -> R With this one I know it is valid but I don't know how to prove it. Also is g(x) a...

So the theorem says: Suppose that ##U## and ##V## are finite dimensional vector spaces, and that ##T:U\to V##, ##S: V \to W##. Then ##\text{dim Ker }ST \le \text{dim Ker }S + \text{dim Ker }T##. Proof: Set ##U_0 = \text{Ker }ST## and ##V_0 = \text{Ker }S##. ##U_0## and ##V_0## are subspaces of...

Homework Statement Let T:[R[/3]→[R[/3] so that when u=[R][/3] and v=(1,2,1), then T(u)=u×v a) Show that T is a linear transformation. b) Find T((3,0,2)) c) Find a basis for Ker( T ). Give a geometric description of Ker( T ). Homework Equations Properties of a linear transformation: i) T(u+v)=...

Hi there! I'm new in the technique of Kernel Estimation, so it could be that the following questions are really elementary. There is something I don't understand about the bandwidths. Using R I have two functions to perform the estimate: kde2d from MASS bkde2D from KernelSmooth Here are my...

Let $V$ be a finite dimensional vector space over a field of characteristic $0$ and let $sym:\bigotimes^k V\to \bigotimes^k V$ be the map defined as $$ sym(\alpha)=\frac{1}{r!}\sum_{\sigma\in S_k}{^\sigma}\alpha $$ where $S_k$ is the permutation group on $k$ letters and ${^\sigma}\alpha$...

I'm trying to solve the exercise below in a book I'm reading. I inverted equation 1.3 to get ## \phi_{\mathbf k}(t)=\int \frac{e^{-i \mathbf k \cdot \mathbf x}}{(2\pi)^{\frac 3 2}} \phi(\mathbf x,t) d^3 \mathbf x ##. Then I put it in I to get: ## I=\int \int d^3 \mathbf x d^3 \mathbf y...

hi guys :D im having trouble with this proof, any hints? let V be a vector space over a field F and let T1, T2: V--->V be linear transformations prove that