Vector-Field Consistency [nb 1] is a consistency model for replicated data (for example, objects), initially described in a paper [1] which was awarded the best-paper prize in the ACM/IFIP...
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Consider the position vector field $\vec{r}=(x,y,z)^T$. What would be a vector potential $\vec{A}$ for this field? I was thinking of something like $\vec{A}=(yz,zx,-xy)^T$, which gives $$\nabla\tim...
$\underline{G}=(8r^7x-5r^3y)\underline{i}+(-8r^7y+5r^3x)\underline{j}$ where $r=(x^2+y^2)^\frac{1}{2}$ How would I express the vector field as cylindrical coordinates? I have looked at various ex...
I wanted to know that in order to calculate the Line Integral of a Vector Field, is it necessary that the Vector Field has to be a Conservative Vector Field?
Let $T: V \to W$ be a linear transformation, Is it necessary for V and W are vector space over same field?, if they are not over same field then what can we say about that?
Johann Borenstein의 The Vector Field Histogram - Fast Obstacle Avoidance for Mobile Robots 내용을 정리한 포스트 입니다. VFH의 대략적인 내용은 다음과 같습니다. VFH(Vector Field Histogram)은 world model로써 2차원 cartesian histogram...
Is there a common way to find an inverse vector field to a known one? For example I have a real vector field defined by the following two equations: $$ x' = x + Δ_x $$ $$ y' = y + Δ_y $$ Where in t...
In wikipedia, the following sentence is in definition of vector field: Given a subset $S$ of $R^n$, a vector field is represented by a vector-valued function $V:S \rightarrow R^n$ in standard cart...
In a Riemannian Manifold $(M,g)$ a vector field $X$ is said to be Killing vector field if $L_X g$=0 and is said to be conformal if $L_X g= fg$ for some smooth real function $f$ on $M$. Also, the no...