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Questions tagged [connections]

In mathematics, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. (Def: https://en.wikipedia.org/wiki/Connection_(vector_bundle))

In mathematics, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. Reference: Wikipedia.

If the fiber bundle is a vector bundle, then the notion of parallel transport must be linear. Such a connection is equivalently specified by a covariant derivative, which is an operator that can differentiate sections of that bundle along tangent directions in the base manifold.

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U(1) connection as definition

My question is what is a U(1) connection? Can the U(1) connection be expanded in terms of the basis? EDIT: i.e., is there a relation between a U(1) connection and a 1-form?
PhilosophicalPhysics
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Calculate days needed for the 4 workers to complete an 80 person-months job

The workload required to develop a system is estimated at 80 person-months if it is carried out by one person. When four staff members with the same productivity work together to develop the system, each member’s productivity is expected to…
f855a864
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Calculate time needed to brute force a password

When the maximum time required to find an 8-character password consisting of only 26 lowercase alphabetic characters in a brute force fashion is 1, the maximum required time is ? if the length of the password is extended to 10 characters.…
f855a864
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Calculate time to fill an empty tank

An empty tank can be filled with water in 20 minutes by using Pipe A or in 30 minutes by Pipe B, and the tank filled with water can be emptied of water in 40 minutes by using Pipe C. When the three pipes A, B, and C work together,…
f855a864
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Map between two sets of points that minimizes their total distance

Let's have a set of $N$ points at positions $\vec{R}_i$, where $i=1...N$. They are displaced into arbitrary positions $\vec{r}_{M(i)}$, where $M(i)=1...N$. The problem is to find a map $M: i \mapsto M(i)$ such that $S = \sum_{i=1}^N…
Roman
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Natural identification between the difference of two principal connections and the difference of corresponding linear connections

$ω_1$ and $ω_2$ are two principal connection form on a principal G-bundle $P→M$. $E→M$ is an associated vector bundle to $P$. $∇_1$ and $∇_2$ are the two linear connections on $E$ corresponded to $ω_1$ and $ω_2$. Then, $ω_1-ω_2$ is a tensorial or…
jw_
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Connections and Projection Maps

Let $M$ be a manifold and let $\pi: TM\rightarrow M$ be the projection map. Taking the pushforward of $\pi$ we obtain a bundle map $$ \pi_\ast: T(TM)\rightarrow TM. $$ Let $$ V=\ker \pi_\ast $$ be the vertical subbundle of $T(TM)$. Let $\nabla$ be…
Gilbert Easton
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Big O notation in calculus and discrete math

Just to connect my knowledge, I want to know is the big O notation in algorithms similar to O(x) in Taylor Maclaurin of function in calculus?
Thong Nguyen Thanh
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Designing a Formula?

QUESTION: The half-life of a drug is the time it takes for a dose to reduce to half its initial amount. A doctor prescribes a 4mg sleeping pill with a half-life of 24 hours. Write down a formula connecting the mass, m, of drug remaining with …
itshanks
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