Dual Definition and 354 Threads

I am struggling to understand the voltages present in the circuit below. So as stated in the diagram, there is 30V AC at the secondary of the transformer, this is equivalent of 42.4Vpeak. The bridge rectifier changes this to DC and drops the voltage down to roughly 26.3Vpeak DC where each diode...

I need windows on my mac to run some modeling programs, but I'm not sure whether go for dual boot or virtual desktop. I have all my programs already installed and I fear that dual boot + installing all the programs again will suck too much memory space... on the other hand I have never enjoyed...

This is from Kreyszig's Introductory Functional Analysis Theorem 2.9-1. Let $X$ be an n-dimensional vector space and $E=\{e_1, \cdots, e_n \}$ a basis for $X$. Then $F = \{f_1, \cdots, f_n\}$ given by (6) is a basis for the algebraic dual $X^*$ of $X$, and $\text{dim}X^* = \text{dim}X=n$...

I have been trying different distributions of GNU/Linux on virtual box. However, they are relatively slow with some lagging, and if I watch something on YouTube, sometimes the video and sound won't be smooth. I allocated 3 GB RAM, and 20 GB of hard disk for each distribution. Probably this is...

Homework Statement Use the relation ##\langle \vec e^a, \vec e_b \rangle = \delta^a_b## and the Leibniz rule to give an expression for the derivative of a dual frame vector ##\frac{\partial \vec e_b}{\partial x^a}## in terms of the connexion components. Homework EquationsThe Attempt at a...

Reading about collapse and Born rule it gives strong feeling that there is semantic mess in QM with the word "measurement". Wikipedia describes Born rule in following way: In its simplest form it states that the probability density of finding the particle at a given point is proportional to the...

Hi everyone!I'm trying to obtain the natural and dual basis of a circular paraboloid parametrized by: $$x = \sqrt U cos(V)$$ $$y = \sqrt U sen(V)$$ $$z = U$$ with the inverse relationship: $$V = \arctan \frac{y}{x}$$ $$U = z$$ The natural basis is: $$e_U = \frac{\partial \overrightarrow{r}}...

Here it is a simple problem which is giving me an headache,Recall from class that in order to build an invariant out of spinors we had to introduce a somewhat unexpected form for the dual spinor, i.e. ߰ψ = ψ†⋅γ0 Then showing that ߰ is invariant depends on the result that (ei/4⋅σμν⋅ωμν)† ⋅γ0 =...

Please help. I do understand the representation of a vector as: vi∂xi I also understand the representation of a vector as: vidxi So far, so good. I do understand that when the basis transforms covariantly, the coordinates transform contravariantly, and v.v., etc. Then, I study this thing...

What's the purpose of this dual coil? It has a blue and red cable. It stood alone, mounted (isolated) on the chassis of a PC PSU. It's in good condition, so I'm keeping it, but what can be achieved with it?

I've been having some trouble with this problem for a while. (Its not a homework or coursework problem) Its a part of an experimental set up that I'm building and this is a simplified version of it. I have a rigid rod which is hinged at a point and can pitch or heave about that location. There...

Good morning and my compliment for their infinite knowledge contained in this forum. I'm struggling to keep being my girlfriend's hero. I have here a nail led 36w UV led lamp that failed last week. Bulbs are tested all ok and connected in two channels each channel in series of 9 LEDs of 2w...

Hello. So due to some life circumstances i was not able to finish all my coursework of my 3-year BS.c program last year. Thus i have about 24 credits I will take next year. My plan was to finish those courses, and then along that take courses in another university, in biochem on the side. That...

(From Hoffman and Kunze, Linear Algebra: Chapter 6.7, Exercise 11.) Note that ##V_j^0## means the annihilator of the space ##V_j##. V* means the dual space of V. 1. Homework Statement Let V be a vector space, Let ##W_1 , \cdots , W_k## be subspaces of V, and let $$V_j = W_1 + \cdots + W_{j-1}...

stereo jack from a computer to a set of computer speakers and driven by a constant tone on a single track in Audacity do both speakers get the same signal in phase? should I copy and paste the signal into two separate tracks and send them left and right to get two identical phase signals left...

There is this bike manufactured in India with a 180CC single cylinder petrol engine with Twin Spark plugs. They highly market their "twin spark technology". Well according to my knowledge, I don't think that will make much difference in performance and efficiency. What do you think? Is this just...

Hi everybody! To be concise -My undergraduate majors are math and physics -I want to go on and do research in physics (probably theoretical/mathematical physics) and be a professor. -My GPA is a 3.98 and Real Analysis and Abstract Algebra will likely drag down my GPA (I'm currently in these...

For work I had to go get a new windows 10 laptop for various reasons. I'd also like to add Ubuntu 16 on it and dual boot. Anyone know of any reasons why this might be a problem? I remember reading a while back concerns about UEFI bios stuff locking up the computer. I'm getting tired...

This is a multiple choice question that, after one incorrect attempt, I got correct; however, I want to actually understand what the explanation means. I'm hoping someone here can help. Homework Statement Two electrons, each with mass m and charge q, are released from positions very far from...

I am a dual mexican and american citizen but I study in Mexico and I need to apply to other colleges for an international exchange. My question to you is: do you think I should apply to other colleges as a mexican or as an american? I'm applying to Canada, Europe, and the US. I was thinking...

If we seek a bijection $$\wedge^p V \to \wedge^{n-p} V$$ for some inner product space ##V##, we might think of starting with the unit ##n##-vector and removing dimensions associated with the original vector in ##\wedge^p V ##. Might this be expressed as a sequence of steps by some binary...

The determinant of some rank 2 tensor can be expressed via the exterior product. $$T = \sum \mathbf{v}_i \otimes \mathbf{e}_i \;\;\; \text{or}\sum \mathbf{v}_i \otimes \mathbf{e}^T_i $$ $$ \mathbf{v}_1\wedge \dots \wedge \mathbf{v}_N = det(T) \;\mathbf{e}_1\wedge \dots \wedge\mathbf{e}_N$$ The...

The following question/thought experiment is based on the dual nature (particle/wave) of electromagnetic radiation. Consider the emisson of a single photon on a 3D grid along the x-axis with its origin at (0,0,0). The only matter in this experiment consists of “electrons” found only in...

I have been trying to prove the following theorem, for a finite dimensional vector space ## X ## and its dual ## X^* ##: Let ## f:X\rightarrow X^* ## be given by ## f(x) = (x|\cdot) ##, where ## (x|\cdot) ## is linear in the first argument and conjugate linear in the second (so I am using the...

I can't understand how de broglie proves that an electron can have wavelength and momentum just like a photon,

Hello all! I've just started to study general relativity and I'm a bit confused about dual basis vectors. If we have a vector space \textbf{V} and a basis \{\textbf{e}_i\}, I can define a dual basis \{\omega^i\} in \textbf{V}^* such that: \omega^i(\textbf{e}_j) = \delta^i_j But in some pdf and...

I'm still exploring which field is for me, and to ask which is better would be pointless. So instead I want to know: what exactly is the difference between a Computer Science and Electrical Engineering Dual Major/Degree as opposed to a Computer Engineering Major? I realize computer engineering...

I am reading Segei Winitzki's book: Linear Algebra via Exterior Products ... I am currently focused on Section 1.6: Dual (conjugate) vector space ... ... I need help in order to get a clear understanding of an aspect of the notion or concept of the dual basis $$ \{ e^*_1, e^*_2, \ ... \ ...

The dark matter crisis: falsification of the current standard model of cosmology Pavel Kroupa (AIfA, Bonn) (Submitted on 11 Apr 2012 (v1), last revised 20 Jun 2012 (this version, v2)) The current standard model of cosmology (SMoC) requires The Dual Dwarf Galaxy Theorem to be true according to...

Homework Statement Homework Equations[/B] The Attempt at a Solution From that point, I don't know what to do. How do I prove linear independence if I have no numerical values? Thank you.

Homework Statement A diesel engine works on the dual combustion cycle and has a compression ratio of 20/1. At the beginning of the compression process the pressure and temperature are 1.0 bar and 22°C respectively. In the cycle, heat is added at constant volume until the pressure has increased...

Apologies if this is a really trivial question, but I've never been quite sure as to the usage of the terminology dual space. I get that given a vector space ##V## we can construct a set of linear functionals that map ##V## into its underlying field and that these linear functionals themselves...

interesting new paper on possible new research direction for LQG http://arxiv.org/abs/1511.07332 Towards self dual Loop Quantum Gravity Jibril Ben Achour (Submitted on 23 Nov 2015) In this PhD thesis, we introduced a new strategy to investigate the kinematical and physical predictions of self...

Homework Statement Using 26.40, show that a pseudovector p and antisymmetric second rank tensor (in three dimensions) A are related by: $$ {A}_{ij} = {\epsilon}_{ijk}{p}_{k} $$ Homework Equations 26.40: $$ {p}_{i} = \frac{1}{2}{\epsilon}_{ijk}{A}_{jk} $$ The Attempt at a Solution This...

Electric and magnetic parts of Maxwell's equations are kind of similar, so physical effects relating these properties have many 'dual' analogues - with exchanged places. For example in Aharonov-Bohm effect, the phase of charged particle depends on side of magnetic flux tube it comes through...

Before I really explain and go into the point of this thread, I'd like to preface it with the fact that I have scoured the forums and read quite a few posts on "Dual Majoring with CS and Physics" and many of them have good advice, but my situation may require more specifics. I've been into...

I have recently put a Dual windows/Linux system on my laptop. One of the packages within Mathematica was only compatible within the Linux environment so it was suggested I do this dual boot. Since the two operating systems are independent (as far as I understand), I will need to reinstall...

Hi everyone, I am trying to make a Summing Amlifier. I have simulated on computer where it is working correctly, but on real circuit it is showing some mal functioning. I am using OP 27 Op Apmp. The circuit diagram is attached. When I try to add DC voltage to AC sine wave, initially sine wave...

I am currently finishing up my undergraduate degrees (in physics and mathematics) and would very much like to do a dual masters in engineering and physics (eventually going on to get my physics PhD). Is this feasible and/or worth it?

Hello all, I'm having a minor annoyance in proving an identity. The identity is the following \star\text{d}\star A_p = \frac{(-)^{p(D-p+1)-1+t}}{(p-1)!}\nabla_\mu A^\mu_{\,\, \mu_1 \cdots \mu_{p-1}}\text{d}^\mu_1\wedge \cdots \wedge \text{d}^\mu_{p-1} I'm stuck at the first step of proving...

Hi everyone, So I'm going through a chapter on dual spaces and I came across this: "A key property of any dual vector ##f## is that it is entirely determined by its values on basis vectors. ## f_i \equiv f(e_i) ## which we refer to as the components of ##f## in the basis ##{e_i}##, this is...

I'm confused by the following passage in our book (translated). An alternative too choosing the normed tangent vectors ##\vec e_i = \frac{1}{h_1}\frac{\partial \vec r}{\partial u_i}## with scale factors ##h_i = \left| \frac{\partial \vec r }{\partial u_i} \right| ## is to choose the normal...

I watched an interesting video on YouTube by veratisirm where he had a meter long metal rod with a huge metal fly wheel on the end of it. Long story short he could barely lift the thing but under full spin he could just about swing the thing like a sword. the only thing was the precession wanted...

So, I understand that the dual space, V^{\ast} of a vector space V over a scalar field \mathbb{F} is the set of all linear functionals f^{\ast}:V\rightarrow\mathbb{F} that map the vectors in V to the scalar field \mathbb{F}, but I'm confused as to the meaning of the term dual?! Is it just that...

Hi, I would kindly appreciate it if someone could help me with my simulation problem. I am trying to simulate dual porosity in coal and the interaction of coal matrix and fracture flow. The problem I'm having is I can't assign separate domains with different pressures for matrix and fracture in...

why in dual cycle heat addition at constant volume process is first then after heat addition at constant pressure process is done?

why light shows both particle and wave nature?

Can anyone describe in detail the exact device used when detecting single photon/electron presence through a slit in a dual slit experiment. For an electron I suspect a coil is used to detect the electron passing through without destroying it, but for a photon, it's not possible to detect a...

Im debating between two options. Background: I started out as ME and then transferred early to EE. Currently I'm 1/3 of the way to an EE bachelor and a few CS classes deep. First I was thinking of doing a CS minor with my EE major (5 years), but then I realized that with an extra year of...

Hi all, Here is my story. My school offers BA and BS for both physics and math. I am currently a junior in the BS programs for both physics and math. The only difference between the two are merely the language courses verses the two science and society courses (S&SC). I have been told about the...