Dual Definition and 373 Threads

Hey guys, I've just started at grad school, and I'm going to upgrade my laptop for graduate school. I'll be doing a lot of coding in FORTRAN, so I definitely need to be running Linux on it. The question is, is it preferable to get a PC and dual boot it or to get a linux laptop, and not...

I didn't get the concept of dual or hybrid nature of nabla? I-e vector differential operator .. Is it means that nabla can produce a vector from scalar field (gradient) and scalar from vector field(divergence) ? What's the concept of Nabla's Dual nature ? Please explain..

I have decided to major my engineering degree in Electrical and Computer Engineering, however I only start this year. I am interested in the field of robotics, specifically the side of the programming, developing intelligent machines and artificial intelligence etc. My question is, would...

In the documentary the Fabric of the Cosmos Leonard Susskind remarks how confused he is that a photon could be both a wave and a particle, he says a rock is a rock, and a wave is a wave (a picture of an ocean wave crashing). How could a rock be a wave? To me the answer is obvious, a wave is...

Hi,i really need help on how to design a dual channel DC power supply that fulfills the following specifications : 1) Operation - User selection between independent adjustment for positive and negative output voltage, and series tracking mode (slave channel tracks the master channel) 2)...

Homework Statement Let v be a vertex of a d-polytope P such that 0 \in intP . Prove that P^* \cap \{y \in \mathbb{R}^d \mid\left < y, v\right>=1\ \} is a facet of P^{*} . Thanks Homework Equations The definitions are: P^*=\{ y\in\mathbb{R}^{d}\mid\left < x...

Hello all. I am in the process of designing a circuit that involves a resistor divider that connects to a buffer to be connected to a DAQ system. This circuit is being made because the input voltage coming in will be in the range of tens of volts, and what I want is a smaller Vpp wave...

If we're working in R^n and we consider the elements of a basis for R^n to be the column vectors of an nxn invertible matrix B, then what is the relationship between B and the matrix whose row vectors represent elements of the corresponding dual basis for R^n*? My guess, which Wikipedia helped...

I've recently been applying to colleges and looking at many of the universities dual core physics/engineering options, however, one of them also offer a "Pre-engineering" program. My question is simply: should I or should I not enter that program, or will the dual core physics/engineering option...

Homework Statement Let V be a finite dimensional vector field over F. Let T:V→V Let c be a scalar and suppose there is v in V such that T(v)=cv, then show there exists a non-zero linear functional f on V such that Tt(f)=cf. Tt denotes T transpose. Homework Equations Tt(f)=f°T...

Homework Statement Dual plate capacitor with two dielectric slabs placed between the capacitors and a battery supply's a voltage across the capacitors. The slabs are not equal in dielectric permeability. What is the charge at the interface of the two slabs? Homework Equations The...

Homework Statement If X and Y are normed spaces, define \alpha : X^* x X^*\rightarrow (X x X)^* by \alpha(f,g)(x,y) = f(x)+g(y). Then \alpha is an isometric isomorphism if we use the norm ||(x,y)|| = max(||x||,||y||) on X x Y, the corresponding operator norm on (X x Y)^*, and the norm...

Bit of background about me. It's a bit long, but I really need advice. I am a 24 year old living in an economically hard hit area of the country. I have dual degrees in psychology and english, and am currently working in a job that doesn't require my degrees. Originally, I went to school...

S={(x,0)|x>0} on R^2-{0},I need to calculate the closed Poincare dual of S. Assume \omega=f(x,y)dx+g(x,y)dy on R^2-{0} have compact support.Then we need to find a form \eta in H^1 (R^2 - {0} ) satisfying \int\limits_S {i^* \omega = \int\limits_M {\omega \wedge \eta } } , The book...

http://farm7.static.flickr.com/6125/6203213456_7daabe9662.jpg" This is my first post and I've never been here so I'm not sure this is where i should post my question, but if I'm wrong, pls correct me. This force sensor is to load my truck ontop of that shaft to determine it's drag force...

Hi, I want to know more about Dual Gate MOSFETs, i.e, their structure, working, advantages etc... Googling "Dual Gate MOSFET" didn't help at all! So please suggest some sources (online) where I can find more information on them. Also, where can I find more information on current...

Hi, Was wondering how dual input power strips work. I've seen them in data center racks, they have 2 mains power inputs wired to separate mains circuits. if one breaker trips then the strip still receives power from the other circuit. Do these strips have both power circuits wired to all the...

Homework Statement Light propagates as waves, but exchanges energy as particles Homework Equations I don't understand the second part, i.e., light exchanges energy as particle. I need the help of members in this regard The Attempt at a Solution

I've been reading Ballentine, Chapter 1. Have I got this the right way around? Taking our inner product to be linear in its second argument and conjugate linear in its first, the (continuous?) conjugate space of a Hilbert space \cal{H} is the following set of linear functionals, each identified...

My background in linear algebra is pretty basic: high school math and a first year course about matrix math. Now I'm reading a book about finite-dimensional vector spaces and there are a few concepts that are just absolutely bewildering to me: dual spaces, dual bases, reflexivity and...

hi, anyone can provide a simple explanation of what is a dual vector space? i have scoured the net and the explanations are all a tad too complicated for my understanding :( thanks

I have a question about mappings that go from a vector space to the dual space, the notation is quite strange. A linear functional is just a linear map f : V → F. The dual space of V is the vector space L(V,F) = (V)*, i.e. the space of linear functionals, i.e. maps from V to F. L(V,F)=...

Howdy, I need help sorting out a plan... again. It has come to my attention, the various opinions on how hard it is for a bachelors in physics to get a job. Here's what i originally had in mind: B.S. physics -> get a job -> M.S. & Ph.D. physics. It is indeed a crude plan but to specify the...

Hello, I am currently a Jr. in high school and I am very interested in physics and computers. I would like to get a Ph.D. in physics (with emphasis of quantum mechanics or particle physics). For a career I would eventually like to build/research dealing with quantum computing, or be a particle...

Hi, I'm trying to understand the natural transformation from V to V**, and the book has the theory but I think I'm needing an example. Lets say V=R^2 a vector space over K=R. B={(1,1),(1,-1)} a basis of V B={x/2 + y/2, x/2 - y/2} a basis of V* v = (3,2) a vector of V I want to get a...

Homework Statement straight wire along z axis carries charge density \lambda traveling in +z direction at speed v. construct field tenor and dual at point (x,0,0_ Homework Equations E=(2\lambda /4\pi\epsilono r)r^ B=(\muo I/2\pir)\phi^ The Attempt at a Solution I just don't get...

Homework Statement show that if V=M \oplus N, then V^*=M^o+N^o 2. The attempt at a solution So I need to prove for any f \in V*, f(\epsilon)=(g+h)(\epsilon), where g\in M^o and h\in N^o. (g+h)(\epsilon)=g(\epsilon)+h(\epsilon)=g(\alpha+\beta)+h(\alpha+\beta)=g(\beta)+h(\alpha), where\alpha...

Homework Statement Find the current in each branch of the circuit shown in the diagram (attached) if: V1 = 1V V2 = 4V R1 = 1\Omega R2 = 2\Omega R3 = 1\Omega Homework Equations V=I*R The Attempt at a Solution Okay, so I know that the voltage will be even across the parallel...

EDIT: finite dimensional only! Hello, I would like to ask a question; I understand that the cannonical "evaluation map" ( (p(v))(f) = f(v) , f is a functional, v in V ) from V -> V** is a "natural" isomorphism ( we don't have to select any bases, the isomorphism relies on no choices ), so V...

Hi: In the case of a finite-dimensional normed space V, it is relatively-straightforward to show that the kernel of any element of V* has 1 . ( Assume DimV=n): We take a linear map L:V-->F ; F the base field. We choose a basis to represent L, then we consider F as a vector...

Hi, Analysts: I was just looking for a nice proof that when V is an infinite-dimensional normed space, then V and V* are not isomorphic ( I think there is an exception if V is a Hilbert Space, by using Riesz Representation ). Also: while V is not always isomorphic to V* in the...

Homework Statement Let V = P_n(F), and let c_0, c_1,..., c_n be distinct scalars in F. For 0 <= i <= n, define f_i(p(x)) = p(c_i). Prove that {f_0, f_1,..., f_n} is a basis for V*. Hint: Apply any linear combination of this set that equals the zero transformation to p(x) =...

As E* is defined in some book as Hom(E, MXR). What could be the isomorphism between dual vector bundle E* and Hom(E, MXR)?

I am building an axial flux generator with dual rotor and single stator. I was doing calculations and have a magnet pole pair question i need help with, there are 12 magnets on each rotor with North pole on one rotor across from South pole on the other rotor. Since there are 24 total magnets...

Homework Statement An emergency supply consists of a small diesel engine driving an alternator. The output of the alternator is rectified and smoothed to produce DC. This has has to supply 10 amps of 110V emergency lighting and charge a 110V battery of internal resistance 2 ohms, If the...

Hello, I'm investigating duality for plane curves, and I came across an 'original' interpretation of the Biduality theorem , that uses the notion of caustic curve. Because everything is still very obscure to me, I try to share the whole with you, in the hope that we can help to fix ideas...

Let V be the space of polynomials of degree 3 or less over \Re. For every \lambda\in\Re the evaluation at \lambda is the map ev_{\lambda} such that V \rightarrow \Re is linear. How do we find the coefficients of ev_{2} in the basis dual to \{1,x,x^2,x^3\}?

Hey guys! I am going crazy... most books don't cover this and instead assume that the manifold is Riemannian or pseudo-Riemannian and has a metric tensor defined on it. I want a "generalized" hodge star. I have an orientable smooth manifold, that's IT. I have heard that there is a way to...

i need a link which can help me better understand primal and dual problems along with simplex Any help would be appreciated Thanks

Let us say we have source that can emit a single photon. We can in principle detect when the photon leaves the source due to the momentum kick. Now let us say this single photon passes through both slits and forms a dot on the far right of the screen. Now if we draw paths through the two slits...

I recently had a conversation with a friend (who for some reason likes number theory) about these split-complex numbers and dual numbers. I'm more into topology, so I've never heard of them and he brought up that the modulus (I've only heard this term used for complex numbers) of the...

why do we use a dual power supply? Why, for instance, do we use +12 and -12 volt instead of just a 12 volt power supply.

I was reading about dual spaces and dual bases in the book Linear Algebra by Friedberg, Spence and Insel (FSI) and they give an example of a linear functional, f_i (x) = a_i where [x]_β = [a_1 a_2 ... a_n] denotes the matrix representation of x in terms of the basis β = {x_1, x_2, ..., x_n} of...

Hello, I had read about the dual nature of electrons and the quantum numbers for some time ago and was always confused. 1-What does dual nature of electron mean? Does it mean that the electron moves in a sort of wave like motion around the nucleus? Where do the sub-shells and orbitals fit in...

I am familiar with the dual slit experiment up to the point where measuring at one slit made the interference pattern collapse. My question is has anyone tried using a sensor of some kind that has no memory or output? Does the observer have to be sentient? I have a feeling someone has...

Finite Dimensional Inner-Product Space Equals its Dual!? Let V be a finite dimensional inner-product space. Then V is 'essentially' equal to its dual space V'. By the Reisz Representation theorem, V is isomorphic to V'. However, I've been told that V=V', which I am having a hard time...

We just had two dual flow toilets installed in our house. They have two modes of flush, a small flow flush for #1 and a somewhat larger flow for #2. The small flow is really good, it uses very little water compared to our old style toilets. However the large flow is insufficient to clean the...

Hey guys, i am looking for some primer on conformal, dual conformal symmetry, respectively. I have to read a lot of stuff about scattering amplitudes for uni and in recent papers people talk a lot about these symmetries... unfortunately i am not so familiar with them, so does any of you know...

So I'm pretty sure I understand the formalism of dual vector spaces. (E.g. there exist objects that operate on vectors and take them to scalars. these objects themselves form a linear vector space). But I'm having difficulty understanding where this comes from intuitively. How would I know...

This is a very silly question. I can't believe I have forgotten. I have a 30v bench power supply and I am looking to test an op-amp running at +/- 15v. I have a supply which has a negative output/ positive output and inbetween a green common/earth output. How do I wire them to produce the +/-...