Dual Definition and 354 Threads

So I've decided that I am going to become a physicist(a theoretical physicist , field is still undecided). I'd like to co-major in either math or engineering so I'd like you guys to evaluate Physics-Math Double Major as opposed to Physics-Engineering Double Major What are the adv/disadv of...

Has anyone in this forum started or finished this kind of program. If so, how did you get in? I imagine it requires perfect GPA and MCAT score, but is there other factors like what your major is or research done as an undergrad?

I'm going to school for chemical engineering with an emphasis in biotechnology, in the hopes of working for a corporation out of school, but eventually founding my own business. As I looked at the curriculum for chem engineering however, I realized I'll have a LOT of free time if I only do the...

Is the dual space a V* a sub set of V?

Hi all, I have - 2 ICs that requires -10v and +10v - 1 IC that requires -5v and +5v How can I power them using one dual dc supply? Thanks!

How to power an OpAmp using two batteries, so there's no connection to mains ground or neutral? This circuit requires ground to force the node connecting the batteries to be at zero potential. How can I achieve the same result without grounding? thanks.

I think I solved it a week ago, but I didn't write down all the things and I want to be sure of doing the things right, plus the excersise of writing it here in latex helps me a loot (I wrote about 3 threads and didn't submited it because writing it here clarified me enough to find the answer...

We recently had a long thread https://www.physicsforums.com/showthread.php?t=666861 about cases where raising and lowering indices isn't completely natural, i.e., where a vector "naturally" wants to be upper-index or lower-index. If you have a metric, then it's pretty clear to me what...

Will two-way SLI GTX 680's (overclocked) run any PC game on max spec @1920x1080 with smooth framerates? I read that the new GPU benchmark is Metro The Last Light. No other PC title will test your hardware like that game..

Hi, I'm learning about vector spaces and I would like to ask some questions about it. Suppose I have a vector space V, and a basis for V \{v_1, ... v_n\}. Then there is a dual space V^* consisting all linear functions whose domain is V and range is ℝ. Then the space V^* has a dual basis \{x_1...

I did a bit of searching and I don't get it. What is really the difference between single supply and dual supply op amps? Voltages are just a potential difference. Op amps usually do not have a ground pin so they should have no idea if I am connecting +-15 V or +30V,0V it should still drive...

Homework Statement Let (X,\|\cdot\|) be a reflexive Banach space. Let \{T_n\}_{n\in\mathbb{N}} be a sequence of bounded linear operators from X into X such that \lim_{n\to\infty}f(T_nx) exists for all f\in X' and x\in X. Use the Uniform Boundedness Principle (twice) to show that...

Homework Statement Let C be a non-empty convex subset of a real normed space (X,\|\cdot\|). Denote H(f,a):=\{x\in X: f(x)\leq a\} for f\in X^* (dual space) and a\in\mathbb{R}. Show that the closure \bar{C} of C satisfies \bar{C}=\bigcap_{f\in X^*,a\in\mathbb{R}: C\subseteq H(f,a)}H(f,a)...

1. X : Banach space Z : closed subspace of X Prove or disprove that X* ⊆ Z* where Z* and X* are dual space of Z and X, respectively. 2. X : normed space and f : X → R : linear functional. Assume that ∃a∈X and r∈(0,1] such that f(B(a,r))=R(Real numbers) where B(a,r) is open...

Hi, All: Let V be a finite-dimensional space, which can be decomposed as: V=Z(+)W . How can we express the dual of V in terms of the duals of Z, W? I think this has to see with tensor products, but I'm kind of rusty here. Any ideas, please?

In an earlier post (https://www.physicsforums.com/showthread.php?t=640804) I remarked on how I was wondering if I should double major in math and physics so I could would be well prepared for a Ph.D. in Mathematical Physics. I also expounded on a couple of (admittedly naive) physical conjectures...

Suppose X is a normed space and X*, the space of all continuous linear functionals on X, is separable. My professor claims in our lecture notes that we KNOW that X* contains functionals of arbitrarily large norm. Can someone explain how we know this, please?

Homework Statement Let va be a dual vector field. Show that the quantity ∂[a vb] transforms as a type (0, 2) tensor under coordinate transformations. Homework Equations wu' = (dxu / dxu') wu The Attempt at a Solution My main problem is that I don't know what the brackets mean...

Just like the title says, what is a dual vector. I am reviewing Panton's "Incompressible Flow", Chapter 3, and a brief section is dedicated to calculating the dual vector and its inverse. Unfortunately, along with many other concepts in this book (if you're into fluids mechanics I don't...

I enrolled at the University of Wisconsin-Eau Claire with the intent of finishing their dual degree program with UW-Madison for physics and nuclear engineering (http://www.uwec.edu/admissions/facts/dualdegree.htm). Heading into my sophomore year, it has become apparent that such a program may...

In short the question I am trying to answer is: 1. do the "waves-functions" from separate particle interfere? 2. do the Schrodinger equations predict the interference pattern caused by the interference of the "wave functions" of two separate particles? The above question is...

Hi ! I want to amplify the output of my hall effect current transducer ( CSLA2CD ). The output of my hall effect sensor is 15.6mVac. And I used a dual rail op - amp to amplify this small ac voltage which the gain is 101 ( as shown in the schematic below ). I tried to simulate using multisim...

Using iteration I've got a satellite flying around two gravity sources. (See picture) When using the iteration over a 100 times I see that TE, total energy slowly sinks so I need to make a correction after each iteration to insure that TE is constant. Trouble is I have several...

Hi all, I encounter a technical problem about tensor calculation when studying general relativity. I think it should be proper to post it here. Riemann curvature tensor has Bianchi identity: R^\alpha_{[\beta\gamma\delta;\epsilon]}=0 Now given double (Hodge)dual of Riemann tensor: G = *R*, in...

{(a_i)_j} is the dual basis to the basis {(e_i)_j} I want to show that ((a_i)_1) \wedge (a_i)_2 \wedge... \wedge (a_i)_n ((e_i)_1,(e_i)_2,...,(e_i)_n) = 1 this is exercise 4.1(a) from Spivak. So my approach was: \BigWedge_ L=1^k (a_i)_L ((e_i)_1,...,(e_i)_n) = k! Alt(\BigCross_L=1^k...

This isn't a homework problem, but it's so simple that it belongs here. Can someone please explain to me bra and ket notation? I've been consulting various books and they are all so abstract. Yesterday, my professor told me that a ket |ψ> represents a column matrix and a bra <ψ| represents a...

Hi, I was working through a Twistor paper and it was explaining the link between holomorphic vector bundles and anti self dual gauges and it had an equation like this, for electro-magnetism. \lambda^a \lambda^b(\frac{\partial A_{b\dot{b}}}{\partial x^{a\dot{a}}}-\frac{\partial...

So I know that the Hodge dual of a p-form A_{\mu_1 \mu_2\cdot \cdot \cdot \mu_p} in d dimensions is given by (*A)^{\nu_1 \nu_2 \cdot \cdot \cdot \nu_{d-p}} = C\epsilon^{\nu_1 \nu_2 \cdot \cdot \cdot \nu_{d-p}\mu_1 \mu_2 \cdot \cdot \cdot \mu_p}A_{\mu_1 \mu_2\cdot \cdot \cdot \mu_p} where C...

Hey everyone, I am currently pursuing a BS in Computer Science and am about half way through. I am really enjoying the program and want to finish it. I have also taken an interest in Biomedical Engineering and was considering starting on a BS in this area after I finished my degree in...

Hey All, Im creating this thread to share some of the information, and hopefully gain some information on dual skin walls. Dual skin walls are a fairly new advancement in facade design in North America, however they are more common in Europe. The first dual skin facade in North America...

trying to prove dual of "there are at least tree points on every line" Hi, Assuming the propositions of incidence: (1) on any two distinct points is at least one line. (2) on any two distinct points is at most one line. (3) on any two distinct lines is at least one point. and the...

Hi everyone, Pardon the neophyte question, but is a one-form the same thing as a dual basis vector? If not, are they related in some way, or completely different concepts/entities? Thank you!

I apologize for not having any attempted work, but I have no idea how to even begin tackling this proof. Any direction would be greatly appreciated! Mike Homework Statement Let V be a vector space, Let W1, ..., Wk be subspaces of V, and, Let Vj = W1 + ... + Wj-1 + Wj+1 + ...

Can anyone explain dual tensor and complex tensor with a simple situation.And even How tensor density is related to transformation of axis..THANKS IN ADVANCE

So if light acts like waves when interacting with huge objects and acts like regular particles when interacting with very small bodies like atoms and electrons.. now I know this might sound silly, but what if the photons were to be in the size of a tennis ball, and the electrons also relatively...

I read things like "When a dual layer DVD burner reads a dual layer disc, the read-laser readjusts its focus past the semi-transparent first layer of physical data, on to an additional layer of data." and "Reflectivity of both recording layers of a dual layer recordable disc is the similar...

I'm wrapping up my first two years at the Community College and I'll have an AS in MET and an AS in MFT. I like the manufacturing and I see good work with it and want to continue with it. My dilemma is whether to go to the expensive private Uni or stick with the State/Regional for the rest of...

I am currently a freshman a liberal arts college and have recently taken an interest in engineering as a possible career path. While my school does not directly offer an engineering degree, it does offer a 3-2 dual degree program at Dartmouth, where I spend my junior year and a 5th year there to...

Hey! New to the forums here, and I wonder if you guys could give me some help. I've got a problem! :D Problem: Let me give you the scenario. I've got some GPS equipment that runs on ignition, constant, and ground. I have a barge that has two motors, and two ignition switches. I need to power...

Homework Statement I attach a word document with the equations because I don't know how to write them on the post. My question reads: Show that Maxwell's equations Eq (1) is equivalent to Eq (3).Homework Equations The first term of Eq 1 reads: F sub alpha beta comma gamma. That means partial of...

Okay so I am given a 3D figure with 5 points. Keep in mind this model has the hyperbolic parallel property and satisfies the incidence axioms. The question is to construct the dual geometry and then to prove or disprove that it is an incidence geometry. My question is how do I go about...

Hey everyone, I am based in the UK and am deliberating whether I should go for a dual honours CS/Maths degree or jump for an Engineering one. I'm aware that in a dual honours while you do more than half of each degree, at the later stages some of the modules are picked so that they go...

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)...

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...