module Definition and 156 Threads

Homework Statement Let S = \{v_{},...,v_{n}\} be a subset of a module M. Prove that N = <<S>> = \{r_{1}v_{1} + ... + r_{n}v_{n} | r_{i} \in R, v_{i} \in S\} is the smallest submodule of M containing S. First you will need to formulate precisely what it means to be the smallest submodule...

Homework Statement Let M be a R-module and I is an ideal in R. Let IM be the set of all finite sums of the form: r_{1}v_{1} + ... + r_{n}v_{n} With r_{i} \in I and v_{i} \in M Is IM a submodule of M? Homework Equations A submodule of an R-module M is a nonempty subset S of M that is...

Hi guys. I am new here. Is there a bluetooth module which you can configure the range of the the module? For example from a 5 meter range to about 1 ft or less... Currently planning on using BTSerial1 Bluetooth module. Any idea of a less expensive and better bluetooth module? Im new to this...

So basically I want to go further into theoretical physics after my BSc. But I don't know what modules would be the best choice. The University I applied for only offers the following module choice, but they state that if I want another selection, the Dean must approve it. 1st year...

I am currently working on an algorithm which will ultimately be able to take as input a 3 matrices, (R,G,B) and convert each pixel value into hue saturation and intensity values. So far I have been able to get all but the hue portion to work properly. Here is the code thus far...

hello, i am doing gear calculations my problem: i get several point numbers for the module of the spur gear din 780 suggest a standard table with modules so i just have to wrap up my calculated modules, for example: 3.91 => 4 ? thank you vm !

Hi, i'm studying a MEng Electrical and Mechanical engineering course in the UK. I've just started second year and have been approved by my advisor to take on an extra module next semester in plasma and astro physics. This module is intended for 4th year physics students and won't count...

Homework Statement z=\frac{(1-3i)^{100} * i * (7-5i)}{5+7i} Homework EquationsFind module and argument of z. The Attempt at a Solution Assuming: |z_1 * z_2| = |z_1||z_2| |z|=\frac{|1-3i|^{100} * |i| * |7-5i|}{|5+7i|} And now calculate each module individually by "Pythagoras theorems"...

You are in training to be an astronaut. In one of your training simulations, your goal is to land a lunar excursion module (LEM) on the surface of the Moon. This LEM has two rocket engines attached to the center of the craft. The engines typically point at angles of 22.0° in opposite directions...

Module "equivalence" There is a problem in a book I'm not quite understanding. Let M be an R-module and let I=Ann(M). Show that M can be regarder as an R/I-Module where scalar multiplication is given by the rule m(I+r)=mr I don't understand what they mean by "regarded as". Am I suppose to...

Take P a free module over an arbitrary ring. Show P is projective. Definition of Projective: If f: M-->N and g: P-->N are module homomorphisms with f surjective, then if P is projective there exists homomorphism h such that h: P-->M with f(h(x))=g(x) for all x. Obviously f has a right...

I want to make my own usb based data acquistion module, and try interfacing it with labview? Now I have a few questions, since i am quite new to it: Where do I get started? Can I do the interfacing(with labview) via parallel port ? or serially ? Can the Module be made using PIC...

First of all, I'm not an electrician, I'm a medical student who occasionally grab a soldering iron for some fun. So if I'm asking something really stupid, I'm sorry. I found scheme forIR transciever on http://www.hardwaresecrets.com/article/86/2 and I'm plannig to build it. I was wondering is...

I am trying to build an electric password box that will trigger a relay when correct order of password is pressed (via push buttons). I am going to use the relay to open the main door of my home electrically (via motors). So if you have any suggestion for the password box, it will be of great...

Hi Does anyone have any experience with ambient power modules? I have a few questions, if anyone could answer any of them i would be most apreciative. 1) do they work? 2) how much power can they output? 3) how small can you make them? 4) how much could you make them for (in mass...

I have just bought an oopic module to control a robot, the problem is the cable for programing has a plug that will not fit into my laptop. http://www.oopic.com/pricing.htm Is there a way around this?

Determine, using the vector components, the module of the vector sum of the four vector data in the figure. Consider = 3V2 inches, b = 3 cm, c = 6 cm and d = 5 cm. Adopt: sin α (alpha) = 0.60; cos α (alpha) = 0.80 and sin 45 degrees = cos 45 degrees = V2/2...

I just ordered a DC to HV DC converter (the F40 model, datasheet here: http://www.emcohighvoltage.com/Fseries.PDF ) from eBay for $50. My intent is to charge capacitors such at the 400V 12,000uF one located here http://www.amazing1.com/capacitors.htm. The converter has output up to 4,000V...

I'm soon starting my 3rd year of my degree. Were allowed to select our modules now, and basically decide what we want to go into, i.e. fluids/thermo, materials, stress analysis etc. Were also given the opportunity to choose one module that is not engineering related. I was thinking about doing a...

Notations: M denotes an abelian group under addtion R denotes a commutative ring with identity ann(?): Let M be an R-module and r∈R v∈M, then ann(v)={r∈R | rv=0} Terms: R-module: a module whose base ring is R torsion element: A nonzero element v∈M for which rv=0 for some nonzero r∈R...

COMSOL RF module: urgent Hi i am a new user to comsol RF module. Actually I a want to model the heating of a material using IR waves... can i use the RF module (which illustrates microwave heating as an example) to model the IR heating...do we have options to change the frequency of wave from...

Hi, all, I am starting with calculating scattering cross sections of metallic nanoparticles. I have some doubt about what type of scattering boundaries conditions and PML to use, since near field shows some surface waves on PML´s inner side and some reflections which affect my far-field...

urgent help needed in COMSOL3.3a-heat transfer module hi friends... I am doing a heat transfer problem in 3D...I have designed a heating device in micro range (exactly similar to the heating device in component library) and kept 3 layers of blocks of material (Si, SiO2, Fe ). I am confused...

Why couldn't a module have a finite basis and an infinite one?

Hi I've started a mechanics module and just wanted to know, what is the difference between Young's Modulus ('e') and the E = Stress/Strain? Thanks! Jase

Hello, Excuse me if I ask something obvious here, but I can't prove it.. Say R is a ring and M an R-module. So, 0 \in M as M is an abelian group. I guess r0=0, no?! Can you tell me how we prove that? Again, sorry if I ask something obvious..

Okay, this is the question that i need to solve using mathematica: Define the function f(n) which counts the number of zeros in n if n is the integer greater than 0. If you input 105, 1005, 10005, find f(n). I want to use Module in this question and I just found out that i have to use...

Homework Statement K is a field with finite characteristic p, G is a finite group, and W is a set that G acts on transitively (so for all x,y in W, there exists g s.t. gx=y). It then says consider M=KW the permutation module. What is KW supposed to mean? I know for a group G that KG is...

Hello, anyone with some experience in Comsol? I have a few basic questions on the RF module thanks!

Let V be a countable dimensional vectorspace over a field F . Let R denote End_F V . Prove that V is a simple R-module. If $ e1 , e2 , . . .$ is a basis of V , then we have a module homomorphism φ_j from R to V , sending f in R to f (e_j ). Find the ker(φ_j) . Find Jac(R). here I...

My definition of an artianian module is : A module is artinian if every decending chain of submodules terminates. Let A be a semisimple ring and M an A-module. If M is a finite direct sum of simple modules then M is artinian. Proof: Suppose that M= S_1+...+S_n where + denotes direct...

could anyone give me a proof of this statement: The module is injective iff it is a direct summand of an injective cogenerator.

So, after looking at all the stuff those geniuses up at NASA came up with, I'm trying to figure out how to get the drag coefficient for the Apollo 13 command module reentry. Heres the stuff I thought were important: Entry-interface 400,000 ft 36,129fps Drogue chutes deploy at...

Homework Statement Suppose M is a D_module and N is a submodule. N is called pure iff for any y \in N and a \in D ax = y is solvable in N iff it is solvable in M. N is a direct summand of M iff there is a submodule K with M = N \oplus K. Prove: (1) If N is a direct summand, then N is pure. (2)...

Homework Statement Suppose M is a D_module and N is a submodule. N is called pure iff for any y \in N and a \in D ax = y is solvable in N iff it is solvable in M. N is a direct summand of M iff there is a submodule K with M = N \oplus K. Prove: (1) If N is a direct summand, then N is pure. (2)...

Homework Statement What would have been the force on the hatch of the Apollo 1 command module (Before the fire) during the "plugs out test" Homework Equations more info 14.8 PSI of pressure outside of the module and 17.5 PSI 1 PSI= 6 894.75729 pascals. 14.8 x 6894.74=102 042.152...

anyone got any tip before the test?? it will happen at march the 5th what is the best way to achieve my best grade possible?

Homework Statement Given an abelian group G with generators x and y, and relations 30x + 105y = 42x + 70y = 0, show it's cyclic and give its order. Homework Equations The Attempt at a Solution I'm guessing the proof basically involves cleverly adding 0 to 0 to show that x = ry or...

Hi.. How to calculate the power rating of PWM pulse train? Reg, Sridhar

Homework Statement Given a few vectors that span a module space, how do you find a set that is a basis for this spanned space consisting of entirely different vectors to the original spanning vectors? The Attempt at a Solution I assume you find what kind of space is spanned by the...

Homework Statement If an R module M is cyclic so M=Rm with annihilator(m)=(p), p prime then can we infer that M is isomorphic to R/(p) without any more infomation?

Let R be a commutative ring, with subring S. Let M be an R-module. Does there exist a S-module N such that N \otimes_S R \cong M as R-modules? Preferably with N a sub-S-module of M? Even better, can we choose such modules N so that if we have an R-module homomorphism f:M --> M' it...

Hi all, Great forum, I have been reading some cool stuff here for about a month. Heres my question: Using induction prove that 5 divides 8^n - 3^n, n Natural Number. I know its true for n = 1, but I get stuck on the n = k+1. I don't know how to proceed from here: 8(8^k) - 3(3^k)...

Hey guys, I'm self-teaching maths to preper myself for the next term of uni, so I'm reading this book on abstract algebra, and somewhere it says that R (the set of real numbers) is not finitely generated as a module over Q (set of rational numbers). Now, I can see that it's not, but i can't...

Obviously having been assigned two different terms indicates these two objects are different but as far as I know, algebra: vector space with the multiplication which takes two elements in vector space and give another in vector space module: vector space over ring(extending from field)...

Consider the following specification: pre n >= 1 post search module(a, n, number) = FOUND(a, number) reads a, n, number changes - mem - Remark: Let i be an integer number. Then, FOUND = 0 iff a does not contain number and FOUND = i iff a[i] = number. search module is the name of...

I have installed Python in a Windows environment and I want to load files to execute them in Python. I have tried "import testprogram.py" and it does load the program and executes it (all the program does is to print something out on the screen) but then there are error messages...

I'm going to take an extra module, from a choice of two, from my university's maths department next year and I was just wondering which is more interesting. The choice is Topology or Abstract Algebra.

hiya a few months ago i got a canon g3, upgrade from a eos 300. first stab in the digital world. now with non digital cams you had a shutter release input, which you could build your own sensors and whatnot for, for taking high speed pics etc etc. it was pretty much a case of applying the...

Hello everyone ! I'm currently working on a problem in Eugene Hecht's Physics book. It's about static fluid and the "compressibility module". I'm not sure this traduction makes sense, because my book is translated into French and I can't find the correct English expression. For those who have...