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    I Partitioning a whole number in a particular way

    Hi, Let W be the sum of all the people's weights, let P be the total number of pizza slices available. If: I have P slices of pizza (P<=W) I have n people I want to split the pizza with I want to use people's weight to determine how many slices they get (more weight -> more slices) I don't...
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    I Physics of a bell siphon

    I'm trying to build a home aquaponics system, and a key component of the design I got off the internet is a bell siphon. So I'm trying to understand the physics of this siphon effect so I can optimize the weight and dimensions of the siphon to fit the size of my system. From what I read on the...
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    Measuring torque acting on motor shaft?

    I have an electric motor that I am using to turn an auger to dispense pet food. I want to measure the average torque required to turn this auger at a given rpm. I know Powerin = Voltage into motor * Current into motor and Powerout = Torque exerted by shaft * RPM of auger and Powerout...
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    Piezoelectric Crystal Shoes?

    I was inspired by this article http://science.howstuffworks.com/environmental/green-science/house-music-energy-crisis1.htm to wonder if one could put piezoelectric crystals in the sole of a shoe and perhaps harness the energy to charge their iPod? Can someone let me know if this is feasible...
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    Calculate attractive force between Cu2+ and O2- ions.

    Homework Statement Calculate the attractive force between a pair of Cu2+ and O2- ions in the ceramic CuO that has an interatomic separation of 200pm. Homework Equations E_A= -\frac{(z_1\cdot e)(z_2\cdot e)}{4\pi\cdot\epsilon_o\cdot r} Where z_1 and z_2 are the valences of the two ion...
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    Finding number of atoms per cm^3 of zinc?

    Homework Statement Zinc has a density of 7.17 Mg/m^3. Calculate (a) the number of Zn atoms per cm^3, (b) the mass of a single Zn atom and (c) the atomic volume of Zn. Homework Equations atomic mass of zinc = 65.39 g/mol The Attempt at a Solution For part (a) I use the fact that...
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    Finding the energy of an electron from n=4 to n=2?

    Homework Statement Find the energy of a He+ electron going form the n=4 state to the n=2 state. Homework Equations E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2} Where m= mass of electron, z= atomic number, e= charge of an electron, n is the energy level. ^ I think those are...
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    Computing energy in the electron of Li 2+?

    Homework Statement Using the Bohr model of the atom, compute the energy in eV of the one electron in Li2+. Homework Equations E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2} Where m= mass of electron, z= atomic number, e= charge of an electron, n is the energy level. ^ I think...
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    Period of an Oscillating Particle

    Homework Statement A particle oscillates with amplitude A in a one-dimensional potential that is symmetric about x=0. Meaning U(x)=U(-x) First find velocity at displacement x in terms of U(A), U(x), and m. Then show that the period is given by ##4\sqrt{\frac{m}{2U(A)}}\int_0^A...
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    Help Understanding Quotient Groups? (Dummit and Foote)

    The definition given is... "Let ##\phi: G \rightarrow H## be a homomorphism with kernel ##K##. The quotient group ##G/K## is the group whose elements are the fibers (sets of elements projecting to single elements of H) with group operation defined above: namely if ##X## is the fiber above...
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    [True or False] Subring of R isomorphic to R/I?

    Homework Statement If ##I## is a proper Ideal in a commutative ring ##R##, then ##R## has a subring isomorphic to ##\frac{R}{I}##. Book says false... Homework Equations ##I## being a proper ideal in ##R## means ##I## is a proper subset of ##R## where (i) if ##a,b\in{R}## then ##a+b\in{R}##...
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    Showing elements of a Principal Ideal Domain are Relatively Prime?

    Homework Statement Let ##R## be a PID and let ##\pi\in{R}## be an irreducible element. If ##B\in{R}## and ##\pi\not{|}B##, prove ##\pi## and ##B## are relatively prime. Homework Equations ##\pi## being irreducible means for any ##a,b\in{R}## such that ##ab=\pi##, one of #a# and #b# must be...
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    Homomorphisms between two isomorphic rings ?

    Homework Statement True or False? Let R and S be two isomorphic commutative rings (S=/={0}). Then any ring homomorphism from R to S is an isomorphism. Homework Equations R being a commutative ring means it's an abelian group under addition, and has the following additional properties...
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    T or F? The prime field of R=Q[sqrt(2)] then Frac(R)=Reals

    Homework Statement If R=\mathbb{Q}[\sqrt{2}], then Frac(R)=\mathbb{R} Homework Equations \mathbb{Q}[\sqrt{2}]=\{a+b\sqrt{2} | a,b\in{\mathbb{Q}}\} Frac(R) is the fraction field of R is basically \{\frac{a+b\sqrt{2}}{c+d\sqrt{2}} | a,b,c,d\in{\mathbb{Q}}\}. The Attempt at a Solution Back...
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    Schools Is Math Grad School Right for Me?

    I can't decide if I want to pursue a PhD in math or not. I like the idea because it would let me keep studying math (interesting), and the challenge would help show me what I am capable of (intellectual potential). But I can't help but wonder if I would be happier if I changed my major to...
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    F^2=f but f=/=1 and f=/=0?

    Homework Statement Show there exists a function f: \mathbb{R} \rightarrow \mathbb{R} s.t. f^2=f but f\neq{0,1}. Homework Equations Here f^2=f means for arbitrary a\in{\mathbb{R}}, f(a)^2=f(a) The Attempt at a Solution I came up with the function f(a)= \begin{cases} 0, & \text{if }a\text{>...
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    Prove that every real number x in [0,1] has a decimal expansion.

    Homework Statement Prove that every real number x in [0,1] has a decimal expansion. Homework Equations Let x\in{[0,1]}, then the decimal expansion for x is an infinite sequence (k_{i})^{\infty}_{i=1} such that for all i, k_i is an integer between 0 and 9 and such that...
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    Is every Subgroup of a Cyclic Group itself Cyclic?

    Homework Statement Are all subgroups of a cyclic group cyclic themselves? Homework Equations G being cyclic means there exists an element g in G such that <g>=G, meaning we can obtain the whole group G by raising g to powers. The Attempt at a Solution Let's look at an arbitrary...
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    Let G be a finite group in which every element has a square root

    Homework Statement Let G be a finite group in which every element has a square root. That is, for each x in G, there exists a y in G such that y^2=x. Prove every element in G has a unique square root. Homework Equations G being a group means it is a set with operation * satisfying...
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    True or False? Every infinite group has an element of infinite order.

    Homework Statement True or False? Every infinite group has an element of infinite order. Homework Equations A group is a set G along with an operation * such that if a,b,c \in G then (a*b)*c=a*(b*c) there exists an e in G such that a*e=a for every a in G there exists an a' such...
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    Schools Types of Applied Math Grad School?

    I was wondering what are the main types of "applied math" I could choose to study in grad school and how I can know which one I would enjoy most? Math Classes I loved were: linear algebra, number theory, intro to real analysis, discrete math, intro to abstract alg Classes I disliked...
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    Y''*y' = x(x+1)

    Homework Statement \frac{d^2 y}{dx^2}\cdot\frac{dy}{dx}=x(x+1), \hspace{10pt} y(0)=1, \hspace{5pt} y'(0)=2 Homework Equations None I can think of... The Attempt at a Solution The only thing I even thought to try was turn it into the form: \frac{d^2 y}{dx^2}{dy}=x(x+1){dx}...
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