Exercise Definition and 578 Threads

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). In Chapter2: Direct Sums and Short Exact Sequences we find Exercise 2.1.6 part (iii). I need some help to get started on this exercise. Exercise 2.1.6 reads as follows: I am...

I've been doing some long bike rides (50+ miles) on routes which include long (several miles) of low to moderate grades, or short distances of 3 to 8% grades. I've experience what smelled like ammonia or amines while exhaling through my nostrils, or while drinking and breathing heavily. I've...

Homework Statement Hi! My problem : There is given substance for which (dV/dT)_p =ap^2,where V-volume,T-temperature,p-pressure,a-const. How much the entropy S will increase if T=const and pressure changes from p1 to p2?Homework Equations The Attempt at a Solution So 1) Mathematically the...

our teacher gave us this exercise but no one could solve it. he said : I hang the weight of 100 g in a spring. it elongates 1 cm. then i hang a 200 g in the spring. it elongates 2cm . what is the original length of the spring? i tried solving it but it just didn't go right.. how do i solve it??

Homework Statement Homework Equations V= iR Kirchoff's law for voltage The Attempt at a Solution On the left-most part of the circuit , I did use KVL (voltage law) and I ended up with Vs = i0 (R1+R2) which basically boils down to i0(2R) since R1 = R2 =R3 ... I'm not even...

Homework Statement We have Vz=6.8 V and Iz=5 mA,rz=20 Ohm,Izk=0.2 mA, R=200 Ohm and the source V= 9 volt a)Find the output voltage when we have the input voltage with the nominal value of 9 Volt. b)Find for the nominal value of the voltage,which is the maximum load current for which the...

I am trying to capitalize the first letter of every word in a sentence. Example. "hey what's up" would be "Hey What's Up". here is my code but nothing is changing the sentence. I thought everything was right. public static String cap(String aString) { String[] sentence = aString.split("...

Exercise 2.1.6 (i) of Berrick and Keating's book An Introduction to Rings and Modules reads as follows:Let M = M_1 \oplus M_2, an internal sum of right R-modules, and let \{ \sigma_1 , \sigma_2, \pi_1 , \pi_2 \} be the corresponding set of inclusions and projections. Given an endomorphism \mu...

Exercise 2.1.5 in Berrick and Keating: An Introduction to Rings and Modules reads as follows: Let M be an abelian group with Mc = 0 for some positive integer c, and put c = ab for coprime integers a,b. Write 1 = ar + bs, and define endomorphisms \alpha and \beta of M by: \alpha (m) = arm...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help with PART 2 of Exercise 1.1.11 (Chapter 1: Basics, page 33) concerning bimodules and endomorphisms... ... Exercise 1.1.11 reads as follows...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help with Exercise 1.1.11 (Chapter 1: Basics, page 33) concerning bimodules and endomorphisms... ... Exercise 1.1.11 reads as...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help with Exercise 1.2.8 (a) (Chapter 1: Basics, page 3o) concerning K^n as a K[T]-module ... ... First, so that MHB readers will understand the relevant notation for the...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help with Exercise 1.1.4 (iii) (Chapter 1: Basics, page 12) concerning matrix rings ... ... Exercise 1.1.4 (iii) (page 12) reads as follows: I can show that M_n (\alpha) is a...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). I need help with Exercise 1.1.4 (ii) (Chapter 1: Basics, page 13) concerning matrix rings ... ... Exercise 1.1.4 (ii) (page 13) reads as follows: I need help with Exercise (ii)...

For those who have read Halmos, in Section 6 Ordered Pairs (page 23 in my book), he gives a non-trivial exercise to find an intrinsic characterization of those sets of subsets of A that correspond to some order in A. I'm curious what that characterization is. A is suppose to be a quadruple...

Hey! :o I have the following exercise: If $p$ is prime, $p \nmid a$, $p \nmid b$, prove that $$a^p \equiv b^p \pmod p \Rightarrow a^p \equiv b^p \pmod {p^2}$$ My idea is the following: $$ a^p \equiv b^p \pmod p $$ $$ a^p \equiv a \pmod p $$ $$ b^p \equiv b \pmod p $$ $$ a \equiv b \pmod p...

For the diagram overleaf solve the problems by at least two different methods. Firstly use you knowledge of the equations of motion for motion under gravity where air resistance is neglected. Secondly, knowing the shape of the curve, find the relationship between height and horizontal...

The problem statement Let ##A ∈ K^{m×n}## and ##B ∈ K^{n×r}## Prove that min##\{rg(A),rg(B)\}≥rg(AB)≥rg(A)+rg(B)−n## My attempt at a solution (1) ##AB=(AB_1|...|AB_j|...|AB_r)## (##B_j## is the ##j-th## column of ##B##), I don't know if the following statement is correct: the columns of...

Homework Statement . Let ##A \in \mathbb C^{m\times n}##. Prove that tr##(A^*A)=0## if and only if ##A^*A=0## (here ##0## obviously means the zero matrix). The attempt at a solution. By definition of the trace of a matrix, the implication ← is obvious. I am having problems proving...

Homework Statement Homework Equations That is my solution: The Attempt at a Solution i solve my problem without ø=30°, I confused what this angle was used to do?

Hi everyone , this exercise was given in one of my midterms , but we didn't correct it and I'm wondering where I went wrong on it : Help will be extremely appreciated : Here is the statement : A block of mass m=2 kg is pushed by a spring with a spring constant of k=650 N/m which is...

A uniform solid sphere of mass M and radius R is rolling without sliding along a level plane with a speed v = 2.30 m/s when it encounters a ramp that is at an angle θ = 27.6° above the horizontal. Find the maximum distance that the sphere travels up the ramp if : 1- the ramp is frictionless...

Hi everyone, my physics final is coming in 3 days:cry: , and I really need to have an answer to this exercise , but I'm stuck ! I don't even understand the problem statement HELP ! A typical fastball is thrwon at approximately 90 mph and with a spin rate of 113 rpm (I don't understand what it...

Jorrie's calculator (Lightcone) makes cosmic history tables which tell you among other things the Hubble times in past years. For convenience let's temporarily use greek Theta Θ to stand for THubble so we don't have to write so much. Basic facts (definitions actually) are that Θ = 1/H and the...

Hi everyone , I'm really stuck with an exercise I can't solve any question and it is really important ! I need help : Two identical billiard balls start at the same height and at the same time and roll along different tracks,as shown in figure attached 1- Which ball has the highest speed...

Given the following premises: {¬p→r∧¬s, t→s, u→¬p, ¬w, u∨w} The conclusion is said to be: ¬t∨w Here are my steps. My conclusion is different from the supposed one, therefore I would appreciate it if any of you can point out my error. Thank You. 1 ¬p→(r∧¬s) Premise 2 p∨(r∧¬s) Implication law...

I am reading Dummit and Foote, Section 15.4 Localization. Exercise 12 on page 727 reads as follows: ------------------------------------------------------------------------------- Let R = \mathbb{R}[x,y,z]/(xy - z^2) , let P be the prime ideal P = (\overline{x}, \overline{y}) generated by...

This is a question for those with Shankar in their disposal. When studying from this book, Exercise 5.1.1 puzzled me. Now, it is easy to solve the exercise from 5.1.9. However, how would we expand psi in terms of the energy eigenfunctions,* if we did not have 5.1.9*, but instead started fresh...

I know that we use fat and other molecules to store energy, and that during exercise we use that energy. I understand that we use that energy by means of a chemical reaction that, among other things, transforms fat in something else. What I wonder is: what is fat ultimately transformed to...

Here is the problem statement: I thought it's a straightforward exercise on the divergence theorem, yet it looks like \operatorname{div} f = 0 . So the surface integral is zero? Am I missing some sort of a trick here? The exercise isn't supposed to be that easy. Any hints are very appreciated!

Hey! :o I got stuck at the following exercise... Could you give me an idea how to show this? Let $G=(V,E)$ be a connected graph and $u,v$ $\epsilon$ $V$.If $d(v,u)=k$,then there is a path $v=v_{1},v_{2},...,v_{k+1}=u$ so that $\{v_{i},v_{j}\}$ doesn't belong in $E$ for $j \geq i+2$...

Homework Statement Has anyone solved the part (d) of 5.6 problem of that book? I am unable to solve it. It asks the reader to prove that the radius ##R## of a rotating cylinder (rotating around its symmetry axis) has to be greater or equal than ##\frac{|S|}{ M } ##, in other words...

I'm looking for some advice for my final year project at university. My project is a design of an exercise machine for wheel chair users . The machine will look like a standard wheel chair but the wheels are a couple of centre meters off the floor. I want to add a mechanism to the wheels which...

I am reading R.Y. Sharp's book "Steps in Commutative Algebra" At the moment I am trying to achieve a full understanding of the mechanics and nature of LEMMA 1.11 and am reflecting on Exercise 1.12 which follows it. LEMMA 1.11 reads as follows: (see attachment)...

hi there, In this Ex ( see attached snapshot ), point b), the poisson bracket equation is not so straightforward to obtain. Please correct my Poisson Bracket expansion here : The first one which is provided is simpler : [ε,η] = εμδμηρ - ημδμερ = ζη and the monster one : [pε,pη] =...

Exercise 19 of Section 15.1 in Dummit and Foote reads as follows: ------------------------------------------------------------------------------ 19. For each non-constant f \in k[x] describe \mathcal{Z}(f) \subseteq \mathbb{A}^1 in terms of the unique factorization of f in k[x] , and...

Hello! I need some help at the following exercise: The language L={l ε {a,b}*:the word l does not contain the subword bba} is regular.Which are the equivalence classes of the relation \approx_{L} ? Also,which is the smallest(as for the number of states) deterministic automata that recognize...

I am reading Dummit and Foote Section 3.1: Quotient Groups and Homomorphisms. Exercise 17 in Section 3.1 (page 87) reads as follows: ------------------------------------------------------------------------------------------------------------- Let G be the dihedral group od order 16. G = <...

Dummit and Foote Section 15.1, Exercise 24 reads as follows: --------------------------------------------------------------------------------------------------------- Let V = \mathcal{Z} (xy - z) \subseteq \mathbb{A}^3 . Prove that V is isomorphic to \mathbb{A}^2 and provide an explicit...

Dummit and Foote Section 15.1, Exercise 24 reads as follows: --------------------------------------------------------------------------------------------------------- Let V = \mathcal{Z} (xy - z) \subseteq \mathbb{A}^3 . Prove that V is isomorphic to \mathbb{A}^2 and provide an explicit...

Dummit and Foote (D&F), Ch15, Section 15.1, Exercise 15 reads as follows: ---------------------------------------------------------------------------------------------------- If k = \mathbb{F}_2 and V = \{ (0,0), (1,1) \} \subset \mathbb{A}^2 , show that \mathcal{I} (V) is the...

Dummit and Foote (D&F), Ch15, Section 15.1, Exercise 15 reads as follows: ---------------------------------------------------------------------------------------------------- If k = \mathbb{F}_2 and V = \{ (0,0), (1,1) \} \subset \mathbb{A}^2 , show that \mathcal{I} (V) is the...

I am reading Dummit and Foote Chapter 15, Section 15.1: Noetherian Rings and Affine Algebraic Sets. Exercise 10 reads as follows: -------------------------------------------------------------------------------------------------------------------- Prove that the subring: k[x, x^2y, x^3y^2...

I am reading Dummit and Foote Chapter 15, Section 15.1: Noetherian Rings and Affine Algebraic Sets. Exercise 9 reads as follows: ------------------------------------------------------------------------------------------------ For k a field show that any subring of a polynomial ring k[x]...

I am reading R. Y. Sharp: Steps in Commutative Algebra, Chapter 5 - Commutative Noetherian Rings Exercise 8.5 on page 147 reads as follows: -------------------------------------------------------------------------------------------------- 8,5 Exercise. Show that the subring \mathbb{Z} [...

Homework Statement could you please check if this exercise is correct? thank you very much :) ##f(x,y)=\frac{ |x|^θ y}{x^2+y^4}## if ##x \neq 0## ##f(x,y)=0## if ##x=0## where ##θ > 0## is a constant study continuity and differentiabilty of this function The Attempt at a Solution...

We're usually just told that exercise is a great way to stimulate the movement of glucose into cells. But how does it do that? I would think that insulin resistance is insulin resistance, exercise or no exercise.

Homework Statement Let ##Q(x)=\sum_{j,i=1}^nC_{ij}x^ix^j ## and ##C_{ij}=C_{ji}; Q(x)>0 \forall x\neq 0## ##f(x)=[Q(x)]^{\frac{p}{2}}## find df(x) The Attempt at a Solution ##Q(x)=\begin{matrix} (c_{11} & c_{12}... & c_{1n}) \\ (... & ... & ...) \\ (c_{n1} & c_{n2} & c_{nn})...

In Section 6.2 of Nicholson: Introduction to Abstract Algebra, Exercise 31 reads as follows: Let E \supseteq F be fields and let u \in E be transcendental over F. (a) Show that F(u) = \{ f(u){g(u)}^{-1} \ | \ f,g \in F[x] ; g(x) \ne 0 \} (b) Show that F(u) \cong F(x) where F(x) is the...

Hi, please refer to the attached image. I am having trouble when doing Exercise 2 Here is what I did: $ \int_{-2}^{2}(f(x)\sin(\frac{m\pi x}{2}))dx = \sin(\frac{m\pi x}{2})a_{0} + \int_{-2}^{2} \sum\limits_{n=1}^\infty (a_{n}(\cos(\frac{n\pi x}{2})\sin(\frac{m\pi x}{2})+b_{n}\sin(\frac{n\pi...