Example Definition and 879 Threads

I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need someone to help me...

...system, I mean as in the Cartesian Vector/Tensor definition. I get that if you have two mutually orthogonal basises which are theta degrees apart and the transformation from one basis to the other follows the same as a rotation by theta degrees i.e: V'i = Rij Vj then it is a Cartesian...

Homework Statement RollingDice. Supposethat 12dice are to be rolled.We shall determine the probability p that each of the six different numbers will appear twice. Each outcome in the sample space S can be regarded as an ordered sequence of 12 numbers, where the ith number in the sequence is the...

Homework Statement A string wraps around a uniform cylinder of mass M, which rests on a fixed plane with angle θ. The string passes up over a massless pulley and is connected to a mass m. Assume that the cylinder rolls without slipping on the plane, and that the string is parallel to the plane...

Hello, I´m a bit math-challenged and just started to brush up on both physics and mathematics simultaneously but I'm still at absolute beginner status and I don't want to go on in the book as long as I can't even figure out such a simple example. I'm using the Giancoli textbook on physics for...

Since I am new to the forum here, I apologize in advance that in case similar example has been explained in another thread. If so, please kindly refer me to the appropriate place to read further. In my example, there will be four reference objects, earth, E, distant star, S, spaceship A, and...

I am reading Joseph J. Rotman's book: A First Course in Abstract Algebra with Applications (Third Edition) ... I am currently focused on Section 3.5 From Numbers to Polynomials ... I need help with Example 3.76 ... ... the example concerns Euclidean rings and their defining characteristics so...

My physics SATII book states that this is not an example of nuclear fusion: 4/2 He + 27/13 Al ⇒30/15 P +1/0 n If this isn't fusion then what is it? (The top number of the division is the mass; the bottom is the atomic number)

I am writing story about Earth set 1000 years in future and I am looking for good example of living animals. So far I had wolves or dogs on my mind, how would they change in 1000 years?

I am reading W. Keith Nicholson's book: Introduction to Abstract Algebra (Third Edition) ... I am focused on Section 4.2:Factorization of Polynomials over a Filed. I need some help with Example 10 on page 215 ... The relevant text from Nicholson's book is as follows:In the above text, we read...

TTree* inputTree = (TTree*)source->Get( "<YourTreeName>" ); Could someone please explain me what the above statements mean? I don't understand what " (TTree*) " does (source is a TFile). Thanks.

Homework Statement A woman pedals her bicycle up a 8-percent grade on a slippery road at a steady speed. The woman and bicycle have a combined mass of 76 kg with mass center at G. If the rear wheel is on the verge of slipping, determine the coefficient of friction μs between the rear tire and...

Homework Statement 1. Explain why a balloon sticks to a wall after being rubbed on your shirt (remember the wall is not metal and does not have "free" electrons") 2. Include a balanced force diagram that includes the electrical force and gravitational force (assume electrical force is twice...

As the potter shapes the mud vessel on his wheel, the wheel applies centrifugal force on the clay.So against this centrifugal force the potter shapes the vessel. Could this be an example of centrifugal force?

I am researching right upper semicontinuous function but I didnt find...Please give some examples...thank a lot

I am have been searching for the of a tensor product of two vectors, but found seemingly conflicting definitions. For example, one source definition was, roughly, that the tensor product of two vectors was another column vector in a higher dimensional space, and another defined the tensor...

Hi I was trying the gram schmidt process on example 1.3.2 page 43 as shown below u1=(3,0,0), u2=(0,1,2), u3=(0,2,5)v1=u1=(3,0,0) v2=u2-proj_(w1) u2=(0,1,2)-((<0,1,2><3,0,0>)/9)(3,0,0) However the top line inner product gives 0...

This is an example at the beginning of the section on the Fundamental Theorem for Line Integrals. 1. Homework Statement Find the work done by the gravitational field \vec{F}(\vec{x}) = -\frac{mMG}{|\vec{x}|^3}\vec{x} in moving a particle from the point (3,4,12) to (2,2,0) along a piece wise...

example of a varible capacitor input op-amp to voltage level circuit. I'm not sure how to turn reactance to a voltage level using an op-amp? :wink:

Hello all. I have almost finished chapter 4 on energy in Taylor's classical mechanics book. But in the last example in this chapter I got confused. Here it is: "A uniform rigid cylinder of radius R rolls without slipping down a sloping track as shown in Figure 4.23. Use energy conservation to...

http://www.nap.edu.au/verve/_resources/Example_Test_Numeracy_Y9_calc.pdf Question 28 says 46 centimeters in the answers but i got 47.5 centimeters

Homework Statement Hi, I've been working through a practice problem for which I used the fundamental theorem of calculus, or one of its corollaries. The setup is a population changing over time. The population, P(t) at t = 0 is 6 billion. The limiting population as t goes to infinity is given...

Homework Statement I'm struggling to perform a symplectic reduction and don't really understand the process in general. I have a fairly solid understanding of differential equations but am just starting to explore differential geometry. Hopefully somebody will be able to walk me through this...

I was reading up classical mechanics in Goldstein but needed some clarifications. I looked online and saw something that bothers me qutie a bit. In the online pdf below, on page 69 (or 74th screen scrolls), it states that Dot Cancellation does not work if the position vector is a function of...

I am baffled by some aspects of the torus ... I hope someone can help ... I am puzzled by some aspects of Singh's treatment of the torus in Example 2.2.5 ( Tej Bahadur Singh: Elements of Topology, CRC Press, 2013) ... ... Singh's Example 2.2.5 reads as follows: My questions related to the...

I had a discussion with my friend. He took an icecream stick and told me that if the stick was held horizontally the stick would break easily but if you held the stick vertically it would be difficult to break the stick. He said that vertically the moment of inertia is more. My question is that...

Would this example be valid in satisfying a relation that is symmetric and anti-symmetric? The relation R = {(1,1),(2,2)} on the set A = {1,2,3} Also, I'm curious to know since relations can both be neither symmetric and anti-symmetric, would R = {(1,2),(2,1),(2,3)} be an example of such a...

As many, I wondered why FTL communication has problems with causality. Went over many posts here in PF, and wasn't satisfied. And then I read this explanation, by Richard Baker: (2015-4-2, link is still active) http://www.theculture.org/rich/sharpblue/archives/000089.html His explanation is a...

Homework Statement A step in this process of proving Sn: 1+4+7+...+(3n-2) = n(3n-1)/2 confuses me. I hope someone can clarify this for me. I do not require the work done, I need clarification on a step only. Thanks! Homework Equations After assuming n=k, we say Sk: 1+4+7+...+(3k-2) =...

Homework Statement So I'm back to my wonderful computational physics course after a brief hiatus and once again, I am teaching myself the material. This unit we are working on some thermodynamics. We've just used the "Leap Frog" method to determine heat transfer of a 100k bar with both ends...

In Munkres book "Topology" (Second Edition), Munkres proves that a function F is a homeomorphism ... I need help in determining how to find the inverse of F ... so that I feel I have a full understanding of all aspects of the example ... Example 5 reads as follows:Wishing to understand all...

Hi I am working on a programming assignment that requires me to implement the successive over-relaxation algorithm. We are given the wikipedia page for this: http://en.wikipedia.org/wiki/Successive_over-relaxation. I have read through the wikipedia page for this numerous times but am still...

I am trying to give some context to medical vaporizers in a literature review I am composing and initially decided to give asthma inhalers and nasal inhalers as examples. I realized however, that some sources on-line were referring to these metered dose inhalers as vaporization devices when...

Show that the galois group for (Complex : Reals) is given by {e, y} where y is y: C-->C is the conjugation automorphism defined by y(z) = z~ (Conjugate of z) for all z in C. if o is an element of gal(C:R) and z = a + bi in C, then o(z) = o(a+bi) = o(a)+o(b)o(i) = a+bo(i) but o(i)^2 = o(i^2) =...

Homework Statement The figure gives the electric potential V(x) along a copper wire carrying uniform current, from a point of higher potential Vs = 9.00 μV at x = 0 to a point of zero potential at xs = 3.20 m. The wire has a radius of 1.50 mm, and copper has a resistivity of 1.69 × 10-8 Ω·m...

I'm having trouble figuring out how the term below boxed in red was eliminated on the left side of the equation as shown below. I reviewed properties of exponential functions, and still can't understand how this term was cancelled. 1. Homework Statement Homework Equations Exponential laws...

Hello! (Wave) I am looking at the proposition: If $(A_n)_{n \in \omega}$ is a sequence of sets and $(f_n)_{n \in \omega}$ is a sequence of functions then: for all $n \in \omega, f_n: \omega \overset{\text{ surjective }}{\rightarrow} A_n$ then there is a function $f: \omega \overset{\text{...

Hello! (Wave) How could we find an example of a directed graph with edges of negative weight for which the Dijkstra's algorithm gives wrong results? (Thinking)

I need some help in fully understanding Example 1, section 4.3 Cauchy Sequences, page 73 of Apostol, Mathematical Analysis. Example 1, page 73 reads as follows: https://www.physicsforums.com/attachments/3844 https://www.physicsforums.com/attachments/3845 In the above text, Apostol writes: "...

I am having a problem understanding an example in kolenkow: an introduction to mechanics. The question I have is on page 71/section 2.9 in the red cover edition. The example is telling me to find the acceleration of the end of the rope and how it is related to the acceleration of the block. I...

Hi! (Smile) According to my notes, a set $A$ is called transitive if the elements of its elements are elements of $A$. For example, the set of natural numbers $\omega$ is a transitive set. Also, if $n \in \omega$ then $n$ is a transitive set since $n=\{0,1,2, \dots, n-1 \}$ and if we take a...

Homework Statement A simple RL circuit in series connected to a source with V(t) = 30Cos(3t+75°)V and is delivering 14.12 W of power. I'm also given the power factor which is pf=0.857 and is lagging. Find the values of R and L Homework Equations P=Vm*Im/2 * pf for power theta =...

Homework Statement An Atwood machine consists of two masses, M and m, which are connected by an inelastic cord of negligible mass that passes over a pulley. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses M and m. Homework Equations...

Are there any tutorials that apply stochastic differential equations to the settings of elementary physics problems ? - for example, an object sliding down a not-frictionless ramp. The ramps of everyday life don't have a constant coefficient of friction. A better model for them would be...

Give an example of a function f:R2-->R , continuous in (0,0), with partial derivatives in (0,0), but not differentiable in (0,0). I was thinking in something like f(x,y)=IxyI

I am looking for a local field of positive characteristic, like Q22 was used in this article: http://8pic.ir/images/s9oiiuqqkq989w3posu9.png in fact, i need an another Example of a local field of positive characteristic like Q22 .

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 2.2 on free modules and need help with Example 5 showing a module with two bases ... ... Thanks to Caffeinemachine, I have largely clarified one issue/problem I had with Example 5, but now have a...

OK. We are producing something and then storing it. The first year, "1" is produced, the second year, "1,1" the third 1,12, so that the production capacity increases 10% per year. How do we convert this into a general formula for how much we have produced in total after year x? It is obviously...

I am reading Paul E. Bland's book, "Rings and Their Modules". In Chapter 1: Basic Properties of Rings and Modules, Bland gives endomorphism rings as a basic example of a ring. The example (Example 7) reads as follows:https://www.physicsforums.com/attachments/3572 I do not feel that I fully...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 2.2 on free modules and need help with Example 5 showing a module with two bases ... ... Example 5 reads as follows:I am having trouble understanding the notation and meaning of M = \bigoplus_{...