Cut Definition and 266 Threads

I'm trying to wrap my head around these Dedekind cuts. The definition is straightforward but I'm a little confused about the downward closure part. ##x \in Q## and ##y<x \Longrightarrow y \in Q## Does that mean that this is not a cut because it is bounded below? {## x \in Q : x>1 \wedge x<2...

Hello. I have a difficulty to understand the branch cut introduced to solve this integral. \int_{ - \infty }^\infty {dp\left[ {p{e^{ip\left| x \right|}}{e^{ - it\sqrt {{p^2} + {m^2}} }}} \right]} here p is a magnitude of the 3-dimensional momentum of a particle, x and t are space and time...

Homework Statement I don't understand the cuts or the views. For example if we make a horisontal cut, which view we should show? http://1.1m.yt/UJasa7v.jpg Homework EquationsThe Attempt at a Solution I have in the book an example that if we make a vertical cut we show the upper view (view...

Homework Statement Draw the objects in in the necessary views using the appropriate cut (section) Are the views correct? Homework EquationsThe Attempt at a Solution https://s13.postimg.org/gjv1jmbsn/20161129_185242.jpg https://s13.postimg.org/z0pgafrqv/20161129_195049.jpg

Homework Statement By using cylindrical coordinate , evaluate ∫ ∫ ∫ zDv , where G is the solid bounded by the cylinder (y^2) + (z^2) = 1 , cut by plane of y = x , x = 0 and z = 0 I can understand that the solid formed , was cut by x = 0 , thus the base of the solid formed has circle of (y^2) +...

i just bought the hardover version of Spacetime physics and i found it contains only 3 chapters out of the supposed 8 that it should contatin, can someone enlighten me on what is going on? is this expected with hardcover versions? that they contain less content? or is it just this textbook? and...

Homework Statement find the slope of tangent line to curves cut from surface z = (3x^2) +(4y^2) - 6 by planes thru the point (1,1,1) and parallel to xz planes and yz planes ... Homework EquationsThe Attempt at a Solution slope of tnagent that parallel to xz planes is dz/dy , while the slope of...

Imagine that we wanted to build a slingshot, using one piece of rubber attached to two hooks - each on a side. We use a rubber, whose spring constant is k. My questions are: 1. If we began to string that slingshot and the rubber would begin to fold, what would happen with the string...

Homework Statement Picture of problem : http://screenshot.sh/ouZAbUeL9Qzmj We have got a desk,mass m1, length L1 and thickness d, and L1>>d. One of it's ends is angled by 45 degree. At the beginning it is put on the other desk which thickness is also d and mass is m2. I have to find final...

Sorry for my english at the beginning. :) I am not really into academic(physic) english. 1. Homework Statement Picture of problem : http://screenshot.sh/ouZAbUeL9Qzmj We have got a desk,mass m1, length L1 and thickness d, and L1>>d. One of it's ends is angled by 45 degree. At the beginning it...

Hello, could someone explain some of the factors, or the calculation, for determining wind turbine cut in speed? I am talking about small wind turbines using with a single bearing on the rotating axis and a permanent magnet generator. A lot of literature targets a cut in speed of 3 m/s without...

How much force is needed to cut in half a tough tool steel beam 5 cm wide and 1 cm thick? Theoretically, the cohesion is low. For example, the surface tension of water is 71 mN/m. Some materials are more cohesive. Quicksilver has surface tension of 450 mN/m. Molten gold and copper have over 1...

Occasionally I want to save a problem which was explained well here into a document outside the forum However, I can't find one of the online editors that seems compatible with the one here on MHB. Also, I have tried to compose a problem from an outside editor and c/p it here but there are...

Homework Statement The integral I want to solve is $$ D(x) = \frac{-i}{8\pi^2}\int dr\,d\theta \frac{e^{-irx\cos\theta}}{\sqrt{r^2+m^2}}r^2\sin\theta$$ which I've reduced to $$ D(x) = \frac{-i}{4\pi x}\int dr \frac{r\sin(rx)}{\sqrt{r^2+m^2}} $$ by integrating over ##\theta##. However, I...

Can the envelope curve (of a family of curves) intersect a member curve of the family at more than one point? It seems possible. Consider the following. Each blue line is a member curve and the red line is the envelope curve. If we modify each blue line such that it has a protrusion like a...

Homework Statement The given question is: Show that a simple graph with at least two vertices has at least two vertices that are not cut vertices.Homework Equations Cut vertices: The removal of cut vertices and all edges incident to them produces a subgraph more connected components than in the...

Homework Statement A spherical fruit has a radius of 1 inch. A slice has surface area of its peel equal to pi/8 . Determine the angle of cut for the slice. Homework Equations I'm sure there is a relevant equation here but I don't know it :-( The Attempt at a Solution So the radius is 1 inch...

That doesn't follow. Selecting a system to study is necessary for most of physics. But it is always a subjective act - since Nature isn't divided into system and the rest of the universe. Most of the time we don't want to consider the universe as a whole but only the particles in a particular...

micromass submitted a new PF Insights post Am I Cut Out for Mathematics or Sciences? Continue reading the Original PF Insights Post.

Homework Statement "Take a tennis ball and cut it into 2 equal halves. Take one of them and cut it again equally. You now have 1 half tennis ball and 2 quarter tennis balls. Glue the 2 quarters to the half, one to its outside (convex) and one to its inside (concave). Design, build and test a...

Hello! I've just received information that there may be a requirement to cut some carbon fiber fabric on the water jet machine in our lab. The party that wants the cutting done, requires an option that's quicker than using shears to cut it. That's pretty much all the information I have at the...

Homework Statement Here is an exercise I came across while studying MaxFlow / MinCut and I'm rather stumped: Designate G = (V, E) as an undirected graph that has at least two vertices. Every edge e on this graph has capacity ce. Pick two arbitrary vertices from G and label them s and t...

Consider the one loop corrections to the propagator and the vertex in ##\phi^4## theory in the attachment The former gives an integral representation proportional to ##\int d^4 k/k^2## in ##4## dimensions while the latter gives a representation ##\int d^4 k/k^2 (k+p)^2## where ##p## is the...

Many times my packed lunch includes an orange of the seedless variety cut into quarters, reassembled, and then wrapped in plastic wrap. About 5 hours latter it is eaten. On a regular basis, today for example, I have noticed that the orange tends to kind of "glue" itself back together again, that...

Homework Statement I am after finding the centroid of the remaining area (hatched) when a circle is cut by a line. I made a diagram in CAD that demonstrates the problem. The idea is that, starting from the bottom of the circle, a cut is taken leaving a remaining shape whose area and...

This is more complicated than it sounds. I'd like to analyse a fracture in a surface body so I need to create a no thickness or infinitesimally small cut/slice if it is possible. Afterwards, I'm planing to analyse stress concentration factor in model environment.

I'm a senior in high school and next year I would like to study mathematics in my capital city. I love studying math in general and I've always gotten A's on my math/physics tests without much preparation. However my parents have always been telling me that I shouldn't do that because there is...

Homework Statement Given a circle with a set diameter, how does one calculate the area of the segment below? Homework Equations The only information available is the diameter (in this particular example it is 14"), You may not use angles. Only the chord length. Thank you for your reply. Miguel

If you buy cut flowers, why might the florist recommend cutting the stems underwater and then transferring the flowers to a vase while the cut ends are still wet? I think cut flowers are flowers cut from a plant. If the stems are cut underwater stems would go. So why wetting if they are cut...

A very basic question: does such a cone, where the broad end is not cut flat but follows the surface of the sphere whose radius is the length of the cone's side, and is centred at the cone's point, have a name?

Homework Statement http://imgur.com/FZM5gqC,RlLeGmP#1 http://imgur.com/FZM5gqC,RlLeGmP#0 Homework Equations f^k_{AB} = \mu_k N_{AB} W_{f,i} = \int_{r_i}^{r_f} \vec{F} \cdot d\vec{r} E^{mech}_f = E^{mech}_i + W^{NC}_{f,i} U_{elastic} = \frac{1}{2} k x^2 The Attempt at a Solution Since the...

Hey physics forums Do you know if you can cut this mono crystalline solar cell in half: https://www.amazon.com/gp/product/B00ISVLPN4/?tag=pfamazon01-20

Homework Statement I am reading Rudin's Principles of Mathematical Analysis (3rd edition) and am working through the construction of ##\mathbb{R}##. In step 6 of his construction, we must first verify that the field properties of multiplication hold for how he defines multiplication for the...

This is a question I have always wanted to ask but was too nervous to. I am currently a EE and Math dual major at an engineering university. I really like EE and thoroughly enjoy the subject and the physics behind it. However, I noticed during lab I tend to struggle more than the other...

Given the function \(f(z) = z^{1/3}\). Can the branch cuts be defined by the rays from zero through the three roots of unity and to infinity?

Hi, I am trying to cut a parabolic curve in a piece of sheet metal using a numerically-controlled cutting machine (basically a very hard rotating router blade). The router blade is 10mm diameter. I want to achieve a parabolic cut in the sheet metal that adheres to the formula y=x^2 The...

The Function To Be Programmed \sigma_m=\frac{4(n_r^2 -1)J_m(n_r k R)}{\pi^2kD_m^+(kR)D_m^-(kR)} where D_m(z)=n_rJ'_m(n_rz)H_m(z)-J_m(n_rz)H'_m(z). The '+'/'-' superscripts indicate the limits as z approaches the branch cut, which lies along the negative imaginary half axis, from the positive...

Homework Statement when the glass is partially cut( as shown in the photo ) , the centre of curvature is inside the denser medium (glass), so the centre of curvature should be lower than point Q in the diagram . am i correct? by saying that the centre of curvature is inside the denser medium...

I was wondering how I would go about working out the energy required to cut a material (e.g. stone or steel) if given a volume, and all the necessary values pertaining to that specific material? For example, how would I work out the amount of energy required to cut a steel block of dimensions...

Hi there I have found an algorithm within the literature that is known as multiple birth and cut. It is in a word fantastic! It seems like it has the potential to solve a problem I have been fighting with. I have been tasked with detecting nuclei in histopathology images and so far the...

Homework Statement Find the electric field due to a half circle of radius R and total charge Q. (a) First estimate by dividing the charge into five equal parts. (b) Repeat for 9 equal parts, (c) Using integral calculus solve exactly.Homework Equations E = kQ/r^2 The Attempt at a Solution...

How to find if a graph has a cut-edge/bridge and cut vertices. In other words, i am mixed up between cut edge and cut vertices? What is the difference and how one can find these in a graph?

What is the Branch cut for the log(z) ? Correct me if I am wrong. I know that the function $f(z) = e^z$ , is periodic function with period $2 \pi $ so to define the function $\log(z) $ we have to restrict the domain of $e^z$ for example taking the points $D : z \in \mathbb{C} $ such that...

Homework Statement Q .Find the tensions in the strings (1), (2) and (3) and the acceleration of the mass ‘m’ just after : (a) string (1) is cut (b) string (2) is cut (c) string (3) is cutHomework Equations The Attempt at a Solution I feel the answer should be (a) T1 = 0 ; T2...

Homework Statement In figure shown, pulleys are ideal m1 > 2 m2. Initially the system is in equilibrium and string connecting m2 to rigid support below is cut. Find the initial acceleration of m2? Homework Equations The Attempt at a Solution In equilibrium, 2T1 = T2 For...

Homework Statement A conducting spherical shell of outer radius a and inner radius 3a/4 is cut in two pieces via a horizontal plane a distance a/2 above the center of the spherical shell, as shown in Figure 1. Let us label "A" the upper part of the shell and "B" the lower part of the shell...

Let α be a Dedekind Cut. w a positive rational.How to prove that there exists a integer n such that nw is a member of α and (n+1)w is not a member of α, using Archemedian propoerty of Q. Suppose p is a member of α. we can find n such that nw < p < (n+1)w. So nw is a member of α. Further I am...

Just covered branch cuts in my undergraduate course but stuck on one of the questions... Find the domain on which f(z) = arccot(z) is single valued and analytic. Now, we've looked at ln(z) in class and I understand the principal of limiting the domain but I'm not having much success and...

what are the dimensions of rectangular beam of volume maximum that can be cut from a trunk in diameter "D" and length "L", assuming that the trunk has the shaped of a straight circular cylinder shape? Answer Width =lenght

The problem is: Consider the area under the curve f(x)=2x-x2 and above the x axis. Find the equation of the line through the origin that cuts this area into two equal parts.