Section Definition and 733 Threads

ik that i have to add the positive and negative ions but the cross section (surface) confuses me how do i resolve this?

On page 105 of Peskin and Schroeder's book it says that the integral over ##d^2b## in the expression: $$d\sigma = \left(\Pi_f \frac{d^3 p_f}{(2\pi)^3}\frac{1}{2E_f}\right) \int d^2b\left(\Pi_{i=A,B} \int \frac{d^3 k_i}{(2\pi)^3}\frac{\phi_i(k_i)}{\sqrt{2E_i}} \int \frac{d^3...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... ... I need some further help in fully understanding some remarks by Browder made after...

The Completeness Proof for First-Order Predicate Logic depends on if $\Phi$ is a set of consistent $\mathcal L$-formulas, then $\Phi$ is satisfiable. How is that constructed? There are a large number of Lemmas working from Machover's text Set theory, Logic and Their Limitations but I'm having...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... ... I need some further help in fully understanding a remark by Browder after Definition 8.9...

Hello, dear friends of mathhelpboards; I stumbled with a striking claim in https://www.cut-the-knot.org/do_you_know/GoldenRatioInYinYang.shtml Sorry, I couldn't paste the pic. The question is if there is an algebraical or trig proof for this claim, as the angle seems to be just 45º. Then, is...

a) I have $$d\sigma=-\beta sin(\theta)d(\theta)+2\gamma sin(\theta)cos(\theta) d\theta$$ and $$d \Omega=2\pi sin(\theta) d \theta$$ so $$\frac{d\sigma}{d \Omega}=-\frac{\beta}{2\pi}+2\gamma cos(\theta)=|f(\theta)|^2$$ b) $$\sigma(\theta)=\alpha+\beta cos(\theta)+\gamma...

I am currently following R.K. Ellis et al.: QCD and Collider Physics, pp. 99 to understand how to arrive at the parton density functions starting from the matrix elements in electron-proton deep inelastic scattering (see figure below). But there seems to be a very fundamental concept that I...

Can anyone help me about cross section calculation of W+W->gamma>l+ l- (leptons), at the tree level? I am stuck to writing amplitude,after written Feynman rules, because of massive vector boson polarization states. How should I do?

I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I need further help with other aspects of Example 1.5, Section 1.2, Chapter III ... Example 1.5, Section 1.2, Chapter III...

I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I need help with some aspects of Examples 1.1 and 1.2, Section 1.2, Chapter III ... Examples 1.1 and 1.2, Section 1.2...

I am reading Theodore W. Gamelin's book: "Complex Analysis" ... I am focused on Chapter 1: The Complex Plane and Elementary Functions ... I am currently reading Chapter 1, Section 4: The Square and Square Root Functions ... and need some help in verifying a remark by Gamelin ... ... The...

I am reading Tom M Apostol's book "Mathematical Analysis" (Second Edition) ... I am focused on Chapter 16: Cauchy's Theorem and the Residue Calculus ... I need help in order to fully understand a remark of Apostol in Section 16.1 ... The particular remark reads as follows: Could someone...

We were asked to label the vasculature structures of a cucumber cross section (complex tissue). I just wanted to know if my labels were accurate. Image attached 1. Xylem 2.— 3. Sieve elements 4. Phloem

What are the cross sections of the DM particle candidates ?

In Landau-Lifsits's book about non relativistic QM it is said that if I have a particle described by a plane wave ##\phi = e^{ikz}## (I think he choses the ##z## direction for simplicity) the wave function after the scattering event is (far from the scattering event) $$\psi \approx e^{ikz} +...

Hi, I analyzed various open cross-section (I, T, L, C) bars using FEA to find maximum shear stress and twist angle. Now I would like to compare these results with approximate hand calculations. Just out of curiosity. However it's not easy to do it analytically. I know about a method of dividing...

I'm trying to understand how CST measures the RCS of an object. If not specified by me, it gives me (with a very brief simulation even for complex objects) graphs, both 3D and 2D, entitled 'Bistatic RCS'. With this wording I think that there is an antenna in a different direction than the one...

If I have impact test data showing energy absorbed by notched specimen, how do I utilize this data while designing. In my case, i am trying to design the valve which closes by striking on valve seat, how do i use the impact test results for this design?

I want to design cross section area required for valve stem when valve is closed under spring force. Valve stem should be designed for buckling load but I am unable to calculate buckling load coming due to impact force coming when valve bangs on valve seat. Valve is having concentric spring. Is...

calculate the moment of inertia of this I section about centriodal axis (##Y_{c}## = 108.4) Where does ##Y_{C}## measurement goes in this I section?

Hi, The following is called normal form of the conic section equation: x²+y²+2ax+2by+c=0 A circle is one of the conic sections when considered as a special of ellipse. I'm confused as to why the the given equation is called "normal form of the conic section equation" when, in my opinion, the...

Say I have two identical circles, both of radii of one, overlapping, as shown in the diagram below: In this diagram, x is the circumference of the circles, and the bit of the bottom circle which is drawn blue (the overlapping bit) is 1/6th of the whole circumference. What I'm looking for is...

I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help in order to understand some...

I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help in order to understand some...

I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help in order to understand the meaning...

I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help with some remarks by Garling concerning a...

I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help with some remarks by Garling concerning a subset...

I have attached the two pages in my notes and I have the following question. 1. Where have the n_t*l gone in 9.9? (According to 9.5 why do they disappear?) 2. Why J_s=sigma_tot J_i? The dimension of flux is per m^2 and sigma is per area too, the dimension is not right...

These are both problems from Royden's Real Analysis. Trying to get through the problems from the Radon-Nikodym Theorem section of the book. Problem 1: Let $(\mu_n)$ be a sequence of measures on a measurable space $(X, M)$ for which there is a constant $c>0$ such that $\mu_n(X)<c, \forall n$...

Andrew Browder in his book: "Mathematical Analysis: An Introduction" ... ... defines a differential form in Section 13.1 which reads as follows: In the above text from Browder we read the following: " ... ... A differential form of degree ##r## (or briefly an ##r##-form) in ##U## is a map...

I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ... I need help in order to fully understand Tu's section on the wedge product (Section 3.7 ... ) ... ... The start of Section 3.7 reads as follows: In the above text from Tu we read the following: " ... ... for...

I know the basic equations of a solenoid carrying a current, the consequences of having an iron core inside one, and how that derives from Ampere's law. But these suggest that the only figure of merit is the cross section area of an iron core and the solenoid, not their shape. Thinking in more...

I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ... I need help in order to fully understand Tu's section on the dual space ... ... In his section on the dual space, Tu writes the following: In the above text from Tu, just preliminary to Proposition 3.1 Tu...

I am reading Jon Pierre Fortney's book: A Visual Introduction to Differential Forms and Calculus on Manifolds ... and am currently focused on Appendix A : Introduction to Tensors ...I need help to understand some statements/equations by Fortney concerning rank one tensors ... Those remarks...

Hello. I am reading DeAngelis - Introduction to particle and astroparticle physics and I have come across a plot showing proton proton cross section vs energy. I am trying to reconcile the statement in the book that says cross section total = cross section elastic whenever there is no available...

In particle physics there is usually a cross section for a particular particle . I came up with a cross section of 1.07 x 10^-42 m^2 for a graviton.

I am reading the book: "Linear Algebra" by Stephen Friedberg, Arnold Insel, and Lawrence Spence ... and am currently focused on Section 2.6: Dual Spaces ... ... I need help with an aspect of Example 4, Section 2.6 ... Example 4, Section 2.6 reads as follows: (see below for details of Section...

I’m having trouble understanding section 30.1 of FLP Vol 1. Particularly the first figure is causing me struggle. I understand magnitude and phase, such as fig 29-9 when 2 waves are added to get an effective resultant vector. But I’m struggling to see how equation 30.3 is applicable when it’s...

I am reading the book: "Vector Calculus, Linear Algebra and Differential Forms" (Fourth Edition) by John H Hubbard and Barbara Burke Hubbard. I am currently focused on Section 1.7: Derivatives in Several Variables as Linear Transformations ... I need some help in order to understand some...

Hello! In most papers that present exclusion plots as cross section versus mass, the plot has a specific shape in which mostly the cross section decreases with mass. I am a bit confused why. If you assume that the density and speed of DM is constant, shouldn't a higher mass (and hence a higher...

Homework Statement I would like to compute the total cross section of a lepton pair production using parton distribution functions. The main problem I am having is the numerical computation and the order of magnitude I am getting as a final answer, which so far definitely indicates that...

I am reading the book: Multivariable Mathematics by Theodore Shifrin ... and am focused on Section 3.1 Partial Derivatives and Directional Derivatives ... I need some help with Example 3 in Chapter 3, Section 1 ... Example 3 in Chapter 3, Section 1 reads as follows:In the above text we read...

I have been trying to find out how the cutoff equation for the T section LC Lowpass filter is derived. I remember from college that f=1/(2pi√(LC)) for an LC circuit. But, with the T section, the cutoff frequency is given by f=1/(pi√(LC)), with L being the sum of the two inductors. My math has...

I am reading Reinhold Remmert's book "Theory of Complex Functions" ... I am focused on Chapter 0: Complex Numbers and Continuous Functions ... and in particular on Section 1.4: Angle-Preserving Mappings ... ... I need help in order to fully understand a remark of Remmert's regarding...

I am reading Reinhold Remmert's book "Theory of Complex Functions" ... I am focused on Chapter 0: Complex Numbers and Continuous Functions ... and in particular on Section 1.3: Scalar Product and Absolute Value ... ... I need help in order to fully understand Remmert's derivation of...

I am reading Reinhold Remmert's book "Theory of Complex Functions" ...I am focused on Chapter 0: Complex Numbers and Continuous Functions ... and in particular on Section 1.2: \mathbb{R}-linear and \mathbb{C}-linear mappings of \mathbb{C} into \mathbb{C} ... ... I need help in order to...

I am reading Reinhold Remmert's book "Theory of Complex Functions" ...I am focused on Chapter 1: Complex-Differential Calculus ... and in particular on Section 2: Complex and Real Differentiability ... ... ...I need help in order to fully understand the relationship between complex and real...

I am reading Reinhold Remmert's book "Theory of Complex Functions" ... I am focused on Chapter 1: Complex-Differential Calculus ... and in particular on Section 2: Complex and Real Differentiability ... ... ... I need help in order to fully understand the relationship between complex and real...

Hi, I am facing issues with my program. Listed below. This is form my masters project. Also in what way can I connect the filleted surfaces shown in fig by a weld or just load or stress transfer connection. fini /clear /title,C160T2B70-1L /prep7 et,1,shell181 r,1,2 mp,ex,1,1.85e5...