What is Section: Definition and 733 Discussions

Beginning of page 303 of Schawrtz's QFT text (section 16.1.1), there's a part on the renormalization of the scalar propagator in ##\phi^3## theory to second order in ##g## the bare coupling. He writes (quote begins): $$M(Q)=M^0 (Q)+M^1 (Q)=\frac{g^2}{Q^2}(1-\frac{1}{32 \pi^2}...

I am reading Tom M Apostol's book "Mathematical Analysis" (Second Edition) ...I am focused on Chapter 12: Multivariable Differential Calculus ... and in particular on Section 12.2: The Directional Derivative ... ...I need help with part of Example 4, Section 12.2 ...Section 12.2, including the...

You guys could put the number of posts by each section, I think we would discover what interests more in the forum and what people study more.

I am reading Steve Awodey's book: Category Theory (Second Edition) and am focused on Section 1.4 Examples of Categories ... I need some further help in order to fully understand some aspects of the definition of the category Rel ... ... The definition of the category Rel ... reads as...

Hi, Please forgive my ignorance but, can somebody please explain the Maxwellian Averaged Cross Section briefly and basically? Thank you in advance.

I am a senior Civil Engineering student in my last study semester and I will begin to send out my resume in hopes of landing a job. I was wondering, is a "Professional Summary" section a standard practice for engineers looking for a job? Thank you in advance.

I am reading Steve Awodey's book: Category Theory (Second Edition) and am focused on Section 1.5 Isomorphisms ... I need some further help in order to fully understand some aspects of the definition of the product of two categories as it applies to the category Groups ... ... The definition...

I am reading Steve Awodey's book: Category Theory (Second Edition) and am focused on Section 1.5 Isomorphisms ... I need some further help in order to fully understand some aspects of Definition 1.4, Page 12 ... ... The start of Section 1.5, including Definition 1.4 ... reads as...

I am reading Steve Awodey's book: Category Theory (Second Edition) and am focused on Section 1.5 Isomorphisms ... I need some further help in order to fully understand some further aspects of Definition 1.3, Page 12, including some remarks Awodey makes after the text of the definition ... ...

I am reading Steve Awodey's book: Category Theory (Second Edition) and am focused on Section 1.4 Examples of Categories ... I need some further help in order to fully understand some further aspects of Section 1.4 Example 13 ... Section 1.4 Example 13 reads as follows: In the above text by...

I am reading Steve Awodey's book: Category Theory (Second Edition) and am focused on Section 1.4 Examples of Categories ... I need some help in order to fully understand some aspects of Section 1.4 Example 13 ... Section 1.4 Example 13 reads as...

How does the emission cross section of an emitting atom (such as Yb atoms in glass) affect the laser performance, namely the slope efficiency (signal power vs absorbed pump power) and laser threshold? Thanks a lot

Homework Statement f f Homework Equations ##a = {v^2}{r}## ##d = vt## The Attempt at a Solution The way I do it is break it down into the curved and straight segment. The bicycle is always traveling at a constant speed. Curved portion: distance ##\frac{\pi R^2}{4}## acceleration ##=...

I am reading Dummit and Foote's book: "Abstract Algebra" (Third Edition) ... I am currently studying Chapter 10: Introduction to Module Theory ... ... I need some help with an Exercise 8(c) of Section 10.1 ... Exercise 8 of Section 10.1 reads as...

I am reading Dummit and Foote's book: "Abstract Algebra" (Third Edition) ... I am currently studying Chapter 10: Introduction to Module Theory ... ... I need some help with an Exercise 8(b) of Section 10.1 ... Exercise 8 of Section 10.1 reads as follows...

Hi, I am taking GRE Physics this year and I am preparing from Conquering GRE Physics book and I have covered everything in that book on Electricity and Magnetism (yet to study Optics and Waves). My question: How much from Griffith Electrodynamics book do I need to study? Or is the material in...

I am reading The Basics of Abstract Algebra by Paul E. Bland ... I am focused on Section 3.2 Subrings, Ideals and Factor Rings ... ... I need help with the proof of Example 2, Section 3.2.12, pages 147 to 148 ... ... Example 2, Section 3.2.12 reads as follows...

Hi guys, apparently I've got both a linear and a subroutine programming error in the code below from lines 20-35? Could someone point me in the right direction. I think one might be the 'CALL wait' instruction, which should be 'CALL delay'? Not really sure as new to this, any help would be much...

I am working on HFSS and designing Antennas for LOW RCS , in all previous works they calculate the S11 parameter for the unit cell then make an array form this unit cell and calculate the RCS , my question is what is the relation between S11 and RCS and why we calculate S11 for the unit...

I am reading Dummit and Foote's book: "Abstract Algebra" (Third Edition) ... I am currently studying Chapter 10: Introduction to Module Theory ... ... I need some help with an aspect of Dummit and Foote's Section 10.3 Basic Generation of Modules, Direct Sums and Free Modules ... ... The...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 1.1 Rings and need some help to fully understand the proof of part of Example 7 on page 10 ... ... Example 7 on page 10 reads as follows:In the above example from Bland we read the following: " ... ...

Known data: In the picture, CD = 10 cm. What is the area of shaded area? Equation: I know, Area of a circle = ##πr^2## Diameter of a circle = ##2πr## Attempt: Here, ## r = 10/2 = 5 ## So, diameter ## = 2πr = 2*3.1416*5 = 31.42 cm ## And area of the circle ## = πr^2 = 3.1416*5^2 = 78.54 cm^2...

Homework Statement Consider scattering of a particle of mass ##m## on the potential $$U(r) = \begin{cases} 0, & r \geq b\\ W, & r < b \\ \end{cases}$$ Where ##W## is some arbitrary chosen constant, and the radius ##b## is considered a small parameter. Find the cross section ##\sigma## in the...

I have found answers on how to calculate the self-inductance of toroid of rectangular cross section, however my question says that "The winding are seen as a thin homogeneous currentlayer around the core" (excuse the translation). What does that mean for N? Does it mean N=1?

I am reading Paul E. Bland's book "Rings and Their Modules" ... Currently I am focused on Section 4.2 Noetherian and Artinian Modules ... ... I need some help in order to fully understand Example 3, Section 4.2 ... Example 3, Section 4.2 reads as follows: My questions are as...

I am reading Paul E. Bland's book "Rings and Their Modules" ... Currently I am focused on Section 4.2 Noetherian and Artinian Modules ... ... I need some help in order to fully understand Example 3, Section 4.2 ... Example 3, Section 4.2 reads as follows: My questions are as...

I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need someone to check my solution to Problem 2(b) of Problem Set 2.1 ... Problem 2(b) of Problem Set 2.1 reads as follows: My attempt at a solution...

I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need help with Problem 2(a) of Problem Set 2.1 ... Problem 2(a) of Problem Set 2.1 reads as follows: I am unsure of my solution to problem 2(a) and need...

I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need help with Problem 1(b) of Problem Set 2.1 ... Problem 1(b) of Problem Set 2.1 reads as follows: I have had difficulty in formulating a rigorous...

I am reading Dummit and Foote's book: "Abstract Algebra" (Third Edition) ... I am currently studying Chapter 10: Introduction to Module Theory ... ... I need some help with an aspect of Example (5) of Section 10.1 Basic Definitions and Examples ... ... Example (5) reads as follows: I do...

I am reading Dummit and Foote's book: "Abstract Algebra" (Third Edition) ... I am currently studying Chapter 10: Introduction to Module Theory ... ... I need some help with an aspect of Example (5) of Section 10.1 Basic Definitions and Examples ... ... Example (5) reads as follows: I...

Hi everyone, I was wondering, is the cross section at Eq 50.25 in http://pdg.lbl.gov/2017/reviews/rpp2017-rev-cross-section-formulae.pdf correct? Because I see a term in the denominator with \frac{1}{s\Gamma} whereas in several other references, the propagator term in the matrix element comes...

Homework Statement [/B] I am having a problem understanding a calculation performed as part of a bigger solution in the design of Slabs. That is, how to determine the centroid of the critical shear section, which consist of 3 planes intersecting to form a 3D model (please see attached...

I am working on deriving expression for deflection of a tapered beam with an elliptic cross-section. Hence, area moment of inertia is a linear function of the beam length. The beam is fixed at one end, and a concentrated force F is applied on its tip at the free end. I am using the known...

Modified from Disquisitiones Arithmeticae, p. 10: Let "*" indicate multiplication and "^" indicate "to the power." For real numbers a, b, c,..., let [a] = a, [a,b] = b*a+1, [a,b,c] = c*[a,b]+[a], [a,b,c,d] = d*[a,b,c]+[a,b], etc. Prove that [a,b,...,l,m]*[b,c,...,l] - [a,b,...,l]*[b,c,...,m]...

I am reading the book "Elementary Real Analysis" (Second Edition, 2008) Volume II by Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner ... and am currently focused on Chapter 11, The Euclidean Spaces \mathbb{R}^n ... ... I need with the proof of Theorem 11.15 on coordinate-wise...

Good day all I'm looking for the proof of stress generated in case of skew bending applied in acircular cross section ( I browsed internet the whole day without finding anything convincing) we use with many thanks in advance!

I was doing the calculations for this: http://fermi.la.asu.edu/PHY531/cylinder/index.html But I can't figure out how to go from \frac{d\sigma}{d\phi} to the total cross section. My guess was that you did the integral from \phi=0 to \phi=2\pi, but that's not helping since I can't tell either how...

I have seen the section sign \S mainly in legal documents. However, an acquaintance is writing a physics paper in which she uses this sign to refer to a section of another paper in which the section sign was not used (sections just being marked off by number), is it OK to use the section sign...

I am reading John B. Conway's book: Ä First Course in Analysis and am focused on Chapter 5: Metric and Euclidean Spaces ... and in particular I am focused on Section 5.2: Sequences and Completeness ... I need some help/clarification with Conway's defintion of completeness of a metric space ...

Homework Statement There is a conductor with the square-shaped area. the Radii are r1 , r2 with width b and resistivity ## \rho_R##. Find the resistance R between A and B 2. Homework Equations ##I = \iint_A\vec J \cdot d \vec A## ## \vec J = \kappa \vec E ## ## \vec E = \rho \vec J## ## V =...

Hi all, I'm writing a fortran 90 program to simulate the Duffing oscillator. I have it working and have produced a cos wave which I expected for D (the driving force) being set to 0. Here's the code: program rungekutta implicit none integer, parameter :: dp = selected_real_kind(15,300)...

I am reading "Introduction to Set Theory" (Third Edition, Revised and Expanded) by Karel Hrbacek and Thomas Jech (H&J) ... ... I am currently focused on Chapter 2: Relations, Functions and Orderings; and, in particular on Section 5: Orderings I need some help with H&J's depiction of...

I am reading "Introduction to Set Theory" (Third Edition, Revised and Expanded) by Karel Hrbacek and Thomas Jech (H&J) ... ... I am currently focused on Chapter 2: Relations, Functions and Orderings; and, in particular on Section 3: Functions I need some help with H&J's depiction of...

I usually read science section in Google news and it's really irritating how lately any time someone "predicts" the world will end they put it on top. But now they really seem to hit the rock bottom. Here's a screenshot and you can see first news is again about "end of the world" although this...

I am reading Micheal Searcoid's book: "Elements of Abstract Analysis" ... ... I am currently focused on understanding Chapter 1: Sets ... and in particular Section 1.2 Relations and Functions ... I need some help in fully understanding some remarks by Searcoid in his sub-section on products...

I was given as a task to solve this question by my teacher (heck if I had the time I would have solved every problem in both Taylor's and Evans's books on PDE); but didn't succeed to the teacher's satisfaction. In the following link there's a presentation of the problem, and in the attachment...

The "Operator Norm" for Linear Transformations ... Browder, Lemma 8.4, Section 8.1, Ch. 8 ... ... I am reader Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra...

The "Operator Norm" for Linear Transfomations ... Browder, page 179, Section 8.1, Ch. 8 ... ... I am reader Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra...

I have come across the term quiet often, but I find it difficult to explain it to myself (or others) and even interpret it... So what is a fiducial cross section? Is it the measured cross section once you factor out the detector acceptance and the different cut-efficiencies (mainly motivated by...