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Electrochemical Impedance Spectroscopy: Experiment, Model, and App
Electrochemical impedance spectroscopy is a versatile experimental technique that provides information about an electrochemical cell’s different physical and chemical phenomena. By modeling the physical processes involved, we can constructively interpre... |
isobars and nuclear saturation Abstract
In this paper, we construct a nuclear interaction in chiral effective field theory with explicit inclusion of the $$\mathrm{{\Delta}}$$-isobar $$\mathrm{{\Delta}}(1232)$$ degree of freedom at all orders up to next-to-next-to-leading order (NNLO). We use pion-nucleon ($${\pi}N$$) ... |
I have regression results about the effect of a treatment on two outcome variables, $N$ and $D$.
The coefficient on $N$ is positive. The coefficient on $D$ is negative.
These results suggest that the effect on $\frac{N}{D}$ should be positive. The treatment increases the numerator, and decreases the denominator.
Howeve... |
For the reaction$$\ce{CaSO4 (s) <=> Ca^2+ (aq) + SO4^{2-} (aq)},$$the appropriate equilibrium constant using activities can be set up as$$K_\mathrm{eq}=\frac{a(\ce{Ca^2+})\,a(\ce{SO4^2-})}{a(\ce{CaSO4})}.$$
The activity $a$ of a pure substances in condensed phases is approximately one, since their behaviour can be ofte... |
LaTeX supports many worldwide languages by means of some special packages. In this article is explained how to import and use those packages to create documents in
Italian.
Contents
Italian language has some accentuated words. For this reason the preamble of your document must be modified accordingly to support these c... |
How can we show that Halting Problem for one-counter additive machines is decidable ?
A simple way is the following:
Suppose that the increments are $+1, -1$; the number of states of the machine is $m$ and the current value of the counter is $n$.
You can notice that if the counter reaches $n+m+1$ without hitting the $0... |
Calculational Exercises
1. Consider \(\mathbb{R}^3 \) with two orthonormal bases: the canonical basis \(e = (e_1 , e_2 , e_3 )\) and the basis \(f = (f_1 , f_2 , f_3)\), where
\[ f_1 = \frac{1}{\sqrt{3}}(1,1,1), f_2 = \frac{1}{\sqrt{6}}(1,-2,1), f_3 = \frac{1}{\sqrt{2}}(1,0,-1) \]
Find the matrix, \(S\), of the change ... |
These exercises are not tied to a specific programming language. Example implementations are provided under the Code tab, but the Exercises can be implemented in whatever platform you wish to use (e.g., Excel, Python, MATLAB, etc.).
### 0. Describing orbits
In an elliptical orbit, the satellite's distance from the obje... |
Intersects of 2 functions
Assuming function $f$ and $g$,
scipy.optimize.fsolve would give an elegant solution:
from scipy.optimize import fsolvedef f(xy): x, y = xy return (y - x ** 2, y - np.sin(x))fsolve(f, [1.0, 1.0])
gives
array([0.87672622, 0.76864886]) is the intersect of $y=x^2$ and $y=\sin(x)$.
Intersects of 2 ... |
The rational numbers $\Q$ are a countable, totally ordered set, so any subset of the rationals is also countable and totally ordered. In fact, the subsets of the rationals are the `only' countable, totally ordered sets!
Example 5.6.1 Let $A=\N\times \N$ using the lexicographic ordering. Under this ordering, $A$ is tota... |
Speaker
Dr Anton Lymanets (University of Tuebingen)
Description
The CBM experiment at the future Facility for Antiproton and Ion Research (FAIR) will explore the properties of nuclear matter at high net baryon densities and at moderate temperature. The key detector – a Silicon Tracking System (STS) – will reconstruct c... |
Journal of Differential Geometry J. Differential Geom. Volume 99, Number 2 (2015), 215-253. On the spectrum of bounded immersions Abstract
In this article, we investigate some of the relations between the spectrum of a non-compact, extrinsically bounded submanifold $\varphi : M^m \to N^n$ and the Hausdorff dimension of... |
LaTeX uses internal counters that provide numbering of pages, sections, tables, figures, etc. This article explains how to access and modify those counters and how to create new ones.
Contents
A counter can be easily set to any arbitrary value with
\setcounter. See the example below:
\section{Introduction} This documen... |
Theorem: Diagonalizable matrices share the same eigenvector matrix $S$ iff $AB=BA$
Proof: $(\Leftarrow)$ Suppose $AB=BA$.
$$ABx=BAx=B\lambda x=\lambda Bx$$ Thus $x$ and $Bx$ are both eigenvectors of $A$, sharing the same $\lambda$. Assume that the eigenvalues of $A$ are distinct (it means the eigenspaces are all one di... |
Answer
$(5, \dfrac{3 \pi}{2})$
Work Step by Step
Here, $r=\sqrt {x^2+y^2}=\sqrt{(0)^2+(-5)^2}= \sqrt {25}=5$ $\tan \theta =\dfrac{y}{x}$ and $\theta=arctan[\dfrac{-5}{0}]$ Thus, $\theta =\dfrac{3 \pi}{2}$ Hence, $(5, \dfrac{3 \pi}{2})$
You can help us out by revising, improving and updating this answer.Update this answ... |
To send content items to your account,please confirm that you agree to abide by our usage policies.If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.Find out more about sending content to .
To send content items to your Kindle, first ensure no-rep... |
In exercises 1 - 2, find a unit normal vector to the surface at the indicated point.
1) \( f(x,y)=x^3,\quad (2,−1,8)\)
Answer: \( (\frac{\sqrt{145}}{145})(12\hat{\mathbf i}−\hat{\mathbf k})\)
2) \( \ln\left(\dfrac{x}{y−z}\right)=0\) when \( x=y=1\)
In exercises 3 - 7, find a normal vector and a tangent vector at point ... |
February 4, 2015
ece1229
No comments
Ampere's law, antenna, antisymmetric, average power, bivector, complex power, constituative relations, continuity equation, cross product, curl, dB, dBi, decibel, directivity, divergence, divergence theorem, dot product, dual, duality, ece1229, electic source, electric dipole, elect... |
i start reading about modular forms of half-integral weight $k/2$ for $\Gamma' \subset \Gamma_0(4)$. As far as i understand these are holomorphic functions $f\colon \mathbb{H} \rightarrow \mathbb{C}$ which satisfies $$f(z)|[\zeta]_{k/2} = f(z)$$ for all $\zeta \in \widetilde{\Gamma}'$, where $\widetilde{\Gamma}'=\lbrac... |
pandas.Series.ewm¶
Series.
ewm(
com=None, span=None, halflife=None, alpha=None, min_periods=0, freq=None, adjust=True, ignore_na=False, axis=0)¶
Provides exponential weighted functions
New in version 0.18.0.
Parameters: com: float, optional
Specify decay in terms of center of mass, \(\alpha = 1 / (1 + com),\text{ for }... |
Based on such demands, I designed a co-pilot which can:
Automatically clustering the clusters; Remove periodic boundary conditions and make the center-of-mass at $(0,0,0)^T$; Adjust the view vector along the minor axis of the aggregate; Classify the aggregate.
After obtaining clusters in step 1, we must remove periodic... |
Heat Equation is
$$Au_{xx} = u_{t},$$ for $-\infty<x<\infty$ and $t>0$. Also, $u(x,0) \rightarrow 0$ as $ x \rightarrow \pm \infty$.
The initial condition:
$$ u(x,0) = \exp{(-|x|)},$$
for $-\infty<x<\infty$.
Want the solution form: (Using the Fourier Transform)
$$u(x,t) = \frac{1}{\pi}\int_{-\infty}^{\infty} \frac{cos(... |
What is the area, in square units, of triangle ABC in the figure shown if points A, B, C and D are coplanar, angle D is a right angle, AC = 13, AB = 15 and DC = 5?
Use Pythagorean Theorem to find DA. So 13^2-5^2=144, and the square root of 144 is 12. So DA must be 12.
Notice that AB has the length of 15 and DA has the ... |
Answer
(a) $m\angle P = 63^{\circ}$ (b) $NP = 13~cm$
Work Step by Step
(a) Since $\angle M \cong \angle Q$, the measure of the angle $m\angle M = 90^{\circ}$ We can see that $m\angle NRQ = 90^{\circ}$ since it is supplementary to $\angle PRN$ Then $m\angle MNR = 90^{\circ}$, since the sum of the four angles in $MNRQ$ i... |
In the general equation of the compressibility factor $Z$, we define $Z$ as $$Z=\frac{pV}{nRT}$$ Here, what is $p$? Is it $p_\text{real}$ or $p_\text{ideal}$? Also, what is $V$? $V_\text{real}$ or $V_\text{container}$?
Both quantities are of the real gas.
Note that for the ideal gas behaviour, the compressibility facto... |
Renormalization Group 8 Lectures Dr V. Niarchos
The course introduces the concept of renormalisation group flow in quantum field theory building on previous lessons about renormalisation in other lectures on QFT. Applications to different field theories, including gauge theories, will be described.
Outline of the cours... |
Communications in Analysis and Geometry Volume 16 (2008) Number 5 Evolution of an extended Ricci flow system
Pages: 1007 – 1048
DOI: http://dx.doi.org/10.4310/CAG.2008.v16.n5.a5
Author Abstract
We show that Hamilton’s Ricci flow and the static Einsteinvacuum equations are closely connected by the followingsystem of geo... |
Is there a good errata for Atiyah-Macdonald available? A cursory Google search reveals a laughably short list here, with just a few typos. Is there any source available online which lists inaccuracies and gaps?
Dear Tim, on page 31 they consider a ring $A$ and two $A$- algebras defined by their structural ring morphism... |
Answer
The weight of the box is 97.1 pounds.
Work Step by Step
The angle of inclination of the ramp with the horizontal is $18{}^\circ $. On resolving the vector into its horizontal and vertical components, the horizontal component will get cancelled and we get $\begin{align} & \sin 18{}^\circ =\frac{30}{x} \\ & x\sin ... |
(b) As it is the case of indirect recursion so let first make it as direct recursion then apply rules of removal of left recursion.
to make it as direct recursion first production remain unchanged while in second production substitute the right hand side of first production wherever it comes.In the question $S$ comes i... |
For the following exercises, use implicit differentiation to find \(\frac{dy}{dx}\).
300) \(x^2−y^2=4\)
301) \(6x^2+3y^2=12\)
Answer:
\(\frac{dy}{dx}=\frac{−2x}{y}\)
Solution: \(\frac{dy}{dx}=\frac{−2x}{y}\)
302) \(x^2y=y−7\)
303) \(3x^3+9xy^2=5x^3\)
Answer: \(\frac{dy}{dx}=\frac{x}{3y}−\frac{y}{2x}\)
304) \(xy−\cos(xy... |
Solve the initial value problem: $$ u_{tt} - u_{xx} = 0 \\ u(x,0) = 0 \\ u_t(x,0) = \begin{cases} \cos \pi (x-1) & \text{if } 1 < x < 2 \\ 0 & \text{otherwise} \end{cases} $$ Find and draw the solution at $t=3$ for
(a). $x\in (-\infty, \infty)$.
(b). $x\in (0, \infty)$ with $u_x(0,t) = 0$.
(c). $x\in (-\infty, 3)$ with... |
I remember when I first learnt that testing for primality is in P (as noted in the paper Primes is in P, which explains the AKS algorithm). Some time later, I was talking with a close friend of mine (who has since received his bachelors in Computer Science). He had thought it was hard to believe that it was possible to... |
AP Statistics Curriculum 2007 Normal Std From Socr
m (→Appendix)
m (→Standard Normal Distribution)
Line 5: Line 5:
* Standard Normal ''density'' function <math>f(x)= {e^{-x^2 \over 2} \over \sqrt{2 \pi}}.</math>
* Standard Normal ''density'' function <math>f(x)= {e^{-x^2 \over 2} \over \sqrt{2 \pi}}.</math>
* Standard ... |
How to Model Different Types of Damping in COMSOL Multiphysics®
In a previous blog post, we introduced various physical phenomena that cause damping in structures and showed how such damping can be represented mathematically. Today, we follow up by looking at how to actually include damping in finite element models.
Ho... |
As already mentioned,$$(\spadesuit) \qquadC(\Bbb{T}) \rtimes_{\alpha} \Bbb{Z}_{2} \cong\{f \in C([0,1] \to {\text{M}_{2}}(\Bbb{C})) \mid\text{$ f(0) $ and $ f(1) $ are diagonal}\}.$$Hence, by the definition of a continuous field of $ C^{*} $-algebras, $ C(\Bbb{T}) \rtimes_{\alpha} \Bbb{Z}_{2} $ is a continuous field of... |
That was an excellent post and qualifies as a treasure to be found on this site!
wtf wrote:
When infinities arise in physics equations, it doesn't mean there's a physical infinity. It means that our physics has broken down. Our equations don't apply. I totally get that
. In fact even our friend Max gets that.http://blo... |
AP Statistics Curriculum 2007 Infer 2Proportions From Socr
(added a link to the Problems set)
m (→Genders of Siblings Example)
Line 66: Line 66:
* Test Statistics: <math>Z_o = {Estimate-HypothesizedValue\over SE(Estimate)} = {\hat{p}_1 - \hat{p}_2 - 0 \over SE(\hat{p}_1 - \hat{p}_2)} = {\hat{p}_1 - \hat{p}_2 - 0 \over ... |
Nonlinear Systems of Equations and Problem-Solving
As with linear systems, a nonlinear system of equations (and conics) can be solved graphically and algebraically for all of its variables.
Learning Objectives
Solve nonlinear systems of equations graphically and algebraically
Key Takeaways Key Points Subtracting one eq... |
2019-10-09 06:01
HiRadMat: A facility beyond the realms of materials testing / Harden, Fiona (CERN) ; Bouvard, Aymeric (CERN) ; Charitonidis, Nikolaos (CERN) ; Kadi, Yacine (CERN)/HiRadMat experiments and facility support teams The ever-expanding requirements of high-power targets and accelerator equipment has highligh... |
Hi, please help:
\({{x+2}\over x^2-2x}-{{2}\over x-2}=-1\)
i need to have X solved...i have no idea...thank you kindly..
solve for X \dfrac{x+2}{x^2-2x} - \dfrac{2}{x-2}=-1
\(\dfrac{x+2}{x^2-2x} - \dfrac{2}{x-2}=-1\)
\(\begin{array}{|rcll|} \hline \dfrac{x+2}{x^2-2x} - \dfrac{2}{x-2} &=& -1 \quad | \quad x-2 \ne 0 \Rig... |
I think there are some important things to remark concerning what you wrote above:
To a). Your calculation is absolutely correct, but the fact that the question as you posted it in your comment speaks about explaining an "obvious" fact in "a few sentences", I would suspect that it aimed more for something like the foll... |
Convergence of global and bounded solutions of a two-species chemotaxis model with a logistic source
College of Mathematics and Statistics, Chongqing University, Chongqing University, Chongqing 401331, China
$\left\{\begin{array}{llll}u_t=\Delta u-\chi_1\nabla\cdot( u\nabla w)+\mu_1u(1-u-a_1v),\quad &x\in \Omega,\quad ... |
I have the following homework question that I am struggling with. I have read the corresponding chapter from the book, but no guidance there.
Consider a linked list $X: X_1 \to X_2 \to X_3 \ldots$. Assume that the cost of examining a particular element $X_i$ is $C_i$. Note that to examine $X_i$, one needs to scan throu... |
We now turn our attention to finding derivatives of inverse trigonometric functions. These derivatives will prove invaluable in the study of integration later in this text. The derivatives of inverse trigonometric functions are quite surprising in that their derivatives are actually algebraic functions. Previously, der... |
Answer
The solution set is $$\{60^\circ, 120^\circ\}$$
Work Step by Step
$$2\sin\theta-\sqrt3=0$$ over the interval $[0^\circ,360^\circ)$ We carry out normal algebra here: $$\sin\theta=\frac{\sqrt3}{2}$$ $$\theta=\sin^{-1}\frac{\sqrt3}{2}$$ Over the interval $[0^\circ,360^\circ)$, there are two values of $\theta$ whose... |
Hint Applet (Trigonometric Substitution) Sample Problem Flash Applets embedded in WeBWorK questions u-subsitution Example Sample Problem with uSub.swf embedded
A standard WeBWorK PG file with an embedded applet has six sections:
A tagging and description section, that describes the problem for future users and authors,... |
Perhaps it would make more sense if it were written as follows:
$$\forall x(hasTail(x) \rightarrow dog(x))$$
Your statement is equivalent to the above statement: $$\begin{align} \lnot \lnot \forall x(hasTail(x) \rightarrow dog(x))&\equiv \lnot \exists x( \lnot(hasTail(x) \rightarrow dog(x)))\tag{1}\\ \\ & \equiv \lnot ... |
The setup is as in this question:
Given a norm $N$ over ${\bf M}_n(\mathbb C)$, it is a natural question to find the best constant $C_N$ such that $$N([A,B])\le C_N N(A)N(B),\qquad\forall A,B\in{\bf M}_n(\mathbb C).$$
Equivalently, $C_N$ is the maximum of $N(AB-BA)$ provided that $N(A)=N(B)=1$.
Given examples of $C_N$ ... |
Electronic Journal of Probability Electron. J. Probab. Volume 23 (2018), paper no. 9, 21 pp. Approximation of smooth convex bodies by random polytopes Abstract
Let $K$ be a convex body in $\mathbb{R} ^n$ and $f : \partial K \rightarrow \mathbb{R} _+$ a continuous, strictly positive function with $\int \limits _{\partia... |
Let $m,n \in \mathbb{N}$ and $m \geq n \geq 2$ and $x_1,x_2,...x_n \in \mathbb{N}_{\geq 1}$ such as $x_1+x_2+...+x_n=m$. Find $\min P$ with $P= \sum_{i=1}^{n} x_i^2.$
closed as off-topic by user9072, fedja, Stefan Kohl, Franz Lemmermeyer, Felipe Voloch Nov 1 '15 at 21:11
This question appears to be off-topic. The users... |
The notation $M = \int \vec F\cdot d\vec r$ elides an important detail: the path along which $F$ is to be integrated. The usual construction is to integrate along a path that starts at a fixed point $p$ and ends at a variable point $x$. But there are two trouble spots with this construction.
The first is not so bad. Ho... |
I have in mind $$\max\left( \sqrt{(x-1) (y-x)}+\sqrt{(1-x) (7-y)}+\sqrt{(y-7) (x-y)}\right)$$ for $x\geq -2\land x\leq 3\land y\geq 0\land y\leq 11 $, of course, taking into account real values of the roots only. In order to avoid complex numbers I consider
f=(Sqrt[(x - 1)*(y - x)] + Sqrt[(7 - y)*(1 - x)] + Sqrt[(x - y... |
Let $M^3$ be a complete riemannian manifold and $\Sigma ^2\subset M^3$ a embedded minimal compact surface. Consider the normal variation $\phi: \Sigma \times \Bbb{R}\to M$ given by
$$\phi(p,t)=\exp_p(tN(p)),$$
when $N$ is a normal vector field along to $\Sigma.$
I want to show that:
Lemma: There is $\delta>0$ such that... |
Solve system of equations
$\begin{cases} 3x^2 + \sin 2y - \cos y - 3 = 0 \\ x^3 - 3x - \sin y - \cos 2y + 3 = 0 \end{cases}$
I tried to use substitution $x = \cos t$ or sth, but I get literally nothing
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in re... |
@Qmechanic answered your question in the comments, but evidently the message did not automatically sink in. Let me try to illustrate it with the routine demonstration you probably were exposed to when learning the uses of the Dirac bra-ket notation.
The short answer is that the tracefulness of the identity in the r.h.s... |
I am writing some Calculus content, and I would like a "big list" of useful functions which are defined by definite integrals, but are not elementary functions.
Two examples of such functions are
$$ \mathrm{Erf}(x) = \frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}\mathrm{d} t $$
which is fundamentally important to statistics, an... |
Difference between revisions of "Conservation of Angular Momentum"
(copied stuff from other conservation of angular momentum page, will redirect other page to this page)
m (Maths formatting)
Line 27: Line 27:
:<math>\mathbf{L_i}=\mathbf{L_f}</math>
:<math>\mathbf{L_i}=\mathbf{L_f}</math>
−
:<math>
+
:<math>= I \omega</... |
It has been stated that the molar conductance($\Lambda_m$) of strong electrolytes is not affected to a greater extent on dilution and so to find the limiting value of molar concentration($\Lambda_m^0$) we can extrapolate the graph of molar conductance vs the concentration ($\sqrt c$). But as the concentration would nea... |
LaTeX:LaTeX on AoPS
LaTeX About - Getting Started - Diagrams - Symbols - Downloads - Basics - Math - Examples - Pictures - Layout - Commands - Packages - Help
This article explains how to use LaTeX in the AoPSWiki, the AoPS Community, and the AoPS Classroom. See Packages to know which packages are prebuilt into the AoP... |
EMV method starts its original form in Mathematics Reflection here:http://reflections.a...irelymixing.pdf
As a matter of fact, the idea of this method is extremely simple, because you are just assumed to rewrite the inequality in form of $a - b,b - c,c - a$, then compare other terms.
The drawback of this method is that... |
Given an initial velocity vi, mass of the cue ball, coefficient of friction between the ball and surface, and the radius from the center as where the cue has struck, how would I determine the change in velocity.
Unfortunately it is not enough to know where the cue has struck the cue ball, as the the spin on the cueball... |
SolidsWW Flash Applet Sample Problem 1
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+ + +
[[Category:Sample Problems]]
[[Category:Sample Problems]]
Revision as of 10:07, 10 August 2011 Flash Applets embedded in WeBWorK questions solidsWW Example Sample Problem with solidsWW.swf embedded
A standard WeBWorK PG file with an embedded applet ... |
An even more ambitious, more stringy type of supersymmetry could actually be more compatible with the LHC data
A year ago or so, we have entered the serious LHC era in which many eyes of high-energy physicists have been refocused from formal, top-down theory to experiments and phenomenology, i.e. to the thinking about ... |
Search strategies for exotic decays of the Higgs boson in the gg+MET final state at the LHC Table of contents: Abstract
In this study, we devise a search strategy for the exotic decay of the 125 GeV
Higgs boson in the $\gamma\gamma+MET$ final state. The studied final state comes in two different topologies: resonant an... |
LHCb Collaboration,; Aaij, R; Adeva, B; Adinolfi, M; Bernet, R; Bowen, E; Bursche, A; Chiapolini, N; Chrzaszcz, M; Dey, B; Elsasser, C; Graverini, E; Lionetto, F; Lowdon, P; Mauri, A; Müller, K; Serra, N; Steinkamp, O; Storaci, B; Straumann, U; Tresch, M; Vollhardt, A; Weiden, A; et al, (2015).
Measurement of $CP$ viol... |
I am trying to determine how to find the tightest upper and lower bounds when using the squeeze theorem. If there is a general technique to determining them I would appreciate the insight. Specifically I have this problem:
$$\lim_{n\to \infty} \sqrt[n]{2\left(\frac12\right)^n+\left(\frac23\right)^n+3\left(\frac12\right... |
Max Koecher (for example, in
The Minnesota Notes on Jordan Algebras and Their Applications; new edition: Springer Lecture Notes in Mathematics, number 1710, 1999), defined a domain of positivity for a symmetric nondegenerate bilinear form $B: X \times X \rightarrow \mathbb{R}$ on a finite dimensional real vector space ... |
My confusion started from thinking the quantum superposition principle.
Several website say that the quantum superposition means all state can be represented as infinity superposition of orthogonal states.
Also, i see that the Hilbert space is a infinity dimension vector space, so I don't have any question at first. (t... |
When you first encountered the trigonometric functions it was probably in the context of "triangle trigonometry,'' defining, for example, the sine of an angle as the "side opposite over the hypotenuse.'' While this will still be useful in an informal way, we need to use a more expansive definition of the trigonometric ... |
I was studying Alexander Holevo's book on
Quantum Systems, Channels and Information, which is a small but terse introduction to Quantum Information Theory. The theory of Tensor products is used almost everywhere so I decided to study the same topic from different books. There is one property that I find hard to prove a... |
Let $A\subset \mathbb{R}^n$ and $B\subset \mathbb{R}^n$ be closed retangles, and let $f:A\times B \rightarrow \mathbb{R}$ be integrable. For $x\in A$ and $y\in B$, and let \begin{equation} \mathscr{L}(x) = \mathbf{L} \int_B f(x, y) dy \end{equation} denote the lower integral of $f$ on $y\in B$. Then $\mathscr{L}$ is in... |
Given $f\colon\mathbb{R} \to \mathbb{R}$, $f$ is differentiable on $\mathbb{R}$ and the $\lim_{x \to \infty}f(x)$ does not exists . show/prove formally that there exists $x_0 \in \mathbb{R}$ such that $f'(x_0)=0$
My strategy is showing that $f$ is not monotonic function because all monotonic functions have limits when ... |
Search
Now showing items 1-2 of 2
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Difference between revisions of "LaTeX:Symbols"
(→Bracketing Symbols)
(→Bracketing Symbols)
Line 332: Line 332:
See that there's a dot after <tt>\right</tt>. You must put that dot or the code won't work.
See that there's a dot after <tt>\right</tt>. You must put that dot or the code won't work.
− + +
addition to the \l... |
Thank you for using the timer!We noticed you are actually not timing your practice. Click the START button first next time you use the timer.There are many benefits to timing your practice, including:
Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that ... |
I need to find when the sun reaches the Zenith at a given latitude.
What I've done so far:
$L=23.5 \cdot \sin(\frac{2\pi}{365.25}\cdot D) $
Here L is the latitude (<23.5) and D is number of days from March 21.
This is based on my understanding that the sun executes SHM around the celestial equator. I then solve this eq... |
The angular resolution of the telescope
really has no direct bearing on our ability to detect Oort cloud objects beyond how that angular resolution affects the depth to which one can detect the light from faint objects. Any telescope can detect stars, even though their actual discs are way beyond the angular resolution... |
This is essentially a follow up motivated by this answer to my question about the gauge transformation interpretation of identity types.
A field $$\psi:\mathcal M\to\mathbb C^n$$ is a section of the $\mathbb C^n$-bundle over the spacetime manifold $\mathcal M$. We have a local gauge transformations $$\psi(x)\mapsto \ps... |
1) Let us work in units where the speed-of-light $c=1$ is one.
In Ref. 1 is derived the radial geodesic equation for a particle in the equatorial plane
$$\tag{7.47} (\frac{dr}{d\lambda})^2+2V(r)~=~E^2, $$
with potential
$$ \tag{7.48} 2V(r)~:=~(1-\frac{r_s}{r})((\frac{L}{r})^2+\epsilon). $$
Here $\epsilon=0$ for a massl... |
1. Solution: For any $\vp\in\ca L(V,\mb F)$, if $\dim \m{range} \vp=0$, then $\vp$ is the zero map. If $\dim \m{range} \vp=1$, then $\vp$ is surjective since $\dim\mb F=1$. Moreover, $\dim…
Exercises 1,2 and 4. For Problem 2, please also see Carson Rogers’s comment. 4. Solution: For any $f\in \ca L(V_1\times \cdots\tim... |
The orthogonal group, consisting of all proper and improper rotations, is generated by reflections. Every proper rotation is the composition of two reflections, a special case of the Cartan–Dieudonné theorem.
Yeah it does seem unreasonable to expect a finite presentation
Let (V, b) be an n-dimensional, non-degenerate s... |
I have the function $$f(x)=\frac{2x}{10+x}$$ and I am asked to find its power series representation which I found to be $$\sum_{n=0}^{\infty} (-1)^{n} *\frac{2x^{n+1}}{10^{n+1}}$$ and I found the radius of convergence to be $R=10$. All until here is clear and easy, but when I am asked to find the 1st few terms I tries ... |
Yes. Denote the entrywise absolute value of a complex matrix $X$ by $|X|$. In general, if $|X|\le Y$ entrywise, then $\rho(X)\le\rho(|X|)\le\rho(Y)$.
Your $P$ is an orthogonal projection. Therefore the moduli of its entries are bounded above by $1$. Hence $|A|\le|B||D|$ and $\rho(A)\le\rho(|B||D|)$. So, it suffices to ... |
First, note that this is not specific to probability or the Stieljes integral. You could have asked the question about a plain vanilla integral $$\int_{-\infty}^\theta f(x)dx = \int_{-\infty}^\infty H(\theta-x)f(x)dx$$ where $H$ is the step function. Actually, we can simplify even further and consider derivative with r... |
While the answer for your particular case depends on a lot of factors, you can estimate how hot an object gets that is facing the sun (and whose back side is insulated) using the Stefan-Boltzmann law. Let us assume that the material is perfectly black (emissivity of 1.0) and facing the sun which delivers approximately ... |
The energy level of the particle in a one-dimensional box are given by $$E_n = \frac{n^2\hbar^2 \pi ^2}{2mL^2} = \frac{n^2 h^2}{8mL^2}.\tag1$$We see that the energy is quantised and dependent on the quantum number $n$. We also see that the energy difference between those levels gets larger with $n$. The only variable i... |
Let $T$ and $\epsilon$ be two independent random variables. Let $R=T+\epsilon$. Given this information, we can derive the posterior distribution $f(T=t|R=r)$. I have the following question: I haven't figure out how to write mathematically the posterior distribution that I am interested in. I will try to describe it fro... |
I really like the proof contained in the paper
Derivation of the Biot-Savart Law from Ampere's Law Using the Displacement Current from Robert Buschauer (2013)
It's simple and it fulfills the role of convincing the reader.
Basically the author works with one point charge $q$ situated in origin of
Z azis $(0,0,0)$. He su... |
The CO2 molecules are trying to change phase, but the surrounding liquid exerts a pressure. If you consider a simplified mechanical equilibrium between a gas bubble and surrounding liquids
$$\Delta P \pi R^2 = \sigma 2\pi R$$
where $\sigma$ is the surface tension, you have a relation between bubble size and the pressur... |
The reason for using $H_0: \mu = 12$ is that, among the set of values that correspond to $\mu \geq 12$, $\mu = 12$ is the most conservative (also called least favorable) configuration.
Let us be more precise what conservative means here. Say we set certain value of the observed statistic $\hat{\mu}$ at which we are wil... |
After I reviewed briefly the so-called black hole wars, and expressed my doubts about black hole complementarity, there are still many things to be said. However, I would like to skip over various solutions proposed in the last decades, and discuss the one that I consider most natural.
All the discussions taking place ... |
I'm trying to find the Fourier transform of $xe^{-\frac{x^2}{2}}$. I was given the hint that when $g(x) = e^{-\pi x^2}$, $\mathcal{F}(g) = g(x)$.
This is how far I have come. So we start off with the usual Fourier transform: $$ \int_{\mathbb{R}} e^{-2 \pi i x \xi} xe^{-x^2/2} \mathrm{d}x $$
Next we do a variable change... |
The Schrödinger equation is the basis to understanding quantum mechanics, but how can one derive it? I asked my instructor but he told me that it came from the experience of Schrödinger and his experiments. My question is,
can one derive the Schrödinger equation mathematically?
The Schrödinger equation is the basis to ... |
In a previous question about differences in Newtonian and GTR gravitional force for the case of star-planet gravitational interactions an
approximate relationship was noted between the expressions for the gravitational force exerted by a star on an orbiting planet (the solution is valid situations with low gravity, slo... |
Differentiation is "linear" meaning you can tackle sums one term at a time. So $\sin(\pi x)$ and $\cos(\pi x)$ can be differentiated separately and then put back together.
As for each of those terms, $\sin(\pi x)$ can be pulled apart as: $y=\sin(u)$ and $u=\pi x$. Then the chain rule says: $$\frac{dy}{dx} = \frac{dy}{d... |
Let's say that you are standing on the ground and you observe two horizontal forces of
equal magnitude, but acting in opposite directions on the block, because of which the net vector sum of all horizontal forces is zero,i.e. $$\sum F_x=0 \implies \left(a_{x}\right)_{net}=0 $$Thus the block moves with constant velocity... |
While I was looking at the periodic table today, I realised that there were gases that were much lighter than helium such as hydrogen. If hydrogen is lighter than helium, why do we insist on using helium in balloons?
As other answers have noted, the only gas lighter than helium is hydrogen, which has some flammability ... |
This page indicates that Greek letters can be inserted into Emacs by using
M-i. However, Emacs 23.2.1 in a Debian Squeeze variant inserts the "tab" character when
M-i is pressed. How can I insert Greek letters such α and β in Emacs?
This page indicates that Greek letters can be inserted into Emacs by using
You can use ... |
Ellipse Geometry – a Problem
I found the following nice problem in my Facebook account. Facebook, however, is a miracle to me and I am always unable to find a posting a second time. Unless you answer something silly like „Following“ it is lost. The best I could find was this link.
The problem is to prove:
The intersect... |
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