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Practical and theoretical implementation discussion.
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I've had a question that I couldn't answer myself and haven't found any formal derivation on the topic. If one has a point light with position \(\vec{c}\) and intensity \(I\), then the irradiance at point \(\vec{p}\) at some surface c... |
I assume that you have a wide-sense stationary discrete-time input noise signal $x(n)$, a linear time-invariant filter with impulse response $h(n)$, and an output noise process $y(n)$. If we assume that $x(n)$ is zero mean (which is not necessary, but makes it easier) and if we model $x(n)$ as perfectly band-limited, w... |
Practical and theoretical implementation discussion.
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I've had a question that I couldn't answer myself and haven't found any formal derivation on the topic. If one has a point light with position \(\vec{c}\) and intensity \(I\), then the irradiance at point \(\vec{p}\) at some surface c... |
Calculate the potential inside a uniformly charged solid sphere of radius $R$ and total charge $q$.
My attempt:
There are several ways to solve this problem but I'm curious as to whether this particular method is applicable.
WLOG let the point $P$ lie on the $z$-axis a distance $z$ from the center of the sphere (origin... |
Practical and theoretical implementation discussion.
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Hi,
I have a simple question as in the title. Why is volumetric emission proportional to absorption coefficient? I often see the volumetric emission term is written as I can also see another representation, volumetric emittance functio... |
I did the following proof earlier and just wanted conformation as to whether it works. The question was to show$$\frac{d}{dx}x^2=2x$$by the difference-quotient definition of a derivative, and then prove that limit with the $\epsilon$, $\delta$ definition for limits.
I said that $$\frac{d}{dx}x^2=\lim_{h\to0}\frac{(x+h)... |
Ex.7.2 Q7 Coordinate Geometry Solution - NCERT Maths Class 10 Question
Find the coordinates of a point \(A\), where \(AB\) is the diameter of circle whose center is \((2, -3)\) and \(B\) is \((1, 4)\)
Text Solution Reasoning:
The coordinates of the point \(P(x, y)\) which divides the line segment joining the points \(A... |
Practical and theoretical implementation discussion.
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I've had a question that I couldn't answer myself and haven't found any formal derivation on the topic. If one has a point light with position \(\vec{c}\) and intensity \(I\), then the irradiance at point \(\vec{p}\) at some surface c... |
There are two prominent uses of the term "average" in algorithm analysis.
Average-case as a special case of expected costs
Here, "average case" just means "expected case w.r.t. uniform distribution". Since we
usually analyse with uniform inputs in mind (everything else is hard, and there's not much reason to prefer one... |
Recently, I read a tutorial about Hough line transform at the OpenCV tutorials. It is a technique to find lines in an image using a parameter space. As explained in the tutorial, for this it is necessary to use the
polar coordinate system. In the commonly used Cartesian coordinate system, a line would be represented by... |
I swear I read the question many times, but I still not quite sure what it is about. So I will try to clarify some things hoping that they are relevant.
First off,
any complex multiple of a wave function indeed describes exactly the same state of a system. This directly follows from the postulate of quantum mechanics w... |
Practical and theoretical implementation discussion.
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I've had a question that I couldn't answer myself and haven't found any formal derivation on the topic. If one has a point light with position \(\vec{c}\) and intensity \(I\), then the irradiance at point \(\vec{p}\) at some surface c... |
Numerical Methods for PDEs: In Occasion of Raytcho Lazarov's 70th Birthday Joseph Pasciak, Texas A&M University An Analysis of Finite Element Approximation to the Eigenvalues of Problems Involving Fractional Order Differential Operators Authors: Bangti Jin, Texas A&M University Raytcho Lazarov, Texas A&M University Jos... |
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I've had a question that I couldn't answer myself and haven't found any formal derivation on the topic. If one has a point light with position \(\vec{c}\) and intensity \(I\), then the irradiance at point \(\vec{p}\) at some surface c... |
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Practical and theoretical implementation discussion.
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I've had a question that I couldn't answer myself and haven't found any formal derivation on the topic. If one has a point light with position \(\vec{c}\) and intensity \(I\), then the irradiance at point \(\vec{p}\) at some surface c... |
I have tried doing this since the past 2 hours. How do I do this?
It's just a straightforward application of the definitions:
$\bullet \,$If $gf$ is injective, then $f$ is injective because $f(a)=f(b)\Rightarrow gf(a)=gf(b)\Rightarrow a=b$.
$\bullet \,$If $gf$ is surjective, then $g$ is surjective because $b\in S\Right... |
I am interested in seeing examples of a space $X$ (preferably a closed smooth manifold, but any finite-dimensional CW-complex would also be of interest) with a vector bundle $\xi\colon E \to X$ on it, so that there is exactly one index $i$ with $w_i(\xi) \neq 0$, and $i$ is bigger than $8$. Here are some remarks:
(1) F... |
No, your "following" is not accurate. You wrote a SB Lagrangean invariant under
O(N)×O(N) (⊂ O(2N)), except for the λ term, which is only invariant under its diagonal subgroup O(N), instead.
The
N φs and the N εs fit into 2 N - vector, $(\vec{\phi},\vec{\epsilon})$, so the symmetry starts as O(2N) but the g term is onl... |
You have to check that two conditions are met:
$\cup \mathcal{B} = X$. $\forall B_1, B_2 \in \mathcal{B}: \forall x \in B_1 \cap B_2: \exists B_3 \in \mathcal{B}: x \in B_3 \subseteq B_1 \cap B_2$.
If these hold for a family $\mathcal{B}$ of subsets of $X$, then this family forms a base for some topology on $X$. And th... |
I'm trying to find the Fourier Transform of the following rectangular pulse:
$$ x(t) = rect(t - 1/2) $$
This is simply a rectangular pulse stretching from 0 to 1 with an amplitude of 1. It is 0 elsewhere. I tried using the definition of the Fourier Tranform:
$$ X(\omega) = \int_0^1 (1)*e^{-j\omega*t}dt $$
However carry... |
Answer
$$-\tan x\cos x=\sin(-x)$$ $\text{C}$ is the answer.
Work Step by Step
$$A=-\tan x\cos x$$ A Quotient Identity related to $\tan x$ states that $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$ That means we can rewrite $A$ as follows: $$A=-\frac{\sin x}{\cos x}\cos x$$ $$A=-\sin x$$ Also, from Negative-Angle Identiti... |
In Python, objects can declare their textual representation using the
__repr__ method. IPython expands on this idea and allows objects to declare other, rich representations including:
A single object can declare some or all of these representations; all are handled by IPython's
display system. This Notebook shows how ... |
Temperature Amount of a substance Luminous intensity
are pretty much bogus fundamental units. The unit temperature is just an expression of the Boltzmann constant (or you could say the converse, that the Boltzmann constant is not fundamental as it is merely an expression of the anthropocentric and arbitrary unit temper... |
While doing some exercises on the variation of the metric tensor $g_{\mu\nu}$ and of its inverse $g^{\mu\nu}$, I came across the following identity:
$$\begin{align} & \delta(g_{\mu\nu}g^{\mu\nu})=\delta g_{\mu\nu} g^{\mu\nu} + g_{\mu\nu}\delta g^{\mu\nu} \overset{!}{=} 0 \\ \iff & \delta g_{\mu\nu} g^{\mu\nu} = - g_{\m... |
Here is a hotch-potch of examples, counterexamples, theorems, ... which I
plagiarized adapted from the answer by some guy with a complicated name to the analogous question for complex analytic spaces. I hope they will give you some intuition for flatness, that "riddle that comes out of algebra, but which technically is... |
Given the Klein Gordon equation $$\left(\Box +m^{2}\right)\phi(t,\mathbf{x})=0$$ it is possible to find a solution $\phi(t,\mathbf{x})$ by carrying out a Fourier decomposition of the scalar field $\phi$ at a given instant in time $t$, such that $$\phi(t,\mathbf{x})=\int\frac{d^{3}x}{(2\pi)^{3}}\tilde{\phi}\left(t,\math... |
Will that affect the quality of speech comparison, and by how much?
That is impossible to tell without knowing what the Node.js thing does internally; I think it's a bit much too ask for us to search for what you meant. As a comment: signal processing in JavaScript sounds like a bad idea, performance-wise
and developme... |
Let $K$ be a complete, algebraically closed non-Archimedean field, and let $p \in K[x]$ be of degree $d > 0$ and norm 1. (Here the norm of a polynomial is the maximum of the norms of its coefficients.)
I am interested in finding unique representations for elements of the affinoid algebra $$A = K \langle x, p^{-1} \rang... |
Answer
$8(\cos(30^{\circ})+i\sin(30^{\circ}))$
Work Step by Step
To find the trigonometric form of a complex number from its Cartesian form, two things must be done. Firstly, the modulus of the complex number must be found. Secondly, the argument of the complex number must be found. To find the modulus of the complex n... |
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1of 1 Fri Apr 26, 2019 10:18 pm Forum: General Development Topic: Point lights and non-diffuse brdfs Replies: 9 Views: 1095
Thanks anyways, I appreciate it. I'll keep looking for a formal proof, and if I find one I'll make sure to link it for future readers.
Fri Apr ... |
The proof will be done in three parts. First we explain the martingale difference method used to obtain concentration inequalities. At some point, we will need to estimate the probability of discrepancy between coupled delayed renewal processes, and thus, the second part of the proof is the explicit construction of a c... |
Lecture: HGX205, M 18:30-21
Section: HGW2403, F 18:30-20 Exercise 01 Prove that \(\neg\Box(\Diamond\varphi\wedge\Diamond\neg\varphi)\) is equivalent to \(\Box\Diamond\varphi\rightarrow\Diamond\Box\varphi\). What you have assumed? Define strategyand winning strategyfor modal evaluation games. Prove Key Lemma: \(M,s\vDas... |
Context.If have an algebraic element $\alpha$ over $\mathbb Q$, and I want to write $\mathbb Z[\alpha]:=\{a+\alpha b,\ a,b\in \mathbb Z\}$ as a quotient ring of the form $\mathbb Z[X]/I$.
Is the following approach correct?
Let $\pi$ be an irreducible of $\mathbb Z[X]$ such that $\pi(\alpha)=0$.
Then let's consider the ... |
Let $e_1,e_2,\dots$ be a Schauder basis for a Hilbert space $(V , \langle \cdot , \cdot \rangle)$. Let $A:V \to V$ be an operator. Finally, let $V_n = {\rm span}( e_1, \dots, e_n)$. Let $i_n : V_n \to V$ be the injection so that $i_n^\dagger$ is the orthogonal projection. Finally, define $A_n = i_n^\dagger \circ A \cir... |
There are a thousand apps for organising your life, calendars, todo lists, note trackers, but the big kahuna, the true Swiss army knife is org-mode. Out of the box, org-mode understands LaTeX and code snippets, todo lists and bookmarks, projects and agendas. Best of all, it comes with a powerful text editor, Emacs! Thi... |
Sign-changing solutions for some nonhomogeneous nonlocal critical elliptic problems
Departamento de Matemática, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile
$ (-\Delta_{\Omega})^{s} u = \left| u\right| ^{\frac{4}{N-2s}}u +\varepsilon f(x)\quad \mbox{in }\Omega, $
$ \Omega $
$ \mathbb... |
freqz uses an FFT-basedalgorithm to calculate the Z-transform frequency response of a digitalfilter. Specifically, the statement
[h,w] = freqz(b,a,p)
returns the
p-point complex frequency response, H( e ),of the digital filter. jω
In its simplest form,
freqz accepts the filtercoefficient vectors
b and
a,and an integer
... |
The following describes my understanding of floating point representations.
(For numbers $b, m, E_{min}, E_{max} \in \mathbb{N} \setminus \{0\}$, $b>1$, $E_{min} \leq E_{max}$...)
Let $F(b, m, E_{min}, E_{max})$ be the set of all real numbers $x \in \mathbb{R}$ that can represented as
$x = \sigma \cdot (\sum_{i=0}^{m-1... |
Construct two functions $ f,g: R^+ → R^+ $ satisfying:
$f, g$ are continuous; $f, g$ are monotonically increasing; $f \ne O(g)$ and $g \ne O(f)$.
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes a minute to sign up.Sign up to jo... |
I've seen Julius' MATLAB code and I know what it does.
Essentially, given an LTI filter with impulse response, $h[n]$, and frequency response:
$$\begin{align} H(e^{j \omega}) &\triangleq \Big| H(e^{j \omega}) \Big| \, e^{j \phi(\omega) } \\&= \sum\limits_{n=-\infty}^{\infty} h[n] \, e^{-j \omega n}\end{align}$$
Then $\... |
Although I've not specifically attempted a \$15\:\text{A}\$ boosted LM317 before, this is along the lines of what I'd try out first. This is roughly taken from the Figure 23 you mentioned:
simulate this circuit – Schematic created using CircuitLab
In this case, I went for the D44/D45 series devices. (The PNP version ha... |
Let $f(x) = \sum_{n=1}^\infty \frac{(-1)^n}{\sqrt n} \arctan\left(\frac{x}{\sqrt n}\right)$. Show that $f(x)$ converges uniformly.
First, it is easy to see that the series converges for every $x$ by Leibniz test.
Now, I'm not so sure how to prove uniform converges. I thought about the fact that $\arctan\left(\frac{x}{\... |
I'm trying to find the field equations for some particular Lagrangian. In the middle I faced the term
$$\frac{\delta \Gamma_{\beta\gamma}^{\alpha}}{\delta g^{\mu\nu}} \, .$$
I know that
$$\delta \Gamma_{\beta\gamma}^{\alpha} = \frac{1}{2}g^{\sigma\alpha}(\nabla_{\beta}(\delta g_{\sigma\gamma}) + \nabla_{\gamma}(\delta ... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
What is Young’s Double Slit Experiment?
Young’s double-slit experiment uses two coherent sources of light placed at a small distance apart, usually, only a few orders of magnitude greater than the wavelength of light is used. Young’s double-slit experiment helped in understanding the wave theory of light which is expla... |
Let $E_\delta =[0,1]^{N-1}\times [0,\delta]$, $p\in [1,\infty)$ and $1/p+1/p'=1$. Let $\varphi\in C^1(E_\delta)$ such that $$\varphi(x)=0,\ \forall \ x\in [0,1]^{N-1}\times \{0\}.$$
By the fundamental theorem of calculus and Holder inequality, if $x'=(x_1,\cdots,x_{N-1})$ and $x=(x',t)$ then $$|\varphi(x)-\varphi(x',0)... |
Ex.9.1 Q16 Some Applications of Trigonometry Solution - NCERT Maths Class 10 Question
The angles of elevation of the top of a tower from two points at a distance of \(4\,\rm{m}\) and \(9\,\rm{m}\) from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is \... |
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... |
There is no need for an epsilon transition, it is a waste of space.
For a regular expression $E$, with resulting automaton $A$, must respect these properties of the transition function, $\delta$:
$A$ has exactly one initial state $q_0$, which is not
accessible$^{*}$ from any state. That is,$$ \delta(q, a) \neq q_0 \qua... |
Gödel has proved the existence of undecidable propositions for any system of recursive axioms capable of formalizing arithmetic. But do we know the logical causes of this state of undecidability? In other words, what are the common or recurrent characteristics of this type of propositions, if any?
This answer is a bit ... |
This is a very nice problem: I struggled with it for some time. I’ll go part way, and you should be able to finish it off.
Certainly $b$ is nonzero, ’cause it’s the constant term of an irreducible quadratic. Now, since the roots of $x^2+ax+b$ are among the roots of $f$, we have $(x^2+ax+b)\big|f(x)$, so we may write $f... |
Let $G$ be a finite group, $L(G)$ its subgroup lattice and $\mu$ the Möbius function.
Consider the Euler totient of $G$ defined as follows: $$ \varphi(G) = \sum_{H \le G}\mu(H,G) |H| $$ Let $X=\{M_1, \dots, M_n \}$ be the set of maximal subgroups of $G$. By applying the Crosscut Theorem with $X$ (see this comment of Ri... |
You'll need to understand the
sampling theorem. In short, each signal has what we call a spectrum¹, which is the Fourier transform of the signal as it comes in time domain (if it is a time signal), or spatial domain (if it is a picture. Since the Fourier transform is bijective, a signal and its transform are equivalent... |
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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 ... |
Suppose that I have 10 kg of plastic/polymer that is non solvable in water. I then divide the plastic/polymer into two equal parts. Let us name the parts A and B in order to identify them. I then proceed to make beads from each part. I make $n_A$ beads of radius $r_A$ from part A. I also make $n_B$ beads of radius $r_B... |
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Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
Page history 12 October 2019 10 October 2019 28 September 2019 20 September 2019 23 August 2019 5 August 2019 17 July 2019 25 June 2019
Dating maintenance tags: {{Full citation needed}}m
+15
→Future potential
-7
→Reduced CO2 emissions: add {{full citation needed}}
+24
→History
-19
→Failure risks: tidy up ref
+92
→top: ... |
The Annals of Applied Probability Ann. Appl. Probab. Volume 29, Number 1 (2019), 326-375. Random switching between vector fields having a common zero Abstract
Let $E$ be a finite set, $\{F^{i}\}_{i\in E}$ a family of vector fields on $\mathbb{R}^{d}$ leaving positively invariant a compact set $M$ and having a common ze... |
Answer
Please see the work below.
Work Step by Step
We know that $v=\sqrt{\frac{\gamma P}{\rho}}$ We plug in the known values to obtain: $v=\sqrt{\frac{(1.29)(48000)}{0.35}}$ $v=420\frac{m}{s}$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
2... |
I am stuck on the following exercise.
It is given that the series $\sum_{n=1}^\infty a_n$ is convergent, but not absolutely convergent and $\sum_{n=1}^\infty a_n=0$. Denote by $s_k$ the partial sum $\sum_{n=1}^k a_n$, k=1,2,... Then
$s_k=0$ for infinitely many k
$s_k>0$ for infinitely many k, and $s_k<0$ for infinitely... |
One can use binomial expansion in combination with the complex extension of trig functions:
$$\cos(xy)=\frac{e^{xyi}+e^{-xyi}}{2}=\frac{a^{xy}+a^{-xy}}2$$
Using $a=e^i$ for simplicity.
We also have:
$$(a+a^{-1})^n=\sum_{i=0}^{\infty}\frac{n!a^{n-i}a^{-i}}{i!(n-i)!}=\sum_{i=0}^{\infty}\frac{n!a^{n-2i}}{i!(n-2i)!}$$
Whic... |
Can anyone help me with this exercise, please?
A topological space $X$ is said to be irreducible if $X\neq\emptyset$ and if every pair of non-empty open sets in $X$ intersect, or equivalently, if every non-empty open set is dense in $X$. Show that $\text{Spec}(A)$ is irreducible if and only if the nilradical of $A$ is ... |
Is there an example of an eigenfunction of a linear time invariant (LTI) system that is
not a complex exponential? Justin Romberg's Eigenfunctions of LTI Systems says such eigenfuctions do exist, but I am not able to find one.
All eigenfunctions of an LTI system can be described in terms of complex exponentials, and co... |
Find the number of irreducible monic polynomials of degree $2$ over a field with five elements.
Please anyone help me.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
Find... |
We know that there are Whitehead theorem for homotopy and homology theory.
Is there the Whitehead theorem for cohomology theory for 1-connected CW complexes?
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.Sign up to join this community
We know that there ar... |
I'm going to assume you were just handed this schematic and asked to perform some tasks. The results you got do not sound correct for the circuit. (It's not a great design. But it's enough to get by.)
The first thing to check is the voltage of the power supply. If this is a \$9\:\text{V}\$ battery that was sitting on a... |
Ex.13.5 Q2 Surface Areas and Volumes Solution - NCERT Maths Class 10 Question
A right triangle, whose sides are \(3 \,\rm{cm}\) and \( 4\,\rm{cm}\) (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate.)
Te... |
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D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
Let $X,Y$ be two disjoint closed sets on $\mathbb{R}$ such that $X\cup Y = [a,b]$. Show that $X= \emptyset$ or $Y = \emptyset$.
Here's what I've got by now:
Let $k \in X\cup Y$. Therefore $k \in X$ or $k \in Y$. Suppose that $X \neq \emptyset$ and $k \in X$, hence $k \notin Y$ which implies that $k \in \mathbb{R} \setm... |
Ex.6.3 Q6 Triangles Solution - NCERT Maths Class 10 Question
In Figure , if \(\Delta \mathrm{ABE} \cong \Delta \mathrm{ACD}\), show that \(\Delta ADE \sim \Delta ABC\).
Diagram
Text Solution Reasoning:
As we know if two triangles are congruent to each other;their corresponding parts are equal.
If one angle of a triangl... |
I'll list two approaches, either of which should work.
Projected gradient descent
One general approach would be to use projected gradient descent, which provides a way to accommodate these kinds of constraints. For specific kinds of constraints there may be a better way.
Let's recall how we train neural networks. We ha... |
Three-dimensional antenna radiation patterns. The radial distance from the origin in any direction represents the strength of radiation emitted in that direction. The top shows the directive
pattern of a horn antenna
, the bottom shows the omnidirectional
pattern of a dipole antenna
.
In the field of antenna design the... |
Similar to this question: Applications of connectedness I want to collect applications of compactness.
E.g.: compact + discrete => finite, which can be used to prove the finiteness of the automorphism group of polarized abelian varieties.
MathOverflow is a question and answer site for professional mathematicians. It on... |
Juan Maldacena wrote a popular essay on gauge symmetries and their breaking:
The next Maldacena may arrive from Zimbabwe.
Analogously, we learn that Maldacena's work with gauge theories was helped by the chronic inflation in his homeland, Argentina. The persistent monetary inflation and currency reforms – something tha... |
Ex.3.6 Q2 Pair of Linear Equations in Two Variables Solution - NCERT Maths Class 10 Question
Formulate the following problems as a pair of equations, and hence find their solutions:
(i) Ritu can row downstream \(20\,\rm{ km}\) in \(2\) hours, and upstream \(4 \,\rm{km}\) in \(2\) hours. Find her speed of rowing in stil... |
I am taking input from an electret mic amplified using LM358 amplifier from my PIC16F877A's ADC unit. I am getting the readings in Volts from the ADC which ranges from 2.5V to 5V. How can I convert these readings into dB?
DB SPL is a pressure measuring unit.
You can't convert a voltage to an DB SPL reading unless you k... |
I need help with what seems like a pretty simple integral for a Fourier Transformation. I need to transform $\psi \left( {0,t} \right) = {\exp^{ - {{\left( {\frac{t}{2}} \right)}^2}}}$ into $\psi(0,\omega)$ by solving:
$$ \frac{1}{{2\pi }}\int_{ - \infty }^{ + \infty } {\psi \left( {0,t} \right){e^{ - i\omega t}}dt} $$... |
Rather than answer the question numerically I have outlined the four different cases,
reversible / irreversible and isothermal / adiabatic.
In adiabatic changes no energy is transferred to the system, that is the heat absorbed or released to the surroundings is zero. A vacuum (Dewar) flask realises a good approximation... |
Oceanic Basin Modes: Quasi-Geostrophic approach¶
This tutorial was contributed by Christine Kaufhold and Francis Poulin.
As a continuation of the Quasi-Geostrophic (QG) model described in the other tutorial, we will now see how we can use Firedrake to compute the spatial structure and frequencies of the freely evolving... |
You started off correctly but in flow used the wrong result that $\lim_{x \to 3}f(x) = f(3)$. This is not known in advance as we don't know whether $f$ is continuous or not. Another problem is that you are trying to deal with both $x \to 3^{-}$ and $x \to 3^{+}$ separately. This is required only when the definition of ... |
I am confused about, what I believe, refers to passive and active transformations in QM. What I have understood so far is that the matrix elements $\langle \psi| \hat{H}|\phi\rangle$ should remain unchanged under transformations; this implies that $\hat{H} = \hat{U}^\dagger \hat{H} \hat{U}$.
On the other hand, under ce... |
There ought to be a diagram showing how the angle $\theta$ is defined. Nevertheless, the boundary condition which you have been given is confusing.
The diagram above shows a vertical plane through the centre of the spherical electrode. There is
cylindrical symmetry here, so a cylindrical co-ordinate system is the obvio... |
Consider the following two polynomials \begin{align} p(s)&:=s^n+\alpha_{n-1}s^{n-1}+\cdots+\alpha_1s+\alpha_0,\\ q(s)&:=s^{n-1}+\alpha_{n-1}s^{n-2}+\cdots+\alpha_2 s+\alpha_1, \end{align} where $\alpha_{0},\dots,\alpha_{n-1}$ are positive real numbers.
Assume that $p(s)=sq(s)+\alpha_0$ is Hurwitz, i.e., every root $\la... |
A hypothetical diatomic molecule has a binding length of $0.8860 nm$. When the molecule makes a rotational transition from $l = 2$ to the next lower energy level, a photon is released with $\lambda_r = 1403 \mu m$. At a vibration transition to a lower energy state, a photon is released with $\lambda_v = 4.844 \mu m$. D... |
In "A Classical Introduction to Modern Number Theory" by Ireland and Rosen, a very close bound is obtained by completely elementary means.
Assum $p_n \le x < p_{n+1}$, where $p_i$ denotes the $i$'th prime. By definition, $\pi(x) = n$.
Considers the numbers up to $x$: $\{1,2,\cdots, x \}$. They are divisible only by pri... |
I have a question form my teachers, and I cannot understand why I can find out the modulation index form the figure.
The question provide a Figure like this:
And the information signal is a sinusoidal test signal with peak amplitude $6\ \rm V$ and is applied to an AM-DSB-C modulator, the Fourier spectrum of the modulat... |
Let
$\Omega\subseteq\mathbb{R}^n$ be a bounded domain $H:=W_0^{1,2}(\Omega)$ be the Sobolev space $|\;\cdot\;|_p$ be the seminorm $$|u|_p^p:=\int_\Omega|\nabla u|^p\;d\lambda^n\;\;\;\text{for }u:\Omega\to\mathbb{R}\;\text{weakly differentiable}$$ on $L^p:=L^p(\Omega)$ $\left\|\;\cdot\;\right\|_p$ be the $L^p$-norm
From... |
Illinois Journal of Mathematics Illinois J. Math. Volume 48, Number 1 (2004), 89-96. On the geometry of positively curved manifolds with large radius Abstract
Let $M$ be an $n$-dimensional complete connected Riemannian manifold with sectional curvature $K_M\geq 1$ and radius $\operatorname{rad}(M)>\pi /2$. For any $x\i... |
Logarithms and Exponentials
log computes logarithms, by default natural logarithms,
log10 computes common (i.e., base 10) logarithms, and
log2 computes binary (i.e., base 2) logarithms. The general form
log(x, base) computes logarithms with base
base.
log1p(x) computes \(\log(1+x)\) accurately also for \(|x| \ll 1\).
e... |
Nonrelativistic solutionThe variables used will be$x$ for the distance travelled$v$ for velocity$a$ for acceleration ($1~\mathrm{g}$)$t$ for the time$c$ for the speed of light.Non brakingAssuming the velocity you arrive at does not matter we take the equation$$x = \frac12 a t^2\ .$$Solve for $t$:$$t = \sqrt{\frac{2x}{a... |
Thermodynamics has always been a tough thing for me. There are lots of assumptions in this subject (those assumptions, I know, are necessary, I know the science of thermodynamics is a very practical science).
First Law of Thermodynamics states mathematically: $$\Delta U=Q+W$$ (with proper sign conventions must be used)... |
Using currently available fuels and technology and an unlimited budget. How big would a rocket without stages have to be to make it to a stable orbit? and how big would a rocket without staged have to be to escape Earth's gravity? "edited" - or for the easier question how big would the rocket have to be if it was massl... |
In
classical thermodynamics the change in internal energy is defined by the first law as$$\Delta U = q + w$$so that only the difference in $U$ is known; $q$ is the heat absorbed by the 'system' and $w$ the work done on the system.
For example in a closed system (no exchange of matter with environment) we can write for ... |
A simple illustration of the trapezoid rule for definite integration:$$ \int_{a}^{b} f(x)\, dx \approx \frac{1}{2} \sum_{k=1}^{N} \left( x_{k} - x_{k-1} \right) \left( f(x_{k}) + f(x_{k-1}) \right). $$
First, we define a simple function and sample it between 0 and 10 at 200 points
%matplotlib inlineimport numpy as npim... |
Let $\phi$ be a convex function on $(-\infty, \infty)$, $f$ a Lebesgue integrable function over $[0,1]$ and $\phi\circ f$ also integrable over $[0,1]$. Then we have:
$$\phi\Big(\int_{0}^{1} f(x)dx\Big)\leq\int_{0}^{1}\Big(\phi\circ f(x)\Big)dx.$$
I am thinking about a counterexample that the converse of this statement.... |
I'm trying to understand lines in affine and projective space in order to solve problems 2.15 and 4.13 in Algebraic Curves by William Fulton: https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf&ved=2ahUKEwiI3drj-NHhAhXJxIsKHQSMC9QQFjAAegQIAhAB&usg=AOvVaw0_YBJKOU-rk2... |
The Annals of Probability Ann. Probab. Volume 22, Number 1 (1994), 160-176. Survival Asymptotics for Brownian Motion in a Poisson Field of Decaying Traps Abstract
Let $W(t)$ be the Wiener sausage in $\mathbb{R}^d$, that is, the $a$-neighborhood for some $a > 0$ of the path of Brownian motion up to time $t$. It is shown... |
Violino, Giulio, Ellison, Sara L, Sargent, Mark, Coppin, Kristen E K, Scudder, Jillian M, Mendel, Trevor J and Saintonge, Amelie (2018)
Galaxy pairs in the SDSS - XIII. The connection between enhanced star formation and molecular gas properties in galaxy mergers. Monthly Notices of the Royal Astronomical Society, 476 (... |
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