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Recently I have decided to study EM processes with massive spin-1 boson represented by a field $\hat {W}_{\mu}$.
At the first time I have used minimally modified lagrangian: $$\tag 1 \hat {L} = |\partial_{\mu}\hat {W}_{\nu} - \partial_{\nu}\hat {W}_{\mu}|^{2} + m^{2}|\hat {W}|^{2} \to \hat {L}_{m} = |\hat {D}_{\mu}\hat... |
not ice how one two compone nts acting together give one original Siding plan as their resultant.
Step 3 :
magnets
ferrofluid rare earth magnets rare earth magnets magnetic toys magnetic balls magnet balls strong magnet magnetic bracelet strong magnets magnetic bracelets magnetic bracelets magnetic name tags
Now we cth... |
not ice how one two compone nts acting together give one original Siding plan as their resultant.
Step 3 :
magnets
ferrofluid rare earth magnets rare earth magnets magnetic toys magnetic balls magnet balls strong magnet magnetic bracelet strong magnets magnetic bracelets magnetic bracelets magnetic name tags
Now we cth... |
In what follows, we step forward to the generation of a (input) random field $g\in L^P(\Omega,\Sigma, \mathbb{P}; \mathcal{X})$ with realisation in a Banach space $\mathcal{X}=\mathcal{X}(D)$ defined on some Lipschitz domain $D\subset\mathbb{R}^2$ for some $1<P< \infty$. For example we have $\mathcal{X} = L^\infty(D)$ ... |
Remember that an oracle machine isn't really a "complete object" - basically anything interesting we might ask of it
depends on what oracle we feed it. For example, whether an oracle machine $\Phi_e^-(e)$ halts or not depends in general on what oracle it's working with.
So let me rephrase the fact you're starting with:... |
Let $E$ be a dense subset of a metric space $X$, and let $f$ be a uniformly continuous
real function defined on $E$. Prove that $f$ has a continuous extension from $E$ to $X$.
Could the range space $\mathbb{R}^1$ be replaced by any metric space?
Proof: I solved the first part of problem but I am interested in a second ... |
Let $\Omega\subset\mathbb{R}^d$ be open,and $P(D)=\operatorname{\sum_{|\alpha|\le N}}f_{\alpha}D^{\alpha}$ be an elliptic differential operator. Rudin proves in
Functional Analysis Part II the Regularity Theorem for Elliptic Operators that if $f_{\alpha}$ are smooth and $f_{\alpha}$ are constants for $|\alpha|=N$, then... |
I have a vector field $\vec v=(x^2+y^2+z^2)(x \hat x+y \hat y +z \hat z)$, and I need to computed the integral of $\Delta \cdot \vec v$ over the region $x^2+y^2+z^2 \le 25$. I see that $\vec v=r^2\vec r$ which is $\vec v=r^3 \hat r$. The way I tried to compute the integral was like this:
$$\int r^3\hat r \cdot d\vec a ... |
mihaild
Avatar from Batllestar Galactica series.
Moscow, Russia
Member for 8 years, 9 months
1 profile view
Last seen Apr 7 at 18:17 Communities (11) Top network posts 14 Guessing each other's coins 13 Big O /Right or wrong? 10 Finding $f$ such that $f(f(f(f...(x)))) = x$ 10 Sum of signature of elements of $S_n$ is $0$... |
The null points where electric field is zero must lie inside the triangle and on the axes of reflection symmetry.
Consider a triangle with side $2a$. Suppose a null point P lies on the axis through charge 3, as in the diagram below.
Because of symmetry, the horizontal components of the electric fields at P due to charg... |
I have a number of measurements of the same quantity (in this case, the speed of sound in a material). Each of these measurements has their own uncertainty.
$$ v_{1} \pm \Delta v_{1} $$ $$ v_{2} \pm \Delta v_{2} $$ $$ v_{3} \pm \Delta v_{3} $$ $$ \vdots $$ $$ v_{N} \pm \Delta v_{N} $$
Since they're measurements of the ... |
I) On a general symplectic manifold $({\cal M},\omega)$ (typically called
phase space by physicists), one can locally choose a symplectic potential $\theta\in \Gamma(T^{*}{\cal M}|_{\cal U})$, which is a one-form such that
$$\tag{1} \mathrm{d}\theta~=~\omega,$$
cf. Poincare Lemma. Here ${\cal U}\subseteq {\cal M}$ deno... |
I'm not convinced that a neural network is necessarily the right tool for this. When you have a hammer, it's tempting to think that everything looks like a nail... but sometimes the answer is "No, you dummy, that's a screw, use a screwdriver, not a hammer."
So, I'll comment on several kinds of methods you could explore... |
Sorry for the newbie inquiry but I'm having a little trouble making sense of stationarity and how a the presence of a time trend impacts this. I'm working on a model for operating margins and as a first step I want to determine if the original series is stationary before proceeding. I first fitted a simple linear trend... |
Suppose that 10 volunteers have done an intelligence test; here are the results obtained. The mean obtained at the same test, from the entire population is 75. You want to check if there is a statistically significant difference (with a significance level of 95%) between the means of the sample and the population, assu... |
The Annals of Statistics Ann. Statist. Volume 19, Number 3 (1991), 1626-1638. Inference for the Crossing Point of Two Continuous CDF's Abstract
Let $\mathscr{F}$ denote the set of cdf's on $\mathbb{R}$ with density everywhere positive. Let $C_A = \{(F,G) \in \mathscr{F} \times \mathscr{F}$: there exists a unique $x^\as... |
In calculus, I know that one defined the differential quotient$$\frac{dy}{dx} := \lim\limits_{h \rightarrow 0}{\frac{y(x+h)-y(x)}{h}}$$I learned that it is
not a quotient, but can be treated as one in many cases which you can prove like$$ \frac{dy}{dx} = {\frac{dx}{dy}}^{-1} \quad or \quad \frac{dy}{dx} \frac{dx}{dt} =... |
There are several ways of testing for coeliac disease, a metabolic disorder in which the body responds to gluten proteins (gliadins and glutenins) in wheats, wheat hybrids, barley, oats and rye. One diagnostic approach looks at genetic markers in the HLA-DQ (Human Leukocyte Antigen type DQ), part of the MHC (Major Hist... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
Difference between revisions of "Carmichael number"
(Erdős upper bound)
m
Line 1: Line 1: − + Revision as of 08:48, 22 February 2013
A composite natural number for which modulo , whenever is relatively prime to . Thus they are pseudo-primes (cf. Pseudo-prime) for every such base . These numbers play a role in the theor... |
Let's Cover Homotopy (an apologetic revisionary tale)Mathematics · What am I doing? The structure of these posts
This post is not really building off of the theory from my previous post (homology pt 1), but it’s about the same subject. It turns out we were using a book I didn’t really like too much, so I switched to so... |
Assume that we have a non-empty finite lattice $(L,\leq)$ and a monotone Boolean-valued function $f : L \rightarrow \mathbb{B}$ (i.e, for every $x,y \in L$, if $f(x)=\mathbf{true}$ and $x \leq y$, then $f(y) = \mathbf{true}$).
What is an efficient algorithm to compute the
frontier set of $f$, i.e., the elements $x \in ... |
When attempting to prove that a number is the infimum of a set, the proof normally follows as follows:
1)show set is bounded below by $t$.
2)assume $s$ is also a lower bound, but $s>t$ 3)show $s$ is in the set therefore obtaining a contradiction.
However in this question: show that $\inf \{2 + \frac 2 n \mid n \in \Bbb... |
I am reading "Topological Field Theory of Time-Reversal Invariant Insulators" by Qi, Hughes, and Zhang (https://arxiv.org/abs/0802.3537). It argues that time reversal invariant (TRI) insulators in 2+1 and 3+1 dimensions are descendants of the fundamental TRI insulator in 4+1 dimensions. When it discusses quantum hall e... |
In set theory, we have the phenomenon of the
universal definition. This is a property $\phi(x)$, first-order expressible in the language of set theory, that necessarily holds of exactly one set, but which can in principle define any particular desired set that you like, if one should simply interpret the definition in ... |
The useful properties of kernel SVM are not universal - they depend on the choice of kernel. To get intuition it's helpful to look at one of the most commonly used kernels, the Gaussian kernel. Remarkably, this kernel turns SVM into something very much like a k-nearest neighbor classifier.
This answer explains the foll... |
A note on global existence to a higher-dimensional quasilinear chemotaxis system with consumption of chemoattractant
1.
School of Mathematics and Statistics Science, Ludong University, Yantai 264025, China
2.
School of Mathematics and Statistics, Beijing, Institute of Technology, Beijing 100081, China
$\left\{ \begin{a... |
Abstracts Andreas Bjorklund, Lund University
Title:
Faster 3-coloring for diameter two Abstract
The complexity of 3-coloring an n-vertex graph of diameter two is unknown. That is, its decision version is not known to be NP-complete, yet the fastest known algorithms are far from polynomial. Mertzios and Spirakis [http:/... |
The CIR process is given by the SDE $$ \mathrm dr_t = \theta(\mu-r_t)\mathrm dt + \sigma\sqrt{r_t}\mathrm dW_t $$ where $W_t$ is a Brownian motion. I am interested in finite-difference schemes of simulating trajectories of this process, for example I tried the Euler-Maryama scheme $$ r_{t+\Delta t} \approx r_t + \theta... |
Correction Open Access Published: Correction to: Some generalizations for \((\alpha-\psi,\phi)\)-contractions in b-metric-like spaces and an application Fixed Point Theory and Applications volume 2018, Article number: 4 (2018) Article metrics
1078 Accesses
1 Citations
The original article was published in Fixed Point T... |
Let $(X,\mathscr T)$ be topological space with dense subset $D$ and a closed,relatively discrete subset $C$ such that $\mathscr{P}(D)\precsim$ $C.$ Then $(X,\mathscr T)$ is not normal.
Notations and definition in the theorem:-
$X\sim Y$- There is a bijection map from $X$ to $Y$.
$X\precsim Y-$ There is a subset $Y'$ of... |
Similar triangles
How I wish I could show this problem in drawing. This problem has to deal with the concept of similar triangle.
In a diagram, PQ//YZ. PQ is parallel to YZ,
|XP| = 2cm, |PY| = 3cm, |PQ|= 6cm and the area of triangle $\displaystyle XPQ = 24cm^2$
Calculate the area of trapezium PQZY.
Let me describe the ... |
The original article rightfully neglects the cost of DES computations (there are less than $2^{90}$) and everything except memory accesses to its
Table 1 and Table 2. I go one step further: considering that Table 1 is initialized only once and then read-only, it could be in ROM, and I neglect all except the accesses to... |
Definition:Partitioning
Jump to navigation Jump to search
Then $\family {S_i}_{i \in I}$ is a
Definition
Let $S$ be a set.
Let $\family {S_i}_{i \mathop \in I}$ be a family of subsets of $S$ such that:
$(1): \quad \forall i \in I: S_i \ne \O$, that is, none of $S_i$ is empty $(2): \quad \displaystyle S = \bigcup_{i \ma... |
I will try to give an approach to this integral using complex analysis:
First of all we would like to have a form of the integral which is most easily tractable by contour integration, which (at least for me) means that
One way of doing so, is exploiting the parity of the integrand and transform $y\rightarrow 1/x$. We ... |
This question already has an answer here:
Proof with 3D vectors 2 answers
Let $a = \begin{pmatrix}x_a\\y_a\\z_a\end{pmatrix}$, $b = \begin{pmatrix}x_b\\y_b\\z_b\end{pmatrix}$, and $c = \begin{pmatrix}x_c\\y_c\\z_c\end{pmatrix}$. Show that $(x_a,y_a,z_a)$, $(x_b,y_b,z_b)$, and $(x_c,y_c,z_c)$ are collinear if and only i... |
Differentiation
This course is aimed at teaching concepts, but some advanced mathematics is required. One important skill is to be able to “graphically differentiate” functions. This means identifying the tangent line at a particular point, and finding the slope of the tangent line using
\[\text{slope} = \dfrac{\text{r... |
Assume you want to create a security which replicates the implied volatility of the market, that is when $\sigma$ goes up, the value of the security $X$.
The method you could use is to buy call options on that market for an amount $C$.
We know that call options have a positive vega $\nu = \frac{\partial C}{\partial \si... |
Dec 9. http://web.stevens.edu/algebraic/MADAY2016/
Dec 2.M.
Nov 18.
Nov 11. Shamgar Gurevich (Madison and Yale)
Nov 4 Title: Random nilpotent groups.
Oct 28. Dima Savchuk (University of South Florida)
Oct 21. Pascal Weil, CNRS and Université de Bordeaux
Oct 14. CUNY has Tuesday schedule
Sep 23. Ben Steinberg (CCNY)
Sep... |
I understood that One-Time Pad (OTP) encryption ensures perfect secrecy. However, I couldn't find any real-world examples where the OTP is used.
Also, which are some real-world examples where it won't be suitable to use an OTP.
Cryptography Stack Exchange is a question and answer site for software developers, mathemati... |
Let's assume that signal you are analysing is sinusoid with amplitude $A$:
$x=a\sin{2\pi f_{0} t}$
Its RMS value of amplitude is then: $\dfrac{a}{\sqrt{2}}$ as you noticed in your code. Before performing DFT it is good practice to window signal as it decreases leakage, etc.
After transforming this signal into frequency... |
In
Mostly Harmless Econometrics: An Empiricist's Companion (Angrist and Pischke, 2009: page 209) I read the following:
(...) In fact, just-identified 2SLS (say, the simple Wald estimator) is approximately
unbiased. This is hard to show formally because just-identified 2SLS has no moments (i.e., the sampling distributio... |
The set of integers $\Bbb Z$ under ordinary addition is cyclic. Both $1$ and $-1$ are generators. But I am a bit confused how can $1$ generate $0$ and how $-1$ generates $0$? What is the order of $1$ and $-1$ on this group of integers?
The subgroup generated by a set of elements of a group is the smallest subgroup that... |
Computing Stiffness of Linear Elastic Structures: Part 1
Today, we will introduce the concept of structural stiffness and find out how we can compute the stiffness of a linear elastic structure subjected only to mechanical loading. In particular, we will explore how it can be computed and interpreted in different model... |
The reason you can't prove your proposed algorithm correct is because.... it actually is not a correct algorithm for this problem. If you try running it on a small example of network flow graph with more than one unique min cut, you'll see immediately what goes wrong. In particular, this algorithm fails on
every flow g... |
I need to solve this equation (find $\lambda$) using numerical methods:
$\displaystyle N_0e^{\lambda}+v\frac{e^{\lambda}-1}{\lambda}-N_1 = 0$
All other terms are constant and known.
N0 = 1000000; v = 435000; N1 = 1564000;
I need to solve it by using bisection, false position, newton Raphson and fixed point. I have alre... |
If $f:\mathbb{R}\to\mathbb{R}$ and every point takes a local maximum value, it's a fact that the local maximum values of a real function can only have countable, so if we assume $f$ is continuous we have $f$ must be constant. My question is, if $f$ isn't continuous, can we prove there must be some interval that $f$ is ... |
I am reading the book of Hassan Khalinl
Nonlinear Systems (chapter 8.1. Center Manifold Theorem).
In Example 8.2 the author states a system
$$\dot{y}=yz$$ $$\dot{z}=-z+ay^2,$$
in which $a\in \mathbb{R}$.
As the linearized system at $(0,0)$ is already diagonal and y is associated with the eigenvalue which is zero. We ca... |
I was stuck on (b) until I realized that the inequality is misstated: it should be
$$\sum_{i=1}^k\frac{a_{N+i}}{s_{N+i}}\ge 1-\frac{s_N}{s_{N+k}}\;.$$
To see this, note that $\sum_{i=1}^ka_{N+i}=s_{N+k}-s_N$, and the partial sums are increasing, so
$$\sum_{i=1}^k\frac{a_{N+i}}{s_{N+i}}\ge\sum_{i=1}^k\frac{a_{N+i}}{s_{N... |
A loan was taken out on 1 September 1998 and was repayable by the following scheme: The first repayment was made on 1 July 1999 and was £1000. Thereafter, repayments were made on 1 November 1999, 1 March 2000, 1 July 2000, 1 November 2000, etc until 1 March 2004, inclusive (note that the loan was fully repajd on 1 Marc... |
Watching a video by the "mathematicalmonk" on the web, I was wondering how to answer this kind of questions:
Given $X_1,\ldots,X_n\sim \mathcal{N}\left(\mu,\sigma^2\right)$. Assume that $\mu$ is unknown. Using the square loss $\mathcal{L}\left(a,b\right)=\left(a-b\right)^2$:
1) Does $\hat{\sigma}^2=\frac{1}{n}\sum_{i=1... |
Until now we have talked about our everyday experience of magnetic fields originating from what are called
permanent magnets. But magnetic fields and electric charges are intimately linked, as we will soon see in greater detail.For now we will switch gears and consider how a charged particle behaves in a magnetic field... |
In standard cosmology models (Friedmann equations which your favorite choice of DM and DE), there exists a frame in which the total momenta of any sufficiently large sphere, centered at any point in space, will sum to 0 [1] (this is the reference frame in which the CMB anisotropies are minimal). Is this not a form of s... |
Taking$$m\frac{d^2x}{dt^2} = - kx - \gamma v + F(t) + \eta$$and writing this as$$\mathrm{d}\mathbf{x}_t= A\mathbf{x}_t\mathrm{d}t + \mathbf{F}_t\mathrm{d}t + \sigma\mathrm{d}W_t$$where $\mathbf{x}_t = (x, v)^\mathrm{T}$, $A = \begin{pmatrix}0 & 1 \\ -\frac{k}{m} & -\frac{\gamma}{m}\end{pmatrix}$, $\mathbf{F}_t = (0, F(... |
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Let be an array of rowwise independent, but not necessarily identically distributed, random variables with =0 for all k and n. In this paper, we povide a domination condition unde... |
I would disagree on a few counts.
I don't think it's "probably" possible to prove $P \neq NP$. I certainly don't think it's impossible, but Gödel's incompleteness theorems tell us that there are some sentences in a logical system which are true but which can't be proven.
You ask if there have been proofs to Computer Sc... |
I have an $n$-manifold $M$ which is foliated by leaves $F_\alpha$ of dimension $p$ and a path $\gamma:[0,1]\to M$. You can take without problems $\gamma$ to be injective. Is the following statement true?
Claim:There exists a neighborhood $U$ of the image of $\gamma$ and a foliation $L_\beta$ of $U$ of dimension $n-p$ s... |
Let $\mathscr{T}$ be an elementary topos (I use the definition of a Cartesian closed, finitely complete category with a subobject classifier). Let $a$ be any object (that's not isomorphic to $0$) of $\mathscr{T}$, and $0$ the initial object. Is any arrow of the form $f: 0 \to a$ a monomorphism? I believe the answer is ... |
I am trying to prove that for
any choice of reals $a$ and $b$ such that$a \neq b $the function $f(x) := \sin(ax) - \sin(bx)$ has $|f(x)| \geq 1$ for some $x>0$
(This is not an exercise question but something I am trying to prove for myself. Plots with Wolfram Alpha seem to indicate it might be true, and so counterexamp... |
I made a high voltage DC supply which people may be interested in. It uses an Ebay Chinese ZVS resonant driver and a custom transformer, which then feeds a bridge rectifier and output inductor. At 35 V input the no-load output is 1 kV. I ran it for a while at 400V 0.375A with no difficulties (150W). The transformer sta... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
The code you found is unfortunately written and explained in a very confusing way, most notably in a way that, in my humble opinion, misses the entire point of Bucketsort.
Let $A$ be an array of $n$ elements, taken from the ordered set $(S, \le)$. Bucketsort is a sorting algorithm that sorts $A$ in linear time with pro... |
Let $\to_\beta$ be $\beta$-reduction in the $\lambda$-calculus. Define $\beta$-expansion $\leftarrow_\beta$ by $t'\leftarrow_\beta t \iff t\to_\beta t'$.
Is $\leftarrow_\beta$ confluent? In other words, do we have that for any $l,d,r$, if $l \to_\beta^* d\leftarrow_\beta^* r$, then there exists $u$ such that $l\leftarr... |
Learning Objectives
By the end of this section, you will be able to:
Describe the right-hand rule to find the direction of angular velocity, momentum, and torque. Explain the gyroscopic effect. Study how Earth acts like a gigantic gyroscope.
Angular momentum is a vector and, therefore,
has direction as well as magnitud... |
Let $m_1 = \underbrace{ \{0,1\}^n \times \cdots \times \{0,1\}^n }_{L\text{ times}}$ be a message of space $\mathcal{M}^L$, where $\mathcal{M} = \{0,1\}^n$.
Let $c_1$ be the encryption of $m_1$ using CBC mode.
Let $x \in \mathcal{K}$ be some binary string.
Finally, let $m_2$ be another message such that:
$m_2[1] = m_1[... |
You are referring to the following problem:$$H = \{ (\langle M \rangle, w, t) \mid \text{$M$ accepts $w$ in time at most $t$} \}$$where $t$ is binary encoded. You should note this is
not the (classical) halting problem, but, rather, the bounded version of the halting problem. The halting problem itself cannot be comple... |
This question already has an answer here:
(The questions are below the question heading)
I actually agree with it - that is not to say that $\mathbb{Q}$ isn't countable.
Reasoning The definition of bijection is a useful starting point, and it is easy to see that $\mathbb{Z}$ is countable. I shall denote this as $\mathb... |
Answer: not known.
The questions asked are natural, open, and apparently difficult; the question now is a community wiki.
Overview
The question seeks to divide languages belonging to the complexity class $P$ — together with the decision Turing machines (TMs) that accept these languages — into two complementary subclass... |
The positivity condition is not there just so that "programs terminate", as you put it (what programs?), but to make sure the type is well defined in the first place. The inductive definitions define the
smallest type satisfying an equation. That is, we put into the type only those things which are prescribed by the cl... |
As you know, the identity$$(a+b)(a-b) \;\; = \;\; a^2 - b^2$$shows that if you start with $a+b$ and multiply by $a-b,$ you'll get an expression that contains only even powers of $a$ and $b.$ Also, if you start with $a-b$ and multiply by $a+b,$ you'll get an expression that contains only even powers of $a$ and $b.$
One ... |
I had an exam today and one of my question was:
Give a function $f$ that is Riemann integrable but not Lebesgue integrable
How is it possible ? I always thought that Riemann $\implies $ Lebesgue, isn't it ?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals ... |
Matrices consist of elements of some field. However, if we have a matrix $A\in M_{m,n}(F)$, it is sometimes useful to look at each row as a vector from $F^n$, i.e., we can view the matrix as $$A=\begin{pmatrix}\vec r_1\\\vec r_2\\\vdots\\\vec r_m\end{pmatrix}.$$ (Doing the same thing with columns make sense, too. I wil... |
OpenCV 3.1.0
Open Source Computer Vision
In this tutorial you will learn how to:
Principal Component Analysis (PCA) is a statistical procedure that extracts the most important features of a dataset.
Consider that you have a set of 2D points as it is shown in the figure above. Each dimension corresponds to a feature you... |
This is one of those questions that is much trickier than it appears, many different people contributed to the formulas as we write them today. The short answer, that doesn't really do justice to history, is that only Euler presented volume formulas in this form in his textbooks after 1737.
The principal step was no do... |
Motviation
Suppose we observe survival/event times from some distribution \[T_{i\in1:n} \stackrel{iid}{\sim} f(t)\] where \(f\) is the density and \(F(t)=1-S(t)\) is the corresponding CDF expressed in terms of the survival function \(S(t)\). We can represent the hazard function of this distribution in terms of the dens... |
I'm having a pretty hard time with this. I'm asked to show that, in the category of
sets with exactly 17 elements, no two objects have either a direct product nor direct sum. Part of me doesn't even believe this statement—but whenever I try to come up with a direct product, I get snagged.
Let $(C, \alpha, \beta)$ be a ... |
Let $S=\{1,2,3,4,5,6,7,8,9,10\}$, $P=\{y \in \mathbb N : y \text { is a prime number}\}$, consider the map $f$ defined as follows: $$\begin{aligned} f:x\in S \rightarrow f(x) \in \wp (P) \end{aligned}$$ and $$\begin{aligned} f(x)=\{y \in P: y \mid x\} \end{aligned}$$
Let $X=\{1,4,5,8,10\}$ and $f(X)=\{\{\emptyset\}, \{... |
I am having trouble and I am unsure how to solve this PDE. $x\frac{\partial v}{\partial x} +y\frac{\partial v}{\partial y} = 2xy(x^2-y^2)$ I know you will use method of characteristics, but I am being thrown off by the function on the right side.
I think I already answered to a question like this, but where ?.
Change $... |
Prove that there is no Homomorphism from $\Bbb Z_8 \oplus \Bbb Z_2$ onto $\Bbb Z_4 \oplus \Bbb Z_4$?
Suppose that $\phi$ is an onto homomorphism between the two sets.
Then $\phi(\Bbb Z_8 \oplus \Bbb Z_2) = \Bbb Z_4 \oplus \Bbb Z_4$ because it's onto and $|\phi(\Bbb Z_8 \oplus \Bbb Z_2)| = |\Bbb Z_4 \oplus \Bbb Z_4| = 1... |
Tikhonov regularization and ridge regression are terms often used as if they were identical. Is it possible to specify exactly what the difference is?
Tikhonov regularizarization is a larger set than ridge regression. Here is my attempt to spell out exactly how they differ.
Suppose that for a known matrix $A$ and vecto... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
Your equation #1 is $$(R+2\lambda x)i=B\ell v=B\ell \frac{dx}{dt}$$ Solving for $x$ as a function of time, and assuming $x(0)=0$, we get $$R+2\lambda x(t)=R e^{kt}$$ where $k=\frac{2\lambda i}{B\ell}$. The velocity of the bar is $v(t)=v_0e^{kt}$ where the initial velocity is $v_0=\frac{iR}{B\ell}$.
We do not need to fi... |
The probability that an arithmetic Brownian motion process $dt = \mu dt + \sigma dW$ hits an upper Barrier $U$ before it hits a lower barrier $L$ is given by
$$ \mathbb{P}(\tau_U\leq \tau_L) = \frac{\text{Y}(x_0)-\text{Y}(L)}{\text{Y}(U)-\text{Y}(L)} $$ where $$ \text{Y}(x) = exp(\frac{-2\mu x}{\sigma^2}) $$
But what i... |
Why, when calculating the conditional probability of A given B, do we assume that the probability of B is greater than zero?
We have
$$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
If $P(B)=0$ then the RHS is undefined.
Also, if we're given that $B$ happens then it cannot be the case that $P(B)=0$. That's a contradiction.
Here ... |
Quadratic Equations Practise solving quadratic equations algebraically with this self-marking exercise.
This is level 6; Three terms and the roots are not necessarily integers. You can earn a trophy if you get at least 7 correct.
For this exercise
all answers should be rounded to three significant figures.
Instructions... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
Why is there a phase difference between resistor and capacitor? I am looking for the conceptual reason behind this. What does a phase difference of \$\pi/2\$ show conceptually? According to me, the one with positive phase difference would reach to its peak value earlier than the another, but how do we come to know the ... |
This question already has an answer here:
Is there a way to simplify $\det(D + C)$, where $D,C$ are square matrices of matching dimensions, $D$ is diagonal (with different diagonal elements, $D_{ij} = \delta_{ij}d_i$), and $C$ is a constant matrix, that is, all entries $C_{ij}=c$ are equal to the same number?
To be mor... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
Both loops oscillate without any loss of energy.
In loop A the voltage across $C_1$ varies sinusoidally between $0$ and $2\epsilon$. The angular frequency of oscillation is $\omega_0=\frac{1}{\sqrt{LC}}$. So the voltage across $C_1$ at time $t_1$ after connection with the battery is $\epsilon (1-\cos\omega_0 t_1)$. See... |
We know that Pythagoreans in Ancient Greece discovered that the square root of two is an irrational number. Why was that discovery historically significant? What value was that knowledge to the Ancient Greeks?
I do not agree on some details of the interpretation regarding the discovery of the irrationality of $\sqrt{2}... |
Hi I'm just consider the difference between groups and rings when it comes to direct product. And want to check this is right or not.
Let $A_i \le B_i$ [The $A_i$ is a subobject(Subring or Subgroup) of the $B$]
It is obvious that
$A_i \le B_i \Rightarrow \Pi _{i=1} ^{n} A_i \le B(=\Pi _{i=1} ^{n} B_i)$
Then question is... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
Enthalpy $H$ is defined so that $\Delta H = q_P$, the heat at constant pressure. This is convenient for constant-pressure calorimetry---it makes it possible to track energy changes without considering volume changes in the system.
$$\begin{align*}\Delta U &= q + w & \text{(first law)}\\\Delta U_P &= q_P + w_P & \text{(... |
NOTE : This excerpt comes form Hormander's text, An Introduction to COmplex Analysis of Several Variables. STATEMENT: (Runge approximation theorem)Let $\Omega$ be an open set in $\mathbb{C}$ and $K$ a compact subset of $\Omega$. The following conditions on $\Omega$ and $K$ are equivalent:
(a) Every function which is an... |
Given the Minkowski metric $\eta$ the Lorentz Transformation $\Lambda$ satisfies $$\eta=\Lambda^{T}\eta\Lambda$$ which in index form may be written $$\eta_{\mu\nu}=(\Lambda^{T})_{\mu}^{\,\,\alpha}\eta_{\alpha\beta}\Lambda^{\beta}_{\,\,\nu}$$$$\eta_{\mu\nu}=\eta_{\alpha\beta}\Lambda^{\alpha}_{\,\,\mu}\Lambda^{\beta}_{\,... |
Research Open Access Published: A generalization of Hegedüs-Szilágyi’s fixed point theorem in complete metric spaces Fixed Point Theory and Applications volume 2018, Article number: 1 (2018) Article metrics
1809 Accesses
Abstract
In 1980, Hegedüs and Szilágyi proved some fixed point theorem in complete metric spaces. I... |
I try to prove the Jech's "Set theory", exercises 12.11:
12.11. If $\kappa$ is an inaccessible cardinal, then $V_\kappa\models \text{there is a countable model of ZFC}$. My attempt. Since $(V_\kappa,\in)$ is a model of ZFC, by Löwenheim-Skolem theorem theorem there is a countable model $(A,R)$ which elementary equivale... |
March 4th, 2019, 11:18 AM
# 1
Newbie
Joined: Mar 2019
From: Romania
Posts: 1
Thanks: 0
Need some help to solve this limit
Hi everyone,
I have a problem that I don't know how to solve - ideally without using l'Hospital. Can you pls help?
March 5th, 2019, 06:38 AM
# 2
Math Team
Joined: Dec 2013
From: Colombia
Posts: 7,68... |
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