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In the classical linear model with $$Y=X\beta +\epsilon,$$ where $Y \in \mathbb{R}^n$ is the observation, $X\in \mathbb{R}^{n\times p}$ is the known covariates, $\beta \in \mathbb{R}^p$ is the unknown parameter with, $p < n$, and $\epsilon \in \mathbb{R}^{n}$, $\epsilon \sim \mathcal{N}(0,\sigma^{2}I)$.
The classical l... |
True or False Problems of Vector Spaces and Linear Transformations Problem 364
These are True or False problems.
For each of the following statements, determine if it contains a wrong information or not. Let $A$ be a $5\times 3$ matrix. Then the range of $A$ is a subspace in $\R^3$. The function $f(x)=x^2+1$ is not in ... |
Mechanical Properties of Solids Hooke's law and Elastic Moduli For a given material longitudinal strain : Shear strain : Bulk strain = 1 : 2 : 3 Elastic limit is the maximum value of stress with in which a body can regain its original size and shape. Hooke's law states that with in the Elastic limit stress is directly ... |
Let $E$ be a vector bundle, with $X$ base space and $p:E\to X$ a surjective projection.
Let $x\in X$ be given. Let $U_1, U_2$ be two neighborhoods of $x$ in $X$ which carry local trivializations, that is, $$\varphi_1:p^{-1}(U_1)\cong U_1 \times V_1$$and $$ \varphi_2:p^{-1}(U_2)\cong U_2 \times V_2$$ are two homeomorphi... |
This question already has an answer here:
I would like the limits to be vertically above and below the summation sign. I also need a larger summation sign... This is currently what I have:
$x^2sin(x) = \sum_{n=-\infty\atop n\ne \pm 1}^\infty \dfrac {4i(-1)^{n}n}{(n^2 - 1)^2} $
Any help appreciated! |
Published May 2002,February 2011.
1. Introduction
Do the angles of a triangle add up to 180 degrees or $\pi$ radians? The answer is 'sometimes yes, sometimes no'. Is this an important question? Yes, because it leads to an understanding that there are different geometries based on different axioms or 'rules of the game ... |
This is essentially an addition to the list of @4tnemele
I'd like to add some earlier work to this list, namely Discrete Gauge Theory.
Discrete gauge theory in 2+1 dimensions arises by breaking a gauge symmetry with gauge group $G$ to some lower
discrete subgroup $H$, via a Higgs mechanism. The force carriers ('photons... |
So, I've wondered if there are irrationals where I can calculate some digit $n\in\mathbb{N}$ when given only the $k_n\in \mathbb{N}_0$ ($k_n<n-1$) digits before them. Preferrably $k_n\in o(n)$.
I think this is one of the problems which is easy to state but hard to answer.
So of course, if $k_n$ would be positive and fi... |
On the complex plane $\mathbb C$ consider the half-open square $$\square=\{z\in\mathbb C:0\le\Re(z)<1,\;0\le\Im(z)<1\}.$$
Observe that for every $z\in \mathbb C$ and $p\in\{0,1,2,3\}$ the set $(z+i^p\cdot\square)$ is the shifted and rotated square $\square$ with a vertex at $z$.
Problem.Is it true that for any function... |
I would like to know what the equation is for as series of infinite terms which are multiplied by the order of the terms: $$ \sum_{i=0}^{\infty} \sum_{j=0}^{\infty}(ij) a^ib^j $$ $a$ and $b$ are both fractions. Thanks to the answers provided on the question " Simple approximation to a series of infinite terms ", I assu... |
LHCb is one of the four big experiments operating at LHC and it's mainly dedicated
to measurements of $C\!P$ violation and to the search for new physics in the decays of
rare hadrons containing heavy quarks. The LHCb collaboration has recently published a result which shows for the first time a compelling 5.3 $\sigma$ ... |
How come it's possible to get Metropolis-Hastings acceptance rates close to 1 (for example, when exploring a unimodal distribution with a normal proposal distribution with too-small SD), after burn-in is over? I see it in my own MCMC chains but I don't understand how it makes sense. It seems to me that after reaching t... |
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Note by Azimuddin Sheikh 7 months, 1 week ago
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and th... |
Current Electricity Ohm’s law and it's Limitations, Resistivity and it's Temperature Dependency Resistance depend up on current and potential difference. Reciprocal of resistance is conductance \tt (G) = \frac{1}{R} Unit of conductance is (ohm) −1. Specific resistance \tt P = \frac{R A}{l} Unit of specific resistance =... |
We define a $2\times 2$ Givens rotation matrix as:
$${\bf G}(\theta) = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) &\cos(\theta) \end{bmatrix}.$$
On the other hand, we define a $2\times 2$ hyperbolic rotation matrix as:
$${\bf H}(y)=\begin{bmatrix} \cosh( y) & \sinh( y) \\ \sinh( y) &\cosh( y) \end{bma... |
Modular Arithmetic (MA) has the same axioms as first order Peano Arithmetic (PA) except $\forall x (Sx \ne 0)$ is replaced with $\exists x(Sx = 0)$. (http://en.wikipedia.org/wiki/Peano_axioms#First-order_theory_of_arithmetic).
MA has arbitrarily large finite models based on modular arithmetic. All finite models of MA h... |
Note: This question was asked in stats.stackexchange.com and math.stackexchange.com, with expired bounties on both sites.
Given a sequence of iid random variables $X_i$ (without loss of generality from $U(0,1)$), an integer $k \ge 1$ and some $p \in (0,1)$, construct the sequence of random vectors $Z^{(j)}$, $j=0,1,...... |
We try to analyze the average correlation of a portfolio as it can be found here in section 2 b), the same formula which is also used by the CBOE to calculate implied correlations:
$$ \rho_{av(2)} = \frac{\sigma^2 - \sum_{i=1}^N w_i^2\sigma_i^2}{2 \sum_{i=1}^N \sum_{j>i}^N w_i w_j \sigma_i \sigma_j} $$
EDIT:Assuming th... |
Differential and Integral Equations Differential Integral Equations Volume 20, Number 8 (2007), 927-938. Nonexistence results for classes of elliptic systems Abstract
We consider the system \[ -\Delta u = \lambda f(u,v); \, x \in \Omega \] \[ -\Delta v = \lambda g(u,v); \, x \in \Omega \] \[ u = 0 = v; \, x \in \partia... |
In a typical supervised learning problem we have a fixed volume of training data with which to fit a model. Imagine, instead, we have a constant stream of data. Now, we could dip into this stream and take a sample from which to build a static model. But let's also imagine that, from time to time, there is a change in t... |
First of all, Ryanair has more than 700,000 flights per year now, but not during their entire 35 year existence. The total number of flights you give is therefore too high.
Assuming aircraft accidents are purely statistical (which is
not true, of course), one can estimate the number of accidents you expect using a Pois... |
Here's a bit of an elaboration on my earlier comment.
You can see $SO_3$ as the quotient of a unit $3$-ball by the antipodal map on the boundary. This is realized explicitly by the exponential map for $SO_3$. The tangent space to the identity of $SO_3$ is all $3\times 3$ matrices $H$ such that $H^T=-H$. Up to conjugati... |
I have a matrix $A \in \mathbb{R}^{n \times n}$ and would like to know about the relationship between the $\| A \|_\infty$ (i.e., the maximum element of the matrix) and the operator-induced norm $\| A \|$.
I know that the following upper-bound holds (from Matrix Norm Inequality): $ \| A \|_\infty \leq \sqrt{n} \| A \| ... |
No, this is not true, not even for closed points. Consider $\Bbb P^1_k$. Then $A=k$ and $\mathcal{O}_{\Bbb P^1_k,pt}\cong k[t]_{(t)}$, and $j^{-1}$ of the maximal ideal is the zero ideal, so the requested localization of $A$ is just $A$, which is very far from $k[t]_{(t)}$. Certainly this will be an isomorphism if $X$ ... |
Hydrogen Structure, Preparation, Properties and Uses of hydrogen peroxide Concentration of H 2O2 :
Physical properties : Boiling point → 152º C Melting point → −0.4º C It is completely miscible in water. It is stored in plastic (or) wax coated glass bottles. Rough surface can decompose H 2O 2 H 2O 2 (Hydrogen peroxide)... |
In my last post, the irrational number
e was used. Let’s define and explain e a bit more in this post.
If you deposit $1 in the bank which pays 100% interest once each year (I need to find this bank!), then at the end of 1 year, you will have the original $1 plus 100% of that which is another $1, for a total of $2. Now... |
Skills to Develop
To learn the concept of the sample space associated with a random experiment. To learn the concept of an event associated with a random experiment. To learn the concept of the probability of an event. Sample Spaces and Events
Rolling an ordinary six-sided die is a familiar example of a
random experime... |
The Navigation Algorithm¶
This section describes the navigation algorithm in detail.
Global Path Planner¶
A global planner problem in the Isaac framework is decomposed in three classes: the Planner Model, the Visibility Graph Algorithm, and the Optimizer.
Planner Model¶
A planner model (engine/gems/path_planner/Planner... |
Question
f(x) = sin 2x, 0 < x < \[\pi\] .
Solution
\[\text { Given }: \hspace{0.167em} f\left( x \right) = \sin 2x\]
\[ \Rightarrow f'\left( x \right) = 2 \cos 2x\]
\[\text { For a local maximum or a local minimum, we must have }\]
\[f'\left( x \right) = 0\]
\[ \Rightarrow 2 \cos 2x = 0\]
\[ \Rightarrow \cos 2x = 0\]
\... |
Abbreviation:
DLO
A
is a structure $\mathbf{A}=\langle A,\vee,\wedge,f_i\ (i\in I)\rangle$ such that distributive lattice with operators
$\langle A,\vee,\wedge\rangle$ is a distributive lattice
$f_i$ is
in each argument: $f_i(\ldots,x\vee y,\ldots)=f_i(\ldots,x,\ldots)\vee f_i(\ldots,y,\ldots)$ join-preserving
Let $\ma... |
$\newcommand\Q{\mathbb Q}$I have a series of questions related to sum of $k$-powers of algebraic numbers (it is actually only one question that I try to weaken/strengthen the conditions). Suppose we know the following $$\sum_{i=1}^n a_i^k \in \Q$$ for algebraic number $a_i$'s for which not all of them are in $\Q$. Then... |
skills to develop
To learn how to apply formulas for estimating the size samples that will be needed in order to construct a confidence interval for the difference in two population means or proportions that meets given criteria.
As was pointed out at the beginning of Section 7.4, sampling is typically done with defini... |
I have been going through Certifiable quantum dice: or, true random number generation secure against quantum adversaries by Umesh Vazirani and Thomas Vidick. They have used entangled particles as shared resources for a quantum nonlocal game aka CHSH game. Because of the acronym CHSH I assumed that the game was proposed... |
I have the following $d$-dimensional integral:
$$\displaystyle \int_{\mathbb{R^d}} |x|^{-d/2}|b-x|^{-d/2}J_{d/2}(\rho |x|)J_{d/2}(\rho |b-x|)\mathrm{d}x,$$
where $|\cdot|$ denotes the Euclidean norm on $\mathbb{R}^d$, and $x, b \in \mathbb{R}^d$, $\rho > 0$ does not depend on $x$, and $J_{d/2}$ denotes the Bessel funct... |
(a) Find all $3 \times 3$ matrices which are in reduced row echelon form and have rank 1.
First we look at the rank 1 case.For a $3 \times 3$ matrix in reduced row echelon form to have rank 1, it must have 2 rows which are all 0s. The non-zero row must be the first row, and it must have a leading 1.
These conditions im... |
I am looking at constructible points in abstract algebra, particularly in $\mathbb{C}$. Alongside a proof of a theorem, I came across this expression which I cannot work out how it's been derived. It just comes out as follows, but some notations;
$L(z_1,z_2)$ represents the straight line that connects points $z_1,z_2 \... |
Is the impulse response of a LINEAR
TIME-VARIANT system unique? I know that it's unique for the L.T.I case!!! Advance thanks for the HELP....
Is the impulse response of a LINEAR
With the input-output relationship of a linear time-varying system given by
$$y(t)=\int_{-\infty}^{\infty}h(t,\tau)x(t-\tau)d\tau\tag{1}$$
it ... |
There does not always exist a matching with your property in a bipartite graph.
Consider for example the graph $G = (V, E)$ where
$V = \{a_1, a_2, a_3, b_1, b_2, b_3, c_1, c_2, d_1, d_2, x\}$ and $E = \{a_1, a_2\} \times \{c_1, c_2, x\} \cup \{b_1, b_2\} \times \{d_1, d_2, x\} \cup \{(a_3, c_1), (a_3, d_2), (a_3, x), (... |
Are there any differences between the study of Calculus done by Newton and by Leibniz. If so please mention point by point.
Newton's notation, Leibniz's notation and Lagrange's notation are all in use today to some extent they are respectively:
$$\dot{f} = \frac{df}{dt}=f'(t)$$ $$\ddot{f} = \frac{d^2f}{dt^2}=f''(t)$$
Y... |
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∫0∞x2e−x2 dx \large \int_0^\infty x^2 e^{-x^2} \, dx ∫0∞x2e−x2dx
If the value of the integral above is equal to πAB \dfrac{\pi^A}{B}BπA, where AAA and BBB are rational numbers, find a×ba\times ba×b.
Problem Loading...
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Set Loading... |
ISSN:
1547-5816
eISSN:
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Journal of Industrial & Management Optimization
October 2011 , Volume 7 , Issue 4
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Abstract:
We present explicit optimality conditions for a nonsmooth functional defined over the (properly or weakly) Pareto set associated with a multi-obje... |
For some positive integer constants $n, k$ and $t$, I want to find the values for $n_1, \ldots, n_t$, all positive integers, that maximize the following sum :
$$ \sum_{i = 1}^t (n_i)^k $$
such that $n_i \geq 1$ for each $i$ and $\sum_{i = 1}^t n_i = n$. So, what's the best way to pick the $n_i$'s ?
It feels like the ri... |
I think I've figured this out. The point is that, the rigorous meaning one can draw from the formal covariance of $J^\mu$ is that the momentum-space coefficient functions of $J^\mu$ (i.e. the functions in front of monomials of $a_p$ and $a^\dagger_p$) transform covariantly under the change of variable $p\to \Lambda p$.... |
Fortunately your scenario is rather simple, your camera is on a line directly perpendicular above and centered on the quad you're concerned about. So what you want is for the quad to fill the whole screen, I assume (more or less) exactly the whole screen, i.e. the size of your projected quad in window space is your ent... |
Let $U=\{1,\ldots, u\}$ be a
universe of elements for some $u\in \mathbb N$.Given some $n\in\mathbb N$, we are interested in computing some function $f:U^{\le n}\to\mathbb R$ over range queries.
In the Range Query problem we get an integer array $A[1,\ldots,n]\in U^n$ and wish to compute queries that takes as input par... |
For $k \ge 4$, the expected time until the first duplicate is $O(\sqrt{n})$. This leaves the case $k=3$ [Edit: The case of $k=3$ is resolved below with a construction with expected first duplicate at about $n/4$].
Let $D_i$ be the number of duplicates in the first $i$ values. The expected time until the first duplicate... |
Structure of Atom Nature of electromagnetic radiation and Photoelectric effect
Nature of Light : Different Theories Newton's Corpuscular Theory : Light comes out of the source as small particles called corpuscles. It traces in straight lines. Huygen's Wave Theory : According to Huygen, light has wave character. He comp... |
Difference between revisions of "SageMath"
m (→Install Sage package: flag for deletion)
m (→3D plot fails in notebook: flag for deletion)
Line 152: Line 152:
=== 3D plot fails in notebook ===
=== 3D plot fails in notebook ===
+ +
If you get the following error while trying to plot a 3D object:
If you get the following ... |
The
Manin constant is defined for elliptic curves over $\Q$ which are optimal. Let $E$ be an optimal elliptic curve of conductor $N$, let $f$ be the modular form associated to $E$, and let $\varphi:X_0(N)\to E$ be the associated modular parametrization. Let $\omega_E$ be the Néron differential on $E$. Then the pull-bac... |
Rudin's Real and Complex Analysis Chapter 3 Exercise 4 is:
Assume that $\varphi$ is a continuous real function on $(a,b)$ s.t. $$\varphi\left(\frac{x+y}{2}\right)\leq \frac{\varphi(x)+\varphi(y)}{2}$$ for all $x,y\in(a,b)$. Prove that $\varphi$ is convex.
The conclusion does not follow if continuity is omitted from the... |
Logarithms confuse many of my students so I thought it is time to explain these. I touched on these before on a post about inverse operations, but let’s add some more detail.
Let’s first define some terms here. Consider the expression
x 2. Here, x is raised to the power of 2. x is the base and 2 is the exponent, power,... |
Since the homomorphism $\bar{\phi}:M/IM \to N/IN$ is surjective, for any $b\in N$ there exists $a\in M$ such that\[\bar{\phi}(\bar{a})=\bar{b}, \tag{*}\]where $\bar{a}=a+IM$ and $\bar{b}=b+IN$.By definition of $\bar{\phi}:M/IM \to N/IN$, we have\[\bar{\phi}(\bar{a})=\overline{\phi(a)}=\phi(a)+IN.\]Thus, it follows from... |
Digital Signal Processing - Dec 2014
Electronics & Telecom Engineering (Semester 5)
TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory. (2) Attempt any four from the remaining questions. (3) Assume data wherever required. (4) Figures to the right indicate full marks.
Answer any one question from Q1 and Q... |
Useful links: How vortex bound states affect the Hall conductivity of a chiral px ± ipy superconductor
This work extend our understanding of the anomalous charge response, c
xy of chiral superconductors. It is established that in order to correctly apply the Streda formula for calculating c xy it is necessary to employ... |
(Previous related question: Finding mathematically the ground state density in DFT)
I am studying the density optimisation procedure (in particular for Orbital-Free DFT) this thesis.
The derivative of the energy is given as:
$$\frac{\delta E[n(r)]}{\delta n(r)} = v(r) + v_i(r) + \frac{1}{2}(3\pi^2)^{2/3}\left(n(r)\righ... |
Kinetic Theory of Gas Kinetic Theory of an Ideal Gas and Degree of freedom Kinetic theory of gas equation \tt PV=\frac{1}{3}mN\ V^2_{RMS} where P is the pressure exerted by the gas and V is the volume “m” is the mass of molecule. N is the total number of molecules V RMSis Rms velocity. If volume and temperature of a ga... |
The problem:
Input: An $n \times n$ matrix of 0's and 1's, and a position posof this matrix (i.e. a pair of integers $i,j$ with $1 \leq i,j \leq n$)
Output:
YES if there exists a path through
adjacentmatrix entries $\dagger$, starting at pos, covering each matrix entry with a 1 exactly once, and not covering the matrix... |
Gödel's constructible universe ($L$) is defined using definable power set operator in first order logic ($\mathcal{L}_{\omega ,\omega}$). One can produce such a universe in infinitary logics in the same way using corresponding notions of formulas and definability. Obviously $L$ becomes larger when the logic has more ex... |
In a standard portfolio optimization setting, an efficient frontier is formed for the mix of asset weights which result in the greatest (expected) portfolio return with least amount of (expected) portfolio volatility.
Technically any point on that frontier can be considered efficient in the absense of a risk-free rate.... |
The correlation coefficient, \(r\), tells us about the strength and direction of the linear relationship between \(x\) and \(y\). However, the reliability of the linear model also depends on how many observed data points are in the sample. We need to look at both the value of the correlation coefficient \(r\) and the s... |
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Now showing items 1-10 of 15
A free-floating planet candidate from the OGLE and KMTNet surveys
(2017)
Current microlensing surveys are sensitive to free-floating planets down to Earth-mass objects. All published microlensing events attributed to unbound planets were identified based on their short timescale (bel... |
Find the smallest relation containing the relation $\{ (1,2),(2,1),(2,3),(3,4),(4,1) \}$ that is:
Reflexive and transitive Reflexive, symmetric and transitive
Well my first attempt:
Reflexive: $ S_1 = \{ (1,1),(2,2),(3,3),(4,4) \}$ Symmetric: $ S_2=\{ (3,2),(4,3),(1,4) \}$ Transitive: $S_3= ? $Is where I'm stuck.
So th... |
i have this exercice: Let $f\in L^2(\mathbb{R}^n)$. 1- Prouve that the equation $\Delta u - u = \dfrac{\partial f}{\partial x_i}$ admeit a unique solution $u \in H^1(\mathbb{R}^n)$?
2- Prouve the exustance of constant $C \geq 0$ such that $||u||_{H^1} \leq C ||f||_{L^2}$?
3- Prouve the existante of a constant $M \geq 0... |
(a) Prove that $T:V\to V$ is a linear transformation.
To prove $T$ is a linear transformation, we need to show the following properties.
For any $X, Y\in V$, we have $T(X+Y)=T(X)+T(Y)$.
For any $X\in V, r\in \R$, we have $T(rX)=rT(X)$.
To check condition 1, let $X, Y \in V$. Then we have\begin{align*}T(X+Y)&=A(X+Y)-(X+... |
I have it set up so I place my mouse in the center of where I want the spiral to be, then I press enter to start the program, then define the radius initially and how much it grows each time it goes around.
I use \$\sin(\theta)\$ = opposite / hypotenuse and \$\cos(\theta)\$ = adjacent / hypotenuse to find how much my c... |
This week¶
This week's highlight is a paper on imitation learning: Learning Self-Correctable Policies and Value Functions from Demonstrations with Negative Sampling, chosen again for pragmatic reasons. The problem my team is currently working on has both reasons for wanting high sample efficiency: training would be pro... |
A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.
bidibangboom Posts: 34 Joined: May 10th, 2019, 6:38 pm
triple poster
Code: Select all
#C A... |
In my last post, you saw that a 90° angle is called a right angle. This is the angle made by the two lines at the corner of a square. Now a triangle is a shape that has three angles inside. A basic property of any triangle is that all the internal angles add up to 180°:
But this post is about triangles where one of its... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
I've created a figure that displays a "timeline" that contains specific points as well as ranges. The only thing that I want to add (but don't know how) are dots/circles/squares at the points (at 0, theta * s, theta*s+w and z). Also, I would like to center the timeline. When I wrap the tikzpicture in the figure environ... |
Introduction to Optical Prisms
Prisms are solid glass optics that are ground and polished into geometrical and optically significant shapes. The angle, position, and number of surfaces help define the type and function. One of the most recognizable uses of prisms, as demonstrated by Sir Isaac Newton, consists of disper... |
ISSN:
1556-1801
eISSN:
1556-181X
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Networks & Heterogeneous Media
March 2008 , Volume 3 , Issue 1
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Abstract:
The classical Lighthill-Whitham-Richards (LWR) kinematic traffic model is extended to a unidirectional road on which the maximum density $a(x)$ represents road inhom... |
Warning: I am not a physicist.
As Dan Hulme already explained, light can't travel through metals, so dealing with IOR is a lot more...
complex. I will answer why that happens and how to calculate the reflection coefficient.
Explanation: Metals are filled with free electrons. Those electrons react to external fields and... |
I'm receiving "Limit controls must follow a math operator" error. Googled it, tried, nothing helped. Appears on Overleaf 2.0, using makefile in Cent OS, Fedora. Using pkgs
geometry, amsmath, amsthm, amssymb, amsfonts, verbatim, babel (czech), inputenc (utf8), fontenc (IL2)
l.99 ...� $\lim\limits_{n\to\infty}$ a $\Pi\li... |
Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2,\beta_3\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.
Basis of coefficient ring in terms of a root \(\nu\) of \(x^{4}\mathstrut -\mathstrut \) \(2\) \(x... |
Before answering the question more or less directly, I'd like to point out that this is a good question that provides an object lesson and opens a foray into the topics of
singular integral equations, analytic continuation and dispersion relations. Here are some references of these more advanced topics: Muskhelishvili,... |
Find the Matrix Representation of $T(f)(x) = f(x^2)$ if it is a Linear Transformation
Problem 679
For an integer $n > 0$, let $\mathrm{P}_n$ denote the vector space of polynomials with real coefficients of degree $2$ or less. Define the map $T : \mathrm{P}_2 \rightarrow \mathrm{P}_4$ by\[ T(f)(x) = f(x^2).\]
Determine ... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Continuation 2 has been added, with seemingly ideal results.
Ben Aveling’s solution.inspired three new solutions (“Continuations”)to this surprisingly playful puzzlethat is interestingly reminiscent ofBenford’sandZipf’slaws.$\require{begingroup} \begingroup \def\safeMathJax{\text{\endgroup error}} \def \p {{\kern 1mu p... |
I am a sophomore. A friend and I ran across a kinetic chemistry exercise. We solved it in a slightly different way and we can't come to an agreement on who is right. We would appreciate some help:
Destruction of stratospheric ozone as determined by using the steady-state approximation.
The balance of ozone in the strat... |
Abbreviation:
BDLat
A
is a structure $\mathbf{L}=\langle L,\vee ,0,\wedge ,1\rangle $ such that bounded distributive lattice
$\langle L,\vee ,\wedge \rangle $ is a distributive lattice
$0$ is the least element: $0\leq x$
$1$ is the greatest element: $x\leq 1$
Let $\mathbf{L}$ and $\mathbf{M}$ be bounded distributive la... |
51 0 1. Homework Statement
How did [itex]\frac{1}{2}x[/itex] come from at k=1?
2. Homework Equations 3. The Attempt at a Solution
because k=1 will make the first term at denominator 2(k-1) = [itex]\frac{0}{0}[/itex]
Yes. The [itex]\ \frac{1}{2}x\ [/itex] comes from the fact that the first term has the form 0/0 as k → 1... |
When I face a writing task, my two big failure modes are either not starting at all and dragging my feet indefinitely, or writing far too much and having to cut it down to size later. In the latter case, my problem isn’t just that I go off on tangents. I try to answer every conceivable objection, including those that o... |
Under what conditions is it possible, using a suitable change of variables, to eliminate 1st order terms in an elliptic partial differential equation, so that the equation involves the 2nd derivatives, the dependent variable, and independent terms only?
To be concrete, consider the elliptic equation $-\Delta u + \sum_i... |
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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 ... |
The answer is yes, to both questions.
First question first. For any geodesic $n$-gon $P$ on $M$, i.e., a simply connected region of $M$ whose boundary consists of $n$-geodesic arcs, define
$$ \delta(P)= \mbox{sum of the angles of $T$}-(n-2)\pi. $$
Note that if $M$ were flat, then the defect $\delta(P)$ would be $0$. Th... |
Bed inversion¶
To compute the initial ice thickness \(h_0\), OGGM follows a methodology largely inspired from [Farinotti_etal_2009], but fully automatised and relying on different methods for the mass-balance and the calibration.
Basics¶
The principle is simple. Let’s assume for now that we know the flux of ice \(q\) f... |
I am studying inverse kinematics. But I wonder the suggested equations. (The following equations are taken from 'Computer Animation Algorithms and Techniques Third Edition Page, 181')
To better control the kinematic model such as encouraging joint angle constraints, a control expression can be added to the pesudoinvers... |
Oscillations and Waves Transverse and longitudinal waves Transverse wave: A wave in which the particles of the medium vibrate at right angles to the direction of propagation of wave is called a transverse wave.This wave travel in the form of crests and troughs.
Longitudinal wave: A wave in which the particles of the me... |
I found the derivation for two point and three point perspective here on this site, even though it says review on one point perspective, it doesn't give a link to previous pages, but I'd like to know how the matrix for one point perspective was derived. If possible please give me a detailed derivation for this projecti... |
See e.g. :
[page 7]
Definition 2.1.2 A sequent is an expression ($Γ \vdash \psi$) where $\psi$ is a statement (the conclusion of the sequent) and $Γ$ is a set of statements (the assumptions of the sequent). We read the sequent as ‘$Γ$ entails $\psi$’. The sequent ($Γ \vdash \psi$) means
There is a proof whose conclusio... |
This was shown by Hardy back in 1903/1904.
A mention of it can be found here: Quarterly Journal Of Pure And Applied Mathematics, Volume 35, Page 203, which is somewhere in the middle of a long paper.
Here is a snapshot in case that link does not work:
Note, the integral is slightly different, but I suppose it won't be ... |
$B$-meson light-cone distribution amplitudes and radiative leptonic decay
Pre-published on: 2019 July 18
Published on: 2019 October 04
Abstract
We present the recent developments of $B$-meson light-cone distribution amplitudes (LCDAs) including their definition, classification, evolution, equations of monition (EOMs), ... |
is
related to the significance level of the finding. The coefficient? (Since none of those are true, is likely that the population mean is zero or near zero. occur only rarely: less than one out of 300 observations on the average. standard use the mean scores.
interval includes zero then the effect will not be statisti... |
Fill in each blank unshaded cell in the diagram below with a positive integer less than 100, such that every consecutive group of unshaded cells within a row or column is an arithmetic sequence.
This problem is from the USAMTS Round 3 problem set.
Puzzling Stack Exchange is a question and answer site for those who crea... |
I'm not entirely sure what I'm doing wrong here, I'm using a
\kill'd line to mark the tabs first, but it's still giving me an undefined tab position error.
The error is reported for line 0 so I'm not sure which of these is causing it.
\begin{framed}\begin{tabbing}tabs \= tabs \= tabs \killGive $a$ the value 2.Give \emp... |
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Now showing items 1-1 of 1
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 ... |
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Now showing items 1-5 of 5
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
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