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ISSN:
1078-0947
eISSN:
1553-5231
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Discrete & Continuous Dynamical Systems - A
July 2001 , Volume 7 , Issue 3
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Abstract:
We consider a special $2 \times 2$ viscous hyperbolic system of conservation laws of the form $u_t + A(u)u_{x} = \varepsilon u_{x x}$, where $A(u) = Df(u... |
Difference between revisions of "Geometry and Topology Seminar"
(→Spring Abstracts)
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===Bena Tshishiku===
===Bena Tshishiku===
"TBA"
"TBA"
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===Autumn Kent===
===Autumn Kent===
Revision as of 14:58, 31 January 2017 Contents 1 Fall 2016 2 Spring 2017 3 Fall Abstracts 4 Spring Abstracts 5... |
radianmeasure is the ratio of two lengths, it is a unitless measure. For example, suppose the radius were 2 inches and the distance along the arc were also 2 inches. When we calculate the radian measure of the angle, the “inches” cancel, and we have a result without units.
\( \require{cancel}\)
\[\theta \, \text{radian... |
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:342-382, 2019.
Abstract
We consider the sorted top-$k$ problem whose goal is to recover the top-$k$ items with the correct order out of $n$ items using pairwise comparisons. In many applications, multiple rounds of interaction can be costly. We res... |
This is a neat question and I've thought about it before. Here's what we came up with:
You run your algorithm $n$ times to get outputs $x_1, \cdots, x_n \in \mathbb{R}^d$ and you know what with high probability a large fraction of $x_i$s fall into some good set $G$. You don't know what $G$ is, just that it is convex. T... |
Current browse context:
physics.flu-dyn
Change to browse by: References & Citations Bookmark(what is this?) Physics > Fluid Dynamics Title: Equilibrium and stability of two-dimensional pinned drops
(Submitted on 21 Aug 2019 (v1), last revised 22 Aug 2019 (this version, v2))
Abstract: Superhydrophobicity relies on the s... |
Pfleiderer, C.; Fai\ss{}t, A.; {von L̈ohneysen}, H.; Hayden, S. M.; Lonzarich, G. G.
Title:
Field Dependence of the Specific Heat of Single-Crystalline {{ZrZn2}}
Abstract:
We present measurements of the specific heat C of a single crystal of ZrZn2 in the range 2\textendash{}30K, at magnetic field B up to 14T. For B=0 a... |
There has been a great deal of excitement among topologists about the proof of the Virtual Haken Theorem, and in fact of the Virtual Fibering Theorem (for closed hyperbolic 3-manifolds, but I'm guessing they will soon be proven in full generality). The proof is lucidly discussed in Danny Calegari's blog. The theorems s... |
I want to generate a list of simple trigonometric questions in
TeXForm, for example, as follows.
Evaluate the following expressions.\begin{enumerate}\item $\sin 30^\circ$\item $\sec 90^\circ$% ... others go here ...\item $\csc 315^\circ$\end{enumerate}
So I can just copy and paste it to my LaTeX input file to create a ... |
I'm using Mathematica 9 and its Control Systems functionality.
I've searched the references extensively but seem not to be able to find any examples of state space model parameters estimation. All examples show models parametarized already or when they are given symbolic parameters they are not simulated.
So my questio... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
Answer
$59$ meters
Work Step by Step
Let $h$ be the height of the building. $h=\dfrac{50}{(\cot 32^{\circ}-\cot 53^{\circ})}$ This gives: $h=\dfrac{50}{(1.6000335-0.753554)}$ $h \approx 59$ meters Hence, the height of the building is $59$ meters.
You can help us out by revising, improving and updating this answer.Updat... |
A typical atom consists of three subatomic particles: protons, neutrons, and electrons (as seen in the helium atom below). Other particles exist as well, such as alpha and beta particles (which are discussed below). The Bohr model shows the three basic subatomic particles in a simple manner. Most of an atom's mass is i... |
Here we want to give an easy mathematical bootstrap argument why solutions to the time independent 1D Schrödinger equation (TISE) tend to be rather nice. First formally rewrite the differential form$$-\frac{\hbar^2}{2m} \psi^{\prime\prime}(x) + V(x) \psi(x) ~=~ E \psi(x) \tag{1}$$into the int...
[Some time travel comme... |
I am told that Fourier showed that we can represent an arbitrary continuous function, $f(x)$, as a convergent series in the elementary trigonometric functions
$$f(x) = \sum_{k = 0}^\infty a_k \cos(kx) + b_k \sin(kx)$$
Also, suppose that $\{\phi_n(x)\}^\infty_{n = 0}$ is a set of orthogonal functions with respect to a w... |
The Monster is the largest of the 26 sporadic simple groups and has order
808 017 424 794 512 875 886 459 904 961 710 757 005 754 368 000 000 000
= 2^46 3^20 5^9 7^6 11^2 13^3 17 19 23 29 31 41 47 59 71.
It is not so much the size of its order that makes it hard to do actual calculations in the monster, but rather the ... |
An inclusive reference of transformation matrices for basic OpenGL work. It is intended as a quick reference while coding OpenGL without libraries.
There are many tutorials and guides online that explain how to use these matrices and mathematic fundamentals. If you are new to the subject, I recommend reading this artic... |
This set of Advanced Network Theory Questions and Answers focuses on “Advanced Problems on Network Theorems – 2”.
1. A network contains linear resistors and ideal voltage source s. If values of all the resistors are doubled, then voltage across each resistor is __________
a) Halved b) Doubled c) Increases by 2 times d)... |
Radar engineering details radar sensorradar antennaradar sensors
Radar engineering details are technical details pertaining to the components of a radar and their ability to detect the return energy from moving scatterers — determining an object's position or obstruction in the environment.wikipedia
50 Related Articles... |
Applied/ACMS/absS18 Contents 1 ACMS Abstracts: Spring 2018 ACMS Abstracts: Spring 2018 Thomas Fai (Harvard) The Lubricated Immersed Boundary Method
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elasti... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
Definition:Null Set Contents Definition
Let $\left({X, \Sigma, \mu}\right)$ be a measure space.
Family of Null Sets
The family of
$\mu$-null sets, $\left\{{N \in \Sigma: \mu \left({N}\right) = 0}\right\}$, is denoted $\mathcal N_{\mu}$. Definition in $\R^n$ A set $E \subseteq \R^n$ is called a null set if for any $\eps... |
Keywords
copositive matrix, extreme ray, zero support set
Abstract
Let $A \in {\cal C}^n$ be an exceptional extremal copositive $n \times n$ matrix with positive diagonal. A zero $u$ of $A$ is a non-zero nonnegative vector such that $u^TAu = 0$. The support of a zero $u$ is the index set of the positive elements of $u$... |
I'm trying to understand how a Gaussian Process with a squared exponential covariance function can be obtained from Bayesian Linear Regression with a Gaussian prior $N(0,\sigma_p^2 I)$ on the parameters and an infinite number of basis functions. I'm following the proof in chapter four of
Gaussian Processes for Machine ... |
How to Generate Random Surfaces in COMSOL Multiphysics®
To easily generate random-looking geometric surfaces, the COMSOL Multiphysics® software provides a powerful set of built-in functions and operators, such as functions for uniform and Gaussian random distributions and a very useful
sum operator. In this blog post, ... |
A Belyi-extender (or dessinflateur) is a rational function $q(t) = \frac{f(t)}{g(t)} \in \mathbb{Q}(t)$ that defines a map
\[ q : \mathbb{P}^1_{\mathbb{C}} \rightarrow \mathbb{P}^1_{\mathbb{C}} \] unramified outside $\{ 0,1,\infty \}$, and has the property that $q(\{ 0,1,\infty \}) \subseteq \{ 0,1,\infty \}$.
An examp... |
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Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
The Monster is the largest of the 26 sporadic simple groups and has order
808 017 424 794 512 875 886 459 904 961 710 757 005 754 368 000 000 000
= 2^46 3^20 5^9 7^6 11^2 13^3 17 19 23 29 31 41 47 59 71.
It is not so much the size of its order that makes it hard to do actual calculations in the monster, but rather the ... |
On a power-type coupled system of Monge-Ampère equations
DOI: http://dx.doi.org/10.12775/TMNA.2015.064
Abstract
$$
\begin{cases}
\det D^{2}u_{1}={(-u_{2})}^\alpha & \hbox{in $\Omega,$} \\
\det D^{2}u_{2}={(-u_{1})}^\beta & \hbox{in $\Omega,$} \\
u_{1}<0,\ u_{2}<0& \hbox{in $\Omega,$}\\
u_{1}=u_{2}=0 & \hbox{on $ \parti... |
A
tetrahedral snake, sometimes called a Steinhaus snake, is a collection of tetrahedra, linked face to face.
Steinhaus showed in 1956 that the last tetrahedron in the snake can never be a translation of the first one. This is a consequence of the fact that the group generated by the four reflexions in the faces of a te... |
This question already has an answer here:
Prove the map has a fixed point 2 answers
Let $(X,d)$ be compact. Show: for a map $f$ that when $\forall x, y \in X$ with $x\neq y$
$d(f(x),f(y))<d(x,y)$ is fulfilled.
Then $f$ has a unique fixed point.
Mathematics Stack Exchange is a question and answer site for people studyin... |
Here we want to give an easy mathematical bootstrap argument why solutions to the time independent 1D Schrödinger equation (TISE) tend to be rather nice. First formally rewrite the differential form$$-\frac{\hbar^2}{2m} \psi^{\prime\prime}(x) + V(x) \psi(x) ~=~ E \psi(x) \tag{1}$$into the int...
[Some time travel comme... |
This is a heuristic explanation of Witten's statement, without going into the subtleties of axiomatic quantum field theory issues, such as vacuum polarization or renormalization.
A particle is characterized by a definite momentum plus possible other quantum numbers. Thus, one particle states are by definition states wi... |
Article Title Keywords
Doubly substochastic matrices, Sub-defect, Maximum diagonal sum
Abstract
Let $\Omega_n$ denote the convex polytope of all $n\times n$ doubly stochastic matrices, and $\omega_{n}$ denote the convex polytope of all $n\times n$ doubly substochastic matrices. For a matrix $A\in\omega_n$, define the s... |
Mr yannick stoll (LAPTh)
18/03/2015, 19:30
Theory
YSF (Young Scientists Forum)
We investigate the consequences at low energies of a new MSSM-SU(5) induced symmetry relation in the up-squark sector. We show that this relation is not too much spoiled by the RGE running down to the electroweak scale and is kept relatively... |
By "measure of correlation", in this context, we mean the
mutual information$$I(X:Y)=H(X)+H(Y)-H(X,Y)=H(X)-H(X|Y).$$
Let us consider a few different classical scenarios and try to work out how this quantity should be computed for quantum states.
Full correlation
In the case in which observing $Y$ gives full information... |
Now, I kinda wonder, if I am going to proof to some one that 1 + 2 + ... + 100 = 5050, how can I do that? Here one way to do it.
First line up two line of sum this way, one from 1 to 100, another from 100 to 1.
1 + 2 + 3 + ... + 100 100 + 99 + 98 + ... + 1 --------------------------------------- 101 + 101 + 101 + ... +... |
Iiris Sundin,Peter Schulam,Eero Siivola,Aki Vehtari,Suchi Saria,Samuel Kaski;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:6046-6055, 2019.
Abstract
Machine learning can help personalized decision support by learning models to predict individual treatment effects (ITE). This work studie... |
The
integral symbol: Contents History[edit]
The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz in 1675 in his private writings;
[1] [2] it first appeared publicly in the article " De Geometria Recondita et analysi indivisibilium atque infinitorum" (On a hidden geometry and analysis of ind... |
The alternating group $A_5 $ has two conjugacy classes of order 5 elements, both consisting of exactly 12 elements. Fix one of these conjugacy classes, say $C $ and construct a graph with vertices the 12 elements of $C $ and an edge between two $u,v \in C $ if and only if the group-product $u.v \in C $ still belongs to... |
Perturbation theory is a method for continuously improving a previously obtained approximate solution to a problem, and it is an important and general method for finding approximate solutions to the Schrödinger equation. We discussed a simple application of the perturbation technique previously with the Zeeman effect.
... |
Angular resolution spatial resolutionresolutionresolvedresolving powerRayleigh criterionresolution limitspot sizeappears ascriteriondiffraction limited
Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to ... |
Li-Yorke chaos for dendrite maps with zero topological entropy and
ω-limit sets
University of Carthage, Faculty of Sciences of Bizerte, Department of Mathematics, Jarzouna, 7021, Tunisia
Let
X be a dendrite with set of endpoints $E(X)$ closed and let $f:~X \to X$ be a continuous map with zero topological entropy. Let $... |
For the better part of the 30ties, Ernst Witt (1) did hang out with the rest of the ‘Noetherknaben’, the group of young mathematicians around Emmy Noether (3) in Gottingen.
In 1934 Witt became Helmut Hasse‘s assistent in Gottingen, where he qualified as a university lecturer in 1936. By 1938 he has made enough of a nam... |
print("Python (and any language-specific) code still works as expected")
As does non-language code.
You may notice that there's a sidebar to the right (if your screen is wide enough).These are automatically generated from the headers that are present in your page.The sidebar will automatically capture all 2nd and 3rd l... |
I am working through Milnor's Characteristic classes and am currently working problems on the topic of oriented bundles and euler class. I am having trouble computing the euler class of the tangent bundle of a sphere. (The actual question is in the third paragraph)
The first part which worked out fine for me was to sho... |
This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Advanced Problems on Network Theorems – 1”.
1. The temperature coefficient of a metal as the temperature increases will ____________
a) Decreases b) Increases c) Remains unchanged d) Increases and remains same View Answer
Explanation: We ... |
Event detail Student Algebraic Geometry Seminar: Geometry of the moduli space of curves of genus \(g\)
Seminar | April 17 | 4-5 p.m. | 891 Evans Hall
Ritvik Ramkumar, UC Berkeley
Given a variety \(X\) it's a basic question to ask if it's rational i.e. admits a birational map \( P^n \to X \) for some \(n\). For curves a... |
We have associated to a subgroup of the modular group $PSL_2(\mathbb{Z}) $ a
quiver (that is, an oriented graph). For example, one verifies that the fundamental domain of the subgroup $\Gamma_0(2) $ (an index 3 subgroup) is depicted on the right by the region between the thick lines with the identification of edges as ... |
Currently I am going through the proof of the Stein-Weiss interpolation theorem for a seminar paper and in particular through the proof of Lemma 1 which begins at page 320 (I will use a particular function for $\Phi$). First I will establish the setting:
Let $S := \{z \in \mathbb{C} : 0 < \text{Re }z < 1\}$ and $F$ be ... |
Part 4 in the quest for the hydrogen molecule
In this part I would like to focus on the energy of a particle. A particle can have kinetic and potential energy. Suppose a particle is in a state \(|\psi\rangle\) where it has energy \(E\), then how does that state look like? Is there only one such state or are there many?... |
Compression after Lempel and Ziv (LZ78)
When reading about sequence learning and the prediction of elements in a time series you inevitably cross paths with the area of sequence compression at some point, and so did I. In the present post I’d like to outline a classical compression algorithm, the 1978 version of the se... |
The term ``blue moon'' in the present context describes rare events,
i.e. events that happen once in a blue moon. The blue moon ensemble approach was introduced by Ciccotti and coworkers as a technique for computing the free energy profile along a reaction coordinate direction characterized by one or more barriers high... |
Polygon is a word derived from The Greek language, where poly means many and gonna means angle. So we can say that in a plane, closed figure with many angles is called a polygon. The given diagram is how a polygon looks like:
There are many properties in a polygon like sides, diagonals, area, angles, etc. Lets know how... |
Last time we have that that one can represent (the conjugacy class of) a finite index subgroup of the modular group $\Gamma = PSL_2(\mathbb{Z}) $ by a
Farey symbol or by a dessin or by its fundamental domain. Today we will associate a quiver to it.
For example, the modular group itself is represented by the Farey symbo... |
NTS ABSTRACTSpring2019
Return to [1]
Jan 23
Yunqing Tang Reductions of abelian surfaces over global function fields For a non-isotrivial ordinary abelian surface $A$ over a global function field, under mild assumptions, we prove that there are infinitely many places modulo which $A$ is geometrically isogenous to the pr... |
The particle-in-a box model is used to approximate the Hamiltonian operator for the \(\pi\) electrons because the full Hamiltonian is quite complex. The full Hamiltonian operator for each electron consists of the kinetic energy term \(\dfrac {-\hbar ^2}{2m} \dfrac {d^2}{dx^2}\) and the sum of the Coulomb potential ener... |
Hitchhiker Server Sky Test Orbits
Testing the first server sky thinsat arrays may be challenging - they don't belong in a common orbit, they won't last long below 1000 km altitude due to ram drag. It would be nice to deploy the first tests at M288, but that will require a custom launch.
Instead, let's dispense as a co-... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
Consider the scattering of a quantum particle in one dimension, caused by a step in the potential (this appears in many undergrad level QM books):
$$ V(x) = \begin{cases} V_1 & x<0 \\ V_2 & x>0\end{cases}. $$
The particle is incident from the left, so it's wavefunction is:
$$ \psi(x) = \begin{cases} e^{i k_1 x} + r e^{... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
A
tetrahedral snake, sometimes called a Steinhaus snake, is a collection of tetrahedra, linked face to face.
Steinhaus showed in 1956 that the last tetrahedron in the snake can never be a translation of the first one. This is a consequence of the fact that the group generated by the four reflexions in the faces of a te... |
In the microcanonical ensemble, the entropy \(S\) is a natural function of \(N\),\(V\) and \(E\), i.e., \(S=S(N,V,E)\). This can be inverted to give the energy as a function of \(N\), \(V\), and \(S\), i.e., \(E=E(N,V,S)\). Consider using Legendre transformation to change from \(S\) to \(T\) using the fact that
\[T= \l... |
I decided to start working on my own answer after I asked the question, so here's the result of a few days' work.
An excellent (and very recent) paper regarding accretion is Debnath (2015), which can be applicable at least for material gathered onto the surface of the red dwarf.
Debnath assumes a static
1, spherically ... |
The answer to my question is as follows. The Hamiltonian given by
$$H^{can} = \lim_{\rho \to \pi/2} (cos\rho)^{2-d}\int d^{d-1}\Omega \dfrac{h_{tt}}{16\pi G_N}$$
is a surface term, which is characteristic of gravity. In general the Hamiltonian can have a volume term which has contribution from the Hamiltonian density a... |
\[ E[X] = \sum_{i=1}^{\infty} x_i p(x_i) \]
The standard deviation is the square root of the variance, and the variance is given in terms of the expected value.
\[ Var(X) = E[X^2] - (E[X])^2 \]
Except that $$E[X^2]$$ is of course completely different from $$(E[X])^2$$, but it gets worse, because $$E[X^2]$$ makes
no not... |
Definition:Null Relation Definition $\mathcal R \subseteq S \times T: \mathcal R = \O$ That is, no element of $S$ relates to any element in $T$: $\mathcal R: S \times T: \forall \tuple {s, t} \in S \times T: \neg s \mathrel {\mathcal R} t$ Also known as
This is also sometimes referred to as
a trivial relation by some a... |
Keywords
Inverse eigenvalue problem, nonnegative matrix, prescribed diagonal entries
Abstract
The problem of the existence and construction of nonnegative matrices with prescribed eigenvalues and diagonal entries is an important inverse problem, interesting by itself, but also necessary to apply a perturbation result, ... |
Cone is a three-dimensional structure having a circular base where a set of line segments, connecting all of the points on the base to a common point called apex. A cone can be seen as a set of non-congruent circular discs that are stacked on one another such that ratio of the radius of adjacent discs remains constant.... |
ISSN:
1551-0018
eISSN:
1547-1063
All Issues
Mathematical Biosciences & Engineering
2006 , Volume 3 , Issue 1
Select all articles
Export/Reference:
Abstract:
Zhien Ma's love for mathematics has strongly shaped his educational pursuits. He received formal training from the strong Chinese School of Dynamical System over a... |
Following the along the same lines as benguin, let $m$ denote the betting amount and let $A,B$ be multiples of $m$ for simplicity. WLOG assume $m=1$ and adjust $A,B$ accordingly so they simply denote a number of steps to either win or lose. This much simpler setup can be transformed back again to cover all cases anyway... |
Self-Consistent Schrödinger-Poisson Results for a Nanowire Benchmark
The
Schrödinger-Poisson Equation multiphysics interface simulates systems with quantum-confined charge carriers, such as quantum wells, wires, and dots. Here, we examine a benchmark model of a GaAs nanowire to demonstrate how to use this feature in th... |
The other answers here, describing oxygen toxicity are telling what can go wrong if you have too much oxygen, but they are not describing two important concepts that should appear with their descriptions. Also, there is a basic safety issue with handling pressure tanks of high oxygen fraction.An important property of b... |
In economics, the
consumption function describes a relationship between consumption and disposable income. [1] Algebraically, this means C = f(Y_{d}) where f \colon \mathbb{R} \to \mathbb{R} is a function that maps levels of disposable income Y_{d}—income after government intervention, such as taxes or transfer payment... |
A group G is said to have a
factorization if there exist proper subgroups $A$ and $B$ such that $G = AB = \{ ab \ | \ a \in A, b \in B \}$.
The paper Factorisations of sporadic simple groups (by Michael Giudici) provides the classification of all the factorizations of the sporadic simple groups. We observe there that o... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
In The Da Vinci Code, Dan Brown feels he need to bring in a French cryptologist, Sophie Neveu, to explain the mystery behind this series of numbers:
13 – 3 – 2 – 21 – 1 – 1 – 8 – 5
The Fibonacci sequence, 1-1-2-3-5-8-13-21-34-55-89-144-… is such that any number in it is the sum of the two previous numbers.
It is the mo... |
I am trying to use
\prod in math display mode but it appears large (larger than I want it to be) but when I use
\mathsmaller from the
relsize package the letter appears on right side of it instead of below. Is there any way to make the symbol smaller while the character remains below the symbol?
I am trying to use
I do... |
With sufficient worldbuilding, your creatures could be affected by
Electric Imbalance Syndrome (EIS)
Similar to amflare's answer, but differing in that Electric Imbalance Syndrome is biological in nature instead of affecting whatever happens to be unlucky enough to be nearby when the sun decides to screw everyone over.... |
In AP Calculus, we saw the following derivatives: \[\sin’ x = \cos x \\ \cos’ x = -\sin x\]
That is, the derivative of the sine is the cosine, and the derivative of the cosine is the opposite of the sine.
I showed one way to see why this is true using Desmos. The purple line is the tangent, while the black dot is the s... |
Here we want to give an easy mathematical bootstrap argument why solutions to the time independent 1D Schrödinger equation (TISE) tend to be rather nice. First formally rewrite the differential form$$-\frac{\hbar^2}{2m} \psi^{\prime\prime}(x) + V(x) \psi(x) ~=~ E \psi(x) \tag{1}$$into the int...
[Some time travel comme... |
I am using AucTeX to write LaTeX and I have fontification enabled. The highlighting of marcos works but while macros like
\begin are highlighted using font-lock-keyword-face all math macros ( \sum, \leq to mention a few) are highlighed using font-lock-sedate-face that is reserved for ``unknown'' macros.
On the other ha... |
I'll assume we want a cryptographic hash giving security in the Random Oracle Model; collision-resistance and preimage-resistance follows. Collision-resistance alone rules out CRC, regardless of size.
The standard technique would be to split the file into blocks, distribute them with index to the participants, which ha... |
Answer
$-192$
Work Step by Step
$\sum_{i=1}^{24} (17-2i)=-2 \times \sum_{i=1}^{24} i+\sum_{i=1}^{24} (17)$ $=(-2) \times \dfrac{(24) \times (24+1)}{2}+17 \times (24)$ $=(-2) \times \dfrac{(24) \times (25)}{2}+17 \times (24)$ $=-600+408$ $=-192$
You can help us out by revising, improving and updating this answer.Update ... |
This set of Network Theory Questions & Answers for Exams focuses on “Advanced Problems on Reciprocity Theorem”.
1. In Reciprocity Theorem, which of the following ratios is considered?
a) Voltage to current b) Current to current c) Voltage to voltage d) No ratio is considered View Answer
Explanation: The Reciprocity The... |
We start with half-hourly \(u_*\)-filtered and gap-filled NEE_f values. For simplicity this example uses data provided with the package and omits \(u_*\) threshold detection but rather applies a user-specified threshold.
With option
FillAll = TRUE, an uncertainty, specifically the standard deviation, of the flux is est... |
Lots of the answers so far have focused on the economic reasons why a floating city is impossible. But what about physical reasons?
Aerodynamic Levitation
As a first approximation, we can treat the city as an air bearing. There are a couple formulas that we can take from an intro fluid flow class to calculate the amoun... |
ISSN:
1930-5346
eISSN:
1930-5338
All Issues
Advances in Mathematics of Communications
May 2014 , Volume 8 , Issue 2
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Export/Reference:
Abstract:
A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and ... |
Category:Supremum Metric Let $S$ be a set.
Let $M = \left({A', d'}\right)$ be a metric space.
Let $d: A \times A \to \R$ be the function defined as:
$\displaystyle \forall f, g \in A: d \left({f, g}\right) := \sup_{x \mathop \in S} d' \left({f \left({x}\right), g \left({x}\right)}\right)$
where $\sup$ denotes the supre... |
Acoustic Topology Optimization with Thermoviscous Losses Today, guest blogger René Christensen of GN Hearing discusses including thermoviscous losses in the topology optimization of microacoustic devices.
Topology optimization helps engineers design applications in an optimized manner with respect to certain
a priori o... |
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Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
October 2005 , Volume 13 , Issue 5
Special Issue
Recent Development on Differential Equations and Dynamical Systems: Part II
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Abstract:
We will classify the path connected components of spaces of... |
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J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
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Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
A Belyi-extender (or dessinflateur) is a rational function $q(t) = \frac{f(t)}{g(t)} \in \mathbb{Q}(t)$ that defines a map
\[ q : \mathbb{P}^1_{\mathbb{C}} \rightarrow \mathbb{P}^1_{\mathbb{C}} \] unramified outside $\{ 0,1,\infty \}$, and has the property that $q(\{ 0,1,\infty \}) \subseteq \{ 0,1,\infty \}$.
An examp... |
Yesterday, Jan Stienstra gave a talk at theARTS entitled “Quivers, superpotentials and Dimer Models”. He started off by telling that the talk was based on a paper he put on the arXiv Hypergeometric Systems in two Variables, Quivers, Dimers and Dessins d’Enfants but that he was not going to say a thing about dessins but... |
Differentiating a function is usually regarded as a discrete operation: we use the first derivative of a function to determine the slope of the line that is tangent to it, and we differentiate twice if we want to know the curvature. We can even differentiate a function negative times—ie integrate it—and thanks to that ... |
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Measurement of $W$ boson angular distributions in events with high transverse momentum jets at $\sqrt{s}=$ 8 TeV using the ATLAS detector
(Elsevier, 2017-02)
The $W$ boson angular distribution in events with high transverse momentum jets is measured using data collected by the ATLAS ... |
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