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Answer
$7.99\ g/cm^3$
Work Step by Step
If the diameter is 9.40 mm, the radius (half of it) is $4.70\ mm=0.470\ cm$. The volume of the sphere is: $V=\frac43\pi r^3=0.435\ cm^3$ The given mass is 3.475 g, so the density is: $\rho=m/V=7.99\ g/cm^3$
You can help us out by revising, improving and updating this answer.Updat... |
In last week’s discussion of proofs by contradiction and nonconstructive proofs, we showed:
Theorem: There exist irrational numbers \(x\) and \(y\) with the property that \(x^y\) is rational.
However, our proof was
nonconstructive: it did not pinpoint explicit values for \(x\) and \(y\) that satisfy the condition, inst... |
Well-Posedness and Ill-Posedness Problems of the Stationary Navier–Stokes Equations in Scaling Invariant Besov Spaces 227 Downloads Abstract
We consider the stationary Navier–Stokes equations in \(\mathbb {R}^n\) for \(n\geqq 3\) in the scaling invariant Besov spaces. It is proved that if \(n<p\leqq \infty \) and \(1\l... |
A quadratic equation can be defined as a equation of a second degree, which implies that it comprises of minimum one term that is squared. The definite form is
ax² + bx + c = 0; where in x is an unknown variable and a,b,c are numerical coefficients.
Quadratics Equation Examples
Beneath are the illustrations of quadrati... |
In Frankel's paper: "Manifolds with positive curvature", he proved the following theorem:
If $M^n$ is complete Riemannian manifold with positive sectional curvature, and $V^r$, $W^s$ are two compact totally geodesic submanifolds. If $r+s\ge n$ then $V$ and $W$ have a non-empty intersection.
The proof is by contradictio... |
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I need some help with the following problem:
Let $X$, $Y$, and $Z$ are independent circularly symmetric complex Gaussian random variable with zero mean and unit variance, i.e., $X$, $Y$, and $Z \sim CN(0, 1)$.
These random variables can be represented in polar form as \begin{equation} X=r_1 e^{i \alpha}\\ Y=r_2 e^{i \b... |
(A)dS exchanges and partially-massless higher spins
Artikel i vetenskaplig tidskrift, 2008
We determine the current exchange amplitudes for free totally symmetric tensor fields $\vf_{\mu_1 ... \mu_s}$ of mass $M$ in a $d$-dimensional $dS$ space, extending the results previously obtained for $s=2$ by other authors. Our ... |
Say I have a neural network with some unknown number $N$ of hidden layers. Assume I know the structure (e.g. feedforward, convolutional, or recurrent) of the first $k$ of these hidden layers but know nothing about the remaining $N-k$ layers. (I also don't know $N$.) Assuming the weights in the unknown part are fixed, t... |
As it can be shown, the equations for the irrep with zero mass and helicity 2, -2 respectively can be given in a form $$ \tag 1 \partial^{\dot {b}a}C_{abcd} = 0, \quad \partial^{\dot{b}a}C_{\dot{a}\dot{b}\dot{c}\dot{d}} = 0. $$ Here $C_{abcd} = C_{(abcd)}, C_{\dot{a}\dot{b}\dot{c}\dot{d}} = C_{(\dot{a}\dot{b}\dot{c}\do... |
Suppose you have a car traveling on a banked curve with friction. The curve makes an angle $\theta$ with the horizontal and has coefficient of static friction $\mu$.
Suppose we wish to calculate the minimum speed at which the car can travel so that it does not slip down the curve towards the center of the circular race... |
1. 11, 23, 47, 83, 131, . What is the next number?a. 145
b. 178
c. 176
d. 191
Explanation:
11,23,47,83,131
23–11 = 12
47–23 = 24
83–47 = 36
131–83 = 48
Therefore, 131+60=191
2. A series of book was published at seven year intervals. When the seventh book was published the total sum of publication year was 13, 524. Firs... |
I have an expectation given as: $\mathbb{E}\left(S_{T}\mathbb{1}_{S_{T}\geq K} \right)$
where $K$ is just an arbitrary number (i.e. the strike price, but that's unimportant) and $S$ can be modelled by the equation $S_{t} = \exp((r-\frac{1}{2})t + \sigma W_{t})$. Also, the expectation is under the $\mathbb{P}$-measure, ... |
Suppose we have an SU(N) non abelian gauge theory coupled with a multiplet of complex scalar fields $\Phi$. The lagrangian would be
$$ L= - \frac 12 \text{Tr } F_{\mu\nu}F^{\mu\nu} + |D_\mu \Phi|^2 - V(\Phi)$$
where $D_\mu$ is the covariant derivative: $D_\mu \Phi = \partial_\mu \Phi +ig A_\mu^at_a \Phi$, $A_\mu$ is th... |
Say that we have a system evolving over discrete timesteps.
The quantity we are interested is X and is given by a distribution $P_X$. This distribution is evolving temporally, and we have a nonlinear equation $F$ that gives us this evolution.
$P_{\Delta X}(x;n) = F\big(~P_X(x;n)~,~P_X(x;n-1)~\big)~~~,~~~n \in \mathbb{N... |
It took me quite some time to clearly understand the experiment you're describing.
Actually, pouring a full bottle in a container is a quite intriguing thing.
Consider the following starting configuration :
This of course is an unstable situation, as the pressure $P_0$ cannot be at the same time the pressure of the air... |
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One of the main lessons of category theory is that whenever you think about some kind of mathematical gadget, you should also think about maps
between gadgets of this kind. For example, when you think about sets you should also thin... |
№ 9
All Issues Exact values of the best (α, β) -approximations of classes of convolutions with kernels that do not increase the number of sign changes Abstract
We obtain the exact values of the best $(\alpha , \beta )$-approximations of the classes $K \ast F$ of periodic functions $K \ast f$ such that $f$ belongs to a ... |
Is there a closed-form expression for the distribution of the Sample Kurtosis of data sampled from Gaussian distribution? i.e.,
$P(\hat{K}<a)$ where $\hat{K}$ is the sample kurtosis.
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data... |
27 February 2012, 05:58
Today’s Theorem comes thanks to Simon, because he is stupid. It is given without proof, because I don’t know how to prove it, and my book doesn’t have a proof. I probably don’t even know what it says.
Theorem: Suppose that a function $f$ is represented by a power series in $x – x_0$ that has a n... |
My nice nats Collection
context $F$ in ${\bf D}\longrightarrow{\bf C}$ context $G$ in ${\bf C}\longrightarrow{\bf D}$ definiendum $\langle\alpha,\beta\rangle$ in it inclusion $\alpha:FG\xrightarrow{\bullet}1_{\bf C}$ inclusion $\beta:1_{\bf D}\xrightarrow{\bullet}GF$ Discussion
That silly name … I made it up.
The natur... |
Cross-posted from my blog.
The purpose of this post is to lay out some of the stuff I wish someone had explained to me when I was first learning about electronics. This is a pretty entry-level introduction, intended by me to ‘fill in the gaps’ with regard to basic operating principles. Opamps are not all that complicat... |
1. We construct a public-key bit-encryption scheme that is plausibly semantically secure, but is not circular secure. The circular security attack manages to fully recover the private-key. The construction is based on an extension of the Symmetric External Diffie-Hellman assumption (SXDH) from bilinear groups, to $\ell... |
This question focuses on translating/adapting custom defined MATLAB code for creating a CorrelationMatrix to Mathematica.
Software and hardware used: Mathematica Version 10.3.0.0 Computer: Mac Pro (Late 2013) Processor: 3.5 GHz 6-Core Intel Xenon E5 Memory: 32 GB 1866 MHzDDR3 Graphics: AMD FirePro D500 3 GB Background
... |
Difference between revisions of "User:Nikita2"
m
m
(4 intermediate revisions by the same user not shown) Line 3: Line 3: −
I am Nikita Evseev
+
I am Nikita Evseev Novosibirsk, Russia.
My research interests are in [[Mathematical_analysis | Analysis]] and [[Sobolev space|Sobolev spaces]].
My research interests are in [[M... |
I have a glmer model that I am performing contrasts on. My model has four factors (emotion, gender, filter, ageGroup). No interactions. I have been using
lsmeans(x, spec, contr='pairwise')) (and)
lsm within
glht) to get lsmeans and to do pairwise contrasts within-factors. I am also interested in comparing the means fro... |
№ 9
All Issues Volume 63, № 2, 2011
Ukr. Mat. Zh. - 2011. - 63, № 2. - pp. 147-155
The best quadrature formula is found for the class of convex-valued functions defined on the interval [0, 1] and monotone with respect to an inclusion.
Ukr. Mat. Zh. - 2011. - 63, № 2. - pp. 156-164
The solvability of the inhomogeneous D... |
[This is the 6th post in the current series about Wythoff’s game: see posts #1, #2, #3, #4, and #5.
Caveat lector: this post is a bit more difficult than usual. Let me know what you think in the comments!]
Our only remaining task from last week was to prove the mysterious Covering Theorem: we must show that there is ex... |
So what are spin-networks? Briefly, they are graphs with representations ("spins") of some gauge group (generally SU(2) or SL(2,C) in LQG) living on each edge. At each non-trivial vertex, one has three or more edges meeting up. What is the simplest purpose of the intertwiner? It is to ensure that angular momentum is co... |
I know that if I have two differentiable functions $f, g$ then the functions $(f + g)$ and $fg$ are also differentiable. I would like to find a way how to argue about the function $h$ where \begin{equation} f(x) = (hg)(x) := h(x)g(x) \quad \text{and } f,g \text{ are differentiable} \end{equation}
For a start I can conc... |
Consider some (4, say) distinguishable particles. If we wish to distribute them into two exactly similar compartments in an open box, then the priori probability for a particle of going into any one of the compartments will exactly 1/2 as both compartments are identical. If the four particles are named as a , b, c and ... |
Consider the Peano axioms. There exists a model for them (namely, the natural numbers with a ordering relation $<$, binary function $+$, and constant term $0$). Therefore, by the model existence theorem, shouldn't this suffice to prove the consistency of first order arithmetic? Why is Gentzen's proof necessary?
The axi... |
№ 9
All Issues Volume 63, № 9, 2011 Estimates for the norms of fractional derivatives in terms of integral moduli of continuity and their applications
Ukr. Mat. Zh. - 2011. - 63, № 9. - pp. 1155-1168
For functions defined on the real line or a half-line, we obtain Kolmogorov-type inequalities that estimate the $L_p$-no... |
Vertex degree Function
context $G=\langle V,E,\psi\rangle$ … undirected graph
definiendum $ \mathrm{dom}\ d = V $
range $ u,v\in V, u\neq v $ range $ e\in E $
definiendum $ d(v):=\left|\{e\ |\ \exists u.\ \psi(e)=\{u,v\}\}+2\ \mathrm{card} \{e\ |\ \psi(e)=\{v,v\}\}\right| $ Discussion
The value $d_G(v)$ is the number o... |
Search
Now showing items 1-10 of 26
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... |
This was a sub-question in my previous post that I ask separately now.
In
Introduction to Conformal Field Theory by Blumenhagen and Plauschinn (springer link) the Virasoro algebra is introduced the central extension of the Witt algebra. They give the central extension $$\widetilde{\mathfrak{g}} = \mathfrak{g}\oplus \ma... |
To round off our series on round objects (see the first and second posts), let’s compute the sphere’s surface area. We can compute this in the same way we related the area and circumference of a circle two weeks ago. Approximate the surface of the sphere with lots of small triangles, and connect these to the center of ... |
Abstract
Double quantum dots (DQDs) are a versatile platform for solid-state physics, quantum computation and nanotechnology. The micro-fabrication techniques commonly used to fabricate DQDs are difficult to extend to the atomic scale. Using an alternative approach, which relies on scanning tunneling microscopy and spe... |
Large deviations for stochastic 3D Leray-$ \alpha $ model with fractional dissipation
1.
School of Mathematical Sciences, Nankai University, 300071 Tianjin, China
2.
School of Mathematics and Statistics, Jiangsu Normal University, 221116 Xuzhou, China
In this paper we establish the Freidlin-Wentzell's large deviation p... |
Newspace parameters
Level: \( N \) = \( 3311 = 7 \cdot 11 \cdot 43 \) Weight: \( k \) = \( 1 \) Character orbit: \([\chi]\) = 3311.h (of order \(2\) and degree \(1\)) Newform invariants
Self dual: Yes Analytic conductor: \(1.65240425683\) Analytic rank: \(0\) Dimension: \(1\) Coefficient field: \(\mathbb{Q}\) Coefficie... |
In these cases:
$$
r(x,y) = \bigvee \\{a \in A : \; \Delta(a) \leq_{A\times A} (x,y) \\}
$$
$$
l(x,y) = \bigwedge \\{a \in A : \; (x,y) \leq_{A\times A} \Delta(a) \\}
$$
You're assuming that you can just take infima \\(\bigwedge\\) and suprema \\(\bigvee\\). In a simple lattice \\((L, \wedge, \vee)\\) you don't have th... |
AliPhysics 4e47bdd (4e47bdd)
Scripts used in the analysis Algorithms Corrections Monte-carlo code Mid-rapidity tracklet code for dN/deta Tasks Topical
file AliAODForwardMult.h Per-event \( N_{ch}\) per \((\eta,\varphi)\) bin. file AliFMDEventPlaneFinder.h file AliForwardUtil.h Various utilities used in PWGLF/FORWARD. f... |
I've got a few measurements $\vec{x}$ for some real-world value $\hat{x}$. These measurements have some uncertainty, and are correlated. Given these estimates, and their covariances, I want to take some kind of weighted average of the estimates
$$\bar{x} = \sum_i w_i x_i = \vec{w} \cdot \vec{x}$$
Naturally, I want my w... |
I just stumbled upon the definition of the center Z of a group G: $$Z= \{x \in G \mid xz = zx \text{ for all } z \in G\}$$ The name “center” seems to suggest that there is some kind of geometric interpretation of the concept which I fail to see. My question is the following: is there some intuition/motivation behind th... |
№ 9
All Issues Volume 64, № 3, 2012
Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 291-306
We study the relationship between the isomorphism of quivers and properties of their spectra. It is proved that two simple strongly connected quivers with at most four vertices are isomorphic to one another if and only if their character... |
This is my first study about signal analysing. I'm very confused about filter order. My problem is how can I know whether its 12-th order, or 2nd order like the book says so? I already knew that slope has 2 choises whether its in n multiples of -6n dB/oct or -20n dB/dec. If the slope is -20 dB/dec then the second order... |
This question results from the discussion following a previous question: What is the connection between partial least squares, reduced rank regression, and principal component regression?
For principal component analysis, a commonly used probabilistic model is $$\mathbf x = \sqrt{\lambda} \mathbf{w} z + \boldsymbol \ep... |
In short, my question is why does a spurion analysis work to produce the correct symmetry breaking terms regardless of the high energy physics?
The context that this question arose is from an Effective Field Theory course (for more context, see here, Eq. 5.50). Consider the QCD Lagrangian,
\begin{equation}
{\cal L} _{ ... |
Synchronization for stochastic differential equations with nonlinear multiplicative noise in the mean square sense
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
We provide a more clear technique to deal with general synchronization problems for SDEs, whe... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
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... |
LaTeX Lambda24 Credit Royalty
Convert latex math notation to lambda functions in Python!
Language
Python 3.x
Metrics
API Calls - 1,882 Avg call duration - 1.00sec
Permissions
The Algorithm Platform License is the set of terms that are stated in the Software License section of the Algorithmia Application Developer and A... |
I have panel data for counts of new firms in different regions for six years. I am estimating a static poisson regression with multiplicative fixed effects$^*$; I have also tried to estimate a dynamic model by introducing a lagged dependent variable, but could not make that latter model work. Now, I would like to test ... |
I have this info but I don't understand anything
The coordinates and why those are the specific angles
You have the same polar co-ordinates for (3, 4) and (-4, 3) - this is incorrect. For (-4, 3), the angle would be more than 90. For (-4, 3), the polar co-ordinates would be (5, 90+53).
The purpose of any co-ordinate sy... |
I'm going to go a bit overboard here and give you the sketch of how vectors are geometrically constructed, since I think it's helpful to know. While writing this I found I was phrasing things very carefully, which means: you may need to reread parts of this in a quiet corner if it doesn't all make sense at first.
Suppo... |
I guess by "bosons" you're referring to gauge bosons?
If so then start with some matter field $ \psi(x)$ which transforms under the gauge group. For local gauge transformations the gauge group element $g$ is spacetime dependent $g(x)$, and the transformation is $$\psi(x) \longrightarrow \psi'(x) = g(x)\psi(x).$$
Deriva... |
Modeling a Continuous-Time System with Matlab
Many of us are familiar with modeling a continuous-time system in the frequency domain using its transfer function H(s) or H(jω). However, finding the time response can be challenging, and traditionally involves finding the inverse Laplace transform of H(s). An alternative ... |
Gauge theories describe the connectivity of a space with small, symmetric extra dimensions
Start with an infinite cylinder (the direct product of a line and a small circle). The cylinder can be twisted. To avoid appealing to concepts that I'm trying to explain, I'll just say that the cylinder is made of wire mesh: even... |
After the answers by joshphysics and user37496, it seems to me that a last remark remains.
The quantum relevance of the universal covering Lie group in my opinion is (also) due to a fundamental theorem by Nelson. That theorem relates
Lie algebras of symmetric operators with unitary representations of a certain Lie grou... |
Complete measure space Set
context $X $
definiendum $ \langle X,\Sigma,\mu\rangle $ … complete measure space over $X$
postulate $ \langle X,\Sigma,\mu\rangle $ … measure space
$\mu(N)=0$ $N'\subseteq N $
postulate $ N'\in\Sigma $ Discussion
In a complete measure space, subsets of null-sets can also be measured (and the... |
Incorrect theorem: Suppose $A$ is a real matrix, if $\forall x \neq 0,\ x \in \Bbb R^n,\ x^TAx > 0$, then all eigenvalues $> 0$. False proof: If $Ax = \lambda x$, then $$ x^TAx = \lambda x^Tx = \lambda ||x||^2> 0$$
Since $||x||^2> 0$, so $\lambda > 0$ q.e.d.
So I'm pretty sure this isn't true, since we can take a rotat... |
Let us now take a closer look at the
hex-fractal we sliced last week. Chopping a level 0, 1, 2, and 3 Menger sponge through our slanted plane gives the following:
This suggests an iterative recipe to generate the hex-fractal. Any time we see a hexagon, chop it into six smaller hexagons and six triangles as illustrated ... |
1. The perimeter of a equilateral triangle and regular hexagon are equal. Find out the ratio of their areas?a. 3:2
b. 2:3
c. 1:6
d. 6:1
Correct Option: bExplanation:
Let the side of the equilateral triangle = $a$ units and side of the regular hexagon is $b$ units.
Given that, $3a = 6b$ $ \Rightarrow \dfrac{a}{b} = \dfr... |
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly.
The best-known stochastic process to which stocha... |
Encouraged by Hilmar, I've decided to update the answer with all the steps necessary to calculate the Reverberation Time from a scratch. Presumably, it will be useful for others interested in this area. Obviously, it is the simplest approach because more advanced are definitely beyond a scope.
In the beginning, you mus... |
I've been using
Mathematica for a while now, and there are multiple common tasks that I end up doing. I'd like to learn how to convert them into functions so that I can store them in some file and load them at startup.
Most of these common tasks involve taking a set of equations and doing something with them. Thing is,... |
B̈oni, P.; Mook, H. A.; Martínez, J. L.; Shirane, G.
Title:
Comparison of the Paramagnetic Spin Fluctuations in Nickel with Asymptotic Renormalization-Group Theory
Abstract:
The paramagnetic spin fluctuations in Ni have been investigated at small momentum q and energy transfer $\Elzxh\omega$ by means of inelastic-neut... |
Difference between revisions of "Mean field models"
(I can't believe there was not an entry about this... work in progress)
(→Mean field solution of the Ising model)
Line 3: Line 3:
==Mean field solution of the Ising model==
==Mean field solution of the Ising model==
−
A well-known mean field solution of the [[Ising mo... |
I'm working through example 3.2 of Zangwill's Modern Electrodynamics and have come across a change in integration variables that I just can't seem to get. The example has two different change distributions related by $ \rho_b(\lambda \mathbf{r}) = \rho_a(\mathbf{r})$ and asks for the relationship between the electric p... |
I don't see why Gauss' Law holds for volumes that contain no source or sink. I am trying to understand Gauss' Law as a general effect of any vector field, so I would appreciate if any answers do not centrally focus on electrostatics.
For an arbitrary 3-dimensional region $R$ placed in a vector field
F, the divergence t... |
Improved Three Bin Exact Frequency Formula for a Pure Real Tone in a DFT
Introduction
This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by extending the exact two bin formulas for the frequency of a real tone in a DFT to the three bin case. This article is a direct exte... |
Main question: I've been reading about communication games a lot, and I'm wondering if there are good criteria to select between two separating-ish equilibria. I think of a separating equilibria as coordination equilibria among types. So, if we grant that these types successfully coordinate, why wouldn't we grant that ... |
I believe there are some big misunderstandings in the question...
First: usually error terms are , additive not multiplicative.
There are the so-called
multiplicative error models (MEM), but I don't think it's the case here, because usually in MEM the multiplicative error is time-dependent (i.e., $\epsilon_{t} \in [0, ... |
In general relativity and for its Einstein-Hilbert action, we usually ask that the metric variations $\delta g_{\mu \nu}$ cancel on the boundary $\partial \, \Omega$ of some region $\Omega$ of the spacetime manifold ($\delta g_{\mu \nu} = 0$). But if the variations are of
compact support, why can't we also ask that the... |
Per cent is derived from the Latin word ‘per centum’ meaning ‘per hundred’. It is represented by the symbol % and means 100. If we say 1% that means 1 out of 100 or one part of a complete quantity. In chapter 7 of ICSE Class 8 Maths, you will learn all the concepts related to Percent and Percentage. Also, you will solv... |
Stupid Question: If I'm given a non-euclidean space, such as $S^n $ (n-dimensional unit sphere), with the the uniform measure $\mu$ on it.
I'm also given a function $f:S^n \to \mathbb{R} $ that is bounded, by a constant $C$ . As an analogous to the Lebesgue measure case, can I say that: $ \int_{S^n } f d\mu \leq C \mu ... |
Getting Started¶
MathJax allows you to include mathematics in your web pages, either using TeX and LaTeX notation, or as MathML. To use MathJax, you will need to do the following things:
Obtain a copy of MathJax and make it available on your server. Configure MathJax to suit the needs of your site. Link MathJax into th... |
Transvection A transvection is a linear mapping $f$ of a (right) vector space $V$ over a skew-field $K$ with the properties
$$\def\rk{\textrm{rk}\;}\rk(f-E) = 1\quad\textrm{and}\quad \textrm{Im}(f - E)\subseteq \ker(f-E),$$ where $E$ is the identity linear transformation. A transvection can be represented in the form
$... |
Let us now take a closer look at the
hex-fractal we sliced last week. Chopping a level 0, 1, 2, and 3 Menger sponge through our slanted plane gives the following:
This suggests an iterative recipe to generate the hex-fractal. Any time we see a hexagon, chop it into six smaller hexagons and six triangles as illustrated ... |
First, the critical dimension. There are many ways (seemingly inequivalent ways but ultimately bound to give the same result) to calculate $D=10$ for the superstring that mirror the methods to calculate $D=26$ for the bosonic string.
For the bosonic string, one may use a conformally invariant world sheet theory. Becaus... |
A classical question on signals and systems, for which I provide you one method of solution.
Now given an LTI system, and its input $x[n]$ and output $y[n]$, the fundamental approach to determine the impulse response $h[n]$ involves the utilisation of a frequency domain approach to assert $H(e^{jw}) = Y(e^{jw})/X(e^{jw... |
I will give two explanations for why games crop up so fruitfully, one explanation from mathematics and the other arising from evolutionary biology.
The mathematical explanation for why games crop up in mathematics is that the truth of a complex statement
$$\forall x_0 \exists y_0 \forall x_1 \exists y_1 \cdots \varphi(... |
View Answer
question_answer1) Suppose that the division \[x\div 5\] leaves a remainder 4 and the division \[x\div 2\] leaves a remainder 1. Find the ones digit of x. play_arrow
View Answer
question_answer2) Find the number of digits in the square root of 4489. (Without any calculation). play_arrow
View Answer
question_... |
I am studying for my qualifiers, and I ran into this question from a previous year's exam.
$\textbf{Question:}$
Consider a two-consumer two-good pure exchange economy. Both preferences are locally non-satiated and convex. Prove or disprove the following statement: if $(x_1,x_2)$ and $(\hat{x}_1,\hat{x}_2)$ are two diff... |
First off, I want to warn you just a little bit about putting battery systems in parallel. It's usually not a good idea because often the two batteries (or battery systems) don't have exactly the same voltage. If they are different, then the one with the larger voltage will supply some current into the battery with the... |
E.g. if I know that my topology is that of a hyperboloid, how much freedom do I have left for my choice of the metric? And the other way around: if my metric is some conformal factor times the unit hyperboloid how much freedom do I have left in my choice for the topology? Am I forced to conclude that the topology of th... |
I have a discrete time stochastic process, where at each time the state of the system $X_t$ is given by: $$ X_t = f_\theta(X_{t-1},\epsilon_t), \; \; \text{for} \; t = 1,\dots,T $$ and, for example, the perturbations $\epsilon_t$ are i.i.d. $N(0,\sigma_e)$. So the state of the system at each time is a function (paramet... |
Python is available on any Linux/Unix machine including department machines and Macs.
You can download and install python on your own computer by following instructions at http://www.python.org
You can use the Python interpreter interactively by typing
python at a terminal window.Ipython is a nicer front end to python ... |
Hello, I've never ventured into char before but cfr suggested that I ask in here about a better name for the quiz package that I am getting ready to submit to ctan (tex.stackexchange.com/questions/393309/…). Is something like latex2quiz too audacious?
Also, is anyone able to answer my questions about submitting to ctan... |
I came across John Duffield Quantum Computing SE via this hot question. I was curious to see an account with 1 reputation and a question with hundreds of upvotes.It turned out that the reason why he has so little reputation despite a massively popular question is that he was suspended.May I ...
@Nelimee Do we need to m... |
Let $(\Omega,\mathcal F, P)$ be such a probability space that for every event $A\in\mathcal F$, the events that are independent to $A$ form an algebra $\mathcal B_A$ ($\Omega\in\mathcal B_A$). Independence to $A$ implying (I hope I get this right) for every finite $\mathcal C\subseteq\mathcal B_A$ $$P\left (A\cap\bigca... |
The Chaplygin sleigh problem is very popular in nonholonomic mechanics (more details can be seen in Bloch,
Nonholonomic Mechanics and Control, Springer, New York, 2015, section 1.7, pp 29-30),
The Chaplygin sleigh is a rigid body moving on two sliding posts and one knife edge
The equations are:
$\qquad v =\dot{x}\cos\t... |
@egreg It does this "I just need to make use of the standard hyphenation function of LaTeX, except "behind the scenes", without actually typesetting anything." (if not typesetting includes typesetting in a hidden box) it doesn't address the use case that he said he wanted that for
@JosephWright ah yes, unlike the hyphe... |
Problem Statement:-
Find the set of real values of $x$ for which $$x^{(\log_{10}x)^2-3\log_{10}x+1}\gt1000$$
Correct Approach:-
Domain of $x^{(\log_{10}x)^2-3\log_{10}x+1}\implies x\gt0$
Now, $$x^{(\log_{10}x)^2-3\log_{10}x+1}\gt1000$$
Taking $\log_{10}$ on both sides, we get
$$((\log_{10}x)^2-3\log_{10}x+1)(\log_{10}x... |
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History and Feedback Christian Lawson-Perfect 2 years, 2 months ago
Saved a checkpoint:
I'd like a description of how you decide if a root is a surd or not, like "$\sqrt{a}$ is a surd because there is no whole number $b$ such that $b^2 = a$".
Similarly for part
b), ... |
S Bhattacharyya
Articles written in Pramana – Journal of Physics
Volume 60 Issue 1 January 2003 pp 47-52 Reasearch Articles
Analysis of a part of the meteorite which fell at Dergaon (India) on March 2, 16.40 local time (2001) is presented with the help of FTIR, absorption and atomic spectra. The FTIR spectrum exhibits ... |
Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Normal Distribution having location parameter $\mu_{10\times 1} = (1,1,\dots,1)$ and the scatter parameter $\Sigma = I_{10}$, where $I_{10}$ is the $10 \times 10$ identity matrix.
My question is relat... |
In order to analyze the magnitude of earthquakes or compare the magnitudes of two different earthquakes, we need to be able to convert between logarithmic and exponential form. For example, suppose the amount of energy released from one earthquake were 500 times greater than the amount of energy released from another. ... |
Multiplicity Results for the Biharmonic Equation with Singular Nonlinearity of Super Exponential Growth in ℝ 4 21 Downloads Abstract
We consider the following elliptic problem of exponential-type growth posed in an open bounded domain with smooth boundary
B 1 (0) ⊂ ℝ 4: \((P_\lambda)\begin{cases}\Delta^{2}u = \lambda(u... |
The key point here is that without an air gap an inductor will saturate if you try to put any current through it so inductance will fall and you can't store any energy.
The term "Flyback Transformer" is a little misleading and its more useful to consider it as coupled inductors rather than a transformer because the act... |
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