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This question is intended to kind of rekindle this old question, which was apparently very hard didn't receive a satisfactory answer. I'm aware that the hope of a definite answer is quite slim, but I'm still very curious to know:
Suppose $f:U\to \Bbb R$ is a function, $U$ is an open subset of $\Bbb R^n$, and $x_0\in U$... |
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Edit this page" (or just " edit") link at one of its edges. This will bring you to a page with a text box containing the wikitext: the editable source code from which the server produces... |
We were doing $\ce{O2}$ estimation by Winkler's method
The procedure and reactions involved in this experiment are: Carefully fill a 300-mL glass stoppered bottle brim-full with sample water. Immediately add 2mL of manganese sulfate to the collection bottle. Add 2 mL of alkali-iodide reagent (NaOH + KI) in the same man... |
I am trying to solve the equation
$\frac{d}{dt}V(t)=r(t)V(t)+\pi-\mu(x+t)(b_d-V(t))$
numerically using the R function 'ode'. This is a Thiele differential equation for a life insurance reserve with premium rate $\pi$, mortality intensity $\mu$ (for an $x+t$ year old), death benefit $b_d$ and interest rate process $r$.
... |
First of all, rates of convergence are usually given in the form$$ \|u-u_h\| \leq C N^\alpha,$$rather than equality. Furthermore, rates are
asymptotic, i.e., only have to hold for $N\to \infty$. This means that you're unlikely to find a single $C$ and $\alpha$ such that your equation holds.
Another reason why your appr... |
Category: Ring theory Problem 624
Let $R$ and $R’$ be commutative rings and let $f:R\to R’$ be a ring homomorphism.
Let $I$ and $I’$ be ideals of $R$ and $R’$, respectively. (a) Prove that $f(\sqrt{I}\,) \subset \sqrt{f(I)}$. (b) Prove that $\sqrt{f^{-1}(I’)}=f^{-1}(\sqrt{I’})$
Add to solve later
(c) Suppose that $f$ i... |
I felt I needed to write an additional answer to try to clear my mind about the question. Here is the try, step by step. Caveat: for simplicity, I used the same notation $C$ of a function of reals $u$ and $v$, for its rewriting in $x=u+iv$ and $\bar x$, and on complex $x$ alone. I hope it is not confusing for the reade... |
Consider the system of equations formulated in a previous question (optical fibers continuity of tangent field components across the core-cladding interface):
$$ \left\{ \begin{array}{c} e_z^{(1)}(r,\phi)|_{r = a} = e_z^{(2)}(r,\phi)|_{r = a}\\ e_{\phi}^{(1)}(r,\phi)|_{r = a} = e_{\phi}^{(2)}(r,\phi)|_{r = a}\\ h_z^{(1... |
Category: Group Theory
Group Theory Problems and Solutions.
Popular posts in Group Theory are:
Problem 625
Let $G$ be a group and let $H_1, H_2$ be subgroups of $G$ such that $H_1 \not \subset H_2$ and $H_2 \not \subset H_1$.
(a) Prove that the union $H_1 \cup H_2$ is never a subgroup in $G$.
Add to solve later
(b) Pro... |
As a quick note, the equations of motion that come from that Lagrangian are
$$\frac{d}{dt}\left(\dot q_1 + \dot q_2\right) = -2kq_1^3$$$$\frac{d}{dt}\left(\dot q_2 + \dot q_1\right) = -2kq_2^3$$
The Dirac procedure for singular Lagrangians goes as follows:
Step 1: Calculate the generalized momenta as usual$$p_1 \equiv ... |
I am intrigued by this question because it gets at the heart of so many grey areas of the financial system in which it becomes almost impossible to know how many assets derive their values from some unseen or ill-prescribed, but presumed extant, underlying process.
Calibration can be interpreted as means of deriving an... |
...
The Giant Radio Array for Neutrino Detection (GRAND) is a planned large-scale observatory of ultra-high-energy (UHE) cosmic particles, with energies exceeding 10^8 GeV. Its goal is to solve the long-standing mystery of the origin of UHE cosmic rays. To do this, GRAND will detect an unprecedented number of UHE cosmi... |
Current browse context:
physics.soc-ph
Change to browse by: References & Citations Bookmark(what is this?) Physics > Physics and Society Title: Epidemic SIR model on a face-to-face interaction network: new mobility induced phase transitions
(Submitted on 21 Mar 2018 (v1), last revised 24 May 2018 (this version, v3))
Ab... |
(a) If $AB=B$, then $B$ is the identity matrix. (b) If the coefficient matrix $A$ of the system $A\mathbf{x}=\mathbf{b}$ is invertible, then the system has infinitely many solutions. (c) If $A$ is invertible, then $ABA^{-1}=B$. (d) If $A$ is an idempotent nonsingular matrix, then $A$ must be the identity matrix. (e) If... |
Various stringed instruments of Chinese make on display in a shop.
String instruments or stringed instruments are chordophones. Some common instruments in the string family are violin, guitar, sitar, electric bass, viola, cello, harp, double bass, rabab, banjo, mandolin, ukulele, and bouzouki. History
Early string inst... |
The rate of turn is inversely proportional to the (True) airspeed. For an aircraft in a level, coordinated turn, the rate of turn is given by
$\mathrm{Rate\ of\ turn} = \frac{1091 \tan\theta}{V}$
where
Rate of turn is in degrees per second, $\theta$ is the bank angle in degrees, and $V$ is the TAS in knots.
So, as the ... |
For what values of $x$ is the number $121$ a square in base $x$?
This is a very easy question, but I still think it's pretty fun. Perhaps it's something to pass on to younger people who are taking algebra.
Puzzling Stack Exchange is a question and answer site for those who create, solve, and study puzzles. It only take... |
For a given set of filter specifications, we generally obtain the filter system function, $$H(z)$$, assuming that the filter coefficients can be represented with infinite precision. However, when implementing the filter in the real world, we have to use a finite number of bits to represent each coefficient of $$H(z)$$.... |
Recommended Level
Beginner
Nodal Analysis
Nodal analysis is a form of analysis that uses Kirchhoff’s Current Law (KCL) and node equations to solve for circuit voltage values where the schematic diagram does not have any conductor paths crossing. A term typically used for this purpose is said to represent a planar circu... |
You need to evaluate $H(z)$ on the unit circle $z=e^{iw}$ in order to get the frequency response (assuming that the system is stable, i.e. the region of convergence contains the unit circle). But your $\mathcal{Z}$-transform looks a bit unusual because for causal signals (or filter impulse responses) you should get neg... |
A complete combinatorial proof using Allen's comment:
Let $(W,S)$ be a Coxeter system, and let $Dem(T) \in W$ be the
Demazure product or greedy product of a word $T$ in $S$.
Claim: $Dem(T)$ is the unique Bruhat maximal element in the set $\big\{ \prod Q : Q \subseteq T\big\}$ (where $Q\subseteq T$ means that $Q$ is a s... |
stat946w18/Implicit Causal Models for Genome-wide Association Studies Contents 1 Introduction and Motivation 2 Implicit Causal Models 3 Implicit Causal Models with Latent Confounders 4 Likelihood-free Variational Inference 5 Empirical Study 6 Conclusion 7 Critique 8 References 9 Implicit causal model in Edward Introduc... |
For a harmonic oscillator in one dimension, there is an uncertainty relation between the number of quanta $n$ and the phase of the oscillation $\phi$. There are all kinds of technical complications arising from the fact that $\phi$ can't be made into a single-valued and continuous operator (Carruthers 1968), but roughl... |
stat946w18/Implicit Causal Models for Genome-wide Association Studies Contents 1 Introduction and Motivation 2 Implicit Causal Models 3 Implicit Causal Models with Latent Confounders 4 Likelihood-free Variational Inference 5 Empirical Study 6 Conclusion 7 Critique 8 References 9 Implicit causal model in Edward Introduc... |
14 0 Homework Statement A yo-yo is placed on a conveyor belt accelerating ##a_C = 1 m/s^2## to the left. The end of the rope of the yo-yo is fixed to a wall on the right. The moment of inertia is ##I = 200 kg \cdot m^2##. Its mass is ##m = 100kg##. The radius of the outer circle is ##R = 2m## and the radius of the inne... |
Tagged: linear algebra Problem 26
In this problem, we will show that the concept of non-singularity of a matrix is equivalent to the concept of invertibility.
That is, we will prove that: (a)Show that if $A$ is invertible, then $A$ is nonsingular. (b)Let $A, B, C$ be $n\times n$ matrices such that $AB=C$.
Prove that if... |
Hi everyone!
I have a problem at hand that needs to calculate a series of covariant derivatives like
\nabla_{\alpha} \nabla_{\beta} \nabla_{\gamma} \nabla_{\lambda}\partial_{\nu}\phi
Where \nabla is the usual covariant derivative in GR and \partial is the usual partial derivative.
In fact, this expression is a term of ... |
The setting is basically earth. Our planet is unfortunately on a collision course with a large asteroid. However, humans have discovered and decoded a message from an ancient, advanced alien race (our parents). These aliens have left behind technology and knowledge that could save the planet, but this technology is enc... |
Notch Filters
Typical target reflectance is as high as possible in the high reflectance range and as small as possible in the rest of the specified spectral range.
Design approaches: rugate type coatings and conventional multilayer stacks. The advantage of the rugate and quasi-rugate coatings is that they suppress ripp... |
Problem 15
Let $p_1(x), p_2(x), p_3(x), p_4(x)$ be (real) polynomials of degree at most $3$. Which (if any) of the following two conditions is sufficient for the conclusion that these polynomials are linearly dependent?
(a) At $1$ each of the polynomials has the value $0$. Namely $p_i(1)=0$ for $i=1,2,3,4$. (b) At $0$ ... |
I want to get a better grasp of what a rigorous formal proof is. So I was hoping to find proofs of interesting results using natural deduction or Hilbert system or similar. The "interesting result" could be anything from infinitude of primes to Lagrange's theorem. "Interesting result" is not $x \wedge y \implies y \wed... |
In statistical mechanics, for a system of $N$ particles $x_1, \ldots, x_N$ in three dimensions, the Gibbs free energy is defined in terms of the Hamiltonian $H$ as $$ G = -k_\mathrm B T \log \int_{\mathbb{R}^{3N}} \mathrm e^{-H(x_1, \dots, x_N)}\,\mathrm dx_1 \dots \mathrm dx_N.$$ People talk about the "free energy dif... |
Here is an example (the group $H_K^\mathbf{Q}$ defined below, which is actually a split extension abelian-by-countable).
Let $(Q,\le)$ be a total ordering. Let $K$ be a countable (possibly finite) field. Let $V^Q_K=K^{(Q)}$ be the free $K$-module with basis $(e_q)_{q\in Q}$. Let $G^Q_K$ be the group of $K$-module autom... |
Note: I first posted question on math.stackexchange and I got one reply, which was a bit helpful (I'm still trying to understand it fully), but did not explore the two solution cases that I mentioned. Besides I would appreciate additional insight on this question, which I hope its not too trivial for mathoverflow. Than... |
Tagged: normal subgroup If a Half of a Group are Elements of Order 2, then the Rest form an Abelian Normal Subgroup of Odd Order Problem 575
Let $G$ be a finite group of order $2n$.
Suppose that exactly a half of $G$ consists of elements of order $2$ and the rest forms a subgroup. Namely, suppose that $G=S\sqcup H$, wh... |
Article - Physically Based Rendering
Introduction
The pursuit of realism is pushing rendering technology towards a detailed simulation of how light works and interacts with objects.
Physically based rendering is a catch all term for any technique that tries to achieve photorealism via physical simulation of light.
Curr... |
Given a Boolean function $f$ over the set of variables $X =\{ x_1,...,x_n \}$, the influence of $x_i$ is defined as the probability that changing only $x_i$ on random input changes $f$.
Given a function $f$ presented in $\text{CNF}$, and a coordinate, are there any known methods for determine if the coordinate has posi... |
Definition(1). Let $\mathscr{L}$ be a first-order language. An $\mathscr{L}$-theory $T$ is said to have quantifier-elimination whenever if for all $\mathscr{L}$-formula $\phi(\bar{x})$ there exists a quantifier-free $\mathscr{L}$-formula $\psi_\phi(\bar{x})$ such that $$T\models \forall \bar{x}\left(\phi(\bar{x})\leftr... |
I am a new LaTeX user. I already searched through the topic and I have not found an answer yet. I am using the
exercise package to build a large Multiple Choice math question set complete with an answer key and full explanations. This is the format of a typical Multiple Choice question:
\item \(\frac{19^2+19}{19}\)\beg... |
Let's assume that an excess of 2 cm of water evaporates across the entire surface of the Earth, and settles at an altitude of 3000 m. It is possible to compute the increased moment of inertia of the Earth, and thus the theoretical slowdown.
Moment of inertia of the earth can be found from data on the NASA website http:... |
Hybrid Interaction Point Process Model
Creates an instance of a hybrid point process model which can then be fitted to point pattern data.
Usage
Hybrid(...)
Arguments …
Two or more interactions (objects of class
"interact") or objects which can be converted to interactions. See Details.
Details
A
hybrid (Baddeley, Turn... |
Legacy code is a concern for any company with a reasonably size team pretty quickly. In this article Wayne Lobb from Foliage provides us with industry metrics with respect to code growth (Unfortunately need to register to download). The quick summary is that on average a developer can either create…
December 2011
The f... |
amp-mathml
Displays a MathML formula.
Required Script
<script async custom-element="amp-mathml" src="https://cdn.ampproject.org/v0/amp-mathml-0.1.js"></script>
Supported Layouts container Examples amp-mathml.amp.html
This extension creates an iframe and renders a MathML formula.
<amp-mathml layout="container" data-form... |
States of Matter: Gases and Liquids Melting and Boiling Points, Molecular Speeds Most Probable Velocity C p (or) Vp:
\tt C_p=\sqrt{\frac{2RT}{M}}=\sqrt{\frac{2PV}{M}}=\sqrt{\frac{2P}{d}}
RMS Velocity (C or u): \tt u=\sqrt{\frac{u_1^2+u_2^2+u_3^2+...+u_n^2}{n}} \tt PV=\frac{1}{3}\ MC^2 \tt C=\sqrt{\frac{3PV}{M}}=\sqrt{\... |
No, I don't think it's
necessary to use MathJax. In fact, one of our top answerers here doesn't use MathJax at all. This is mostly because answers, and questions, are based in physics and not in maths (though often the maths & physics are intertwined so it's kinda difficult to distinguish them). So if you can explain y... |
Electroweak theory has two coupling constants before and after Spontaneous Symmetry Breaking (SSB) each one for $SU(2)_L$ and $U(1)_Y$, though they are connected by Weinberg angle after SSB. My question is, how is unification complete with two independent couplings before SSB. The motive for unification is a single uni... |
Disclaimer: This is not really an answer, but rather a "long comment". However, I hope it can provide some useful insights. Anyway, I think that this question can be basically considered a duplicate of Is there a way to obtain the classical partition function from the quantum partition function in the limit $h→0$?.
The... |
I'll summarize the comments from chi, and sketch the proof that
There can be no proof of $\mathrm{False}:=\forall X:*.X$ in the CoC in head normal form. Furthermore, this fact can be proven in a weak theory, say Peano Arithmetic (though the excluded middle is not required).
This fact implies that if the CoC is normaliz... |
I understood the definition of
affine $k$-chain and that he defines $\int \limits_{\Gamma} \omega$ as $(82)$. But I can't understand the last two above examples. What does they mean?
Can anyone explain them detailed?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and prof... |
Let $M,N$ be oriented $d$-dimensional Riemannian manifolds, $M$
compact*, and let $f:M \to N$ be smooth.
Consider the Dirichlet energy functional: $E_{M,N}(f)=\int_M \|df\|^2 \operatorname{Vol}_g$. ($\operatorname{Vol}_g$ is the Riemannian volume form of $M$).
Fix another $d$-dimensional Riemannian manifold $W$.It's ea... |
Let $f$ be measurable, finite a.e, and Lebesgue integrable on $\mathbb{R}$ . Show that for all $\epsilon > 0$ there exists a measurable set $E$ (i.e $\mu(E) < \infty$) such that:
$\int_{E} |f| > \int_{\mathbb{R}} |f| - \epsilon$
My attempt
Suppose that for all $\epsilon > 0$ there exists set of finite measure $E$ such ... |
As you may expect from the title of this section, this will be the most difficult and complicated section of this chapter so far. Our aim will be to calculate the field and potential surrounding a simple dipole.
A simple dipole is a system consisting of two charges, \(+Q \text{ and }−Q\), separated by a distance \(2L\)... |
Radioactive decay is the process by which unstable particles with high mass; fall apart into more stable particles with lower mass. Although the process itself is quantum mechanical in nature, the dynamics of radioactive decay are described by special relativity and are essentially identical to those of an inelastic co... |
The problem is NP-Hard and the reduction is from partition.
So, assume you are given an instance of partition $S=${$x_1,\ldots,x_n$}. Let $t = (\sum_{i=1}^n x_i) / 2$. The question is whether there is a subset of $S$ such that its sum is $t$.
To this end, let $v_0 = (0, 2t, t)$ be a special vector. For every number $x_... |
When we follow the standard textbooks, or tradition, most of us teach the following definition of big-Oh notation in the first few lectures of an algorithms class: $$ f = O(g) \mbox{ iff } (\exists c > 0)(\exists n_0 \geq 0)(\forall n \geq n_0)(f(n) \leq c \cdot g(n)). $$ Perhaps we even give the whole list with all it... |
Someone asked a question about self-avoiding random walks, and it made me think of the following:
Consider a piece that starts at a corner of an ordinary $8 \times 8$ chessboard. At each turn, it moves one step, either up, down, left, or right, with equal probability, except that it must stay on the board, of course, a... |
257 23 Homework Statement Consider object going through circular motion with radial acceleration = ##2m/s## and radius given by ##\frac{4}{2t+2}## Find arc length of object swept through the first two seconds. Homework Equations --
My working:
##s=\int v## ##v= \sqrt{\frac{a_{c}}{r}}=\sqrt{\frac{a_{c}}{\frac{4}{2t+2}}}... |
You might want to have a look at the overlap-add (http://en.wikipedia.org/wiki/Overlap%E2%80%93add_method) and overlap-save (http://en.wikipedia.org/wiki/Overlap%E2%80%93save_method) methods. But, if all you are trying to do is additive synthesis, you don't absolutely have to use the IFFT to generate your signal.
You c... |
It would probably be useful before reading this and the next section to review Chapters 11 and 12.
Figure XVII.12 shows the same system as figure XVII.2, except that, instead of being left to vibrate on its own, the second mass is subject to a periodic force \( F\ =\ \hat{F}\sin\omega t\). For the time being, we’ll sup... |
Question
I have the feeling gas cannot have an equivalent of Ohm's law, tying pressure and throughput via some kind of fluid resistance constant depending on the geometry of the obstacle considered. Certainly because gas can be compressible.
However I need a very rough estimate (not a number from experience, a first or... |
I'm trying to figure out some kind of immunization using a factor model I developed for interest rates. Here is the basic problem. Let's say that we have a bond portfolio containing $N$ bonds with weights $x_i$ and one liability. Call the present value of the liability $P_L$. I'll suppose that the bond prices are given... |
Defining a subgroup of elliptic curves with specific characteristics
Hey,
is there a way, to define a subgroup of an elliptic curve with two or more characteristics? I would like to take an elliptic curve over a finite field of order p and $p^4$, define the r-torsion subgroup (where $r$ is a prime, too) and reduce thos... |
Quasi harmonic approximation¶
Using phonopy results of thermal properties, thermal expansion andheat capacity at constant pressure can be calculated under thequasi-harmonic approximation.
phonopy-qha is the script to runfitting and calculation to perform it. Mind that at leave 5 volumepoints are needed to run
phonopy-q... |
Is it possible to create a Normal Map from a Texture, not a mesh? If so, how?
As I'm working on an Eye, and have already made the textures, I was wondering if it was possible to create Normal Maps out of those Textures.
Blender Stack Exchange is a question and answer site for people who use Blender to create 3D graphic... |
This chapter of our tutorial is about legends. Legends are the classical stories from ancient Greece or other places which are usually devoured by adolescents. They have to read it and this is where the original meaning comes from. The word
legend stems from Latin and it means in Latin "to be read". So we can say legen... |
Sides of a parallelogram: \(a\), \(b\)
Diagonals of a parallelogram: \({d_1},\) \({d_2}\) Consecutive angles: \(\alpha\), \(\beta\) Angle between the diagonals: \(\varphi\)
Diagonals of a parallelogram: \({d_1},\) \({d_2}\)
Consecutive angles: \(\alpha\), \(\beta\)
Angle between the diagonals: \(\varphi\)
Perimeter: \(... |
Calculation of a triple integral in Cartesian coordinates can be reduced to the consequent calculation of three integrals of one variable.
Consider the case when a three dimensional region \(U\) is a type I region, i.e. any straight line parallel to the \(z\)-axis intersects the boundary of the region \(U\) in no more ... |
For maximum sensitivity preamble detection with time referencing, consider using a barker code, or for more choices with longer lengths a PRN (pseudo-random noise) sequence, or for even more choices when more distinction is needed (CDMA) Gold codes are a possibility. (Also not further detailed but have other advantages... |
15.1 Two spaceships are connected by a strong cable. Both ships are initially at rest, and ignite their engines at the same time. Their accelerations are identical at every point in time. Does the cable stay intact?
Hint: use a spacetime diagram to analyze what happens.
15.2 In classical mechanics, the Doppler shift in... |
I'm confused about the impact that a mean reverting stock price process has on the value of an option on it.
Several sources say that there is indeed an impact on the price of an option:
Lo and Wang (1995)
Yet, another source seems to say that mean reversion has no impact on the price of an option:
"The drift term of t... |
This question already has an answer here:
Can anybody show me how to do the boxes in the image attached in latex.
Thanks ahead
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It only takes a minute to sign up.Sign up to join this community
This... |
Consider the following two variants of subset sum problem:
Variant 1
Given a set of $2n$ positive integer elements and a positive integer target $W$, is there a subset with size $n$, whose sum is $W$?
Variant 2
Given a set of $n$ positive integer elements and a positive integer target $W$, where $(\text{the maximum ele... |
In his celebrated paper "Conjugate Coding" (written around 1970), Stephen Wiesner proposed a scheme for quantum money that is unconditionally impossible to counterfeit, assuming that the issuing bank has access to a giant table of random numbers, and that banknotes can be brought back to the bank for verification. In W... |
I have two points. (-1,-5) is one of the minimum points and (3.5,-4) is one of the maximum points. I'm not sure if this is a sin or a cosine function. Please write the equation to this problem.
.I literally just watched a video on how to do this, this is a learning process for me too
I am assuming that you learned the ... |
I have a problem about a general multivariate skew normal distribution. There is a $p\times 1$ vector, $\mathbf{y}=(\mathbf{y}_1',\mathbf{y}_2',\ldots,\mathbf{y}_n')',p>n$, which has the density as
$$f_p(\mathbf{y})\propto\phi_p(\mathbf{y};\boldsymbol{\mu},\Sigma)\prod_{i=1}^n\Phi(c_1+c_2\mathbf{1}'\mathbf{y}_i)=\phi_p... |
I analyzed an unknown Alkali Halide crystal using x-rays from a copper source. I need to find the d-spacing for this crystal, i.e. the interplanar distance between planes of atoms.
I found my $K_\alpha$ and $K_\beta$ peaks and used Bragg's Law to calculate the d-spacing. However, these values do not match. Is this an e... |
Let $S$ be the set of $2^n$ binary $n$-bit strings. For every $x\in S$, let $f(x)$ is the maximal chain of bits 1 in $x$. So Can we find a good upper bound of $$F(n)=\frac{\sum_{x\in S}f(x)}{2^n}$$ Of course, $O(1)\le F(n) \le O(n)$. I think the upper bound is a constant or $O(\log n)$. Can anyone help me?
There is an ... |
Let's derive the proof. Consider you are short an option and long its self-financing delta hedge. You get the portfolio $\Pi$ whose $t$-value verifies$$ \Pi_t = \underbrace{- V_t}_{\text{Short option}} + \underbrace{\Delta_t S_t}_{\text{Long stocks}} + \underbrace{\frac{(V_t - \Delta_t S_t)}{B_t} B_t}_{\text{Residual c... |
removes tags created more than 6 months ago which have been used only a single time. It will run monthly.
Hake's Theorem, due to Heinrich Hake of Düsseldorf in 1921, says that an improper Henstock–Kurzweil integral (aka generalized Riemann integral, gauge integral, Perron integral, or Denjoy integral) on a bounded inte... |
Background
For my thesis, I'm trying to wrap my head around a relatively small field within mathematics called "Stochastic Cooperative Game Theory". To that end, I've read a few papers on the subject, including
Cooperative games with stochastic payoffs (Suijs et al., 1999, link) and Convexity in stochastic cooperative ... |
Is my solution correct?
Question: Find all \(z\), such that \((z+1)^7=z^7\).
My answer: Since \(z\ne 0\), we can divide by \( z^7\) on both sides to get \(\left(\frac{z+1}{z}\right)^7=1\). If we let \(w=\frac{z+1}{z}\), then \(w\) is equal to the \(7^{\text{th}}\) roots of unity. We can manipulate \(w=\frac{z+1}{z}\) b... |
In theoretical population genetics, it is very common to have to assume a model of epistatic interaction. The two most common models are the additive model and the multiplicative model.
Additive model
Under the additive model the fitness $w$ of an individual carrying all $n$ mutations of effects $[s_1,s_2,...,s_n]$ is
... |
It might be thought that there is rather a limited amount that could be written about the geometry of a straight line. We can manage a few Equations here, however, (there are 35 in this section on the Straight Line) and we shall return for more on the subject in Chapter 4.
Most readers will be familiar with the equatio... |
As @nimbus3000 mentions, the shape of the vol curve differs by markets so I won't comment on that here. I'll restrict my comments to the Black(-Scholes) vs. Bachelier section of the question.
You can approximate Normal (Bachelier) vols from Black vols by (there is a second order effect related to the product of the squ... |
First, the term "propagator" is usually defined as the Green's function of the first type, not the second type, i.e. as a solution to the diffential equation $\hat L G = \delta$.
At any rate, those definitions are ultimately equivalent – when the details are correctly written down – because the Green's function defined... |
I'm reading "Antennas and Wave Propagation" by Harish and Sachidananda. They introduce the phasor form of Maxwell's equations:
$$\nabla\times E=-j\omega\mu H$$ $$\nabla\times H = j\omega\epsilon E + J$$ $$\nabla\cdot D = \rho$$ $$\nabla\cdot B = 0$$
First of all they observe that by taking the curl of the first equatio... |
First of all credits:
Latex people for making this beauty happen
Dave at xyloid.org for his vblatex package
The makers of mhchem package
Tormod for being the most unappreciated person who created and manages this chaos every day, also for being a great man and a father
Tormod's family for being the people who appreciat... |
Is there an example of an eigenfunction of a linear time invariant (LTI) system that is
not a complex exponential? Justin Romberg's Eigenfunctions of LTI Systems says such eigenfuctions do exist, but I am not able to find one.
All eigenfunctions of an LTI system can be described in terms of complex exponentials, and co... |
Let $A$, $B$ be two smooth vector bundles of finite rank over a smooth manifold $M$. Let $Diff(A,B)$ be the space of differential operators from $A$ to $B$. Can I talk about "the space of smooth maps from $[0,1]$ to $Diff(A,B)$?
You could use the bijective correspondence between differential operators $L: \Gamma(A) \to... |
This is not a complete answer, just a start as you indicate that you don't even know where to begin.
Let $f\in\Bbb{Z}[x]$ monic. If its image $f_p$ in $\Bbb{F}_p[x]$ is separable and factors as $f_p=\prod_{i=1}^kg_k$, then $\operatorname{Gal}(f)$ contains an element of cycle type $(\deg g_1,\ldots,\deg g_k)$. So it mak... |
In "Classical Mechanics" book by Goldstein, Poole & Safko they develop the formulas of scattering to due to central-force problem.
In page 88, after receiving the expression for the differential cross section
$$ \sigma(\theta) =\frac{s}{sin \theta} |\frac{ds}{d\theta}|$$
They said that the relation between $s$(impact p... |
Consider a probe approaching a planet for a hyperbolic flyby manoeuvre;
The eccentricity of the hyperbolic trajectory can be calculated using the following formula:
$$e = 1 + \frac{r_pv_\infty^2}{\mu_1}$$ $v_\infty$ refers to the probe's hyperbolic excess velocity. $\mu_1$ refers to the standard gravitational parameter... |
Let $T: \R^n \to \R^m$ be a linear transformation.Suppose that the nullity of $T$ is zero.
If $\{\mathbf{x}_1, \mathbf{x}_2,\dots, \mathbf{x}_k\}$ is a linearly independent subset of $\R^n$, then show that $\{T(\mathbf{x}_1), T(\mathbf{x}_2), \dots, T(\mathbf{x}_k) \}$ is a linearly independent subset of $\R^m$.
Let $A... |
Tagged: abelian group
Abelian Group Problems and Solutions.
The other popular topics in Group Theory are:
Problem 616
Suppose that $p$ is a prime number greater than $3$.
Consider the multiplicative group $G=(\Zmod{p})^*$ of order $p-1$. (a) Prove that the set of squares $S=\{x^2\mid x\in G\}$ is a subgroup of the mult... |
This question already has an answer here:
Equation of state of a rubber band 1 answer
Which of these two equations of state are valid?
$$S_1 = L_0 \gamma (\theta E/L_0)^{1/2} - L_0\gamma\left[\frac{1}{2} \left(\frac{L}{L_0}\right)^2 + \frac{L_0}{L} - \frac{3}{2}\right]$$
$$S_2 = L_0 \gamma e^{\theta n E/L_0} - L_0\gamm... |
Answer
$\frac{2x-1}{2x}, x\ne0$
Work Step by Step
Canceling common terms and using exponent rules, we find: $\frac{\sqrt x-\frac{1}{2\sqrt x}}{\sqrt x}=\frac{\frac{2x-1}{2\sqrt x}}{\sqrt x}=\frac{2x-1}{2x}$
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Custom software development is expensive, certainly if you include the cost of the need to maintain lines of code over time. A common strategy is therefore to reuse code that has been created already or share the development and maintenance costs between different parties.Different types of reuseReuse models can differ... |
Mike Spivey
I am a math professor at the University of Puget Sound. My background is in operations research, and I teach typical OR courses such as optimization, modeling, and probability, as well as calculus, statistics, and differential equations.
My math blog,
A Narrow Margin, includes (among other things) discussio... |
It is quiet easy to prove whether C4 has any effect on total capacitance when C2=C3=C5=C6. Here's your circuit:
simulate this circuit – Schematic created using CircuitLab
I will calculate total capacitance Ct of this circuit and if the final result does not contain Cx than it can be omitted, it has no effect. But if th... |
For the symmetrized quantum field theory Lagrangian of the free dirac field
$$\mathcal{L} = i[\overline{\psi}_a,({\partial_\mu}\gamma^\mu \psi)^a] -m[\overline{\psi}_a,\psi^a ]$$
the terms are symmetrized since $\overline{\psi}_a$ and $\psi_a$ do not anti-/commute. Is this the correct symmetrized Lagrangian? Now I trie... |
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