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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21928 | # American Institute of Mathematical Sciences
January 1996, 2(1): 23-52. doi: 10.3934/dcds.1996.2.23
## Evolution equations governed by the subdifferential of a convex composite function in finite dimensional spaces
1 Departement de mathematiques, Universite Montpellier II, 34095 Montpellier cedex 5, France
Recei... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21929 | # Problem: Spiderman, whose mass is 80.0 kg, is dangling on the free end of a 12.0-m-long rope, the other end of which is fixed to a tree limb above. By repeatedly bending at the waist, he is able to get the rope in motion, eventually getting it to swing enough that he can reach a ledge when the rope makes a 60.08 angl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21930 | # Beat Frequency for Police Radar with Special Relativity
"A radar speed trap operates on a frequency $v_o = 109 Hz$. What is the beat frequency between the transmitted signal and one received after reflection from a car moving at v = 30 m/s toward the radar. Do calculations with accuracy to linear terms in v/c."
I'm... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21931 | # Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.h(x) = 19x4 − 419x2 + 18:
1 answer
###### Question:
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leadin... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21932 | # Compound Lorentz transformations
References: Griffiths, David J. (2007), Introduction to Electrodynamics, 3rd Edition; Pearson Education – Chapter 12, Post 18.
The Lorentz transformations can be written in matrix form as
$\displaystyle \Lambda_{x}=\left[\begin{array}{cccc} \gamma & -\beta\gamma & 0 & 0\\ -\beta\ga... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21933 | # Glossary
Argument. An argument is a set of claims that is structured such that some of those claims (known technically as premises) are offered in support of another (known technically as the argument’s conclusion).
Conclusion. The conclusion of an argument is the arguer’s main point, or the thing of which they are... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21934 | # Zero function implies zero polynomial.
I'm trying to help someone with a problem in Apostol's book (Chapter 1 BTW, so before basically any calculus concepts are covered) at the moment and I'm stumped on a question.
I'm trying to prove that if $p$ is a polynomial of degree $n$, that is where $$p(x) = a_0 + a_1x + \c... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_21935 | # For any eight points on an equilateral triangle of side $1$, there's at least one pair of those points at most $1/3$ apart
Let's say we have an equilateral triangle of side length $$1$$. Show that for any configuration of eight points on this triangle (on the sides or in the interior), there is at least one pair of ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13536 | How to formalize a tree problem?
Considering a network of $n$ IT centers $1,...,n$ we can connect by lines which heve different characteristics. Among these charateristics, we take an interrest in the reliability of a line. Thus, let be the error rate $p_{ij}$ which represents the probability for a message channeled b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13537 | # Fermat's Last Theorem
1. Feb 24, 2004
### digiflux
I am trying to get my father's ingenious proof of Fermat's last theorem the recognition that it deserves. Please visit the link below.
www.fermatproof.com
Thanks!
#### Attached Files:
File size:
7.9 KB
Views:
174
2. Feb 24, 2004
### matt grime
I'm not sure w... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13538 | Cross product as result of projections
The cross product between two vectors in $\Bbb{R}^3$ (call them a and b) is denoted a $\times$ b and the result is a vector in $\Bbb{R}^3$ orthogonal to the first two. There are a variety of ways of computing this resultant vector. One way in particular is known from the symbolic... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13539 | ## calc 3, centroids
consider the solid region W=[1,-1]x[-2,2]x[-1,1] in R3
Compute the centroid/center of mass when W is equipped with the density function p(x,y,z)=2
and also when p(x,y,z)=x^2
for both of these i got (0,0,0)...is that right? |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13540 | +0
0
144
5
+941
Aug 12, 2020
#1
0
We can use the sine law to find P1 P2
By the sine law, P1 P2 = sin 15. We can also find P1 P_3 = sin 60, P1 P4 = sin 90, etc.
So (P1 P2)^2 + (P1 P3)^2 + … + (P11 P12)^2 = 12 (sin 15)^2 + 12 (sin 30)^2 + 12 (sin 45)^2 + … + 12 (sin 90)^2 = 42.
Aug 12, 2020
#2
+941
0
Sorry but t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13541 | # Applications of parity formula on connected planar graph
I've been offered the adhering to trouble as homework:
A graph is drawn in the plane and has 78 faces, all of them triangles.
Prove the outer face is not a 19-gon.
We are additionally offered a tip to make use of the formula:|V|-|E|npls|F|= 2 (for planar, a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13542 | # Chapter 13 - Newton's Theory of Gravity - Exercises and Problems - Page 353: 15
On Mars, the astronaut can throw the ball to a height of 39.4 meters.
#### Work Step by Step
We can find the acceleration due to gravity $g_m$ on the surface of Mars. $g_m = \frac{G~M_m}{R_m^2}$ $g_m = \frac{(6.67\times 10^{-11}~m^3/kg... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13543 | # EFX Allocations: Simplifications and Improvements
The existence of EFX allocations is a fundamental open problem in discrete fair division. Given a set of agents and indivisible goods, the goal is to determine the existence of an allocation where no agent envies another following the removal of any single good from ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13544 | # Special case of Forced Harmonic Oscillator
$$\frac{d^2l}{dt^2} + c \frac{dl}{dt} +k= F_0\sqrt{1-l^2}$$
Either a closed form or something like given initial conditions, the max value of $l$. For small $l$, this boils down to simple step response. But for larger variations it doesn't work.
I'm looking for a solution... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13545 | ## Algebraic & Geometric Topology
### Quadratic forms classify products on quotient ring spectra
#### Abstract
We construct a free and transitive action of the group of bilinear forms $Bil(I∕I2[1])$ on the set of $R$–products on $F$, a regular quotient of an even $E∞$–ring spectrum $R$ with $F∗≅R∗∕I$. We show that t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13546 | ## 9.1 Overview
We begin our description of DLMs with a static regression model, wherein the $$i^{th}$$ observation (response variable) is a linear function of an intercept, predictor variable(s), and a random error term. For example, if we had one predictor variable ($$f$$), we could write the model as $$$\tag{9.1} y... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13547 | # Tag Info
Define $\gamma = 1/\beta$, $P=\textrm{precision}$, and $R=\textrm{recall}$. Then $$F_{\beta} = (1 + 1/\gamma^2)\cdot \frac{PR}{P/\gamma^2 + R} = (\gamma^2 + 1) \cdot \frac{PR}{\gamma^2R + P}$$, which is the $F_\gamma$ measure with the roles of $P$ and $R$ switched. So the same reasoning that shows precision... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13548 | # Asymptotic formula for Tate--Shafarevich groups of $p$-supersingular elliptic curves over anticyclotomic extensions
### Antonio Lei (Universite Laval)
Thu Mar 17, 22:00-23:00 (6 months ago)
Abstract: Let $p\ge 5$ be a prime number and $E/\mathbf{Q}$ an elliptic curve with good supersingular reduction at $p$. Under... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13549 | # how to prove if $\lim_{n \rightarrow \infty}a_n=A$, then $\lim_{n \rightarrow \infty}\frac{a_1+…+a_n}{n}=A$? [duplicate]
I know this is a duplicate but I can't understand any of the duplicates.
$\lim_{n \rightarrow \infty} a_n = A$, how to prove if $\lim_{n \rightarrow \infty}a_n=A$, then $\lim_{n \rightarrow \inft... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13550 | ×
# Strange functions
Let $$f_r(x)= x(x-1)(x-2)(x-3) + r$$, where $$r$$ is a real number. Then:
• Does $$f_r(x)$$ have a real root for every value of $$r$$?
• Does $$f_r(x)$$ have a repeated root for finitely many values of $$r$$?
Note by Paramjit Singh
2 years, 8 months ago |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_13551 | # Sphere packings with antipodal (unequal) spheres
Let $\|\cdot\|_2$ denote the Euclidean norm, let $\langle \cdot, \cdot\rangle$ denote the standard dot product, and let $\mathcal{S}^{d-1} = \{\mathbf{x} \in \mathbb{R}^d: \|\mathbf{x}\|_2 = 1\}$ denote the Euclidean unit sphere in $\mathbb{R}^d$. For constants $\alph... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20496 | # Tag Info
7
A is acting as a square-root oracle in that protocol. We can use that oracle to factor $n$ and break the scheme. Suppose you are an attacker that wants to impersonate A. You: Pick a random $m$; Send $m^2$ to A; Compute $p = \gcd(m_1 - m, n)$, thus factoring $n$. This works with probability $1/2$ for each... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20497 | Field
定義
$\mathbf{F}: S \rightarrow \mathbb{R}^n$
Vector fields are one kind of tensor field.
???
$\mathbf{F}(\mathbf{x}) = \mathbf{0}$
$(f \mathbf{F})(\mathbf{x}) = f(\mathbf{x}) \mathbf{F}(\mathbf{x})$
$\mathbf{(F+G)}(\mathbf{x}) = \mathbf{F}(\mathbf{x}) + \mathbf{G}(\mathbf{x})$
張量場
As a tensor is a general... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20498 | # What is the value of $E$ (electric field, in $\rm V/m$) in the equation $E=F/Q$?
Is there a constant value for $$E$$, in terms of $$E=F/Q$$, in units of $$V/m$$ or $$N/C$$, assuming the distance is negligible? (Virtually touching?)
What is the value of E in E=F/Q if the Q is the elementary charge; say an electron, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20499 | Chapter 83
#### Use the following for high yield facts:
• Less then one percent of the body's calcium is in the circulation.
• Only the ionized form of circulating calcium is physiologically active.
• Parathyroid hormone (PTH), vitamin D, and calcitonin are the hormones that control calcium levels.
• IV calcium ca... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20500 | # Is Mathematics Inevitable?: A Miscellany
### Underwood Dudley, Editor
Catalog Code: IMI
Print ISBN: 978-0-88385-566-9
340 pp., Hardbound, 2008
List Price: $57.95 MAA Member:$46.50
Series: Spectrum
This is a collection of gems from the literature of mathematics that shine as brightly today as when they first appear... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20501 | # zbMATH — the first resource for mathematics
Stability and stability domains analysis for nonlinear differential- difference equations. (English) Zbl 0807.34089
If a time-delay system $\dot x(t)= A(t,x(t),x(t-\tau(t))) x(t)+ B(t,x(t),x(t-\tau(t)) x(t- \tau(t)))\tag{1}$ and a vector norm $$p$$ are given, then an overv... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20502 | Home > Standard Error > Linear Fit Standard Error
# Linear Fit Standard Error
## Contents
Retrieved 2016-10-17. ^ Seltman, Howard J. (2008-09-08). Note that the inner set of confidence bands widens more in relative terms at the far left and far right than does the outer set of confidence bands. To illustrate this, l... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20503 | # Second intriangle similar to outer triangle
$$ABC$$ is a triangle. $$A_1B_1C_1$$ is a tiangle inside $$ABC$$ such that $$A_1$$ divides $$BC$$, $$B_1$$ divdes $$CA$$ and $$C_1$$ divides $$AB$$ in $$1:2$$ ratio. A further trianle $$A_2B_2C_2$$ is constructed such that $$A_2$$ divides $$B_1C_1$$, $$B_2$$ divdes $$C_1A_... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20504 | # Critical point of Mabuchi energy functional has zero scalar curvature
I am currently reading the proof of convergence of Kähler-Ricci flow in the case $c_1(M)=0$ from Song, Weinkove. On page 45 he defines the term Mabuchi's $K$-energy functional:
$$\frac{d}{dt}\mathrm{Mab}_{\omega_0}(\phi_t)=-\int_M\dot{\phi}_tR_{\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20505 | How do you decide whether the graphs of the two equations are parallel lines: y=2x-1, y=-2x+1?
Dec 5, 2016
Not parallel
Explanation:
Lines are parallel, if their slope is same.
Slope of y= 2x-1 is 2
Slope of y= -2x+1 is -2.
The slopes are not same (not equal), hence lines are not parallel
Dec 5, 2016
Both lines... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20506 | Mathematics
# A candy machine is filled with candy. The weight of the candy can differ from the desired 84 ounce weight by no more than 0.5 ounces. Solve the absolute value equation given in order to find the heaviest and lightest acceptable weights for the candy machine. |x – 84| = 0.5
#### Quan336
4 years ago
whe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20507 | ###### Example3.2.6
Solve for $$x$$ in $$-2-2(2x+1)\gt4-(3-x)\text{.}$$ Write the solution set in both set-builder notation and interval notation.
Solution
in-context |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20508 | How do you solve -55 - 4n =13?
Jan 11, 2016
color(blue)(n = -17
Explanation:
$- 55 - 4 n = 13$
$- 55 - 13 = 4 n$
$- 68 = 4 n$
$n = - \frac{68}{4}$
color(blue)(n = -17 |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20509 | Classical proof that well-ordering principle is equivalent to complete induction [duplicate]
I want to prove that:
Well ordering principle ⟺ Complete Induction.
I am interested in both directions of the implication. That is, that if every non-empty set contains a least element then if a property P holds for all natu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20510 | ### Home > MC2 > Chapter 6 > Lesson 6.2.7 > Problem6-137
6-137.
Make a table and a graph for the following rule: $y = 3x-2$.
Fill in a table with a few calculated points from the expression.
Graph the points.
Sketch a line that intersects all the points from the table.
1. Explain how you know that there are more ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20511 | ## March 10, 2017
### The Logic of Space
#### Posted by Mike Shulman
Mathieu Anel and Gabriel Catren are editing a book called New Spaces for Mathematics and Physics, about all different kinds of notions of “space” and their applications. Among other things, there are chapters about smooth spaces, $\infty$-groupoids... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2656 | # Transpose of inverse vs inverse of transpose
Is the transpose of the inverse of a square matrix the same as the inverse of the transpose of that same matrix?
• This holds if the underlying ring is commutative as the answers show. If the underlying ring is not commutative, it might fail. Jan 2, 2017 at 16:52
• By wh... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2657 | # Why is zero times vector of reals not zero?
Using the following global assumptions
\$Assumptions = Element[n, Integers] && Element[a, Vectors[n, Reals]] && b == 0 && Element[c, Reals]
I assumed that Refine[a.b]
returns 0. Instead, it returns [a.0], which again according to my knowledge should be a vector of n zer... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2658 | # Why are integrals called integrals?
What is the historical background for this term?
I cannot quite see what is integral about an integral, even if we go back to the viewing it as the area under a curve. It seems to me a strange choice of word.
• An integral gives a measure of the whole space. – Doug Spoonwood May... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2659 | # Evaluate integral by using spherical coordinates
030sqrt(9-x2)sqrt(x2+y2)sqrt(18-x2-y2) (x2+y2+z2)dzdxdy
x=$\rho$sin$\varphi$cosθ
y=$\rho$sin$\varphi$sinθ
z=$\rho$cos$\varphi$
Change the integrand to $\rho$ and integrate wrt d$\rho$dθd$\varphi$
I don't know how to find the limits of integration. Normally I would ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2660 | # Chapter 12 Sequences and Series - 12.1 Define and Use Sequences and Series - 12.1 Exercises - Skill Practice - Page 798: 18
n-th term:$\quad a_{n}=n^{3}+1$ The next term is $\quad a_{5}=126$
#### Work Step by Step
Each term of the given sequence is close to the corresponding terms of $1,\ 8$, $27$, $64$, $...\qqua... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2661 | Examine the consistency of the system of equations: $\quad 5x -y +4z = 5$ $\quad2x + 3y + 5z= 2$ $\quad 5x - 2y + 6z = -1$
Toolbox:
• (i)A matrix is said to be singular if |A|$\neq 0$.
• (ii)If A is a non-singular matrix such that
• AX=B.
• then $X=A^{-1}X$
• Using this we can solve the system of equation which has un... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2662 | # Operator Norm and Sequences ... Another Question ... Browder, Proposition 8.7 ...
#### Peter
##### Well-known member
MHB Site Helper
I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...
I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2663 | ## Seems quite hard
Prove that $\forall p$ prime and $r\in\mathbb{Z}$ $\exists n\in\mathbb{N}$ for which $\binom{2n}{n}\equiv r\pmod{p}$. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2664 | # If $\vec {a}$ and $\vec {b}$ are two vectors, such that $\vec {a}.\vec {b}\le 0$ and $|\vec {a}\times \vec {b}$ then
If $\vec {a}$ and $\vec {b}$ are two vectors, such that $\vec {a}.\vec {b}\le 0$ and $|\vec {a}\times \vec {b}|$ then find the angle between $\vec {a}$ and $\vec {b}$
My Attempt:
Let $\theta$ be the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2665 | Welcome to mathimatikoi.org forum; Enjoy your visit here.
## Inequality
General Mathematics
Riemann
Articles: 0
Posts: 170
Joined: Sat Nov 14, 2015 6:32 am
Location: Melbourne, Australia
### Inequality
Let $x, y,z >0$ satisfying $x+y+z=1$. Prove that
$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} \geq \sqrt{\frac{3}{xyz... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2666 | # Revision history [back]
With a little bit of playing with the code I found that the best way to solve this problem analytically is by specifying prices and income in the var() command. the code I've used is:
x, y, l, p, q, R= var('x, y, l, p, q, R') U = x^7/10 * y^3/10; U m = px+qy; m solve(m == R, y) L = U - l * (... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2667 | # Distribution of ‘unmixed’ parts based on order of the mix
Suppose I have paired observations drawn i.i.d. as $X_i \sim \mathcal{N}\left(0,\sigma_x^2\right), Y_i \sim \mathcal{N}\left(0,\sigma_y^2\right),$ for $i=1,2,\ldots,n$. Let $Z_i = X_i + Y_i,$ and denote by $Z_{i_j}$ the $j$th largest observed value of $Z$. Wh... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2668 | # The count in a bacteria culture was 700 after 20 minutes and 1000 after 40 minutes. What was the initial size of the culture?
##### 2 Answers
Jun 16, 2017
490 microorganisms.
#### Explanation:
I will assume exponential growth for bacteria. This means that we can model the growth with an exponential function:
$f ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2669 |
# Precalculus Review
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
Exercise $$\PageIndex{1}$$
Write down an equation of a line passing through the points $$(1,2)$$ and $$(3,5)$$.
Add answer tex... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2670 | # Revision history of "Science:Math Exam Resources/Courses/MATH152/April 2015/Question B 2 (b)/Solution 2"
• (cur | prev) 20:05, 8 March 2018 . . (837 bytes) (+837). . (Created page with "Let $\lambda_1, \lambda_2, \lambda_3$ denote the three roots of the characteristic polynomial of $A$ (counted with multiplicity)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2671 | # Probability¶
## Overview¶
### Probability Space¶
A probability space: $$(\Omega, \mathcal{F}, P)$$ where
• $$\Omega$$ is the sample space (set of all possible outcomes)
• $$\sigma$$-algebra $$\mathcal{F}$$ is a set of events where each event is an outcome
• $$P$$ is a function giving the probability of an event... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22288 | On the 𝑝-closedness and 𝑝-nilpotency of finite groups
Shuqin Dong , Hongfei Pan and Long Miao
From the journal Journal of Group Theory
Abstract
Let acd(G) and acs(G) denote the average irreducible character degree and the average conjugacy class size, respectively, of a finite group G. The object of this paper is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22289 | # TRIGONOMETRIC FUNCTIONS
In a right angled triangle ABC, ∠CAB = A and ∠BCA = 90° = π/2. AC is the base, BC the altitude and AB is the hypotenuse.
We refer to the base as the adjacent side and to the altitude as the opposite side. There are six trigonometric ratios, also called trigonometric functions or circular fun... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22290 | # 2011 AMC 10A Problems/Problem 22
## Problem 22
Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There are $6$ colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?
$\textbf{(A)}\ 2520\qquad\textbf{(B)}\ 2880\qquad\textbf{(C)}\ 3... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22291 | # Wu's inequality
### Solution 1
Pick point $F\;$ and form triangles with $F\;$ as a common vertex, sides $\{x,y\},\;$ $\{y,z\},\;$ and $\{z,x\},\;$ and angle of $120^{\circ}\;$ between each pair:
Let $[X]\;$ denote the area of shape $X.\;$ By the sine formula for the area of triangle,
\displaystyle\begin{align} [\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22292 | # Showing dual space of a normed space is a normed space
Let $X$ be a Normed Linear Space. The dual space $X^*$ of $X$ is the set of all bounded linear functionals on $X$. It is a normed linear space with the norm $\Vert\varphi\Vert$. (according to notes).
I can show the triangle inequality is true.
Trying to show $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22293 | Change search
Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22294 | EN|RU Volume 18, No 1, 2011, P. 77-84 UDC 519.87 E. A. Monakhova On an extremal family of circulant networks Abstract: We consider the problem of maximization of the number of nodes of circulant networks for a given degree and diameter. The estimate of the diameter of graphs of the best known extremal family of circula... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22295 | # PlanetPhysics/Direction Cosine Matrix
A direction cosine matrix (DCM) is a transformation matrix that transforms one coordinate reference frame to another. If we extend the concept of how the three dimensional direction cosines locate a vector, then the DCM locates three unit vectors that describe a coordinate refer... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22296 | # Difference between Root[] and Solve[]
I am trying to solve the cubic solution, and I could not understand how these two codes are different. One is using Root, and one is using Solve.
Using Root
Solve[
Root[a + b #1 + #1^3 &, 2] == 1/Root[a + b #1 + #1^3 &, 2]
, b]
Using Solve
Solve[
Solve[a + b x + x^3 == 0, x... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22297 | # What is a symmetric monoidal $(\infty,n)$-category?
This question arose from reading Jacob Lurie's "Classification of topological field theories" paper. In that paper, he uses complete $n$-fold Segal spaces as a model for $(\infty,n)$-categories, but he "glosses over" the question what a symmetric monoidal $(\infty,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22298 | # Define the relation $\sim$on $\mathbb{Z}$ by $a \sim b$ if and only if $5a \equiv 2b \pmod{3}$
Define the relation $\sim$ on $\mathbb{Z}$ by $a \sim b$ if and only if $5a \equiv 2b \pmod{3}$.
Prove that $\sim$ is an equivalence relation on $\mathbb{Z}$. Identify the distinct equivalence classes on $\mathbb{Z}/\sim$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22299 | # zbMATH — the first resource for mathematics
Test of fit for Marshall-Olkin distributions with applications. (English) Zbl 1122.62054
Summary: A. W. Marshall and J. Olkin [J. Am. Stat. Assoc. 62, 30–44 (1967; Zbl 0147.38106)] introduced a bivariate distribution with exponential marginals, which generalizes the simple... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22300 | ### Group Theory
In the last quiz, we looked at symmetries of shapes, which are rigid transformations that send the shape to itself. At the end of the quiz, we saw that we could combine symmetries by doing one after the other, and thus form a kind of “multiplication” on the symmetries.
In this quiz, we’ll explore thi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22301 | # Probabilistic Representations of Solutions of the Forward Equations
Rajeev, B and Thangavelu, S (2008) Probabilistic Representations of Solutions of the Forward Equations. In: Potential Analysis, 28 (2). pp. 139-162.
PDF fulltext.pdf Restricted to Registered users only Download (453Kb) | Request a copy
## Abstrac... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22302 |
## 3.8 Reflection principle
Some of this material is in the chapter of [Kunen] called “Easy consistency proofs”.
Let $\phi (x_1, \ldots , x_ n)$ be a formula of set theory. Let us use the convention that this notation implies that all the free variables in $\phi$ occur among $x_1, \ldots , x_ n$. Let $M$ be a set. T... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_22303 | # Diffeomorphic Level sets Of Manifolds
Let $F:M^n \to \mathbb{R}$ be a smooth function admitting only regular values and $(M,g)$ a smooth connected riemannian manifold.
I know that the vector field $\frac{\operatorname{grad}F}{||\operatorname{grad}F||^2}$ defined my means of the metric $g$ is a smooth one.
How can ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20896 | • Corpus ID: 221172698
# Operators coming from ring schemes
@article{Gogolok2020OperatorsCF,
title={Operators coming from ring schemes},
author={Jakub Gogolok and Piotr Kowalski},
journal={arXiv: Logic},
year={2020}
}
• Published 19 August 2020
• Mathematics
• arXiv: Logic
We introduce the notion of a coordinate $\ma... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20897 | ## Identity involving $\sigma(i·j)$
Arithmetic, algebra, number theory, sequence and series, analysis, ...
castrate
Posts: 17
Joined: Mon Aug 19, 2019 2:34 pm
### Identity involving $\sigma(i·j)$
As far as I know, there is an identity involving d(i·j), where d(n) denotes the number of divisors of n:
$d(i·j)=\sum_{x|... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20898 | # How does a conformal mapping preserve angles in hyperbolic geometry?
Suppose I have a sector $D = \{0 < \arg z < \alpha\}$ where $\alpha \leq 2\pi$. If I apply the function $w = \frac{\zeta - i}{\zeta + i}$ from the upper half plane to the unit disc ($\zeta = z^{\frac{\pi}{\alpha}}$), I get that the vertex of the se... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20899 | # The length of the potentiometer wire is l. A cell of emf E is balanced at length $\large\frac{l}{3}$ from the positive end of the wire. If the length of the wire is increased by $\large\frac{l}{2}$, at what distance will the same cell give a balance point
$\begin {array} {1 1} (A)\;\large\frac{l}{3} & \quad (B)\;\lar... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20900 | # Application of maxima and minima
## Practicle application of maxima and minima SlideShare
Maxima & Minima for IIT JEE Preparation Tips. Maxima and minima have practical applications in the fields of engineering, finance, Finding Minima & Maxima: Problems & Explanation Related Study Materials., Maxima and minima mc-... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20901 | Comment
Share
Q)
# If D,E,F are the mid-points of sides BC,CA and AB respectivelyof $\Delta ABC$,then the ratio of the areas of triangles DEF and ABC is
$\begin{array}{1 1}1 : 4\\1 : 2\\2 : 3\\4 : 5\end{array}$
$FE=\large\frac{1}{2}$$BC$
=> $\large\frac{FD}{AC} =\large\frac{1}{2}$
$\large\frac{FE}{BC} = \frac{ED}{AB... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20902 | # Tagged: stabilizer
## Problem 359
Let $P$ be a $p$-group acting on a finite set $X$.
Let
$X^P=\{ x \in X \mid g\cdot x=x \text{ for all } g\in P \}.$
The prove that
$|X^P|\equiv |X| \pmod{p}.$
## Problem 108
Let $\F_p$ be the finite field of $p$ elements, where $p$ is a prime number.
Let $G_n=\GL_n(\F_p)$ be the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20903 | # Finding elementary matrices E1 and E2 such that: B = E1E2A, confused!
1. Oct 30, 2005
### mr_coffee
Hello everyone, i've been searching in this book forever to find an example but no luck. My problem states:
Find two Elementary matrices E1 and E2 such that $$B = E_2E_1A$$
A =
2 3
-1 8
B =
1 11
3 -24
Can someone ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20904 | # jzhao.xyz
.
\_.
/
# Descartes' Meditations
Last updated January 12, 2022
## First Meditation → skeptical doubts
• descartes wants to find a foundation of knowledge that will still stand strong even after doubting the most basic facts about the world
• everything descartes has accepted has true has come through... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20905 | # Definition:Endorelation/General Definition
## Definition
An $n$-ary relation $\RR$ on a cartesian space $S^n$ is an $n$-ary endorelation on $S$:
$\RR = \struct {S, S, \ldots, S, R}$
where $R \subseteq S^n$.
## Also known as
The term endorelation is rarely seen. Once it is established that the domain and codomai... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20906 | • Archived
skeeter
I was helping someone with the following problem...
A projectile is launched from point A at an angle of 25 degrees relative to the horizontal, with initial velocity = 60 ft/s.
Determine the speed of the projectile along its trajectory where its radius of curvature is 3/4 of its radius of curvature ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20907 | # A question dealing with the convexity of functions involving the absolute value
Just beginning to learn convex analysis and optimization, I have some inquiries to make with regard to the absolute value function $f(x)= |x|$. This function is clearly convex, but since we know that $|x|= \max\{x,-x\}$, does this make $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20908 | # Nauseated
+8
388
8
+1037
### Congratulations Alan on Your Moderator’s Star!
Nauseated May 3, 2015
+13
198
1
+1037
### Merry Christmas and Happy Holidays Melody, CPhill , and . . . ah . . . ah . . . Whoever the third answerer is. Alan too.
Nauseated Dec 25, 2014
0
213
3
+1037
### Rosala!! Please! Please come o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20909 | # Harmonic function.
The function $f : \mathbb{R}^n \rightarrow \mathbb{R}$ given by $f(x) = \|x\|^{2-n}$, where $\|~\|$ denotes the Euclidean norm, is harmonic. This is just a simple computation.
My question is: why should we expect this function to be harmonic? In other words, if someone asked you whether this func... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20910 | # DECIDABLE MODELS OF ω-STABLE THEORIES
@article{Andrews2014DECIDABLEMO,
title={DECIDABLE MODELS OF $\omega$-STABLE THEORIES},
author={Uri Andrews},
journal={The Journal of Symbolic Logic},
year={2014},
volume={79},
pages={186 - 192}
}
• U. Andrews
• Published 1 March 2014
• Mathematics
• The Journal of Symbolic Logic... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20911 | say $\displaystyle a_n=(0.999)^{n^4}$, what is the limit as $n$ goes to $\infty$?
say $\displaystyle a_n=(0.999)^{n^4}$, what is the limit as $n$ goes to $\infty$?
$\displaystyle\lim_{n\to\infty}\left(\frac{999}{100 0}\right)^{n^4}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3056 | # ACT Math : How to multiply complex numbers
## Example Questions
### Example Question #38 : Squaring / Square Roots / Radicals
The solution of is the set of all real numbers such that:
Explanation:
Square both sides of the equation:
Then Solve for x:
Therefore,
### Example Question #852 : Algebra
What is th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3057 | #### Vol. 317, No. 2, 2022
Recent Issues Vol. 321: 1 2 Vol. 320: 1 2 Vol. 319: 1 2 Vol. 318: 1 2 Vol. 317: 1 2 Vol. 316: 1 2 Vol. 315: 1 2 Vol. 314: 1 2 Online Archive Volume: Issue:
The Journal Subscriptions Editorial Board Officers Contacts Submission Guidelines Submission Form Policies for Authors ISSN: 1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3058 | # Dyck language
The importance of using parentheses can be illustrated by looking at the following expression:
$((2-1)\cdot(-(1+2))\cdot 4)\div((1+2)\cdot 2)$
There is no ambiguity in computing the result, which is $-2$. If we remove all the parentheses in the expression, we get
$2-1\cdot-1+2\cdot 4\div 1+2\cdot ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3059 | # Method and system for mutual coherent synthetic aperture radiometry
Imported: 21 Feb '17 | Published: 01 Mar '05
Larry K. Lam
USPTO - Utility Patents
## Abstract
Method and system for synthetic aperture radiometry not limited by the Van Cittert-Zernike theorem and the quasi-monochromatic assumption. A radiometer... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3060 | # Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae
## Fundamenta Mathematicae
• Some algebraic equivalent forms of $\mathbb{R} \subseteq L$
• Reducts of Hrushovski’s constructions of a higher geometrical arity
• $L_p$ regular sparse hypergraphs: box norms
• Small mad families whose hyperspaces of their Isbell... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3061 | 1. Sequencs...
The sequence 7, 12, 17, 22... can be generalized with the expression 5n+2. What is another expression that generalizes this sequence?
2. Originally Posted by MATNTRNG
The sequence 7, 12, 17, 22... can be generalized with the expression 5n+2. What is another expression that generalizes this sequence?
$a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3062 | The Composition of Injective, Surjective, and Bijective Functions
# The Composition of Injective, Surjective, and Bijective Functions
Theorem 1: If $f : A \to B$ and $g : B \to C$ are injective then $g \circ f : A \to C$ is injective.
• Proof: Let $x, y \in A$ and suppose that $(g \circ f)(x) = (g \circ f)(y)$. Then... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3063 | # What is the Q function and what is the V function in reinforcement learning?
It seems to me that the $V$ function can be easily expressed by the $Q$ function and thus the $V$ function seems to be superfluous to me. However, I'm new to reinforcement learning so I guess I got something wrong.
## Definitions
Q- and V... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3064 | # Inverse of (1+x) ln(1+x) - x
Define g(x) = (1+x) ln(1+x) - x. One can check that g is strictly monotonically increasing for x>=0 by checking its derivative is ln(1+x). So g is invertible and its inverse is also strictly monotically increasing.
Is there an explicit closed form for its inverse?
With a page of calcul... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3065 | NEWS@SKY (Science&Space News)
Home To Survive in the Universe
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Why to Inhabit Top Contributors Astro Photo The Collection Forum Blog New! FAQ Login
# HD 20468
Contents
### Images
DSS ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3066 | # rotational energy levels
Posted on Ene 1, 2021
The spherical harmonics called $$Y_J^{m_J}$$ are functions whose probability $$|Y_J^{m_J}|^2$$ has the well known shapes of the s, p and d orbitals etc learned in general chemistry. So, although the internuclear axis is not always aligned with the z-axis, the probabili... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3067 | # History of deletion-contraction formula
The following is known as deletion-contraction formula:
Assume $\Gamma$ is a connectted graph with edge $\rho$ then $$t(\Gamma)=t(\Gamma\backslash\rho)+t(\Gamma/\rho),$$ where $\Gamma\backslash\rho$ is $\Gamma$ with the edge $\rho$ removed and $\Gamma/\rho$ obtained from $\Ga... |
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