instruction stringlengths 1 25.7k | response stringlengths 0 1.42k |
|---|---|
what are esr levels | For men above 50 yrs the normal ESR value is below 20, under 50 yrs the normal ESR value is below 15. For women over 50 yrs the normal ESR value is below 30. |
Factor the ideal (35) into a product of prime ideals in the ring of integers of $\mathbb{Q}(\sqrt[3]{2})$. | (35)= (5,\;\alpha-3)\; (5,\;\alpha^{2}-2\alpha-1)\; (7) |
emancipatory pedagogy definition | It refers to a process of teaching that aims to free the teacher and the student from the mental restrictions imposed by the mainstream culture on the way they perceive things. |
Let \( x \) and \( y \) be functions defined on a simply connected (open or closed) portion of the surface of a (unit) sphere. Consider the following system of PDEs:
\[
\|\nabla x\|^2 = \|\nabla y\|^2 = \| \nabla x \times \nabla y \|^2.
\]
Are there non-constant solutions for such a system? Any ideas about how to reduc... | No nonconstant solutions. |
Solve the equation \(\dfrac{1}{\cos x\cos 2x}+\dfrac{1}{\cos 2x\cos 3x}+\dfrac{1}{\cos 3x\cos 4x}=0\). | \;x=\frac{\pi}{3}+n\pi\quad\text{or}\quad x=\frac{2\pi}{3}+n\pi,\qquad n\in\mathbb Z\; |
what is the largest size package | A large package is a parcel or box whose length plus girth is over 84 inches and less than or equal to 165 inches. Length is the longest side of a package. Girth is the distance around the 2 smaller sides of a package. |
Why did baseball catch on so well in Japan, while no other Asian (or non-U.S.) countries embrace it the way? | Just to counter, Baseball is very popular in Korea which has a large and very active professional league. |
where is prince edward island? | St. Lawrence, west of Cape Breton Island, north of the Nova Scotia peninsula, and east of New Brunswick. |
Who directed the Godfather trilogy of films? | Francis Ford Coppola |
On what day were nine people killed in the Emanuel African Methodist Episcopal Church? | June 17, 2015 |
How does a caller to 911 from California able to give an address from Kansas during the swatting incident? Are 911 operators not local? | It is very, very easy in this day and age to use software to make a phone call from either an anonymous number or spoofing a number. Even an anonymous call would have to be taken seriously by a 911 operator since obviously they can't risk the chance of not acting on a reported hostage situation. 911 operators are locat... |
should a default credit account show settled or balance of £0 | No |
Find the expected value of \((e^X - 1)^\alpha\) where \(X\) follows a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), and \(\alpha \in [0,1]\). | \;
\mathbb{E}\big[(e^{X}-1)_{+}^{\alpha}\big]
=\sum_{k=0}^{\infty}(-1)^{k}\binom{\alpha}{k}\,
\exp\!\Big(\mu(\alpha-k)+\tfrac12\sigma^{2}(\alpha-k)^{2}\Big)\,
\Phi\!\Big(\frac{\mu+\sigma^{2}(\alpha-k)}{\sigma}\Big)
\; |
Given a person can do 4 'hard' tasks or 10 'easy' tasks per day, calculate the total number of days required to complete 21 'hard' tasks and 15 'easy' tasks, considering the possibility of mixing task types on the same day. | 7 |
"What weapon is used in Tchaikovsky's ""1812 Overture""?" | Cannon |
Which chemical element comes next in order of atomic number: hydrogen, helium, lithium, ............? | BERYLLIUM |
what kind of whales are in puerto vallarta | The Humpback Whales are in Puerto Vallarta. |
Compute the number of different ways to draw a diagonal line on every face of a regular cube, considering the cube's rotational symmetries. | 8 |
Oral Rehydration Therapy question | > couldn't give people plain water and a capsule with a small amount of electrolytes. salt pills can be irritating, but you're on the right track. But the right track is even easier. You can make the [ideal rehydration fluid](_URL_0_) in your kitchen. > this thought occurred to me after the thousandth time of sipping ... |
Let $K$ be a finite field with $p$ elements. Let $F \in K[x,y]$ be such that (i) $\deg(F) \leq \sqrt{2p}$ and (ii) the curves $F(x,y)=0$, $F(2x,y)=0$, and $F(4x,y)=0$ intersect at at least $(1-\epsilon)p$ points $(x,y)$ in $\mathbb{A}^2(K)$ or $\mathbb{A}^2(\overline{K})$. What can you conclude about $F$? | \;F(x,y)=x\,G(x,y)\ \text{or}\ F(x,y)=(y-\beta)\,G(x,y)\ \text{for some }\beta\in K\; |
Given a labeled cycle graph with \( n \) vertices \( C_n \) and parameters \( a_1, \ldots, a_k \) such that \( a_1 + \cdots + a_k = n \), how many ways can \( C_n \) be decomposed into consecutive paths of lengths \( a_1, \ldots, a_k \)? | \,n\, |
how old is claire ryann | 3 years |
What is the subject of the latest PBS documentary by Ken Burns, which will premiere on public television later this month? | The National Parks |
Simplify the function $f(\mathbf{x})=\mathbf{x}-\mathbf{v}(\mathbf{x}^TD\mathbf{v})$ to the form $f(\mathbf{x})=(I-A)\mathbf{x}$, where $\mathbf{x}$ and $\mathbf{v}$ are column-vectors and $D$ is a matrix. | \( A = \mathbf{v}\mathbf{v}^TD^T \) |
Find a function \( f(x) \) such that:
- \( f(1) = 1 \) (1! terms)
- \( f(2) = a - b \) (2! terms)
- \( f(3) = a^2b - a^2c - b^2a + b^2c + c^2a - c^2b \) (3! terms)
- \( f(4) = a^3b^2c - a^3b^2d - a^3c^2b + a^3c^2d + a^3d^2b - a^3d^2c - b^3a^2c + b^3a^2d + b^3c^2a - b^3c^2d - b^3d^2a + b^3d^2c + c^3a^2b - c^3a^2d - c^3b... | \,f(n)=\prod_{1\le i<j\le n}\bigl(L_{i}-L_{j}\bigr)\, |
Given the linear transformation \( T: \mathbb{R}^2[x] \rightarrow \mathbb{R}^2[x] \) defined by:
- \( T(1) = 1 - 3x^2 \)
- \( T(1 + x) = a + 1 + 4x \)
- \( T(1 + x^2) = -2x^2 - 2 \)
Let \( A = \begin{bmatrix} 1 & 6 & -3 \\ 0 & 4 & 0 \\ -3 & 6 & b \end{bmatrix} \).
Find the values of \( a \) and \( b \) for which ther... | \( a = 3 \), \( b = 1 \) |
is vancouver in united states | Yes |
Solve the congruence:
\[ x \equiv -3 \pmod{289} \]
\[ x \equiv 53424 \pmod{190969} \] | 1772145 |
When i allready have to pee, why do i instantly have to pee even harder when i drink something? | Your brain is telling your body to make room. |
The British hit parade was first published in 1952, what was the first record to be number one? | HERE IN MY HEART |
If water in lungs is a dangerous scenario, would it be bad to breathe in water vapor? | There is always water vapor present in the air we breathe [(humidity)](_URL_0_) so no, it is not bad to breathe water vapor. edit: formatting |
Given the function \( L(t) = \frac{\ln(t+1)}{t+1} \) for \( 0 \leq t \leq 5 \), at what age \( t \) is a child's learning ability increasing most rapidly? | t=0\ \text{years (at birth)} |
Are stars the only main heat source in the universe? | Not an expert, but the Earth's core does not recieve energy from our sun or any other star for that matter and it is significantly hotter than the surface or other things in space. |
is stacee jaxx a real person | No |
when traveling somewhere, why does time seem to go by faster when returning? | If you're going somewhere new then you're unfamiliar with the landscape and landmarks on the way to your destination and can't properly gauge the distance it takes to arrive. As you're coming back you notice significant features between point A and B. This creates progression feedback, sort of like how in a video game ... |
How does a solid state drive work? | The older generations of disk drives painted the surface of a disk or set of disks with a material that could accept a magnetic signal and keep it so it could be read later. You spun the disk and a read-write head interacted with its surface. Solid state drives don't store in magnetic form and they don't have a spinnin... |
how much sugar in one teaspoon honey | A teaspoon contains 6 grams of sugar. |
What is the probability of randomly picking 6 cards from a set of cards with values $2, 3, 4, 5, 6, 7, 8$ (five cards of each value) such that their values sum to less than 20? Cards are drawn without replacement. | \(\frac{2763}{324632}\) |
The Hotel Employees and Restaurant Employees Union (HERE) was a United States labor union representing workers of the hospitality industry, formed in which year, other major employers that contracted with this union included several large casinos, such as Wynn Resorts? | 1891 |
Solve the recurrence relation \( T(n) = T\left(\lceil\frac{n}{\sqrt{2}}\rceil + 1\right) + 1 \) with the initial condition \( T(n) = 1 \) for \( n \leq 8 \). | \( T(n) \approx 2\log_2 n \) |
Let \( k \geq 2 \) and \( N_1, N_2, \ldots, N_k \) be positive integers. Define \( S = \{(a_1, a_2, \ldots, a_k) \in \mathbb{Z}^k : 1 \leq a_i \leq N_i \} \) and \( A = \{1, 2, \ldots, \prod_{i=1}^{k} N_i \} \). Given a bijective map \( f: S \to A \), a change is defined as choosing any two \( s_1, s_2 \in S \) that di... | \( M = \left(\prod_{i=1}^{k} N_i\right) \sum_{i=1}^{k} \left(1 - \frac{1}{N_i}\right) \) |
Construct a linear mapping \( T: \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) such that \( v = (1,1) \in \text{Ker}(T) \) and \( w = (2,1) \in \text{Im}(T) \). Find the matrix of such a mapping with respect to the standard basis. | \(\begin{pmatrix}2 & -2 \\ 1 & -1\end{pmatrix}\) |
On what island did the Missionaries live with citizens of the Marshall Islands? | Ebon |
What are the maximal left ideals of the ring \( R = M_2(\mathbb{Q}) \)? | \,I_{[a:b]}
=\Bigl\{\begin{pmatrix}xa & xb\\ ya & yb\end{pmatrix}
\;\Big|\;x,y\in\mathbb Q\Bigr\}\, |
Evaluate the integral \( \int_0^{\infty} \frac{1}{(x+1)(x+2)(x+3)} \, \mathrm{d} x \). | \(\frac{\ln(4/3)}{2}\) |
What was the name of the Greek shipping tycoon, sometimes known as 'The Golden Greek', who built the first supertankers capable of transporting large quantities of oil? | STAVROS NIARCHOS |
what are the three primary colours | Red, yellow, and blue |
How does social media groups like UNILAD and similar have 10 million fans by just reposting stuff that comes to the Reddit frontpage? | Mainly because they are on Facebook, so a lot more people get to see the content they post. Depending on security settings, chances are you have at least one friend who sees, and potentially likes/shares their post. Because they liked or shared it, everyone on their friends list sees it too, whether they follow the Uni... |
Let \( G = \langle g \rangle \) be a cyclic group of order \( n = 480 = 2^5 \cdot 3^1 \cdot 5^1 \). Let \( H \) be a subgroup of \( G \), and \( m \) be the smallest natural number for which \( g^m \in H \). Determine for which natural numbers \( m \) the order \( |H| \) of \( H \) is divisible by \( 2 \). | \( m = 2^\alpha \cdot p_1^{l_1} \cdots p_k^{l_k} \) where \( \alpha \in \{1,2,3,4\} \) and \( m < 480 \) |
Given the derivative \( f'(x) = 6x^{4.3} + 5x^{-4.5} + 6x^{0.6} \) and the condition \( f(1) = -11 \), find the function \( f(x) \). | \,f(x)=\frac{60}{53}\,x^{5.3}
-\frac{10}{7}\,x^{-3.5}
+\frac{15}{4}\,x^{1.6}
-\frac{21449}{1484}\, |
what is the strongest material commonly used to build bridges? | Engineered cementitious composites, which include cement, sand, water, fiber and chemicals. |
Estimate the number of connected components of a compact surface \( S \) in terms of the number of critical points of a differentiable function \( f: S \longrightarrow \mathbb{R} \) defined on \( S \). | \;c(S)\;\le\;\dfrac{\#\operatorname{Crit}(f)}{2}\; |
what is the definition of thalweg | Thalweg is the line of lowest elevation within a valley or watercourse.he thalweg thus marks the natural direction (the profile) of a watercourse. |
Solve the following partial differential equation explicitly for $\psi: [0, +\infty)\times\mathbb{R}\to\mathbb{C}$:
$$
\frac{i}{a}\psi'_t(t,x) = -\frac{1}{2}\psi''_{xx}(t,x)
$$
with initial condition $\psi(0,x) = \psi_0(x)$. | \;
\psi(t,x)=\frac{1}{2\pi}\int_{\mathbb R}
e^{ikx-i\frac{a}{2}k^{2}t}\,
\widehat\psi_0(k)\,dk\; |
does it matter if one number on your blood pressure is higher than normal and the other not? | Yes |
how lutherans celebrate lent | The worship services during Lent are more subdued to reflect the somber tone of the season. Usually, all mention of the word Alleluia is removed from the Divine Service, including the hymnody. The Hymn of Praise (Gloria in Excelsis) is removed from the liturgy as well. |
The state of Tabasco, where the sauce gets its name, is in which country? | Mexico |
how to cut down a tree safely | An easy way to make your cuts match up is to place a stick in the off-side of your horizontal cut, causing it to stick out a little. Start a cut on your side of the tree, lining up the bottom of your cut with that side of the horizontal cut. You can project your cuts path by looking down the bar. Stop cutting and peek ... |
Evaluate the integral of $\frac{x^3}{x^2+4x+3}$. | \(\frac{x^2}{2} - 4x - \frac{1}{2} \ln|x+1| + \frac{27}{2} \ln|x+3| + C\) |
how do birds breathe | When the bird takes a breath through their mouth or nostrils,air in lungs is sucked into cranial sacs caudal thoracic, cervical, and clavicular. |
Determine the values of $\theta$ for which $\arg(z-4+2i)=\theta$ and $|z+6+6i|=4$ have no common solutions, where $\theta$ ranges from $-\pi$ to $\pi$. | \;\theta\in\bigl(-\pi+2\arctan\frac{2}{5},\;\pi\bigr)\; |
Is it impossible to tie a knot with frictionless rope? | Knots are not made or held together by friction. They are held together by constrains of reality. I would depend of the knot of course. A non-stable knot like a sheepshank probably wouldn't hold up under these conditions, but a stable knot like an overhand knot or figure-8 knot doesn't depend on friction to stay tied. |
Solve the Euler ODE \(x^2y'' - xy' + y = 6x\ln(x)\) and find the particular solution using the method of variation of parameters. Given the homogeneous solution \(y_h = xC_1 + x\ln(x)C_2\), determine the particular solution and compare it with the solution provided by Wolfram Alpha, which is \(C_1x + C_2x\ln(x) + x\ln^... | \(x \ln^3(x)\) |
Which spirit is used as the base for a Mai Tai cocktail? | Rum |
Using the Newton method, calculate the root (zero) of the function $f(x) = e^{2x} - 2x - 1$ with a precision of $0.00001$ starting from the initial point $p_0 = 1$. Determine the number of iterations required to achieve this precision. | 18 |
Determine the range of the function \( f: \Bbb R \rightarrow \Bbb Z \) defined by \( f(x) = \lfloor x \rfloor \), and whether it is one-to-one, onto, both, or neither. Find all cases where \( f(x) = x \). | \( \Bbb Z \) for the range, onto but not one-to-one, and \( \forall x \in \Bbb Z \) for \( f(x) = x \). |
Find the steady-state profile of the function \( u(x, y, t) \) that satisfies the diffusion-decay partial differential equation:
\[ u_t = D \nabla^2 u - \delta u(x, y, t), \quad u(0, 0, t) = u_0. \]
This involves solving the equation:
\[ 0 = D \nabla^2 u - \delta u(x, y, t), \quad u(0, 0) = u_0. \] | \,u(x,y)=u_{0}\;I_{0}\!\Big(\sqrt{\frac{\delta}{D}}\;\sqrt{x^{2}+y^{2}}\Big)\, |
What country is bordered by Macedonia, Greece, Montenegro and Kosovo? | Albania |
Calculate the limit
\[
\lim_{(x,y)\rightarrow(0,0)}\frac{\ln(1+x)+\ln(1+y)}{x+y}.
\] | The limit does not exist. |
What is the maximum of \( w(x) = \prod_{i=0}^8 (x - x_i) \) on the interval \([-1, 1]\), where the nodes \( x_i \) are equidistant with \( x_0 = -1 \) and \( x_8 = 1 \)? | \,\displaystyle \max_{x\in[-1,1]}w(x)\approx 0.018803261046075\; |
which clade is most primitive | Lampreys and hagfishes. |
where was the forest moon of endor filmed | US West Coast, United States. |
Express the normal distribution probability density function \( f_Y(y; \mu, \sigma^2) = \frac{1}{\sqrt{2\pi \sigma^2}} \exp\left(-\frac{(y-\mu)^2}{2\sigma^2}\right) \) in the form \( Y \sim f_Y(y; \theta, \phi) = \exp\left[\frac{y\theta - b(\theta)}{a(\phi)} + c(y, \phi)\right] \). | \displaystyle
f_{Y}(y;\mu ,\sigma ^2)
=\exp\!\Big[
\frac{y\mu-\mu ^2/2}{\sigma ^2}
-\frac{y^{2}}{2\sigma ^2}
-\frac12\ln(2\pi\sigma ^2)
\Big] |
what is the classic sign of an asthma attack | Coughing and Wheezing are the classic sign of an asthma attack. |
Compute the first 5 non-zero end digits of \((10^{12})!\). | 16576 |
Given the integral $\frac{d}{dx}\int_{\pi}^{x^2} \sin(t) \ \text{dt}$, how do you apply the chain rule when the upper bound is a function of $x$, such as $x^2$ or $2x$? | \( 2x \sin(x^2) \) |
In $\mathbb{RP}^4$, given the planes $\pi_1$ and $\pi_2$ and the line $l$ defined by:
\[
\pi_1: \quad x + 3z - s = 0, \quad 2x + 3y + t = 0,
\]
\[
\pi_2: \quad -x + z + 2t = 0, \quad 3x + y = 0,
\]
\[
l: \quad -13x + 3z = 0, \quad 7y + 3t = 0, \quad -38y + 3s = 0,
\]
determine the planes $\pi$ that contain $l$ and inte... | \text{No such plane }\pi\text{ exists (the solution set is empty).} |
Which US author wrote a series of novels about the Women's Murder Club? | James Patterson |
Consider the locus of the complex number \( z \) in the Argand plane given by \( \text{Re}(z) - 2 = |z - 7 + 2i| \). Let \( P(z_1) \) and \( Q(z_2) \) be two complex numbers satisfying this locus and also satisfying \( \arg\left(\frac{z_1 - (2 + i\alpha)}{z_2 - (2 + i\alpha)}\right) = \frac{\pi}{2} \) for \( \alpha \in... | 10 |
wiki how to convert a fraction to a mixed number | Divide the numerator by the denominator. In the example, , divide 11 by 4. 11 ÷ 4 = 2 with remainder 3. The quotient (without the remainder) becomes the whole number part of the mixed number. |
How do antibiotics work and how do doctors know which to prescribe to you? | Its basically depends on the antibiotic or the bacteria. Some antibiotics break down the bacterias cell wall (which causes it to die when it replicates) others prevent them from making energy so they just die from lack of nourishment. |
What family has the Northumberland Vault? | Percy Family |
Given a prime \( p \) and an integer \( n \ge p \), what is the smallest possible degree of a polynomial \( Q \in \mathbb{F}_p[x_1, \dotsc, x_n] \) such that \( Q \) vanishes on every vector \( x \in \{0,1\}^n \) of weight divisible by \( p \)? | 1 |
Why aren't there many games for mac? | The overall goal of pretty much any project from video game developers and publishers is to make money, and they are interested in producing the most money for the investment of the project. Because Windows has been the dominant operating system for the better part of two decades, many companies develop games for Windo... |
restless legs syndrome definition | A nervous system problem that causes you to feel an unstoppable urge to get up and pace or walk. |
How do we "picture something" in our heads? | There is some evidence that mental imagery reactivates parts of visual cortex (including early visual cortex) that are active during perception in a top-down manner due to feedback from higher level visual areas. See the work of Stephen Kosslyn (a simple Google scholar search will turn up a slew of papers from his grou... |
What is the scientific reasoning behind a “bad trip”? | Science barely understands what makes a trip beyond neurotransmitters A bad trip is usually a memory or fabrication of traumatic events in the past or a general awakening to something you are psychically ill prepared for. Like your own finite nature, god-ness, being devoured alive by ants or things even more indescri... |
names of earthquakes and their faults | The San Andreas earthquake and their fault was originally named for a short segment of the fault along the San Francisco Peninsula that lies within San Andreas and Crystal Springs Valleys. |
Solve the differential equation
\[ m = -\dfrac{1}{32}\dfrac{d(p_0p_1)}{dz}(r-z(r-1))^4 - \dfrac{1}{4}\dfrac{dp_0}{dz}(r-z(r-1))^3 \]
where \( r \) and \( m \) are constants, with the boundary conditions:
- For \( z = 0 \), \( p_0 = p_i \) and \( p_1 = 0 \)
- For \( z = 1 \), \( p_0 = 1 \) and \( p_1 = 0 \) |
p_{0}(z)=1+\frac{1-p_{i}}{1-r^{-2}}\;
\Bigl[\frac{1}{\bigl(r-(r-1)z\bigr)^{2}}-1\Bigr],
\qquad p_{1}(z)=0 .
|
How does credit card fraud work? | No. You don't transfer money into a bank account. ---- But often, people will try various things. Some of the most common are: 1. Buy things online 2. Buy gift cards / prepaid credit cards 3. Use it to mass purchase codes online (things like serial codes for digital content, video games, etc) The whole point is you ex... |
doxepin pills | Doxepin is a tricyclic antidepressants, that affects chemicals in the brain that may become unbalanced. |
Given a sequence of complex numbers \( z_n \) representing points in a golden rectangle, where:
- \( z_0 = 0 + 0i \)
- \( z_1 = 1 + i \)
- \( z_2 = \phi + (2 - \phi)i \)
- \( z_3 = 2\phi - 2 \)
- \( z_4 = 1 + (2\phi - 3)i \)
- \( z_5 = (6 - 3\phi) + (2 - a)i \)
Find the limit \( \lim_{n \to \infty} z_n \). | \displaystyle \lim_{n\to\infty}z_n
=\frac{5+3\sqrt5}{10}+i\,\frac{5-\sqrt5}{10} |
What was the term used by crew members in reference to the battleship at Fall River Heritage State Park? | "Big Mamie" |
Derive the Fourier transform of the general Gaussian function \( f(x) = e^{-\frac{ax^2}{2}} \) for \( a > 0 \). | \( \frac{1}{\sqrt{a}} \cdot \frac{1}{\sqrt{2\pi}} e^{-\frac{w^2}{2a}} \) |
Given a set \( A \) with \( n \) elements, let \( B = (P_1, P_2, \ldots, P_m) \) be a tuple of \( m \) non-empty subsets of \( A \) such that \( P_i \cap P_j \neq \varnothing \) for all \( i \neq j \). How many different tuples \( B \) are there? | \displaystyle
\sum_{F\subseteq\binom{[m]}{2}}(-1)^{|F|}
\bigl|\{\,S\subseteq[m]\;:\;S\text{ contains no edge of }F\,\}\bigr|^{\,n} |
What part of the body is also the name of a punctuation mark? | Colon |
Find a system of recurrence relations for computing the number of n-digit quaternary sequences with an even number of 0s and an even number of 1s. |
\begin{aligned}
a_0&=1,\; b_0=c_0=d_0=0,\\
a_n&=2a_{n-1}+b_{n-1}+c_{n-1},\\
b_n&=a_{n-1}+2b_{n-1}+d_{n-1},\\
c_n&=a_{n-1}+2c_{n-1}+d_{n-1},\\
d_n&=b_{n-1}+c_{n-1}+2d_{n-1}\qquad(n\ge1).
\end{aligned}
|
how much does dietary cholesterol matter in raising your cholesterol? | If you have heart disease or are at risk of heart disease, eat less than 200 mg of dietary cholesterol per day. |
Determine if the linear map \( l: P \rightarrow \mathbb{R} \) defined by \( l(p) = \int_0^1 p(t) \, dt \) is continuous and find its norm \( \| l \| \). | 1 |
Find a conformal mapping of the region \( D = \{z : |z − 1| < \sqrt{2}, |z + 1| < \sqrt{2}\} \) onto the open first quadrant. | \,f(z)=\alpha\,\frac{z-i}{z+i}
=e^{-i3\pi/4}\,\frac{z-i}{z+i}
=\frac{1+i}{\sqrt{2}}\;\frac{i-z}{z+i}\, |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 18,472