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시간 제한메모리 제한제출정답맞힌 사람정답 비율
0.1 초 1024 MB107777.778%

## 문제

Deni enjoys playing the game monopoly very much. But the duration of one game is very long – from 5 to 7 hours. So, Deni starts thinking about changing the classical rules. The players in monopoly usually move in one direction from space to space and after some time they return to the beginning, start again and so on. In the new version, the movement will again be from space to space but from the current one there can be several possibilities for the next move. Deni wants to find such directed connections between the spaces, so that a player can never return to a space, where he has been, no matter how he moves (of course, following the rules). In such a way the game will be shorter in duration

She has already begun making the new board – she has chosen the number of spaces N (the spaces are numbered from 1 to N) and she has made a list with M connections (each connection has a direction and there is no connection that connects a space with itself). If space i is connected to space j, then there is no direct connection in the opposite direction, i.e. from space j to space i, and also, there are no other direct connections from space i to space j. Deni thought that she was ready with the new board, but suddenly she noticed that the condition she wants (when you move from space to space, using the connections, you cannot return to a previously visited space) doesn’t hold for her list of connections. She first thought to remove some of the direct connections, but that will result in rewriting the list, which can be really long. That’s why Deni decided to reverse the direction of some of the directed connections.

You are regularly playing monopoly with Deni. That’s why you want to help her by writing the program, which has to tell her which connections to reverse so that the stated condition will hold. The program has to contain the function find_reverse which will be compiled with the jury’s program.

## 구현

The function find_reverse must have the following prototype:

std::string find_reverse (int N, int M, int connections[][2]);

It is called only once by the jury’s program with three parameters: N – the number of spaces in the new board, M – the number of directed connections in Deni’s list and the array connections which has M rows, each consisting of two numbers x and y – the beginning and ending spaces for the directed connection. This function should return a binary string of length M – in the order of the array connections, for each connection you have to put ‘1’ in the string, if the connection has to be reversed and ‘0’, otherwise. If there is more than one solution, you can return any of them.

You have to submit to the system the file monopoly.cpp, which contains implementation of the function find_reverse. The file may contain other functions and code, needed for your program, but it must not contain a main function – main. Also, you should not try to read from the standard input nor try to write to the standard output!

## 제한

• 3 ≤ N ≤ 5 × 105
• 3 ≤ M ≤ 1.5 × 106

## 서브태스크

번호배점제한
115

N ≤ 7, M ≤ 21

240

N ≤ 103, M ≤ 5 × 103

325

N ≤ 105, M ≤ 5 × 105

420

N ≤ 5 × 105, M ≤ 1.5 × 106

## 로컬 테스팅

For local testing you are given the file Lgrader.cpp. You have to place it in the same folder as your program monopoly.cpp and you have to compile together the files Lgrader.cpp and monopoly.cpp. In such a way, you will make a program to check the correctness of your function. The program will require the following sequence of data from the standard input:

• on the first line: two integers – the number of spaces N and the number of connections M of the new board.
• on the last M lines: on each line there have to be two integers x and y – the beginning and ending spaces for each directed connection.

The output of the program will be the binary string that you found.

Input Output Explanation
6 12
1 2
1 5
2 3
2 5
3 4
3 6
4 1
4 5
5 3
5 6
6 1
6 4
100000101011

The connections that are reversed are: (1,2), (4, 1), (5, 3), (6, 1), (6, 4).

The figure above is showing the spaces, firstly, with the directed connections from Deni’s list and, secondly, after reversing the direction of the connections with corresponding ‘1’ in the output. Clearly, in the beginning using the directed connections (1, 2), (2, 3), (3, 4) and (4, 1) we can start from space 1 and moving along these directed connections, we will return to that space. One can see that Deni’s condition holds in the resulting board. Notice that there are other valid solutions:

(4, 1), (5, 3), (6, 1), (6, 4)

(1, 5), (2, 3), (2, 5), (3, 4), (3, 6), (4, 5), (5, 6)

## 제출할 수 있는 언어

C++17, C++14, C++20, C++14 (Clang), C++17 (Clang), C++20 (Clang)

## 채점 및 기타 정보

• 예제는 채점하지 않는다.


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# How to compute Chi-square value and degrees of freedom in Excel?

I am trying to understand the statistical test of the chi-square in Excel. I already made the test but I still don't know how to compute the χ² value and what it means, how to compute the degrees of freedom and how to write a propper APA approved result section. Can anyone help me and explain this in a simple way?

I have a population of n=76. 'Left' = 25 and 'Right' = 51. The hypothesis is you would expect a normal distribution ('Left' =38 and 'Right' = 38). So the question is 'is this distribution a coincidence?' The p < .029. By seeing this outcome I thought there is that is no coincidence that there isn't a normal distribution and it must be due to a variable.

Is it true in this case the degress of freedom is just n-1?

-

This is really more of a statistical question (except perhaps the bit about APA style). As such it probably belongs on stats.stackexchange.com .

A binary variable does not have a "normal distribution". A normal distribution is bell shaped and is relevant to continuous data.

Your null hypothesis is that the population proportions for left and right handers are equal. Thus, if your chi-square value is sufficiently large, then you might reject the null hypothesis and conclude that the population proportions are unequal.

If $k$ is the number of categories (you have two categories), then degrees of freedom for the one sample chi-square test is $k-1$ (i.e., $2-1 = 1$).

The following formula in Excel should give you a p-value. For example if your chi-square value was 22, and your degrees of freedom was 3:

 =1-CHISQ.DIST(22, 3,TRUE)

• the first argument is the chi-square value
• The second argument is the degrees of freedom
• The third argument indicates that a cumulative distribution (CDF) is desired
• Thus by taking 1 minus the value of the CDF you get the probability of getting a chi-square value as large or larger than the observed value.

You can check your formula by looking at existing calculated tables. http://home.comcast.net/~sharov/PopEcol/tables/chisq.html

-
Thank you very much Jeromy! This was very helpful! –  NinaM Mar 11 '13 at 12:32

format: plain


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### MATH 742 : Geometric Analysis

Fall 2019
Here is the syllabus for the course in pdf format.

#### Announcements

We are meeting in Math 0103 starting Monday, August 26.

Office hours Mondays 2-2:50, or by appointment, in 4412.

#### Problem Sets

• HW 1, due 9/11 FINAL

expand collapse

1. Let φ be a coordinate chart on an n-dimensional manifold M defined at a point p. Define tangent vectors by $$v_i(f) = \frac{\partial (f \circ \varphi^{-1})}{\partial x_i} \qquad f \in C^\infty (M)$$ Show that {v1, ..., vn} form a basis for Tp M, the tangent space to M at p.
2. In this problem you are asked to compute tangent spaces of manifolds embedded in Rn+1. In this case, elements of Tp M can equivalently be viewed as vectors in Rn+1, based at p. It is these subspaces of Rn+1 which you are asked to compute below.

a) Show that Tp Sn = p.

b) Recall the notation for the nondegenerate quadratic forms on Rn of index (p,q), where p+q = n: $$Q_{p,q}({\bf x}) = x_1^2 + \cdots + x_p^2 - x_{p+1}^2 - x_n^2$$ Consider the manifolds $$S^{p,q} = \{ {\bf x} \in {\bf R}^{n+1} \ : Q_{p+1,q}({\bf x}) = 1 \}$$ and $$H^{p,q} = \{ {\bf x} \in {\bf R}^{n+1} \ : \ Q_{p,q+1}({\bf x}) = -1 \}$$ Show that Tp Sp,q = p and similarly for Hp,q. Thus both are pseudo-Riemannian manifolds of index (p,q).

3. For a smooth path γ:[a,b] → M,

a) assume that M is Riemannian, and let $$\alpha(t) = \int_a^t \left\| \dot{\gamma}(t) \right\| \ dt$$ Then show that γ composed with α-1 is parametrized by arc length;

b) assume that M is pseudo-Riemannian, and show that a smooth timelike path admits a parametrization by proper time.
4. Compute the Euler-Lagrange equations for the hyperbolic plane in the upper-half plane model $$g_{(x,y)} = \frac{dx^2 + dy^2}{y^2}$$ a) for the energy Lagrangian;

b) for the length Lagrangian.
5. In lecture we computed the matrix of leading coefficients in the Euler-Lagrange equations for the length Lagrangian on an n-dimensional Riemannian manifold: $$\left( a_{km} \right) = \left( \frac{g_{km}}{\left\| \dot{\gamma} \right\|} - \frac{\left( \Sigma_{\ell} g_{k\ell} \dot{\gamma}^\ell \right) \left( \Sigma_{\ell} g_{m\ell} \dot{\gamma}^\ell \right) }{\left\| \dot{\gamma} \right\|^3} \right)$$ Show that the rank of this matrix is n-1.
• HW 2, due 9/25

1. Let γ be a smooth curve in a semi-Riemannian manifold M. Given two coordinate charts $$\varphi = (x_1, \ldots, x_n) \qquad \bar{\varphi} = (\bar{x}^1, \ldots, \bar{x}^n)$$ use our transformation rules for Christoffel symbols to show that $$\varphi \circ \gamma = (\gamma^1, \ldots, \gamma^n)$$ satisfies the geodesic equations in the first coordinates if and only if $$\bar{\varphi} \circ \gamma = (\bar{\gamma}^1, \ldots, \bar{\gamma}^n)$$ satisfies the geodesic equations in the second coordinates.
2. (Postnikov Exer. 12.3) For the Lagrangian $$\mathcal{L} = \dot{x}^2 + \dot{y}^2$$ on the R2, show that the path x = at, y = 0 is an extremal. Let A be the point (a,0), a > 0, on this extremal, and let O be the origin. The integral $$\int_0^1 (\dot{x}^2 - \dot{y}^2) dt$$ over the segment OA of this extremal is equal to a2. Compute that the action over the broken line OBA (correspondingly parametrized), where B is the point (a/2,b/2), b>0, is equal to a2 - b2. Therefore, the segment OA is not a minimum curve, and there is no minimum curve connecting the points O and A for this Lagrangian.
3. Show that a timelike geodesic in a Lorentzian manifold locally maximizes proper time.


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# Thread: formula for a sequence

1. ## formula for a sequence

i am looking for an explicit formula for the sequence given by the following numbers:

0, 1/2, 1, 2/3, 1/3, 0, 1/4, 2/4, 3/4, 1, 4/5, 3/5, 2/5, 1/5, 0, 1/6, etc..

2. I could get upto this:

nth term,$\displaystyle t_n=\frac{d-m}{d}$

where
$\displaystyle d=\left\lceil\frac{\sqrt{8n+1}-1}{2}\right\rceil$

$\displaystyle m=(-1)^d \left( \frac {d(d+(-1)^d)}{2}-n \right)$

someone, please silmpify

3. $\displaystyle d_{n}=\left\lfloor\sqrt{2n}+\frac{1}{2}\right\rflo or$

4. we get the general term of the sequence to be:

$\displaystyle a_{n}$=$\displaystyle \sum_{n=1}^{n}\frac{(-1)^{d_{n}}}{d_{n}}\$

i figured this out yesterday but didn't have the time to learn LaTex. And I had Mr. Fantastic sending me demerits all day long. maybe he could have spent more time helping with this as opposed to sitting in front of his computer sending out demerits!!

5. i will probably get thrown off the site now!! well it was fun learning a little bit of latex!

6. oh yes, one more thing,

$\displaystyle a_{0}$=0.

7. Originally Posted by kkoutsothodoros
we get the general term of the sequence to be:

$\displaystyle a_{n}$=$\displaystyle \sum_{n=1}^{n}\frac{(-1)^{d_{n}}}{d_{n}}\$
I am not able to follow your answer...could you please give example for some values of n.

8. it does seem a little unclear. sorry, i am just learning how to use latex.

let $\displaystyle a_{n}$ = $\displaystyle \frac{(-1)^{d_{n}}}{d_{n}}\$ for n >= 2, $\displaystyle a_{1}$ = 0.

let $\displaystyle s_{n}\$ = $\displaystyle \sum_{n=1}^{n}a_{n}$.

you should get

$\displaystyle s_{1}$ = 0
$\displaystyle s_{2}$ = .5
$\displaystyle s_{3}$ = 1
$\displaystyle s_{4}$ = 2/3
etc.

9. so $\displaystyle s_{n}$ is the general term for the sequence 0, 1/2, 2/2, 2/3, 1/3, 0/3, 1/4, 2/4, 3/4, 4/4, 4/5, 3/5, etc

10. the funny thing is this sequence is just used as a counterexample in a cauchy sequence problem i was looking at. it wasn't that important to get the general term formula. it just bugged me so much that i couldn't let it go. but i guess it's useful that i learned how to get a general term for 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, etc along the way. the general term for this is:

$\displaystyle d_{n}=\left\lfloor\sqrt{2n}+\frac{1}{2}\right\rflo or$

11. Originally Posted by malaygoel
I am not able to follow your answer...could you please give example for some values of n.
is it more clear now?

12. Originally Posted by kkoutsothodoros
the funny thing is this sequence is just used as a counterexample in a cauchy sequence problem i was looking at. it wasn't that important to get the general term formula. it just bugged me so much that i couldn't let it go. but i guess it's useful that i learned how to get a general term for 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, etc along the way. the general term for this is:

$\displaystyle d_{n}=\left\lfloor\sqrt{2n}+\frac{1}{2}\right\rflo or$
your expression and my expession for d(given in post #2) are quite different. And they both work. Can you explain how you got your expression. mine had a simple logic.

13. Consider 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,etc

where the integer m appears m times in the sequence. using the fact that

$\displaystyle 1+2+3+...+n=\frac{n(n+1)}{2}\$ we have $\displaystyle \frac{m(m-1)}{2}\$ < n <= $\displaystyle \frac{m(m+1)}{2}\$

this inequality leads to:

m < $\displaystyle \sqrt{2n}+\frac{1}{2}\$ <= m + 1 which is equivalent to what we are looking for.

14. Originally Posted by kkoutsothodoros
Consider 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,etc

where the integer m appears m times in the sequence. using the fact that

$\displaystyle 1+2+3+...+n=\frac{n(n+1)}{2}\$ we have $\displaystyle \frac{m(m-1)}{2}\$ < n <= $\displaystyle \frac{m(m+1)}{2}\$
Upto here, everything is correct.

Now, how do you get this

m < $\displaystyle \sqrt{2n}+\frac{1}{2}\$ <= m + 1

15. sorry again, this part is a little tricky and i found an error.

multiply $\displaystyle \frac{m(m-1)}{2}\$ < n <= $\displaystyle \frac{m(m+1)}{2}\$ by 2 to get $\displaystyle m^2 - m < 2n <=m^2 + m$. now add 1/4 to both sides and factor to get $\displaystyle m^2 - m + 1/4< 2n + 1/4 <=m^2 + m + 1/4$ or $\displaystyle (m-1/2)^2 < 2n + 1/4 <= (m + 1/2)^2$. take the square root of everything and we get $\displaystyle (m-1/2) < \sqrt{2n + 1/4}\ <= (m + 1/2)$.

add 1/2 to both sides and we get $\displaystyle m < \sqrt{2n + 1/4}\ + 1/2 <= m + 1$.

i just checked it in Excel and the 1/4 is not affecting the result, luckily. it still works if we start with n = 0.

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kidzsearch.com > wiki

# Stephen Hawking

Stephen Hawking

Born Stephen William Hawking
8 January 1942
Oxford, Oxfordshire, Great Britan
Died 14 March 2018 (aged 76)
Cambridge, Cambridgeshire, England
Nationality British
Fields Mathematics, Physics
Institutions University of Cambridge
Alma mater University of Oxford
University of Cambridge
Known for Black holes
Theoretical cosmology
Quantum gravity
Notable awards Prince of Asturias Award (1989)
Copley Medal (2006)

Stephen William Hawking, CH CBE FRS (8 January 1942 – 14 March 2018) was an English theoretical physicist and mathematician. He was born in Oxford. In 1950, he moved to St Albans, Hertfordshire. He was one of the world's leading theoretical physicists.[1] Hawking has written many science books for people who are not scientists.

Hawking was a professor of mathematics at the University of Cambridge (a position that Isaac Newton once had).[2] He retired on 1 October 2009.[3]

Hawking had a motor neurone disease related to his dyslexia,[4] and because of that he could not move or talk very well. The illness worsened over the years and he was almost completely paralysed. He used a wheelchair to move, and an Intel computer to talk for him. He died on 14 March 2018.

## Early life and education

Hawking went to St Albans School, a local public school in Hertfordshire. At 17, he passed an exam to study at Oxford. He studied physics and chemistry there. Because he found it really easy at the beginning, he didn't study a lot for the final exams.

In October 1962 he started his graduate course at Trinity Hall. It was at this time that his illness started to show up. He had difficulties in rowing and then even simply in walking. However, he finished his PhD and wrote about black holes in his thesis. He then got a fellowship (a job as a university teacher) at Gonville and Caius College in 1965.

## Career

Hawking was a cosmologist—someone who studies the structure of the universe (stars and space). He invented important theories about the Big Bang (the start of the universe), black holes and how they work.

Stephen Hawking predicted that black holes eject some radiation (energy), even though they normally swallow everything. That kind of radiation is named "Hawking Radiation."

Hawking also worked on the problem of quantum gravity. Quantum gravity tries to explain how gravity works with quantum mechanics (physics of tiny things.) That is a hard problem that scientists have not solved yet.

Hawking also wrote popular books about science for non-scientists. His first book, A Brief History of Time, sold over ten million copies.

## Death

Hawking died on 14 March 2018 in Cambridge, Cambridgeshire of complications from motor neuron disease at the age of 76.[5] His ashes are buried in Westminster Abbey in London near Charles Darwin and Isaac Newton.[6]

## Selected publications

### Technical

• Singularities in Collapsing Stars and Expanding Universes, with D.W. Sciama, 1969. Comments on Astrophysics and Space Physics. Vol 1
• The Nature of Space and Time with Roger Penrose, foreword by Michael Atiyah, New Jersey: Princeton University Press, 1996,
• The Large Scale Structure of Spacetime with George Ellis, 1973
• The Large, the Small, and the Human Mind, (with Abner Shimony, Nancy Cartwright, and Roger Penrose), Cambridge University Press, 1997, (hardback), (paperback), Canto edition:
• Information Loss in Black Holes, Cambridge University Press, 2005

### Popular

Hawking in 2013
• A Brief History of Time, Bantam Press 1988.
• Black Holes and Baby Universes and Other Essays, Bantam Books 1993.
• The Universe in a Nutshell, Bantam Press 2001.
• On The Shoulders of Giants. The Great Works of Physics and Astronomy, Running Press 2002.
• A Briefer History of Time, Bantam Books 2005.
• God Created the Integers: the mathematical breakthroughs that changed history, Running Press, 2005.

## Notes

General relativity
$G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}$
Einstein field equations
1. A theoretical physicist is someone who uses information from experiments to make predictions about the world.
2. "Stephen Hawking's Universe" (HTML). PBS Online. Retrieved 2008-06-11.
3. Famous dyslexic people: Stephen Hawking
4. "Physicist Stephen Hawking dies aged 76". BBC News. 14 March 2018. Retrieved 14 March 2018.
5. Shirbon, Estelle (20 March 2018). "Stephen Hawking to Join Newton, Darwin in Final Resting Place". London: Reuters. Retrieved 21 March 2018.


text:
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text:
### Recent Submissions

• #### One-dimensional T-preorders

(IOS Press, 2014)
Conference report
Open Access
This paper studies T-preorders by using their Representation Theorem that states that every T-preorder on a set X can be generated in a natural way by a family of fuzzy subsets of X. Especial emphasis is made on the study ...
• #### Indistinguishability operators generated by fuzzy numbers

(Institute of Electrical and Electronics Engineers (IEEE), 2004)
Conference report
Restricted access - publisher's policy
A new way to generate indistinguishability operators coherent with the underlying ordering structure of the real Dine is given in the sense that this structure should be compatible with the betweenness relation generated ...
• #### Eigenvectors and generators of fuzzy relations

(-, 1992)
Conference report
Restricted access - publisher's policy
A new geometric approach to the study of the eigenvectors is provided. The T-eigenvectors of a T-indistinguishability operator are characterized as its generators in the sense of the representation theorem of L. Valverde ...
• #### Fuzzy numbers and equality relations

(IEEE pub., 1993)
Conference report
Restricted access - publisher's policy
A general approach to the concept of fuzzy number associated to a generalized equality on the real line is given. As a result, the use of triangular and trapezoidal fuzzy numbers, among other types, is justified and a ...
• #### ET-Lipschitzian aggregation operators

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Lipschitzian and kernel aggregation operators with respect to the natural Tindistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and ...
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Two ways to approximate a proximity relation R (i.e. a reflexive and symmetric fuzzy relation) by a T-transitive one where T is a continuous archimedean t-norm are given. The first one aggregates the transitive closure R ...
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(IEEE Comp. Int. Soc., 2007)
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Open Access
Lipschitzian and kernel aggregation operators with respect to the natural T-indistinguishability operator ET and their powers are studied. A t-norm T is proved to be ETLipschitzian, and is interpreted as a fuzzy point and ...
• #### La Hoja de cálculo : un entorno para la enseñanza y estudio de relaciones borrosas

(Center for Soft Computing, 2008)
Conference report
Open Access
En este trabajo se estudia la posibilidad de introduir conceptos de teoría de conjuntos borrosos en los currículos correspondientes a distintos niveles de enseñanza. Se hace especial hincapié en la enseñanza de las relaciones ...
• #### Estructura de las similitudes

(Center for Soft Computing, 2008)
Conference report
Open Access
En este artículo se define formalmente el concepto de estructura de similaridad, se cuenta el número de estructuras de similaridades hasta dimensión 5, se propone una nomenclatura y un algoritmo que asigna una estructura ...
• #### Aproximación de Proximidades por Similitudes

(Center for Soft Computing, 2008)
Conference report
Open Access
En este trabajo se presenta un algoritmo para hallar una relaci´on de similitud próxima a una relación de proximidad (i.e.: una relación de tolerancia) R dada. La relación de similitud obtenida es más próxima a R que su ...
• #### Approximating proximities by similarities

(Univ. Malaga, 2008)
Conference report
Open Access
In this paper an algorithm to find a similarity close to a proximity or tolerance relation R is given. The obtained similarity is closer to R than its transitive closure or any transitive opening of R.
• #### Approximate fuzzy preorders and equivalences

(2009)
Conference report
Restricted access - publisher's policy
Although Fuzzy Preorders and Fuzzy Equivalences are well established types of fuzzy relations, they are defined in terms of properties to be fulfilled in a crisp way. In this paper we relax those requirements by making ...


text:
Wed Apr 22 18:58:25 PDT 2009

```I also have the same problem like yours this days when I want to show the interactions using the analysis menu as discribed in manul. But when I do this using the display menu at the top of ADT window( my system is Windows XP, but I don't know yours), the program can show me the interaction graphic in the viewer without any errors warning. Maybe you can try this way as I said.
Best wishes.
Wen

>Hi,
>
>            I am trying to visualize interactions using the .dlg file and
>the .pdbqt file.  I tried both ADT1.5.2 and 1.5.4 versions by choosing
>AD4.1. I have used autodock4 for docking. I searched archives, but I didn't
>find much help. I am posting for the second time.
>
>I  am getting the following error
>
>>>> ERROR *********************************************
>Traceback (most recent call last):
>  File "C:\Program Files\MGLTools
>1.5.2\MGLToolsPckgs\ViewerFramework\VF.py", line 716, in tryto
>    result = apply( command, args, kw )
>  File "C:\Program Files\MGLTools
>1.5.2\MGLToolsPckgs\AutoDockTools\autoanalyzeCommands.py", line 2087, in
>doit
>    self.build()
>  File "C:\Program Files\MGLTools
>1.5.2\MGLToolsPckgs\AutoDockTools\autoanalyzeCommands.py", line 1912, in
>build
>    self.intDescr = InteractionDescriptor(lig, macro, percentCutoff)
>  File "C:\Program Files\MGLTools
>1.5.2\MGLToolsPckgs\MolKit\interactionDescriptor.py", line 46, in __init__
>    self.build(detect_pi=detect_pi)
>  File "C:\Program Files\MGLTools
>1.5.2\MGLToolsPckgs\MolKit\interactionDescriptor.py", line 56, in build
>    self.buildCloseContactAtoms(percentCutoff)              #
>  File "C:\Program Files\MGLTools
>1.5.2\MGLToolsPckgs\MolKit\interactionDescriptor.py", line 65, in
>buildCloseContactAtoms
>    self.macro_atoms, percentCutoff=percentCutoff)
>  File "C:\Program Files\MGLTools
>1.5.2\MGLToolsPckgs\MolKit\distanceSelector.py", line 106, in select
>    bigC = Numeric.resize(c, (lenC, lenC, 3))
>  File "C:\Program Files\MGLTools
>1.5.2\MGLToolsPckgs\numpy\core\fromnumeric.py", line 541, in resize
>    a = concatenate( (a,)*n_copies)
>MemoryError
>
>Orelse is there any other software, I can use for this purpose? Any kind of
>help in this regard is highly appreciable.
>
>Thanks and regards,
>Latha,


text:
# naginterfaces.library.fit.dim1_cheb_eval¶

naginterfaces.library.fit.dim1_cheb_eval(a, xcap)[source]

dim1_cheb_eval evaluates a polynomial from its Chebyshev series representation.

For full information please refer to the NAG Library document for e02ae

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/e02/e02aef.html

Parameters
afloat, array-like, shape

must be set to the value of the th coefficient in the series, for .

xcapfloat

, the argument at which the polynomial is to be evaluated. It should lie in the range to , but a value just outside this range is permitted (see Exceptions) to allow for possible rounding errors committed in the transformation from to discussed in Notes. Provided the recommended form of the transformation is used, a successful exit is thus assured whenever the value of lies in the range to .

Returns
pfloat

The value of the polynomial.

Raises
NagValueError
(errno )

On entry, and .

Constraint: , where is machine precision.

(errno )

On entry, .

Constraint: .

Notes

dim1_cheb_eval evaluates the polynomial

for any value of satisfying . Here denotes the Chebyshev polynomial of the first kind of degree with argument . The value of is prescribed by you.

In practice, the variable will usually have been obtained from an original variable , where and

Note that this form of the transformation should be used computationally rather than the mathematical equivalent

since the former guarantees that the computed value of differs from its true value by at most , where is the machine precision, whereas the latter has no such guarantee.

The method employed is based on the three-term recurrence relation due to Clenshaw (1955), with modifications to give greater numerical stability due to Reinsch and Gentleman (see Gentleman (1969)).

For further details of the algorithm and its use see Cox (1974) and Cox and Hayes (1973).

References

Clenshaw, C W, 1955, A note on the summation of Chebyshev series, Math. Tables Aids Comput. (9), 118–120

Cox, M G, 1974, A data-fitting package for the non-specialist user, Software for Numerical Mathematics, (ed D J Evans), Academic Press

Cox, M G and Hayes, J G, 1973, Curve fitting: a guide and suite of algorithms for the non-specialist user, NPL Report NAC26, National Physical Laboratory

Gentleman, W M, 1969, An error analysis of Goertzel’s (Watt’s) method for computing Fourier coefficients, Comput. J. (12), 160–165


text:
UPSKILL MATH PLUS

Learn Mathematics through our AI based learning portal with the support of our Academic Experts!

$$12$$ pencils to $$28$$ pencils as $$33$$ wallets to $$84$$ wallets .


text:
Project 3 - Fun with Frequencies

By Anthony Sutardja

This project tinkers with images in the frequency domain. I use the approximations of the Laplacian of a Gaussian and Gaussian filters to filter the images.

Sharpening

In order to sharpen images, I used the technique described in class: increasing sharpness by adding a multiple (here described as alpha) of the "detail portion" of the image, which is the original image subtracted from a gaussian filtered version of the image.

(Top left: original image; Top right: sharpen with alpha @ 0.3; Bottom left: sharpen with alpha @ 0.5; Bottom right: sharpen with alpha @ 0.9)

Hybrid Images

The hybrid images are a composite of two images: one image is modified with a low-pass filter (Gaussian) and the other is modified with a high-pass filter (Laplacian of a Gaussian). I used a box appproximation of both of these filters.

Jesus Colbert

The frequency plots of both the original Jesus and Colbert images are shown below.

I applied the low-pass Gaussian filter to the Jesus image, and the high-pass Laplacian of the Gaussian filter to the Colbert image. I chose to approximate cutoff frequencies with $$f_c = \sigma_c = \frac{1}{2 \pi \sigma}$$. From the frequency plots of the filtered images below, we can see that the low-pass and high-pass filters worked on each image. The hybrid image is then combined together with different weightings. My best result is presented below. From up close, you can see the sharp outlines of Stephen Colbert, but from far away you can only see Jesus. Other hybrid images didn't work out as well as the Colbert Jesus hybrid. Colbert Jesus worked out so well because the silhouettes of the two different images align very well. The other images didn't work out as well because they were just so vastly different from each other. Surfer meets Cal logo Cat Person Tony Wu meets Panda Gaussian & Laplacian Stacks Salvador Dali's Lincoln Painting Colbert Jesus The Gaussian and Laplacian stacks for my favorite image clearly distinguishes the separate images of Stephen Colbert and Jesus. Multiresolution Blending (Spline) My implementation of multiresolution blending uses Laplacian and Gaussian stacks (rather than pyramids). Space Desert Both images are processsed into a 5 level Laplacian stack, with each level using a larger and larger sigma. The sigma corresponds to the Gaussian that is used to approximate the Laplician (recall that I approximate the Laplacian by subtracting the Gaussian filtered image from the original image). The next step is to create a Gaussian stack of the image mask. A laplacian stack of the splined image is then composited based on the weighting from the filtered image mask for each level in the stack: $$LN(i, j, d) = mask(i, j, d) * LA(i,j,d) + (1 -mask(i, j,d)) * LB(i,j,d)$$ where $$LN$$ is the new Laplacian stack, $$LA$$$and $$LB$$$ are the Laplacian stacks of the images that we want to blend, and $$d$$\$ is the level of the stack.

The result is a blended image:

Bells and whistles

Color multiresolution blending

See the multiresion blending images to see the results.

While creating the Gaussian stacks (which is used by the Laplacian stacks), I padded the images with a reflected portion of the image. The program then automatically crops the images down to the original size.

References

Picture sources

• http://imagesci.com/img/2013/12/planet-earth-from-space-2705-hd-wallpapers.jpg
• http://500px.com/photo/84429643/chuysky-trakt-in-kurai-steppe-by-vyacheslav-maslov
• http://500px.com/photo/84428591/twin-by-mang-day-
• http://500px.com/photo/84429521/morning-glory-morning-by-daniel-ripplinger
• http://www.sports-logos-screensavers.com/user/California_Golden_Bears2.jpg
• http://cdn.theatlantic.com/static/infocus/surf091411/s01_20153614.jpg
• http://images6.fanpop.com/image/photos/34900000/Cute-Panda-Bears-animals-34915025-2560-1600.jpg


text:
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G = C4○D4×D13order 416 = 25·13

Direct product of C4○D4 and D13

Series: Derived Chief Lower central Upper central

 Derived series C1 — C26 — C4○D4×D13
 Chief series C1 — C13 — C26 — D26 — C22×D13 — C2×C4×D13 — C4○D4×D13
 Lower central C13 — C26 — C4○D4×D13
 Upper central C1 — C4 — C4○D4

Generators and relations for C4○D4×D13
G = < a,b,c,d,e | a4=c2=d13=e2=1, b2=a2, ab=ba, ac=ca, ad=da, ae=ea, cbc=a2b, bd=db, be=eb, cd=dc, ce=ec, ede=d-1 >

Subgroups: 1040 in 164 conjugacy classes, 87 normal (16 characteristic)
C1, C2, C2 [×8], C4, C4 [×3], C4 [×4], C22 [×3], C22 [×10], C2×C4 [×3], C2×C4 [×13], D4 [×3], D4 [×9], Q8, Q8 [×3], C23 [×3], C13, C22×C4 [×3], C2×D4 [×3], C2×Q8, C4○D4, C4○D4 [×7], D13 [×2], D13 [×3], C26, C26 [×3], C2×C4○D4, Dic13, Dic13 [×3], C52, C52 [×3], D26, D26 [×3], D26 [×6], C2×C26 [×3], Dic26 [×3], C4×D13, C4×D13 [×9], D52 [×3], C2×Dic13 [×3], C13⋊D4 [×6], C2×C52 [×3], D4×C13 [×3], Q8×C13, C22×D13 [×3], C2×C4×D13 [×3], D525C2 [×3], D4×D13 [×3], D42D13 [×3], Q8×D13, D52⋊C2, C13×C4○D4, C4○D4×D13
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], C4○D4 [×2], C24, D13, C2×C4○D4, D26 [×7], C22×D13 [×7], C23×D13, C4○D4×D13

Smallest permutation representation of C4○D4×D13
On 104 points
Generators in S104
(1 40 24 32)(2 41 25 33)(3 42 26 34)(4 43 14 35)(5 44 15 36)(6 45 16 37)(7 46 17 38)(8 47 18 39)(9 48 19 27)(10 49 20 28)(11 50 21 29)(12 51 22 30)(13 52 23 31)(53 100 75 84)(54 101 76 85)(55 102 77 86)(56 103 78 87)(57 104 66 88)(58 92 67 89)(59 93 68 90)(60 94 69 91)(61 95 70 79)(62 96 71 80)(63 97 72 81)(64 98 73 82)(65 99 74 83)
(1 56 24 78)(2 57 25 66)(3 58 26 67)(4 59 14 68)(5 60 15 69)(6 61 16 70)(7 62 17 71)(8 63 18 72)(9 64 19 73)(10 65 20 74)(11 53 21 75)(12 54 22 76)(13 55 23 77)(27 82 48 98)(28 83 49 99)(29 84 50 100)(30 85 51 101)(31 86 52 102)(32 87 40 103)(33 88 41 104)(34 89 42 92)(35 90 43 93)(36 91 44 94)(37 79 45 95)(38 80 46 96)(39 81 47 97)
(53 75)(54 76)(55 77)(56 78)(57 66)(58 67)(59 68)(60 69)(61 70)(62 71)(63 72)(64 73)(65 74)(79 95)(80 96)(81 97)(82 98)(83 99)(84 100)(85 101)(86 102)(87 103)(88 104)(89 92)(90 93)(91 94)
(1 2 3 4 5 6 7 8 9 10 11 12 13)(14 15 16 17 18 19 20 21 22 23 24 25 26)(27 28 29 30 31 32 33 34 35 36 37 38 39)(40 41 42 43 44 45 46 47 48 49 50 51 52)(53 54 55 56 57 58 59 60 61 62 63 64 65)(66 67 68 69 70 71 72 73 74 75 76 77 78)(79 80 81 82 83 84 85 86 87 88 89 90 91)(92 93 94 95 96 97 98 99 100 101 102 103 104)
(1 13)(2 12)(3 11)(4 10)(5 9)(6 8)(14 20)(15 19)(16 18)(21 26)(22 25)(23 24)(27 36)(28 35)(29 34)(30 33)(31 32)(37 39)(40 52)(41 51)(42 50)(43 49)(44 48)(45 47)(53 58)(54 57)(55 56)(59 65)(60 64)(61 63)(66 76)(67 75)(68 74)(69 73)(70 72)(77 78)(79 81)(82 91)(83 90)(84 89)(85 88)(86 87)(92 100)(93 99)(94 98)(95 97)(101 104)(102 103)

G:=sub<Sym(104)| (1,40,24,32)(2,41,25,33)(3,42,26,34)(4,43,14,35)(5,44,15,36)(6,45,16,37)(7,46,17,38)(8,47,18,39)(9,48,19,27)(10,49,20,28)(11,50,21,29)(12,51,22,30)(13,52,23,31)(53,100,75,84)(54,101,76,85)(55,102,77,86)(56,103,78,87)(57,104,66,88)(58,92,67,89)(59,93,68,90)(60,94,69,91)(61,95,70,79)(62,96,71,80)(63,97,72,81)(64,98,73,82)(65,99,74,83), (1,56,24,78)(2,57,25,66)(3,58,26,67)(4,59,14,68)(5,60,15,69)(6,61,16,70)(7,62,17,71)(8,63,18,72)(9,64,19,73)(10,65,20,74)(11,53,21,75)(12,54,22,76)(13,55,23,77)(27,82,48,98)(28,83,49,99)(29,84,50,100)(30,85,51,101)(31,86,52,102)(32,87,40,103)(33,88,41,104)(34,89,42,92)(35,90,43,93)(36,91,44,94)(37,79,45,95)(38,80,46,96)(39,81,47,97), (53,75)(54,76)(55,77)(56,78)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74)(79,95)(80,96)(81,97)(82,98)(83,99)(84,100)(85,101)(86,102)(87,103)(88,104)(89,92)(90,93)(91,94), (1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39)(40,41,42,43,44,45,46,47,48,49,50,51,52)(53,54,55,56,57,58,59,60,61,62,63,64,65)(66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91)(92,93,94,95,96,97,98,99,100,101,102,103,104), (1,13)(2,12)(3,11)(4,10)(5,9)(6,8)(14,20)(15,19)(16,18)(21,26)(22,25)(23,24)(27,36)(28,35)(29,34)(30,33)(31,32)(37,39)(40,52)(41,51)(42,50)(43,49)(44,48)(45,47)(53,58)(54,57)(55,56)(59,65)(60,64)(61,63)(66,76)(67,75)(68,74)(69,73)(70,72)(77,78)(79,81)(82,91)(83,90)(84,89)(85,88)(86,87)(92,100)(93,99)(94,98)(95,97)(101,104)(102,103)>;

G:=Group( (1,40,24,32)(2,41,25,33)(3,42,26,34)(4,43,14,35)(5,44,15,36)(6,45,16,37)(7,46,17,38)(8,47,18,39)(9,48,19,27)(10,49,20,28)(11,50,21,29)(12,51,22,30)(13,52,23,31)(53,100,75,84)(54,101,76,85)(55,102,77,86)(56,103,78,87)(57,104,66,88)(58,92,67,89)(59,93,68,90)(60,94,69,91)(61,95,70,79)(62,96,71,80)(63,97,72,81)(64,98,73,82)(65,99,74,83), (1,56,24,78)(2,57,25,66)(3,58,26,67)(4,59,14,68)(5,60,15,69)(6,61,16,70)(7,62,17,71)(8,63,18,72)(9,64,19,73)(10,65,20,74)(11,53,21,75)(12,54,22,76)(13,55,23,77)(27,82,48,98)(28,83,49,99)(29,84,50,100)(30,85,51,101)(31,86,52,102)(32,87,40,103)(33,88,41,104)(34,89,42,92)(35,90,43,93)(36,91,44,94)(37,79,45,95)(38,80,46,96)(39,81,47,97), (53,75)(54,76)(55,77)(56,78)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74)(79,95)(80,96)(81,97)(82,98)(83,99)(84,100)(85,101)(86,102)(87,103)(88,104)(89,92)(90,93)(91,94), (1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39)(40,41,42,43,44,45,46,47,48,49,50,51,52)(53,54,55,56,57,58,59,60,61,62,63,64,65)(66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91)(92,93,94,95,96,97,98,99,100,101,102,103,104), (1,13)(2,12)(3,11)(4,10)(5,9)(6,8)(14,20)(15,19)(16,18)(21,26)(22,25)(23,24)(27,36)(28,35)(29,34)(30,33)(31,32)(37,39)(40,52)(41,51)(42,50)(43,49)(44,48)(45,47)(53,58)(54,57)(55,56)(59,65)(60,64)(61,63)(66,76)(67,75)(68,74)(69,73)(70,72)(77,78)(79,81)(82,91)(83,90)(84,89)(85,88)(86,87)(92,100)(93,99)(94,98)(95,97)(101,104)(102,103) );

G=PermutationGroup([(1,40,24,32),(2,41,25,33),(3,42,26,34),(4,43,14,35),(5,44,15,36),(6,45,16,37),(7,46,17,38),(8,47,18,39),(9,48,19,27),(10,49,20,28),(11,50,21,29),(12,51,22,30),(13,52,23,31),(53,100,75,84),(54,101,76,85),(55,102,77,86),(56,103,78,87),(57,104,66,88),(58,92,67,89),(59,93,68,90),(60,94,69,91),(61,95,70,79),(62,96,71,80),(63,97,72,81),(64,98,73,82),(65,99,74,83)], [(1,56,24,78),(2,57,25,66),(3,58,26,67),(4,59,14,68),(5,60,15,69),(6,61,16,70),(7,62,17,71),(8,63,18,72),(9,64,19,73),(10,65,20,74),(11,53,21,75),(12,54,22,76),(13,55,23,77),(27,82,48,98),(28,83,49,99),(29,84,50,100),(30,85,51,101),(31,86,52,102),(32,87,40,103),(33,88,41,104),(34,89,42,92),(35,90,43,93),(36,91,44,94),(37,79,45,95),(38,80,46,96),(39,81,47,97)], [(53,75),(54,76),(55,77),(56,78),(57,66),(58,67),(59,68),(60,69),(61,70),(62,71),(63,72),(64,73),(65,74),(79,95),(80,96),(81,97),(82,98),(83,99),(84,100),(85,101),(86,102),(87,103),(88,104),(89,92),(90,93),(91,94)], [(1,2,3,4,5,6,7,8,9,10,11,12,13),(14,15,16,17,18,19,20,21,22,23,24,25,26),(27,28,29,30,31,32,33,34,35,36,37,38,39),(40,41,42,43,44,45,46,47,48,49,50,51,52),(53,54,55,56,57,58,59,60,61,62,63,64,65),(66,67,68,69,70,71,72,73,74,75,76,77,78),(79,80,81,82,83,84,85,86,87,88,89,90,91),(92,93,94,95,96,97,98,99,100,101,102,103,104)], [(1,13),(2,12),(3,11),(4,10),(5,9),(6,8),(14,20),(15,19),(16,18),(21,26),(22,25),(23,24),(27,36),(28,35),(29,34),(30,33),(31,32),(37,39),(40,52),(41,51),(42,50),(43,49),(44,48),(45,47),(53,58),(54,57),(55,56),(59,65),(60,64),(61,63),(66,76),(67,75),(68,74),(69,73),(70,72),(77,78),(79,81),(82,91),(83,90),(84,89),(85,88),(86,87),(92,100),(93,99),(94,98),(95,97),(101,104),(102,103)])

80 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 2H 2I 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 13A ··· 13F 26A ··· 26F 26G ··· 26X 52A ··· 52L 52M ··· 52AD order 1 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 13 ··· 13 26 ··· 26 26 ··· 26 52 ··· 52 52 ··· 52 size 1 1 2 2 2 13 13 26 26 26 1 1 2 2 2 13 13 26 26 26 2 ··· 2 2 ··· 2 4 ··· 4 2 ··· 2 4 ··· 4

80 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 2 4 type + + + + + + + + + + + + image C1 C2 C2 C2 C2 C2 C2 C2 C4○D4 D13 D26 D26 D26 C4○D4×D13 kernel C4○D4×D13 C2×C4×D13 D52⋊5C2 D4×D13 D4⋊2D13 Q8×D13 D52⋊C2 C13×C4○D4 D13 C4○D4 C2×C4 D4 Q8 C1 # reps 1 3 3 3 3 1 1 1 4 6 18 18 6 12

Matrix representation of C4○D4×D13 in GL4(𝔽53) generated by

 52 0 0 0 0 52 0 0 0 0 30 0 0 0 0 30
,
 52 0 0 0 0 52 0 0 0 0 52 30 0 0 7 1
,
 1 0 0 0 0 1 0 0 0 0 1 0 0 0 46 52
,
 32 1 0 0 16 32 0 0 0 0 1 0 0 0 0 1
,
 13 39 0 0 12 40 0 0 0 0 1 0 0 0 0 1
G:=sub<GL(4,GF(53))| [52,0,0,0,0,52,0,0,0,0,30,0,0,0,0,30],[52,0,0,0,0,52,0,0,0,0,52,7,0,0,30,1],[1,0,0,0,0,1,0,0,0,0,1,46,0,0,0,52],[32,16,0,0,1,32,0,0,0,0,1,0,0,0,0,1],[13,12,0,0,39,40,0,0,0,0,1,0,0,0,0,1] >;

C4○D4×D13 in GAP, Magma, Sage, TeX

C_4\circ D_4\times D_{13}
% in TeX

G:=Group("C4oD4xD13");
// GroupNames label

G:=SmallGroup(416,222);
// by ID

G=gap.SmallGroup(416,222);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-13,86,297,13829]);
// Polycyclic

G:=Group<a,b,c,d,e|a^4=c^2=d^13=e^2=1,b^2=a^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=a^2*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e=d^-1>;
// generators/relations

׿
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text: c is the speed of light in vacuum - 299 792. The refractive index is simply the bending power of a material. The shader is able to detect and create variations in liquid based on objects and shorelines. You can use the water for shallow pools with the opacity low, or deeper water with the opacity high. Seit den Filmen Jurrasic Park und Terminator wissen wir alle, was 3D Effekte sind. Certain eye structures have refractive properties similar to water or lenses and can bend light rays into a precise point of focus essential for sharp vision. if we capture image for an object located underwater with 1 meter depth and we capture image for the same object with depth 2 meters). You must have seen a prism right , it makes the light split inti the visible electromagnetic spectrum When you enter a swimming pool dont you see something strange under watter , your legs look smaller , if you half submerge a pencil in a bowl of water , it will look broken. Aug 14, 2009 · My first approach has been to use a refraction shader (more or less the one that comes with Unity pro assets) and add that to a plane beneath the character aligned to the water plane. When a beam of light travels between two media having different refractive indices, the beam undergoes refraction, and changes direction when it passes from the first medium into the second. I'm trying to create an OpenGL application with water waves and refraction. The part of the pencil above the water does not distort since the light only has to travel through one medium (air). Jul 13, 2016Oct 31, 2016Jan 5, 2018Feb 4, 2015Apr 15, 2014 hello, i have some problems with my unreal 4 water it's also a thread in the answerhub on the unreal site, but perhaps you can also help me Air has a refractive index of 1 while water has a refractive index of 1. This is useful for things like glass and water, which refract light that Pixel Normal Offset enables refraction for these large flat surfaces, like water, where you do not want this constant offset that is reading from off screen so much. Here is a list of Nodes we need: Scalar Parameter – Name it ‘Murkiness’. 1 Before you get started you can download the test project using the water shader in case you would like to quickly add it to your project or would like to reverse engineer the material. Place the blu tack in the middle of the coin. Thus it covers even more distance than if it were traveling over level ground that does not reflect like water. Nov 19, 2014 · Create a Comment Box and Name it Water Color and attach these nodes like how they are attached above. The velocity of light changes depends on the WebGL Water. When light passes through water and is thus refracted, the water deeper down gets tinted. Arther Omari. . More than 28 million people use GitHub to discover, fork, and contribute to over 85 million projects. com/imagesSee more images of ue4 water refractionUE4 refraction problem and depth fade problem and. Most people would assume that the refractive index of water is known to a high degree of accuracy. Refraction & Light Experiments: Easy Science for Kids. This change in the direction of wave is called refraction of wave. The lower half is all hand-drawn 2D, including water FX, shadows, reflections and creature animation. When a wave passes from one medium to another medium, the wave will change its speed and its direction. My first approach has been to use a refraction shader (more or less the one that comes with Unity pro assets) and add that to a plane beneath the character aligned to the water plane. Unreal Engine Hallways Editor Engineering Sci Fi Runners Foyers Science Fiction Entrance Halls Zelda Water Shader Help - Polycount Forum" See more. And that's a shame. . Where the sea floor rises suddenly, the refraction …Dec 06, 2018 · Water has a refractive index of about 1. Reﬂections and Refractions in Ray Tracing Bram de Greve (bram. Coherent Laser light is different from regular light because the light waves are _____. The part of the wave in shallow water will move slower than the part of the wave in deeper water. In this investigation, n1will be the index of refraction of air, or 1. This blog focuses on shader and blueprint development in Unreal Engine 4 from a tech artist's perspective. A man looks down at a fish length of 20 cm. When light travels from air through water, glass or anything that Fun Science. ) Waves entering a medium with slower wave speed are refracted towards the normal. Snell's law predicts the angle of refraction that light You must have Pro, because the effect is applied at real time over the image rendered behind the transparent object. Index of refraction of any medium is defined as the proportion between the light of speed in vacuum and in the investigated medium. Refractive index of water. This blog focuses on shader and blueprint development in Unreal Engine 4 from a Refraction depth bias is a way to prevent closer objects from rendering into the distorted surface at acute viewing angles. Learn vocabulary, terms, and more with flashcards, games, and other study tools. So it will grab stuff above the water that will wrongly get refracted on the water surface. An example to understand this better is that of placing a straw/stick in a glass of water wherein it to be bent when viewed from any other angle than 90 0 to the surface. The process of editing water flow per-vertex is a little inconvenient because there is no tool for this in UE4 …The absolute index of refraction of a material is defined as the ratio of the speed of light in a vacuum (c) with respect to the speed of light in the material (v). I need to either cast rays from the sun and then the camera and figure out where they intersect, or I need to start from the ocean floor and figure out in which direction(s, if any) I have to go in order to hit the sun or the camera. unrealengine) submitted 2 years ago by xhudaman So I am trying to get more comfortable in the material editor and I wanted to learn how to use refraction. I think that it resembles smoke more than water so I am wondering would you use any base color, or make the whole thing with emiss…Jan 16, 2015 · The first thing I wanted to do with the new UE4 is create a new and improved all-purpose water shader. If you look up pictures of water drops on a window in detail (or, of course, observed them in real life already), you will notice that, due to refraction, the raindrops appear …In the experiment light traveled from the air, through the glass, through the water, through the back of the glass, and then back through the air, before hitting the arrow. Probably because the standard sky from UE4 has a very bright base whenever the light doesn't adjust. The eye's natural (crystalline) lens also bends light rays. True Fish. If you can't run the demo, you can still see it on YouTube. It’s a good method, but recently I had a chance to develop a different approach – this one is strictly shader-based. Separate the words with plus signs (cat +dog) to search for items that may contain cat but must contain dog. Aug 14, 2009 · Hi, I'm trying to do some refraction around our character when he swims in our water. As you sight at the portion of the pencil beneath the water, light travels from water to air, causing refraction. The rivulet of water forming and rolling around the pipe is a static mesh with a custom refraction material, which is animated in Matinee so that it rises from the seam in …Index of Refraction values (IOR) - For use with 3d modeling / rendering and animation applications. This tutorial will go through how to set up a swimmable water volume using a “Physics Volume” in conjunction with a “Post Process Volume” to get the basic look and feel of swimming underwater. Most refraction in the eye occurs when light rays travel through the curved, clear front surface of the eye . n2is the index of refraction of the secondary medium, which in this case will be water. 10 Refraction and IOR ⏬ Adding Refraction and IOR (Index of Refraction) to Materials in Unreal Engine 4. Here is a very simple example showing how Refraction works. Already complete, will be in the next release. Refraction of water waves is the bending of waves due to changes in wave velocity caused by varying water depths underneath. Index of refraction formula. Dec 13, 2012 · Refraction -- A fish under water 1. Different types of medium include air and water. Velocity and wavelength of wave coming from deep part of water tank to shallow part decrease. How To Create An Animated Water Material in UE4 Animated Water Material in Unreal Engine 4 Hey guys, today I’ll be showing you a simple yet effective technique for creating a …Before you get started you can download the test project using the water shader in case you would like to quickly add it to your project or would like to reverse engineer the material. Real-time ambient occlusion, radiosity, global illumination, refraction, etc that's the kind of thing that is (technically) impressive in an engine, but so var very little of this (beautiful) Unreal/Unity/* demos actually deliver that. Stylized Character Production Techniques in UE4 Founder of Thunder Cloud Studio Dzung Phung Dinh did a detailed breakdown of the amazing Pisciasa character, revealing how he worked with materials To make water, you need just 4 things: a mesh, a shader, a normal map, and a script. The top half is a background still from my UE4 river environment. Simple searches use one or more words. 13. Guide for using Refraction in your Materials. Report this video. 3. Unity Pro has the Glass Refraction package, which uses bump maps to define the refraction, and in the wiki you can find this refraction shader, that uses the object geometry instead of …This will cause the decal to blend Base Color, Metallic, Specular, Roughness, Emissive color, Opacity, and Normal. I use it for a small river so I set a trigger collider which enables it when you're close to the water and disables it when it's out of sight. Water Surface Overview in UE4. Material Properties. Dec 15, 2018 · Nice job on this, but let’s talk glass…. Alessa Baker has recently published an amazing little product - Stylized Water Shader for UE4 which gives you a fully customizable, distance field based water for UE4. Play with prisms of different shapes and make rainbows. With this you can blend in an entirely separate material, such as a wavy water puddle, complete with normal map-based muddy building around it. Explain how light bends at the interface between two media and what determines the angle A demonstration of what happens when light travels through water or glass. Is the effect of water Refraction on first image less than the second. Made by Evan Wallace. Over the past few years I have been collecting IOR (Index of Refraction) values I can find for use in 3d rendering applications. The part of the pencil that is placed in the water will appear bent where the pencil and water meet due to Refraction. The Shader for the cornea and conjunctiva outer layer is a transparent material with an IOR of 1. Propagation of waves has both a speed and a direction, called the velocity. g. 8 for all water materials based on experimentation of …UE4: How to Insert, Apply and Use Decals Inside Your Level Tutorial ⏬ Now, learn how to insert and use decals inside your level. 9 Refraction for Sound Waves. SeaWorld Aquatica Orlando Water Park 2015 Tour and Overview | Orlando Florida. This happens because of bending of light Refraction of Waves Waves change direction when passing from one medium to another. Refraction of Waves Waves change direction when passing from one medium to another. Reactive Water is a Blueprint driven Actor that reacts to any movement of an Actor, who interacts with it, by creating foam, small waves and playing a sound at the location. While most "UE4 Tutorial: Light a cinematic scene" See more. This tool looks for lower prices at other stores while you shop on Amazon and tells you where to buy. 0 answers 6 views 0 votes ue4 how to avoid boundary seams with multiple refractive meshes Updated May 01, 2017 14:13 PM. Light travels and bounces off surfaces into our eyes. However, as shown in Fig. 0; Scalar Parameter – Name it ‘Refraction Amount’. Advanced fully functional multi platform material-pack for water - over water surface, underwater, post-process volume, buoyancy, interactions and caustics. Many 3d applications these days allow you to input actual IOR values in order to achieve a more accurate representation of surfaces during rendering of your 3d models. com) November 13, 2006 Abstract When writing a ray tracer, sooner or later you’ll stumble on the problem of reﬂection and transmission. The dead giveaway that tells you when Amazon has the best price. When looking from water to air we see the (usually 180° from horizon to horizon) world above the water as a cone of about 96°. From this definition, we see that the index of refraction is a dimensionless number that is greater than one because c is always greater than v. This is useful for things like glass and water, which refract light that passes through them. Refraction is the "breaking or bending" of waves as it travels to a different density media. H. More info See in Glossary > Water. When the glass is full of water, it acts as a cylindrical convex lens, and produces an inverted image. its scalar so you don't need a normal map, or you could use like blue channel or something. The scale of the water is smaller that a large waterfall, so the look needs to stay smooth till about half way down where it starts to break up and get that white foamy look to it. Nov 28, 2017 · About your question, the problem is not the water but the script for the refraction. See how changing from air to water to glass changes the bending angle. com provides the Science Fair Project Ideas for informational purposes only. 4, meaning light travels twice as fast in a vacuum as it does through a diamond. When RI is used as a detector in HPLC, only isocratic separations can be applied. I am trying to create a hug splash of water like the water you see when a whale breaches. The Refraction input takes in a texture or value that simulates a surface's index of refraction. Water mode (Simple, Reflective, Refractive) can be set in the Inspector. 0: God rays, volumetric light, lens flares & dirt, visor reflections / water droplets, depth of field, night & thermal vision scopes, dynamic wet surfaces with reflections, rainbows and many other effects. During refraction velocity and wavelength of waves change however, frequency of waves stay constant. Swimmable Water Volume. 33 (water) means that light travels 1. If you would like to contribute to this project, please PM me on …If you look up pictures of water drops on a window in detail (or, of course, observed them in real life already), you will notice that, due to refraction, the raindrops appear to …The refraction, dispersion and reflection of sunlight from thousands of water droplets in the air produces a _____. Interactions: Draw on the water to make ripplesRefraction is the bending of something as it travels through a different material. Please try again later. Surface movement and underwater refraction was doneReal-time ambient occlusion, radiosity, global illumination, refraction, etc that's the kind of thing that is (technically) impressive in an engine, but so var very little of this (beautiful) Unreal/Unity/* demos actually deliver that. Like the Max/Vray to Unreal Datasmith workflow, any sort of glass coming over from pretty much any other platform is completely worthless in Unreal Studio; usually giving you horrendous refraction problems. I made HUGE strides in UDK making a vertex-paint water surface that had approximate refraction and appropriate colour wavelength leeching. 0005 for 1°C and for water is about 0. Light travels faster in water than in glass, but slower than in air (air has an refractive index very close to 1 and in CG we almost always treat air as if it was a vacuum). Then attach the Multiply to the Base Color in the Main Board. Reactive Water is a Blueprint driven Actor, which can be easily added to your level by drag and drop it from the content Swimmable Water Volume. Follow. Stain: Only blends Base Color and Opacity. I was using particles to help cover up that transition between the “clear” water using refraction …V 3. 0001). Sites explaining refraction …WATER. Refraction In Materials (self. (1) Mesh The mesh is the water itself, but without a shader and a script, it won't look like water, it'll look like a sheet, basically. 34. The amount of bending depends on the angle at which the light ray strikes the boundary, as well as the refractive indices [3] of the two materials (in this case, air and water). Metallic is set to 0. com/youtube?q=ue4+water+refraction&v=LnLHneZn3qw Feb 4, 2015 Adding Refraction and IOR (Index of Refraction) to Materials in Unreal Engine 4. We will talk about light bending, but there are other things like sound waves and seismic waves (earthquakes) that also refract. Check the Youtube comments for that. Now is a good time to name the nodes. For doing this, I've learned some basic stuff in shader forge, which probably an easy-use tool for me. its scalar so you don't need a normal map, or you could use like blue channel or something. What happens to1. This demo requires a decent graphics card and up-to-date drivers. Next up is the animation part. Light travels in waves, and we call this traveling propagation. 46 km/s, v is …Start studying 25-26 wave refraction. Nope . Prev. [ #UE4 #Environtment ] Alessa Baker has recently published an amazing little product - Stylized Water Shader for UE4 which gives you a [ #UE4 #Environtment ] Alessa Baker has recently published an amazing little product - Stylized Water Shader for UE4 which gives you a fully customizable, distance field based water for UE4. I’ve shown one technique for water droplets in the past by using Forest Pro. I was using particles to help cover up that transition between the “clear” water using refraction …An IOR value of 1. To visualize mirror-like objects, you need to reﬂect your viewing rays. Refraction. When light passes through transparent objects (in this case, the front of the glass, the water, and the back of the glass), it refracts or bends. When the light passes from one material, into another, it bends or refracts i. When light passes from one medium to another, say from air to water, the direction that the light was traveling will The Refraction input takes in a texture or value that simulates a surface's index of refraction. Fancier water - Daylight Water and Nighttime Water in Pro Standard Assets > Water (this needs some Assets from Standard Assets > Water as well). Water Shader Example Project. The first material is your original translucent water material, you need . My question: Is the effects of the Water Refraction are related to the water depth (e. Refraction 入力は、表面の屈折インデックスをシミュレーションするテクスチャまたは値を受け取ります。通過するライトを屈折させるガラスや水などに実用的です。[ #UE4 #Environtment ] Alessa Baker has recently published an amazing little product - Stylized Water Shader for UE4 which gives you a fully customizable, distance field based water for UE4. 33 times slower through water than it does the empty vacuum of space. Outside that 96° cone is a (much darker) reflection from the water below: Navy Diver 2nd Class Ryan Arnold viewed from below. Underwater Caustics (Simple) NOTE - Not happy with the current implementation, needs more work - transferring this back to WIP Caustic effects from light refraction through the water surface projected onto the landscape below. For example, when light crosses through a window, it is refracted and can create a rainbow. Refraction of light in water. Ask Question. refraction should be 1 = no refraction and you go above or below to change refraction index. Reflection And Refraction Reflection Art Edward Weston Distortion Photography Reflection Photography Fine Art Photography Landscape Photography Black And White Photography Komposition (UE4) City Subway Train photographer Suzanne Saroff creates fractured and skewed images of common foods as seen through vessels filled with water and Refraction is the change in direction of a wave, caused by the change in the wave's speed. Fade in distance from the water line. Name one the dark one - Dark_Colour and the light one - Light_Colour. Step 2 – Transparency and Refraction. Japanese GardenNext, import into Unreal and create the six materials (or basically two materials - one water, one nodraw). Let us say the refractive indices of air and water …The index of refraction of red light in water is about 1. Snell's law of refraction can be applied to the refraction light for any two media. Apply these materials to the box faces in the StaticMesh Editor. I've searched a lot online, but still can't find a tutorial or method about making a shader for water with shader forge. Stylized Character Production Techniques in UE4 Founder of Thunder Cloud Studio Dzung Phung Dinh did a detailed breakdown of the amazing Pisciasa character, revealing how he worked with materials More info See in Glossary > Water. In fact, for most materials the smaller the wavelength of the light, the larger the index of refraction, which means smaller wavelength light will bend more than larger wavelength light will in most materials. Water Line Refraction Width: The width of the refraction effect. Therefore, when the depth of water varies under the crest, the wave bends and water wave refraction occurs. Index of refraction for water is equal: IOR = 1,33333 Colour extinction One of the most important aspects of proper water rendering are colour extinction as light goes deeper and deeper and also light scattering. It’ll work best if we animate 2 patterns going opposite each other. Let us say the refractive indices of air and water are n 1 and n 2, respectively. Here's a question in a paper based on refraction of light. To determine whether the light beam is composed of waves or particles, a model for each can be devised to explain the phenomenon (Figure 1). Nov 28, 2018 · GitHub is where people build software. up vote 2 down vote favorite. Report. What Is an Example of Refraction? The formation of a rainbow and the splitting of light when it passes through a prism are examples of refraction. Light refraction Opacity parameters Foam generation where water hits an object (like a landscape) Metallic strength Ocean waves Small waves Customizable normal strength Global scaling parameter, based on the scale of your water plane Water deepness Tessellation (optional)Mar 07, 2016 · Refraction works mostly fine. I am trying to create a hug splash of water like the water you see when a whale breaches. 3 years ago 13 views. Separate the words with spaces (cat dog) to search cat,dog or both. when i use greater values in the depthfade-fade distance than ~250 i get some water Jan 5, 2018 Using the BumpOffset Node with a combination of a Desaturate Node on the panning normal maps and a height parameter, it makes the layer  10 Refraction and IOR - YouTube www. Default Value = 20. The goal is to help other artists grasp more advanced technical concepts through examples. This quick experiment is so fun to do with kids, takes only 5 minutes and is SUPER EASY -- all you'll need is a pencil and a glass of water. refraction of light. The animation was done entirely in Toon Boom Harmony. Refraction is the change in direction of a wave due to a change in speed at the boundary between two media of different density. So the laser grazes the water near the sea level peak say around 10 miles, then is reflected back upward, and arcs over the 'hump' due to refraction. Note also that the water surface is not flat, so it cause a local ripple effect. 33 times faster than light in water, while diamonds have an index of about 2. Also, depending on where you are viewing from, the reflection and refraction indices can change. 99 x 10 8 m/s. However this can increases the disconnect between the surface and where the refraction starts. Elearnin 42,126 viewsAuthor: HannoverViews: 581Images of ue4 water refraction bing. 33. The Refraction input takes in a texture or value that simulates a surface's index of refraction. The Lake Water material is the foundation to understanding the Ocean Material and the Translucent material. Water reflections really …UE4 How to Avoid Boundary Seams with Multiple Refractive Meshes up vote 4 down vote favorite We use multiple box meshes to create our game world in Unreal Engine 4, but we also use those boxes with translucent/sss materials with refraction. So you might want to take that into consideration for best results. 07:00. e. Select an issue UE4 Forums thread with more info: [Community Project] WIP Weather & Ocean Water Shader. You can find more measured values in the Filmetrics Refractive Index Database . Refraction or the bending of light rays explains why objects seen through transparent objects such as glass or water, look deformed. To simulate a lens, you need refraction. In the 28 Days of STEM series, this week's topic is STEM Challenges so we thought we would introduce a science challenge that 'tricks' your eyes. You can make Pyrex glass disappear by immersing it in glycerin or mineral oil. Examples of waves include sound waves and light waves. The problem is that refraction above a value of 1 jumps out of the align I think i didn't get the concept of depthfade vs. This post is the second part in a series leading up to building custom volumetric effects inside of UE4. The phenomenon is most commonly associated with light, but can also apply to sound, or even water, waves. cglyo. Water Line Refraction: Water line refraction scale (better results with small negative values). Sound travels slower in cooler air so the sound waves below are bend toward the surface of the water where the air is cooler. The terrain is as basic as it can be, with the exception that it uses the ddx ddy formula for the normals to make the low poly look. Atmospheric fog with translucent materials is currently just broken, I can use ExponentialHeightFog thoughthis still does some odd things to the far ends of my water plane. Features: - Environment handler (Wind intensity, direction, on/off). How does he appear? 2 A parallel sided glass plate is introduced in the path of a converging beam. Aug 16, 2015 · Reflection and refraction of colored light in water air surface 2, varying incidence angle. Light refraction Opacity parameters Foam generation where water hits an object (like a landscape) Metallic strength Ocean waves Small waves Customizable normal strength Global scaling parameter, based on the scale of your water plane Water deepness Tessellation (optional)Nov 19, 2014 · Create a Comment Box and Name it Water Color and attach these nodes like how they are attached above. False Fish. I am trying to make a shader for outdoor water in my project. I can't seem to solve it for some reason. com does not make any guarantee or representation regarding the Science Fair Project Ideas and is not responsible or liable for any loss or damage, directly or indirectly, caused by your use of such information. Refraction is seen most often when a wave passes from one medium to a different medium. UE4: How to Insert, Apply and Use Decals Inside Your Level Tutorial ⏬ Now, learn how to insert and use decals inside your level. What we are seeing here is a physics concept called refraction, or the bending of light. Meaning ideally you'd mask out the caustics in primary light shadowed areas. Still Life Game, Art Studies, Unreal Engine, Game Environment, Game Art, Zbrush, Charts, Engineering, Projects. Wesson oil has a higher index of refraction than water (n = 1. 33, meaning that light in a vacuum travels about 1. Index of Refraction Values:  Unreal Engine 4 Animated Water Refraction on Vimeo vimeo. However the GrabPass will grab everything rendered in the scene. It causes a huge drop in FPS. 2. thats refraction . The same formula is used for the water. Strong caustics are usually the result of direct lighting filtering through the refraction from the water above. Refraction for Water WavesBoth reflection and refraction are also dependent on another parameter - angle of incidence, or θi. 1is the incident angle, defined The refractive index depends on temperature, and typically decreases as temperature increases (for organic solvents this decrease is about 0. I also like to tone down refraction the depth fade so it doesnt cause a seam at intersection. well polycount. Stylized Water Shader gives you a fully customizable, distance field based water that is able to detect and create variations in liquid based on objects and shorelines. I think that it resembles smoke more than water so I am wondering would you use any base color, or make the whole thing with emiss… The best example of Refraction can be seen by placing part of a pencil in water. This is the angle between the incident light and the normal to the air-water interface inside the first medium, water. 33), but a lower mass density, so it floats on water. July 11, 2014 Condensation shader for Vray. Plug the Dark_Colour into a Linear Interpolate or Lerp node (which you can find by right clicking the grid and typing lerp or in the Material Editor Reference). An IOR value of 1. We’ll manipulate our normal map to create the illusion of waves on the water surface. 5 - Part 2 of 5 Create a water shader in Maya How To 9 Free Skin 3d models found. Below are the settings used for defining the materials properties to render correctly with the instructions provided. Hi. com › Unreal Engine2. The index of refraction for the oil is very close to the index of refraction for glass. The glass material is exceedingly simple for how good it looks. Sound waves bend when passing into cooler or warmer air because the speed of sound depends on the temperature of the air. These are free to use for any purpose, even commercially, without need for attribution. Translucent water with depth fade with reflection doesn't seem to play nice right now. With refraction, to see the relationship between the angle of incidence and the refracted angle, we also need to know the indices of refraction for the two mediums the light is traveling through. The shallower the water, the slower the wave speed. This tutorial will give you an overview and example on how to create a translucent water shader and has been updated to be compatible for engine version 4. Light refraction is the bending of light, or the change in direction of the rays as it moves past a boundary. The change in direction or bending of a light wave passing from one transparent medium to another; caused by the change in wave’s speed is known as “Refraction”. ask. The refractive index equation is n = c / v, where. Education. Surface movement and underwater refraction was done© All rights reserved. Nov 01, 2016 · Refraction of light explained through cup water and coin - Science experiments for kids - Duration: 1:39. The problem statement, all variables and given/known data 1 A fish under water obliquely sees a fisher-man standing on the bank of a lake. Surface movement and underwater refraction was done Game Over Due to a severe clash of personalities and wildly divergent goals and priorities for Brackenwood, the working relationship deteriorated beyond repair and I made the decision to end the Dashkin project on Oct 24, 2018. 00. 33, but the index of refraction of blue light is closer to about 1. Surface movement and underwater refraction was doneSwimmable under water/surface for Skeletal Meshes. 1, the published literature reveals significant differences in the values of refractive index of water for a given wavelength. (The relationship is a complex one, but near shore speed is approximately proportional to the square root of depth. The Latin word "fract" in refraction means to break. com/90116704Mar 26, 2014 Testing an animated water refraction shader for use in our Dystopia project. Snell's law of refraction is the relationship between the angles of incidence and refraction with respect to the refraction indices of two different media. This video showcases the refraction effect made for a water shader in Unreal Engine 4, this is in real time and very cheap for the processor and video card. Also, we can add the same nodes as Opacity for controlling our material’s Refraction. Refractive index of water wrt air (water n air)= 4/3 Refractive index of glass wrt air (glass n air) = 3/2 Refractive index of glass How fast does light travel, and does it travel faster in water or air? The fastest thing in the whole universe is the speed of light in a vacuum (like outer space!), clocking in at a great 2. Observing Objects in Water - Java Tutorial An object seen in the water will usually appear to be at a different depth than it actually is, due to the refraction of light …Disclaimer and Safety Precautions Education. The top half is a background still from my UE4 river environment. This feature is not available right now. 0 answers 5 views 0 votes Alternatives to bloom for glow?July 11, 2014 Condensation shader for Vray. A pencil placed in a beaker of water looks bent due to refraction of light. The Prefab uses an oval-shaped Mesh for the water. Explore bending of light between two media with different indices of refraction. Glass is by far the most difficult material to get correct in Unreal, and yours looks fantastic. I personally use scene color node but there is nothing wrong with refraction and built in post process ones. This is fairly easy to make, definitely the easiest of the four. His eye is 2m above the surface of the water ($\mu = 4/3$) an the fish is 2m below the surface shown in the figure. You can adjust the Refraction Depth Bias in the following two places inside UE4. Dec 13, 2018 · Water cut off effect in UE4 Updated August 31, 2018 15:13 PM. refraction. The index of refraction depends not only on density but also on the chemical composition of a material. Oct 20, 2018 · Refraction is the bending of waves as they pass from one medium to another, due to a change in their speed. Position the blu tacked coin in the center of your pot so that it is secured down (will not move when you pour water into the pot). Light will change the angle it moves as it goes through air into water, or vice versa. degreve@gmail


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# We know that, f:RR to RR satisfies f′(x)=f(x) for all x in RR then f(x)=A e^x What is a function f:RR^d to RR^d, analogous to the exponential function, if x in RR^d was a d dimensional vector?

We know that, $f:\mathbb{R}\to \mathbb{R}$ satisfies ${f}^{\prime }\left(x\right)=f\left(x\right)$ for all $x\in \mathbb{R}$ then $f\left(x\right)=A{e}^{x}$
What is a function $f:{\mathbb{R}}^{d}\to {\mathbb{R}}^{d}$, analogous to the exponential function, if $\mathbf{x}\in {\mathbb{R}}^{d}$ was a d dimensional vector?
Is there a name given to such functions whose derivatives are the same as the function itself?
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There is a problem with defining a derivative of a map as a map between the same spaces as the original map. Given a map $f:{\mathbb{R}}^{m}\to {\mathbb{R}}^{n}$ its differential at a point $p\in {\mathbb{R}}^{m}$ (if it exists) is a linear map $Df\left(p\right):T{\mathbb{R}}^{m}\to T{\mathbb{R}}^{n}$ of tangent spaces. If m=1 then f is a vector-valued function and its differential is also a vector-valued function. In this case we can define
${f}^{\prime }\left(t\right)=\left({f}_{1}^{\prime }\left(t\right),...,{f}_{n}^{\prime }\left(t\right)\right)$
which is in fact the differential at the point t. Note that here we identify the space ${\mathbb{R}}^{n}$ with the space of linear maps $T\mathbb{R}\to T{\mathbb{R}}^{n}$ which is (luckily) n-dimensional. But if m>1 then this space of linear maps is no more n-dimensional and we can not define the derivative of a map in the same way we do in single variable calculus.


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Industrial Utility Efficiency

# Leaks

## Protect Profits with Compressed Air Leakage Best Practices

This article discusses leak assessments and the barriers to effective leak management. Some best practices will be discussed as suggested tips to help you get the most of your leakage reduction efforts. We all hear it time and time again, leakage reduction is one of the first things we can do to reduce compressed air system electrical costs. Yet almost every industrial compressed air system assessment finds high levels of leakage, and too often plant maintenance staff are fully aware they have a problem but fail to act.

## Fix Air Leaks to Keep Profits in Food and Beverage Applications from Vanishing into Thin Air

“A single ¼-inch leak in a compressed air line can cost a facility from \$2,500 to more than \$8,000 per year. Locating and fixing leaks will result in significant savings depending on pressure requirements and energy costs.”

## Milk Products Plant Finds 52 Percent Potential Savings

A food processor was having compressed air problems, so they invited a compressed air auditor into their plant for an assessment and to help them size future permanent air compressors. The plant was experiencing low air pressure and detecting water in the compressed air lines despite having a desiccant air dryer. The auditor thoroughly analyzed the compressed air system production equipment and did end-use assessment and leakage detection. This article discusses the findings leading to a potential cost savings of 52% of the current level.

## Culture Building with ENERGY STAR® Energy Treasure Hunts

There are many reasons why the U.S. Environmental Protection Agency (EPA) ENERGY STAR® Energy Treasure Hunts have proven successful in helping companies save energy and natural resources, but one that rises to the top is their ability to build a culture of energy efficiency throughout an organization.