arxiv_id
stringlengths 0
16
| text
stringlengths 10
1.65M
|
|---|---|
# Using xacro to automate inertial calculations sequence/float error
Running Ubuntu 16.04 with ROS-Kinetic I am trying to automatically calculate inertial values for a simulated robot. The purpose is to be able to change the dimensions and have the inertia automatically calculated. Here is my macro
<xacro:macro name="cuboid_inertial" params="mass length width height">
<inertial>
<mass value="${mass}"/> <inertia ixx="${0.83*mass*(${width}+${height})}"
ixy="0.0"
ixz="0.0"
iyy="${0.83*mass*(${length}+${height})}" iyz="0.0" izz="${0.83*mass*(${width}+${length})}" />
</inertial>
</xacro:macro>
I have xacro properties as follows.
<xacro:property name="base_link_length" value="0.50"/>
<xacro:property name="base_link_length_sqrd" value="${base_link_length}*${base_link_length}"/>
<xacro:property name="base_link_width_sqrd" value="${base_link_width}*${base_link_width}"/>
<xacro:property name="base_link_height_sqrd" value="${base_link_height}*${base_link_height}"/>
When I try to run the macro it comes up with an error. My link tags...
<link name="base_link">
<visual>
<geometry>
<box size="${base_link_length}${base_link_width} ${base_link_height}"/> </geometry> <material name="grey"/> </visual> <collision> <geometry> <box size="${base_link_length} ${base_link_width}${base_link_height}"/>
</geometry>
</collision>
The error is unexpected EOF while parsing (<string>, line 1) when evaluating expression '(.82)*${mass' edit retag close merge delete ## Comments Somehow the error you posted doesn't seem to correspond to the code you posted in your macro. Your numbers are different and your parentheses and braces are different. ( 2018-06-05 16:30:54 -0600 )edit 1 This seems like a duplicate of #q293296. If it is, please close either this one, or #q293296, so we avoid split discussions. ( 2018-06-06 06:21:56 -0600 )edit ## 1 Answer Sort by » oldest newest most voted The following for your macro works on my system: <xacro:macro name="cuboid_inertial" params="mass length width height"> <inertial> <mass value="${mass}"/>
<inertia
ixx="${0.83*mass*(width+height)}" ixy="0.0" ixz="0.0" iyy="${0.83*mass*(length+height)}"
iyz="0.0"
izz="${0.83*mass*(width+length)}" /> </inertial> </xacro:macro> I also changed the property block: <xacro:property name="base_link_length" value="0.50"/> <xacro:property name="base_link_width" value="0.30"/> <xacro:property name="base_link_height" value="0.35"/> <xacro:property name="base_link_length_sqrd" value="${base_link_length*base_link_length}"/>
<xacro:property name="base_link_width_sqrd" value="${base_link_width*base_link_width}"/> <xacro:property name="base_link_height_sqrd" value="${base_link_height*base_link_height}"/>
Notice that I've changed the location of the ${} sets in your calculations. more ## Comments Thank you! Just as a followup, in xacro. When you use${} is everything inbetween the brackets in the xacro namespace so all variables are essentially global variables? Sorry if that does not make sense.
( 2018-06-06 09:29:04 -0600 )edit
The \${} is used for math expressions and for substituting property values. For math expressions, anything inside the braces is evaluated with Python
( 2018-06-07 09:15:05 -0600 )edit
By default all properties and macro arguments are locally scoped (properties only visible within the single xacro file and macro args only visible within the macro). However you can pass a scope attribute to expand these to the parent scope: http://wiki.ros.org/xacro#Local_prope...
( 2018-06-07 09:18:30 -0600 )edit
|
|
# FAQ
January 01, 2020 | info
### Can I earn more than your performance?
Of course! Our performance shows close to close returns, but almost always there are differences between signal’s closing price and low (MAE for longs),and high (MFE for longs).
If you can catch those differences, then your performance can be much higher than we record.
Also, read my post on MAEs and MFEs.
### What is the minimum capital required?
You can calculate your minimum capital required using this formula:
minimum_capital = (MAE + bitcoin_price + max_drawdown) * leverage_factor
For example, if Bitcoin costs 5,000, average MAE is 200, and drawdown is 30%, then:
minimum_capital = (200 + 5000 + 0.3*5000) = 6,700
So, minimum capital for 1 bitcoin would be 6,700 USD, for 0.1 - 670 USD, for 0.01 - 67 USD and so on.
This is only minimum recommendation, in most cases you need more than just that. But if you will be able to catch sometimes huge MAE and MFE, then you’ll grow that quickly.
### How to interpret signal values?
Signal 1 means ‘buy’ or ‘hold’, -1 - sell short, 0 - close existing positon.
Signal below 1 means that you should downscale your usual position size. For example, if you trade 10 Bitcoins for strategy A, and signal is 0.25, then you should buy 2.5 Bitcoins instead of 10.
### Where can I see live returns?
We have API endpoints for live trading strategies returns, updated every day. Or you can just visit performance page, where you’ll find charts of the returns. Charts are also updated daily.
### When are tradign signals updated?
Bitcoin trading signals are generated 0:02 GMT time each day.
### What is best strategy to use?
It depends on your risk aversion. Trading has one rule - higher returns are always associated with higher risk. For example, Bitcoin Pi 2.0 most of the years generated over 50 percent a year, but with hefty 35 percent max drawdown. If you are not feeling well with 35 percent drawdown, then just go for another strategy.
For most users I would recommend to just use portfolio of strategies, because it uses many models and distributes its risk among them.
### Where I can find statistics about the strategies?
Performance page listing the stats has links to strategy description pages, which also include live strategy statistics.
### I have a question, how I can ask?
Please use my contact form located here.
### Are returns shown in stats and charts reinvested?](
No, returns are not reinvested by default, unless stated otherwise.
It is easy to mislead with reinvested returns, because reinvestments are always generating more than the strategy itself, and I believe in showing the reality, not just the time value.
Also, you need to note, that if you reinvest, drawdowns also will grow exponentially.
### I don’t understand anything about APIs, can I still use your system?
Of course! I have created a helper app just for you.
Or you can just get signals via SMS/ email with Pro and higher plans.
### How much of a PnL shown is in sample and out of sample?
All strategies have half in sample and half out of the sample until March, 2020. Since March, 2020 everything is out of sample (“almost live”).
“Almost live”, because results don’t account for a negligible (<1%) probability that some orders won’t hit limit price.
All charts and data are updated daily with yesterday’s (last week’s) PnL.
Some strategies have risk filters (like F, One, One 2.0), but generally filters aren’t working good compared with naked strategies, because they are often lagging.
All our strategies are event based, so if no Bitcoin fundamentals change, their performance shouldn’t change much.
### Are all systems long only?
For now, yes, except for arbitrage strategies.
### Are all systems on Bitcoin only?
For now, yes, except for arbitrage strategies, because all other instruments are highly correlated with Bitcoin with worse performance than Bitcoin.
### What Sharpe formula is used?
$$sharpe = (returns \div volatility) \times \sqrt{365}$$
### What optimization techniques are used?
As majority of the strategies are event based, no optimization is used. If lagging indicators are used, they are generally “half optimized” - having values that are divided by 10.
It is because I don’t believe in an optimization. If the alpha performs, it will perform regardless of parameters used. Best way to improve risk profile is to just use diversification between strategies.
|
|
# Gradient of the point with x coordinate
I am not even sure where to begin on solving this question
f(x) = $ax^2$ + bx + c, where a = -32, b = 9 and c = 14. What is the gradient of the point, with x coordinate 11, on the graph of y = f(x)?
-
Do you know about differentiation? – user39572 Oct 17 '12 at 14:26
@J.G. Yes I know a little about differentiation,This is more of a fixed point topic – JackyBoi Oct 17 '12 at 14:28
Then differentiate $f$, the gradient will be $f'(11)$ (given any differentiable function $f$, the gradient at $x=a$ is defined as $f'(a)$) – user39572 Oct 17 '12 at 14:29
Hint: plug the given $a,b,c$ into your function, differentiate with respect to $x$, and set $x=11$
-
Would my answer be correct? – JackyBoi Oct 17 '12 at 14:41
@JackyBoi: Yes it would. Doing the differentiation symbolically saved you some computation, usually a good thing. – Ross Millikan Oct 17 '12 at 14:43
Ya actually the answer was something like this according to the given formula
In general, if f(x)= $ax^2$ + bx + c then the gradient at any point on the graph of y=f(x) is given by f prime (x) = 2ax + b
so in the above sums case it will be 2(-32)(11)+9 = -695
-
|
|
# Sentence Examples with the word molecular formula
Its vapour density agrees with the molecular formula C302, and this formula is also confirmed by exploding the gas with oxygen and measuring the amount of carbon dioxide produced (see Ketenes).
The molecular formula of a compound, however, is always a simple multiple of the empirical formula, if not identical with it; thus, the empirical formula of acetic acid is CH 2 O, and its molecular formula is C2H402, or twiceTCH 2 O.
There is some doubt as to the molecular formula of fulminic acid.
View more
That orthoboric acid is a tribasic acid is shown by the formation of ethyl orthoborate on esterification, the vapour density of which corresponds to the molecular formula B(0C2H5)3; the molecular formula of the acid must consequently be B(OH) 3 or H 3 B0 3.
This fact, coupled with the determination of the vapour density of the gas, establishes the molecular formula CO.
|
|
Enhanced heat transfer in the convergent rectangular channels with ∧/∨-shaped ribs on one wall
Title & Authors
Enhanced heat transfer in the convergent rectangular channels with ∧/∨-shaped ribs on one wall
Lee, Myung-Sung; Yu, Ji-Ui; Jeong, Hee-Jae; Choi, Dong-Geun; Ha, Dong-Jun; Go, Jin-Su; Ahn, Soo-Whan;
Abstract
The effect of the rib angle-of-attack on heat transfer in the convergent channel with $\small{{\vee}/{\wedge}}$-shaped ribs was examined experimentally. Four differently angled ribs (a
Keywords
$\small{{\vee}/{\wedge}}$-shaped rib;Convergent rectangular channel;Heat transfer;Total friction factor;Rib angle-of-attack;
Language
Korean
Cited by
References
1.
S. W. Ahn, H. K. Kang, S. T. Bae, and D. H. Lee, "Heat transfer and friction factor in a square channel with one, two, and four ribbed walls," ASME Journal of Turbomachinery, vol. 130, 034501-5, pp. 1-5, 2008.
2.
J. C. Han, S. Ou, J. S. Park, and C. Lei, "Augmented heat transfer in rectangular channels of narrow aspect ratios with rib turbulators," International Journal of Heat and Mass Transfer, vol. 32, no. 9, pp. 1619-1630, 1989.
3.
A. E. Momin, J. Saini, and S. Solanki, "Heat transfer and friction in solar air heater duct with V-shaped rib roughness on absorber plate," International Journal of Heat and Mass Transfer, vol. 45, no. 16, pp. 3383-3396, 2002.
4.
J. C. Han, Y. Zhang, and C. Lee, "Augmented heat transfer in square channels with parallel, crossed, and V-shaped angled ribs," ASME Journal of Heat Transfer, vol. 113, no. 3, pp. 590-596, 1991.
5.
B. Wang, W. Q. Tao, Q. W. Wang, and T. T. Wong, "Experimental study of developing turbulent flow and heat transfer in ribbed convergent/divergent square ducts," International Journal of Heat and Fluid Flow, vol. 22, no. 6, pp. 603-613, 2001.
6.
M. S. Lee, S. S. Jeong, S. W. Ahn, and J. C. Han, "Effects of angled ribs on turbulent heat transfer and friction factors in a rectangular divergent channel," International Journal of Thermal Sciences, vol. 84, pp. 1-8, 2014.
7.
M. S. Lee and S. W. Ahn, "Effects of rib angles on heat transfer in a divergent square channel with ribs on one wall," Journal of the Korean Society of Marine Engineering, vol. 39, no. 6, pp. 609-613, 2015.
8.
S. J. Kline and F. A. McClintock, "Describing uncertainty in single sample experiments," Mechanical Engineering, vol. 75, pp. 3-8, 1953.
9.
F. W. Dittus and L. M. K. Boelter, "Heat transfer in automobile radiators of the tubular type," University of California (Berkeley), Publication of Engineering, vol. 2, p. 443, 1930.
10.
M. S. Lee, S. S. Jeong, S. W. Ahn, and J. C. Han, "Turbulent heat transfer and friction in rectangular convergent/divergent channels with ribs," AIAA Journal of Thermophysics and Heat Transfer, vol. 27, no. 4, pp. 660-667, 2013.
11.
F. P. Incorpera and D. P. Dewitt, Fundamental of Heat and Mass Transfe", 4th ed., John Willy and Sons, Inc., p. 424, 1996.
|
|
## Algebraic Number Theory Study Group/Seminar
Dear fellow grad students and postdocs,
I'm hoping to organize a meeting between those of us with interests
related in some way to algebraic number theory. If interested,
please get in touch by emailing me at falfaisa@math.toronto.edu.
Cheers,
Faisal
## University of Toronto Operations Research Group Event
I am writing to you on the behalf of University of Toronto Operations Research Group (UTORG). UTORG is a student-run organization located in the Department of Mechanical and Industrial Engineering at the University of Toronto. We organize academic seminars and workshops to serve the interests of the academic community at UofT. Below are the two upcoming UTORG events. Detailed information can be found in the attached document. I would appreciate it if you could forward this posting to your graduate students and others who you think would be interested.
Thank you,
Derya Demirtas
Speakers: Jonathan Li, PhD candidate in MIE, joining University of Ottawa;
Sharareh Taghipour, PhD (1T1) and postdoc in MIE, joining Ryerson University;
Vahideh Abedi, PhD candidate in Rotman, joining California State University at Fullerton
Date: Thursday June 14
Time: 3 p.m.
Location: MC310
UTORG » Grad School Application Seminar
Speaker: Velibor Mišić, (BASc IndE 0T9+PEY, MASc 1T2)
Date: Thursday June 21
Time: 6 p.m.
Location: MC310
## Organizing a study group in “class field theory”
This summer, we will have running a learning seminar in class field theory (with an emphasis on the local theory). Our main (proposed) resources will be the lectures in the classic “Algebraic Number Theory” of Cassels-Frolich, Serre’s “Local Fields”, Cassels’ “Local Fields”, and the notes of J. Milne.
I figure that the first half of the summer can be spent ramping up on the relevant algebraic number theory, reviewing the theory of local fields, and learning about group cohomology. Then, in the second half we can dive right in to local class field theory.
If you are interested and want to take part, please contact me at “josh.seaton@hotmail.com”. We will have an organisational meeting in the first week of May.
Joshua.
## Learning Seminar in Geometric Invariant Theory
Dear all,
James Mracek and myself are organizing a learning seminar on Geometric
Invariant Theory in the summer term. GIT (Geometric Invariant Theory) is a
powerful technique that was developed by Mumford in the 1960s to construct
moduli spaces in algebraic geometry. Since then, GIT has emerged as not
only an important tool in algebraic geometry, but also in symplectic
geometry and arithmetic geometry. We plan to cover some subset of the
following topics:
- Different notions of quotients (categorical, good, geometric, etc)
- Reductive Group Actions and Classical Invariant Theory (Hilbert's 14th
problem, etc)
- Linearization of group actions
- Stability and numerical criterion for stability (Hilbert-Mumford criterion)
- Construction of moduli spaces using GIT (moduli of quiver
representations, moduli of genus g curves, etc)
- GIT in symplectic geometry (GIT quotient vs symplectic quotient,
Kahler/hyperkahler quotients; cf. Mumford Chapter 8)
- GIT in arithmetic contexts (abelian schemes)
We plan to use the following sources:
- Dolgachev: Lectures in Invariant Theory
- Mumford/Fogarty/Kirwan: Geometric Invariant Theory
- Mukai: An Introduction to Invariants and Moduli
I would like to have an organizational meeting for all those who are
(james.mracek@utoronto.ca) or myself (kl6@math.toronto.edu) if you are
interested in attending so we can set up on potential meeting times. Also
please feel free to make comments on choice of topics and sources.
Thanks very much,
Kevin
## Geometry Reading Group for Graduate Students
Hello All:
I would like to invite you all to a reading group in geometry that will be focusing on
isoperimetric/diastolic/systolic inequalities.
We will be meeting this Friday in the BA6180 at 11a.m. and every subsequent
Friday at the same time.
This Friday, we will be discussing a short paper by Ivanov and Burago:
On asymptotic isoperimetric invariants of tori, by Burago and
Ivanov, http://arxiv.org/abs/1005.1392
If you are interested, please attend.
In the future, we plan to discuss work such as:
Generalizations of the Kolmogorov-Barzdin embedding estimates, by
Guth and Gromov, http://arxiv.org/abs/1103.3423
Minimax problems related to cup powers and Steenrod squares, by
Guth, arXiv:math/0702066
Volumes of balls in large Riemannian manifolds, by Guth,
http://arxiv.org/abs/math/0610212
Overlap Properties of Geometric Expanders, by Gromov et al.
http://arxiv.org/abs/1005.1392
Filling length in finitely presentable groups, by Gersten and Riley
arXiv:math/0008030
The gallery length filling function and a geometric inequality for
filling length, by Gersten and Riley
http://journals.cambridge.org/abstract_S0024611505015649
We look forward to having you,
Dominic Dotterrer
3rd Year Ph.D. Candidate
Department of Mathematics
University of Toronto
d.dotterrer@gmail.com
## The wClips Seminar
Dear Students and Others,
With help from my students, in the next semester I will be running the "wClips
Seminar", which will be a combination of a class, a seminar, and an
experiment. All are invited to join; we will be meeting on Wednesdays at noon
at a location that will soon be announced (on the URL below) and the first
meeting will take place in the first week of classes, on Wednesday January 11,
2012.
The "class" part of this affair is that we will slowly and systematically go
over my in-progress joint paper with Zsuzsanna Dancso, "Finite Type Invariants
of W-Knotted Objects: From Alexander to Kashiwara and Vergne" (short "WKO",
and see http://www.math.toronto.edu/drorbn/papers/WKO/), section by section,
lemma by lemma, and covering all necessary prerequisites as they arise (though
a certain amount of mathematical maturity will certainly be assumed). Though
wClips will not be on the departmental course listing and you cannot take it
for credit.
The "seminar" component is the usual. Occasionally people other than me will
be telling the story.
The "experiment" part is that every lecture will be video taped and every
blackboard will be photographed and everything will be immediately put on the
WKO website, so that at the end we will have along with the paper a "video
companion" - series of video clips explaining every bit of it. The paper will
be mathematically self-contained, yet in addition every section thereof will
include a link/reference to the corresponding clip in its video companion. And
every video clip will have its written counterpart in one of the sections of
the paper.
Feel free to join or follow remotely at
http://www.math.toronto.edu/drorbn/papers/WKO/! Also, please let me know if
you want to be added to the wClips mailing list.
Best,
Dror.
## Studc Fields Trip, Dec. 9 – CMS 2011 Winter Meeting
Dear Students,
On behalf of the Fields Undergraduate Network and the Canadian
Mathematical Society's Student Committee, I would like to invite
you to four math events that are being held this Friday.
Lecture by Professor Craig G. Fraser on the
History of Complex Analysis,
10:00 a.m. - 12:00 p.m. (James Room)
Lunch with Professor Fraser at Richtree (444 Yonge Street),
12:15 p.m. - 2:00 p.m.
Panel Discussion on the Role of Mathematics in Industry,
2:30 p.m. - 3:45 p.m. (Windsor Room)
CV Writing Workshop (pre-register here,
http://cms.math.ca/Events/winter11/student_workshop),
4:00 p.m. - 5:30 p.m. (James Room)
All events (except lunch) take place at the Delta Chelsea Hotel,
which is located at 33 Gerrard Street.
If you'd like to come to lunch, please RSVP by this Thursday at
noon to richard.cerezo@alumni.utoronto.ca
Lastly, please follow the links below to see posters for the events,
Lecutre on the Origins of Complex Analysis Poster
(http://www.flickr.com/photos/63196321@N07/6461977219/in/photostream/lightbox/)
Panel Discussion and CV Workshop Poster
(http://www.flickr.com/photos/63196321@N07/6461976291/in/photostream/lightbox/)
Sincerely,
Richard Cerezo
richard.cerezo@alumni.utoronto.ca
## Math Union Talk: November 8th, Stephen Smale
Dear Math Students,
Next Tuesday Nov. 8, Fields Medalist Stephen Smale will be giving a talk to the mathematics students here, both undergraduate and graduate, in the Adel Sedra Auditorium (BA1160). It will start at 2:10p.m., with refreshments to be served at 2:00p.m. Prof. Smale will be giving an exposition on ‘Smale’s Problems’. This is a compilation of 18 important open problems for 21st-century mathematicians to keep in mind, just like those of Hilbert that were proposed for the 20th century.
For more information on Smale’s Problems, check out:
http://en.wikipedia.org/wiki/Smale’s_problems
http://www6.cityu.edu.hk/ma/people/smale/pap104.pdf
Josh Seaton, U of T Math Union
josh...@utoronto.ca
## Atmospheric Physics Seminar
Hello everyone,
Professor Marek Stastna from University of Waterloo
will be visiting the Atmospheric Physics Group at the physics department
next week and will be the first of the Atmospheric physics Noble seminar
series this year.
Professor Stastna's talk will be next Monday (September 19) at 4 pm in
Mp609 (see below for more info) and we would like to invite you to attend
this seminar.
Coffee,tee and cookies will be served on Monday at 3:50 in the
coffee/printer room on the sixth floor.
Best,
Ali Mashayek (on behalf of the Atmospheric Physics Noble Committee)
Link to the event page:
http://www.physics.utoronto.ca/research/atmospheric-physics/atmosp-monday-seminars/internal-gravity-waves
Link to Marek's web page:
http://www.math.uwaterloo.ca/~mmstastn/Welcome.html
Title and abstract:The benefits of high order methods for simulating
internal wave dynamics: from the lake scale to bottom boundary layer
interactions
The presence of a stable density stratification is the fundamental
property of both the atmosphere and natural bodies of water on scales
ranging from those associated with small-scale turbulence to those large
enough so as to be affected by the Earth's rotation. In this talk I will
discuss the numerical simulation of stratified fluid dynamics with a focus
on internal wave processes. I will describe the benefits of high-order
methods, both for purely numerical simulation and for instances where it
is coupled with semi-analytical theory to derive new results. In
particular I will discuss fully nonlinear trapped waves over topography,
the instability of the bottom boundary layer beneath internal solitary
waves and the weakly non-hydrostatic dynamics of small to mid-sized lakes
such as those typically found on the Canadian Shield. Throughout, I will
introduce the necessary technical vocabulary and will attempt to explain
the reasons for the various mathematical developments.
## Learning Seminar on 3-Manifolds
I'm organizing a learning seminar for the remainder of the summer in the topology and geometry of 3 dimensional manifolds.
It's just something that I would like to know more of, and I think it would be more interesting/fun if I can convince some
people to join me. The idea is to start from scratch and get as far as we can in the remaining 2 months. If any of you is
interested please email me and I'll set an organizing session as soon as possible. (In fact, if you already have preferred times
also send them.)
Cheers,
Pablo
(pablo.carrasco@utoronto.ca)
|
|
Zariski tangent space of a scheme as the vector space of derivations - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T13:09:44Z http://mathoverflow.net/feeds/question/87150 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/87150/zariski-tangent-space-of-a-scheme-as-the-vector-space-of-derivations Zariski tangent space of a scheme as the vector space of derivations Dima Sustretov 2012-01-31T17:41:07Z 2012-02-01T11:17:36Z <p>A standard lemma says that for a scheme $X$ of finite type over an algebraically closed field $k$ the set of derivations <code>$\mathcal{O}_{X,x} \to \kappa(x)=k$</code>, is isomorphic to the Zariski tangent space <code>$(\mathfrak{m}/\mathfrak{m}^2)^*$</code> where $\mathfrak{m}$ is the maximal ideal of $\mathcal{O}_{X,x}$.</p> <p>The left-to-right inclusion is the natural one, but proving that it is bijective is depedent on one of the forms of the Nullstellensatz from which one deduces that <code>$\mathcal{O}_{X,x} \cong k \oplus \mathfrak{m}$</code>. This already breaks down when $k$ is not algebraically closed and $\kappa(x)$ is a finite extension of $k$.</p> <p>I wonder if there are other interesting situations when this lemma doesn't work, i.e. when the inclusion $\mathrm{Der}(\mathcal{O}_{X,x},\kappa(x)) \hookrightarrow (\mathfrak{m}/\mathfrak{m}^2)^*$ (as $\kappa(x)$-vector spaces) is proper.</p>
|
|
## Operator algebras associated to modules over an integral domain.(English)Zbl 06848506
Summary: We use the Fock semicrossed product to define an operator algebra associated to a module over an integral domain. We consider the $$C^*$$-envelope of the semicrossed product, and then consider properties of these algebras as models for studying general semicrossed products.
### MSC:
47L40 Limit algebras, subalgebras of $$C^*$$-algebras
### Keywords:
semicrossed product; integral domain; module
Full Text:
### References:
[1] W. Arveson, Operator algebras and measure preserving automorphisms, Acta Math. 118 (1967), 95-109. · Zbl 0182.18201 [2] W. Arveson and K. Josephson, Operator algebras and measure preserving automorphisms. II, J. Funct. Anal. 4 (1969), 100-134. · Zbl 0186.45903 [3] N. Brown and N. Ozawa, $$C^*$$-algebras and finite-dimensional approximations, Graduate Studies in Mathematics, 88. American Mathematical Society, Providence, RI, 2008. · Zbl 1160.46001 [4] H. Choda, A correspondence between subgroups and subalgebras in a discrete $$C^*$$-crossed product, Math. Japonica 24 (1979), 225-229. · Zbl 0418.46049 [5] J. Cuntz and X. Li, The regular $$C^*$$-algebra of an integral domain, Quanta of maths, 149-170 Clay Math. Proc. 11 Amer. Math. Soc., Providence RI, 2010. · Zbl 1219.46059 [6] K. Davidson and E. Katsoulis, Isomorphisms between topological conjugacy algebras, J. Reine Angew. Math. 621 (2008), 29-51. · Zbl 1176.37007 [7] K. Davidson and E. Katsoulis, Semicrossed products of simple $$C^*$$-algebras, Math. Ann. 342 (2008), 515-525. · Zbl 1161.47057 [8] K. Davidson and E. Katsoulis, Operator algebras for multivariable dynamics, Mem. Amer. Math. Soc. 209 (2011), no. 982. · Zbl 1236.47001 [9] K. Davidson and E. Katsoulis, Dilation theory, commutant lifting, and semicrossed products, Doc. Math. 16 (2011), 781-868 · Zbl 1244.47063 [10] K. Davidson, A. Fuller, and E. Kakariadis, Semicrossed products of operator algebras by semigroups, Memoirs Amer. Math. Soc. 239 (201X). · Zbl 1385.47027 [11] B. Duncan, Operator algebras associated to integral domains, New York J. Math. 19 (2013), 39-50. · Zbl 1294.47097 [12] B. Duncan and J. Peters, Operator algebras and representations from commuting semigroup actions, J. Operator Theory 74 (2015), 23-43. · Zbl 1389.47111 [13] A. Fuller, Nonself-adjoint semicrossed products by abelian semigroups, Canad. J. Math. 65 (2013), 768-782. · Zbl 1352.47046 [14] E. Kakariadis and E. Katsoulis, Isomorphism invariants for multivariable $$C^*$$-dynamics, J. Noncommut. Geom. 8 (2014), 771-787. [15] M. Landstad, D. Olesen, and G. Pedersen, Towards a Galois theory for crossed products of $$C^*$$-algebras, Math. Scand. 43 (1978), 311-321. · Zbl 0406.46056 [16] J. Peters, Semicrossed products of $$C^*$$-algebras, J. Funct. Anal. 59 (1984), 498-534. · Zbl 0636.46061 [17] J. Peters, The $$C^*$$-envelope of a semicrossed product and nest representations, Operator structures and dynamical systems, 197-215, Contemp. Math., 503, Amer. Math. Soc., Providence RI, 2009. · Zbl 1194.46096 [18] S. Roman, Advanced linear algebra, third edition, Graduate Texts in Mathematics, 135, Springer, New York, NY, 2008. · Zbl 1132.15002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
|
|
## FANDOM
1,099 Pages
A parametric equation is an equation where the coordinates are expressed in terms of a, usually represented with $t$ . The classic example is the equation of the unit circle,
\begin{align}x&=\cos(t)\\y&=\sin(t)\end{align}
Parametric equations are commonly used in physics to model the trajectory of an object, with time as the parameter. They are also used in multivariable calculus to create curves and surfaces.
## Properties and applications
Parametric equations are often represented in terms of a radius vector $R$ , reducing the need for multiple equations. For example, the unit circle can also be represented as
$\vec R(t)=\cos(t)\mathbf{\hat i}+\sin(t)\mathbf{\hat j}$
with $\mathbf{\hat i},\mathbf{\hat j}$ being the unit vectors in the $x,y$ directions respectively.
Surfaces can also be parameterized by using two parameters, often represented by $u$ and $t$ . For example the surface on the right is known as a catenoid, and has the equation
$\vec R(t)=\cosh(t)\cos(u)\mathbf{\hat i}+\cosh(t)\sin(u)\mathbf{\hat j}+t\mathbf{\hat k}$
Another common parametric surface is the unit sphere, which has the equation
$\vec R(t)=\sin(t)\cos(u)\mathbf{\hat i}+\sin(t)\sin(u)\mathbf{\hat j}+\cos(t)\mathbf{\hat k}$
## Calculus with parametric curves
### Derivatives
The derivative of a parametric function with respect to $x$ is equal to
$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}},\ \frac{dx}{dt}\ne0$
The second derivative is equal to
$\frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{dy}{dx}\right)=\dfrac{\dfrac{d}{dt}\left(\dfrac{dy}{dx}\right)}{\dfrac{dx}{dt}}$
### Arc length
The arc length of a parametric curve is equal to
\begin{align}\int\limits_a^b\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}dt\end{align}
or
\begin{align}\int\limits_a^b\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2+\left(\frac{dz}{dt}\right)^2}dt\end{align}
in $\R^3$ .
### Area
The area between a parametric curve and the x-axis is equal to
$\int\limits_a^b y(t)x'(t)dt$
provided $x'(t)$ is never 0.
|
|
# Tag Info
An AR(1), once the time series and lags are aligned and everything is set-up, is in fact a standard regression problem. Let's look, for simplicity sake, at a "standard" regression problem. I will try to draw some conclusions from there. Let's say we want to run a linear regression where we want to approximate $y$ with $$h_(x) = \sum_0^n \theta_i x_i = ... 4 There is a lot of ways to understand why stationarity allows to apply usual time series analysis. Here is one more. Very often, the theoretical justification of what you do in time series need to be able to identify the mean formula and the expectation:$$\frac{1}{N}\sum_{n=1}^N X_n \underset{N\rightarrow +\infty}{\longrightarrow} \mathbb{E} X, $$where the ... 3 Volatility changes over time. Even if daily returns are normal, assuming the conditional volatility each day is known, the unconditional distribution of daily returns will have excess kurtosis. For example, if daily returns have a standard deviation of 1%, 90% of the time, and a standard deviation of 3%, 10% of the time, the presence of the high-volatility ... 2 In the case of application in finance, usually, GARCH is used in estimating realized volatility of returns based on the weight we would like to give to each past observation. Ultimately after estimating (calibrating) the parameters of the model to an existing time-series, GARCH is used for forecasting multi-step ahead return (future) volatility. Different ... 2 I am not sure to understand your question. But as far as I understand it. If you have a dataset with Y,K,L,M over a set of corporates over some years, you can estimate A using a log-log regression, since the following model is compatible with your Coob-Douglas specification:$$\log Y=a \log K + b \log L + c \log M + \log A.$$It is clearly the ... 2 I am a professor too and I did work with Siemens Corporate Technology which provides the quantitative technology for their copper and electricity trading (Siemens being one of the biggest players in this area in Europe). They are mainly using sophisticated neural networks. We also published a paper together, see my answer here: What types of neural networks ... 2 Consider the following AR(1) process with i.i.d. normal errors that have zero mean and finite variance \sigma^2>0,$$ x_t = (1-\rho)\mu + \rho x_{t-1} + \epsilon _t$$Now suppose \rho = 1/2 and \mu = 1. This process does not have a unit root, and it is not mean stationary. At any point in time, the process has finite variance, although as time ... 2 1) Spurious autocorrelation of non-synchronous trading data was analyzed in this article: http://www.amazon.com/An-econometric-analysis-nonsynchronous-trading/dp/1245789457 During some time intervals a lot of trades occur and during some nothing happens(so prices are stale). So serial correlation of traded prices may be present but this may be due to stale ... 1 Write the series in the answer as (x_t - \mu) = \rho (x_{t-1} - \mu) + \varepsilon_t then if \rho=.5 and \varepsilon_t is N(0,\sigma^2), (x_t - \mu) is stationary with mean 0 and variance \frac{\sigma^2}{1-\rho}. A time series process can have a deterministic part and a pure random part. The definition of stationarity (strict or strong or ... 1 For Engle-Granger, I can see that you are returned a vector of 2 elements for each of the output arguments, hence you run two tests there. For the sake of clarity and the education of people interested in the post, we can say that: Since your hValues are both zero, we can say that there is a failure to reject the Null Hypothesis, which in this case is ... 1 A naive reason has been explained by Nassim Nicholas Taleb in his book titled Black Swan. In a deeper look, one should be aware that no historical data analysis can truly estimate the real tail risk of financial markets. By the same token, standard deviation, max drawdown, expected shortfall, VaR, Conditional Var... No single or combination of such ... 1 What you could do is to apply the methods of portfolio risk analysis. If you buy n stocks with percentages w_i,i=1,\ldots,n then your portfolio return is r = \sum_{i=1}^n w_i r_i. Dealing with investment strategies I would not include an expected profit in the VaR calculation and put \mu=0 for this reason. To calculate the volatility of your ... 1 If the returns are N(\mu,\Sigma) distributed, then WML\sim N(0,\sigma), because the equally-weighted \mu's cancel while \Sigma=\sqrt{w \Sigma w'} with w=\{1/n...1/n\}. So your new VaR becomes:$$\mbox{VaR}\left(\alpha\right)_{WML}=\Phi^{-1}\left(\alpha\right)\cdot\sigma$$Your sampling formula from above remains still valid though, just with ... 1 Concidering 22 days of trading per month you have approximatly 132 days of trading. I highly doubt that this will be sufficient for any forecasting. The sample might be too small. Have a look here: http://research.stlouisfed.org/wp/2012/2012-008.pdf Erdemlioglu, Laurent and Neely used the data of ~10 years to conduct their survey. 1 Well, given that either LM or BHHH is supposed to stop when the Kuhn-Tucker condition is satisfied, I infer it has to be stepwise. I would say otherwise if, say, they were potentially using something like SALO (simulated annealing with local optimization), where one algorithm could profitably run in full as a sub-step of the other. 1 Extreme events in financial markets, like the crash of 1987, occur more frequently in the real world than a normal distribution would predict. The economic facts that drive those extreme events are varying. Such extreme declines have been observed over many different time periods (Tulip-mania for instance), which suggests that it is more likely inherent to ... 1 I would say that you can use Johansens methods to test for rank of co-integration matrix. There are tests for that. If there is no co-integration vector present and both series are I(0) then there is no co-integration. Series still might have some short-run dynamics. If series are I(1) and no con-integration vector is present then modeling these series by ... 1 In most of the literature on the information content of various volatility estimator the relevant question is whether a particular estimator can predict (is correlated) with future realized volatility. Hence, the testing regression would be$$ RV(t,T) = \alpha + \beta VOL(t) + \epsilon(t) where RV(t,T) is an estimate of the realized volatility from t to ...
|
|
## IsTim Group Title Use the first principles definition to determine the first derivative of sqrt(2x-1) 2 years ago 2 years ago
1. IsTim Group Title
This is as far as I got:|dw:1340139301477:dw|
2. mashe Group Title
Let's look at the definition: $\lim_{h \rightarrow a} f(x)=[f(x+h) -f(x) ]/h$
3. IsTim Group Title
Ok.
4. mashe Group Title
Your f(x) = sqrt(2x-1), and a=0. So you want to find the limit of f(x) as h approaches 0
5. IsTim Group Title
How do I know a=0?
6. mashe Group Title
So you have $\lim_{h \rightarrow 0} \sqrt(2x-1)= \sqrt (2(x+h)-1) - \sqrt (2x-1)/h$ where h is the denominator and everything else is on top, the numerator
7. IsTim Group Title
As for your latter instructions. I understand, and have reached past that point. The reaffirmation is appreciated.
8. mashe Group Title
Look at the third picture here: http://www.intmath.com/differentiation/3-derivative-first-principles.php and the explanation below it states why a=0
9. IsTim Group Title
Ok. I think I understand; The IROC is 0 at a right. Let's continue.
10. IsTim Group Title
Hello?
11. myininaya Group Title
Where are you at @IsTim ? $\lim_{h \rightarrow 0}\frac{\sqrt{2(x+h)-1}-\sqrt{2x-1}}{h}$ This is where you at right?
12. myininaya Group Title
You need to rationalize the numerator. We are trying to manipulate this problem so that when we plug in 0 for h we don't get 0 on the bottom.
13. myininaya Group Title
Think there is something wrong ... because you should be able to get that h canceled
14. myininaya Group Title
$\lim_{h \rightarrow 0}\frac{\sqrt{2x+2h-1}-\sqrt{2x-1}}{h} \cdot \frac{\sqrt{2x+2h-1}+\sqrt{2x-1}}{\sqrt{2x+2h-1}+\sqrt{2x-1}}$
15. myininaya Group Title
So that is what you did?
16. IsTim Group Title
Yes, that was my previous step before this.
17. myininaya Group Title
$\lim_{h \rightarrow 0} \frac{(2x+2h-1)-(2x-1)}{h(\sqrt{2x+2h-1}+\sqrt{2x-1})}$ Is this what you got next?
18. IsTim Group Title
I then cancelled out 2a and -2a.
19. myininaya Group Title
what else cancels?
20. myininaya Group Title
on top!
21. IsTim Group Title
I forgot to cancel 1 and -1.
22. myininaya Group Title
yep! :)
23. myininaya Group Title
So that means we have $\lim_{h \rightarrow 0}\frac{2h}{h(\sqrt{2x+2h-1}+\sqrt{2x-1})}$ Correct?
24. IsTim Group Title
yes.
25. myininaya Group Title
Do you know what to do from here?
26. IsTim Group Title
Yes. thank you very much.
|
|
# What is energy resolution
Nyasha
Can someone explain the concept of energy resolution to me, especially in gamma cameras. Thanks.
Staff Emeritus
Can someone explain the concept of energy resolution to me, especially in gamma cameras. Thanks.
Where did one find a reference to gamma cameras?
Nyasha
Where did one find a reference to gamma cameras?
Well, l am reading a thesis on them and the author keeps on referring to energy resolution as a % FWHM. So l really don't understand what this means.
billschnieder
Generally speaking, energy resolution refers to the degree of monochromaticity. So if we say the particles have an energy say e, actually they are not all the same energy rather they are spread in a gaussian distribution around e with e representing the mean. The smaller the sigma of the distribution, the higher the energy resolution and the bigger the sigma the lower the energy resolution. % FWHM (~2.35σ ) is often used instead of sigma to represent the resolution especially since the distribution is not always gaussian but can be lorentzian or a mixture.
http://en.wikipedia.org/wiki/Gamma_spectroscopy#Detector_resolution
Last edited:
Nyasha
Generally speaking, energy resolution refers to the degree of monochromaticity. So if we say the particles have an energy say e, actually they are not all the same energy rather they are spread in a gaussian distribution around e with e representing the mean. The smaller the sigma of the distribution, the higher the energy resolution and the bigger the sigma the lower the energy resolution. % FWHM (~2.35σ ) is often used instead of sigma to represent the resolution especially since the distribution is not always gaussian but can be lorentzian or a mixture.
http://en.wikipedia.org/wiki/Gamma_spectroscopy#Detector_resolution
So generally speaking, the lower the %FWHM the better the camera is ?
Mentor
A smaller FWHM might come with some disadvantages elsewhere, but in general, a smaller value there gives a better energy resolution, which can help in the analysis.
M Quack
FWHM means Full Width at Half Maximum. When talking about the resolution of a detector, this means that a beam of monochromatic=monoenergetic photons or particles will produce a Gaussian (or other) distribution of *detected* (or apparent) energies.
In spectroscopy this is significant, as it is sometimes necessary to distinguish gamma lines with close-by energies. If, roughly speaking, the resolution is worse than the energy difference, then the detector cannot tell the lines appart.
For many detectors, the resolution is related to the energy of the detected particle or photon. That is why the FWHM is given as percentage of the particle's energy.
Staff Emeritus
Well, l am reading a thesis on them and the author keeps on referring to energy resolution as a % FWHM. So l really don't understand what this means.
Is this related to synchrotron radiation imaging or gamma ray imaging/tomography?
Nyasha
Is this related to synchrotron radiation imaging or gamma ray imaging/tomography?
It is related to gamma ray imaging.
Bob S
In the attached sodium-iodide spectrum for cesium -137, the FWHM resolution is about 50 keV, or 7,5%. You can also see the Compton backscatter peak and the Compton edge. The energy resolution depends on the size and type of detector, and the gamma energy.
See http://en.wikipedia.org/wiki/File:Caesium-137_gamma_ray_NaI_scintillator_spectrum.jpg [Broken]
Last edited by a moderator:
Staff Emeritus
|
|
• Magoosh
Study with Magoosh GMAT prep
Available with Beat the GMAT members only code
• Free Veritas GMAT Class
Experience Lesson 1 Live Free
Available with Beat the GMAT members only code
• 1 Hour Free
BEAT THE GMAT EXCLUSIVE
Available with Beat the GMAT members only code
• Free Practice Test & Review
How would you score if you took the GMAT
Available with Beat the GMAT members only code
• 5-Day Free Trial
5-day free, full-access trial TTP Quant
Available with Beat the GMAT members only code
• 5 Day FREE Trial
Study Smarter, Not Harder
Available with Beat the GMAT members only code
• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE
Available with Beat the GMAT members only code
• Reach higher with Artificial Intelligence. Guaranteed
Now free for 30 days
Available with Beat the GMAT members only code
• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code ## 640 to 770 - How I Tamed the Beast (Q50, V46, IR8) tagged by: thePaleKing This topic has 3 member replies thePaleKing Newbie | Next Rank: 10 Posts Joined 05 Oct 2015 Posted: 2 messages Upvotes: 5 #### 640 to 770 - How I Tamed the Beast (Q50, V46, IR8) Mon Nov 02, 2015 3:12 pm I just took the GMAT this morning and got my unofficial score of 770 and thought I'd share my tips while it's all still fresh in my head. The most important thing I've learned on my journey is that different things work for different people and it takes a good amount of time to figure out what works best for you. All in all I spent about 300-400 hours over the past 4 months preparing for the GMAT, but I'll try to keep this short and focus on the few things that I feel got me to the next level. After 2 weeks of studying I was hovering around 640, after another month I was stuck around 680, a couple weeks after that I took my first official test and got a 710. I studied another 5 weeks doing mostly official guide and a few subject specific items and got 770. My Tips for You: 1. In quant, shoot to have 25-30 minutes left for your last 10 quant problems. This will ensure you can finish the quant section relaxed and the last 10 questions should be in what the GMAT perceived to be your "range" so getting the last 10 right is important. Being relaxed after quant is essential to maximize your verbal score. 2. Manhattan GMAT practice exams are tough, the highest I ever scored on one was a 700 and I got a 770 on the real thing. That being said, they are a great way to practice. You can either pay$50 for 6 practice exams or buy one of the subject books (sentence correction in my case) and you get access to 6 practice exams for free - this is your first intelligence test for business school so choose wisely.
3. For Critical Reasoning do not read the question stem before the stimulus, I elaborate more on this below.
4. When taking the actual exam, train yourself to not waste time - hide the timer, you will know when you are wasting time. Naturally your brain fatigues toward the end of each section, plan for this and move quicker in the beginning. When I got the V46 score I accidentally went over on my 8 minute break by 2 minutes, I could have freaked out but I stayed cool and made up the time on my first 10 questions when my brain was fresh.
5. In the 2 weeks before your exam, try to do 80% or more of your problems out of the official guide. There will be subtle differences between your unofficial study materials and the official guide, especially for verbal. Be sure you are used to the way GMAC likes to ask the questions.
6. Do keep an error log but do wait until you've been studying for at least a month before starting one otherwise it will be way too big. Wait until you are comfortable with each question type before really homing in on the more subtle mistakes you are making.
My background:
I'm an accountant with a degree in economics.
Resources:
Magoosh Premium - $100 (best value for money) Veritas Prep Live Online Course - ~$1600
Official Guide + Supplements - $50 PowerScore GMAT Critical Reasoning Bible -$20 (100% essential)
Manhattan GMAT Sentence Correction - $30 I originally planned on signing up for an expensive GMAT course from either Manhattan or Veritas, but while I did my research on which one I would buy I thought I'd start with Magoosh because$100 seemed like a drop in the bucket compared to the cost of an expensive course. I highly recommend this for everyone, whether you're on a budget and this is your full course or you've done an expensive course and need an additional question bank. There are video explanations to each question which makes reviewing answers much less exhausting plus the video lessons are well organized for targeting subjects in needed. Mike McGarry, the instructor in just about all the video lessons and video answers, is an EXTREMELY intelligent person with a background in education and you will pick up on this quickly. Overall the main thing Magoosh is lacking in is educating people more on the psychology of the GMAT, however, I will say the best part about these guys is that they don't shy away from suggesting outside resources such as the Manhattan GMAT books, they really want you to get your best score. Also, Mike has published some great 1-month, 3-month and 6-month study plans in their blog.
Veritas Prep Live Online Course:
For anyone interested in paying for one of the "expensive" courses, I highly recommend the Veritas Live Online course. First of all, Veritas starts out from the beginning getting you up to speed on the psychology of the GMAT and if you really want to break through the 700-720 level you need to develop a deep understanding of the GMAT psychology. In addition, the live online format was a fantastic interface that allowed for great communication with the instructor and the rest of the class - the chat box on the side of the screen makes the class much more efficient that an in-person classroom. There's also a teacher's assistant in every class so that anyone having trouble with a concept can get help without slowing down the rest of the class. Ethan was my instructor and he's the man, I'd elaborate but I already wrote an official review on him so there's no need.
PowerScore Critical Reasoning Bible:
I noticed by CR score was hovering around the 60th percentile so I got this book after reading a couple other blog posts out there and this improved my score exponentially. On the first real GMAT test I took where I got a 710, I paid for the score breakdown and my CR score was 96th percentile... enough said.
***If there is anything you take away from my post, this is it: DO NOT READ THE QUESTION STEM BEFORE READING THE STIMULUS - I got this tip from this book and it saves you a ton of time: 1. you need to fully understand the argument before answering the question and reading the question stem will only distract from the argument 2. 50% of the time you can already determine the type of question that will be asked after you read the stimulus so it would be a waste of time to read the question stem anyway.***
(Note: Veritas and Manhattan both recommend reading the question stem first, do not do this)
Manhattan GMAT Sentence Correction:
The main reason I got this was because if you buy 1 MGMAT book you get access to 6 free MGMAT practice exams. The sentence correction book was a good refresher but I had already studied a lot of sentence correction through Magoosh and Veritas so it was more of a review.
Rohit Singh Newbie | Next Rank: 10 Posts
Joined
02 Aug 2011
Posted:
2 messages
Test Date:
25 September 2016
GMAT Score:
760
Fri Nov 13, 2015 4:50 am
Could you please let us know how much time did you spend on the PowerScore bible and how much time did you spend on CR overall?
_________________
Good Luck & Gopdspeed,
RS
thePaleKing Newbie | Next Rank: 10 Posts
Joined
05 Oct 2015
Posted:
2 messages
5
Tue Nov 03, 2015 9:24 am
@oquiella
I used the OG 2016 books, however, this is nearly identical to the 2015 so either is fine. I suggest getting a new version of either book and use the access code in the back of the book to access the problems online at https://gmat.wiley.com/ - this is much easier than doing the problems while flipping through the book.
For the CR Bible, I already had already been through the Veritas book before I started so I had a base, but I still read the CR Bible from the beginning. The first couple of chapters are vital to understand the PowerScore approach to GMAT logic. They mention that you should at least read the 5 most important CR question type chapters if you are on a time crunch. I read those 5 chapters first then later on I would refer back to the other chapters if I noticed myself missing the less common question types when doing the OG (such as bold face and mimic the argument questions). Only referring back to the CR bible when I noticed myself missing a particular question type was a good strategy for me. Also, I didn't need to do much rereading of the chapters because the information stuck pretty well and I was able to apply it immediately.
Good Luck!
oquiella Master | Next Rank: 500 Posts
Joined
12 May 2015
Posted:
164 messages
3
Tue Nov 03, 2015 6:10 am
thePaleKing wrote:
I just took the GMAT this morning and got my unofficial score of 770 and thought I'd share my tips while it's all still fresh in my head. The most important thing I've learned on my journey is that different things work for different people and it takes a good amount of time to figure out what works best for you. All in all I spent about 300-400 hours over the past 4 months preparing for the GMAT, but I'll try to keep this short and focus on the few things that I feel got me to the next level. After 2 weeks of studying I was hovering around 640, after another month I was stuck around 680, a couple weeks after that I took my first official test and got a 710. I studied another 5 weeks doing mostly official guide and a few subject specific items and got 770.
My Tips for You:
1. In quant, shoot to have 25-30 minutes left for your last 10 quant problems. This will ensure you can finish the quant section relaxed and the last 10 questions should be in what the GMAT perceived to be your "range" so getting the last 10 right is important. Being relaxed after quant is essential to maximize your verbal score.
2. Manhattan GMAT practice exams are tough, the highest I ever scored on one was a 700 and I got a 770 on the real thing. That being said, they are a great way to practice. You can either pay $50 for 6 practice exams or buy one of the subject books (sentence correction in my case) and you get access to 6 practice exams for free - this is your first intelligence test for business school so choose wisely. 3. For Critical Reasoning do not read the question stem before the stimulus, I elaborate more on this below. 4. When taking the actual exam, train yourself to not waste time - hide the timer, you will know when you are wasting time. Naturally your brain fatigues toward the end of each section, plan for this and move quicker in the beginning. When I got the V46 score I accidentally went over on my 8 minute break by 2 minutes, I could have freaked out but I stayed cool and made up the time on my first 10 questions when my brain was fresh. 5. In the 2 weeks before your exam, try to do 80% or more of your problems out of the official guide. There will be subtle differences between your unofficial study materials and the official guide, especially for verbal. Be sure you are used to the way GMAC likes to ask the questions. 6. Do keep an error log but do wait until you've been studying for at least a month before starting one otherwise it will be way too big. Wait until you are comfortable with each question type before really homing in on the more subtle mistakes you are making. My background: I'm an accountant with a degree in economics. Resources: Magoosh Premium -$100 (best value for money)
Veritas Prep Live Online Course - ~$1600 Official Guide + Supplements -$50
PowerScore GMAT Critical Reasoning Bible - $20 (100% essential) Manhattan GMAT Sentence Correction -$30
I originally planned on signing up for an expensive GMAT course from either Manhattan or Veritas, but while I did my research on which one I would buy I thought I'd start with Magoosh because \$100 seemed like a drop in the bucket compared to the cost of an expensive course. I highly recommend this for everyone, whether you're on a budget and this is your full course or you've done an expensive course and need an additional question bank. There are video explanations to each question which makes reviewing answers much less exhausting plus the video lessons are well organized for targeting subjects in needed. Mike McGarry, the instructor in just about all the video lessons and video answers, is an EXTREMELY intelligent person with a background in education and you will pick up on this quickly. Overall the main thing Magoosh is lacking in is educating people more on the psychology of the GMAT, however, I will say the best part about these guys is that they don't shy away from suggesting outside resources such as the Manhattan GMAT books, they really want you to get your best score. Also, Mike has published some great 1-month, 3-month and 6-month study plans in their blog.
Veritas Prep Live Online Course:
For anyone interested in paying for one of the "expensive" courses, I highly recommend the Veritas Live Online course. First of all, Veritas starts out from the beginning getting you up to speed on the psychology of the GMAT and if you really want to break through the 700-720 level you need to develop a deep understanding of the GMAT psychology. In addition, the live online format was a fantastic interface that allowed for great communication with the instructor and the rest of the class - the chat box on the side of the screen makes the class much more efficient that an in-person classroom. There's also a teacher's assistant in every class so that anyone having trouble with a concept can get help without slowing down the rest of the class. Ethan was my instructor and he's the man, I'd elaborate but I already wrote an official review on him so there's no need.
PowerScore Critical Reasoning Bible:
I noticed by CR score was hovering around the 60th percentile so I got this book after reading a couple other blog posts out there and this improved my score exponentially. On the first real GMAT test I took where I got a 710, I paid for the score breakdown and my CR score was 96th percentile... enough said.
***If there is anything you take away from my post, this is it: DO NOT READ THE QUESTION STEM BEFORE READING THE STIMULUS - I got this tip from this book and it saves you a ton of time: 1. you need to fully understand the argument before answering the question and reading the question stem will only distract from the argument 2. 50% of the time you can already determine the type of question that will be asked after you read the stimulus so it would be a waste of time to read the question stem anyway.***
(Note: Veritas and Manhattan both recommend reading the question stem first, do not do this)
Manhattan GMAT Sentence Correction:
The main reason I got this was because if you buy 1 MGMAT book you get access to 6 free MGMAT practice exams. The sentence correction book was a good refresher but I had already studied a lot of sentence correction through Magoosh and Veritas so it was more of a review.
Hello,
Congratulations on your awesome score! I know it must be good to take a weight off. Can you tell me which edition of Official guide you used and How long and how you utilized the CR Bible (i.e. Did you just do questions or read the whole book a few times before grasping the subject)? Lastly what schools would you like to apply to?
### Best Conversation Starters
1 lheiannie07 80 topics
2 LUANDATO 62 topics
3 ardz24 52 topics
4 AAPL 47 topics
5 Roland2rule 43 topics
See More Top Beat The GMAT Members...
### Most Active Experts
1 Jeff@TargetTestPrep
Target Test Prep
134 posts
2 Brent@GMATPrepNow
GMAT Prep Now Teacher
131 posts
3 GMATGuruNY
The Princeton Review Teacher
130 posts
4 Rich.C@EMPOWERgma...
EMPOWERgmat
128 posts
5 Scott@TargetTestPrep
Target Test Prep
110 posts
See More Top Beat The GMAT Experts
|
|
# X is a compact metric space, which of the following must be true?
$X$ is a compact metric space, $f$ is a continuous function from $X$ $\rightarrow$ $X$, which of the following must be true?
A. $f$ has fixed point
B. $f$ is a closed map
C. $f$ is uniformly continuous
I know C is right by compactness. What about the others?
-
Hint:
• For A, consider a two-element set $\{x,y\}$ with the discrete metric.
• For B, use that closed subsets of compact spaces are compact, that compact subsets of Hausdorff spaces are closed, and that the continuous image of a compact set is compact.
-
So B is right？As any closed set in compact metric space is also compact. – Jebei Apr 8 '13 at 11:02
Yes, B is right, though you would probably want to expand a bit on the argument to get full credit for the solution. – Zev Chonoles Apr 8 '13 at 11:04
For a non-discrete counterexample to A, consider $X=S^1$ and think about rotations. More generally, any nontrivial rotation of $\mathbb R^n$, with $n$ odd, about the origin has only the origin as a fixed point. So take $X=\mathbb D_1 -D_2$ with D_1 a closed disk about the origin and $D_2$ an open disk of smaller radius about the origin.
-
but $\mathbb R^n$-$\{0\}$ isn't compact anymore, even if you replace $\mathbb R^n$ by $D^n$. – Stefan Hamcke Apr 8 '13 at 11:11
@Ittay: I think that in order for rotations of $S^n$ not to have fixed points, you need $n$ to be odd (or, technically, $n=0$ also works, which is really the same thing as my example of a two-point discrete set). – Zev Chonoles Apr 8 '13 at 11:15
Thank you both for the remarks, I made some correction. – Ittay Weiss Apr 8 '13 at 11:17
@ZevChonoles I like your observation that this is really your example in higher dimensions. – Ittay Weiss Apr 8 '13 at 11:18
@IttayWeiss Why n must be odd？ – Jebei Apr 8 '13 at 13:57
|
|
1. ## Series
I have only done simpler series before so this is new to me. Grateful for help, Thanks!
Determine the value of M so that the given series converges.
2. Originally Posted by Duffman
I have only done simpler series before so this is new to me. Grateful for help, Thanks!
Determine the value of M so that the given series converges.
If you simplify
$\frac{n+1}{n-6} + \frac{n+1}{n+7} - 2 - \frac{M}{n} = \frac{42M-(M-85)n-(M-1)n^2}{n(n-6)(n+7)}$
LCT with $\sum_{n=7}^{\infty} \frac{1}{n}$ will show it diverges for all values of M except $M = 1$ and if so, then
$\frac{n+1}{n-6} + \frac{n+1}{n+7} - 2 - \frac{M}{n} = \frac{42+84n}{n(n-6)(n+7)}$
LCT with $\sum_{n=7}^{\infty} \frac{1}{n^2}$ will show it converges.
3. By the divergence theorem the limit of the inside term needs to be zero in order to have convergence.
Therefore,
$\lim \frac{42M-(M-85)n-(M-1)n^2}{n(n-6)(n+7)} = 0 \implies M = 1$.
|
|
## General Paper Help: Making LaTeX Look Like Word
LaTeX has a very distinct style that is somewhat different from what your professors expect and want their student's papers to look like. Some professors will not accept papers without ragged right text, 12 pt font, and 1 inch margins. I recommend asking your professor for their guidelines before you write your first paper. Once you have their guidelines, the options below will help you make your paper's format exactly what they want.
### Changing the Font Type or Size
LaTeX allows you to change the font type and size in the preamble of your document. (The preamble is the section before \begin{document}, and where most of the global formatting commands are made.) This will affect your document's font size globally, but you can use the relative sizing for local changes. By default, your paper will be in Computer Modern (a font invented by Donald Knuth, the inventor of TeX) and 11pt. For something different, you will have to insert options and packages in the preamble. To change the font size, add the desired font size between the square brackets of the document class declaration. Remember, font size must be of the form "12pt", "11pt", or "14pt".
\documentclass[12pt]{article}
To change the font, you will need to add the font's package to your document by putting \usepackage{ packagename} in the preamble:
\documentclass[12pt]{article}
\usepackage{times}
\begin{document}
The body of your document!
\end{document}
avantgar bookman courier helvetic newcent palatino times zapfchan
### Alignment
#### Ragged Right Text
LaTeX uses its professional typesetting engine to perfectly justify your text, just like professionally published books and journals. However, many professors prefer unjustified text that is aligned with the left edge and the right edge ragged, commonly known as ragged right or left-aligned text. To give your paper a ragged right edge, use the raggedright environment.
\begin{raggedright}
\parindent=0.5in
[You must have a blank line here for the package to work]
Aware of no military grounds for keeping the Jupiter missiles in Turkey, Kennedy informed Ormsby-Gore that he would have to see whether political developments would enable him to do a deal on the reciprocal closing of bases''.
And so goes the rest of your paper...
[You must have a blank line here for the package to work]
\end{raggedright}
It will produce text like the following:
#### Other Justifications
To make things centered, you will want to use the center environment:
\begin{center}
This is centered text.
\end{center}
Similarly, the environment flushright aligns the text on the right edge of the document.
### Adjusting the Margins
While LaTeX has very generous (nearly 2 inch) margins by default, most professors prefer one inch margins all around so they can easily judge the true length of a paper. Use the fullpage package to make your paper conform to your professor's expectations. Include the \usepackage{fullpage} in the preamble of your document and you're set!
### Doublespacing
There are many packages in LaTeX that will doublespace your paper, but setspace does the best job of ignoring headings, figures, and other parts of the text you do not want doublespaced. Make sure to include the package at the top (in the preamble): \usepackage{setspace}.
Use the command \doublespacing to make the text doublespaced. Use the command \singlespacing to return to singlespaced text. If you place either command unseparated from the text as part of a paragraph, it will only apply to the paragraph it is in. However, if is separated by an empty line, it will apply to everything after it. The command \onehalfspacing will create less space between each line than doublespacing, about equivalent to Word's 1.5 spacing. (See an example on the Introduction to LaTeX page)
### Creating a Title Page
You can make a title page using the \maketitle command, which grabs the author and title that you have defined in the preamble and creates a title page automatically. Here's an example document that utilizes this:
\documentclass[11pt]{article}
\title{The Title of Your Paper}
%\date{}
%When commented out, the current date is printed. Uncomment to print no date or to specify a date inside the curly braces
\ begin{document}
\maketitle
\pagebreak
The rest of the paper
\end{document}
To get a page that looks like this (click on the image to see it bigger):
Alternately, you can make a title page by centering text and changing the size as you see fit, then adding a page break. Here's one such title page:
\begin{document}
\begin{center}
\begin{huge}The Title of Your Paper\end{huge}\\
The Date (or \today)\\
\end{center}\\
\end{document}
To get a page that looks like this (click on the image to see it bigger):
### Inserting Space
You may wish to leave a large gap between paragraphs for whatever reason. To do this, you can add a command after a line break (\\) or use the command \vspace:
Right below here will be a 3in gap\\*[3in]
Below here will be a gap 5 cm tall \vspace{5cm}
When specifying any space, be sure to give the unit of measurement and do not leave a space between the number and the unit. In addition to the absolute values of inches (in), centimeters (cm), millimeters (mm), you can also use relative values em and ex. Em is the width of a capital M in the current font, and ex is the height of a lower case x in the current font. Mathematicians might also want to use a mu, 18 of which are equal to one em, for precise positioning in mathmode.
### Long Quotes
Long quotes should go in the quote environment, intuitively enough. The quote is set off by blank lines and horizontal space, just like you learned to do in high school.
Text not in the quote.
\begin{quote}
Quoted text, lots of it
Another paragraph, if necessary
\end{quote}
More text not in the quote. Be that analytical machine!
That gives something like this:
### Footnotes
Whenever you need a footnote, just use \footnote{}. Anything within the bracket will be in the footnote. Here's an example:
Aware of no military grounds for keeping the Jupiter missiles in Turkey, Kennedy informed Ormsby-Gore that he would have to see whether political developments would enable him to do a deal on the reciprocal closing of bases.\footnote{Ormsby-Gore was the British Ambassador to the United States during the Kennedy Presidency.Ormsby-Gore knew Kennedy well from his time in London where his father, Joseph P. Kennedy, had served as American Ambassador.}
The above LaTeX code produces this output:
|
|
# Undecidability of irreducibility of infinite families of integer polynomials?
A recent question, Is irreducibility of polynomials $$\in\mathbb{Z}[X]$$ over $$\mathbb{Q}$$ an undecidable problem? was quickly answered in the negative. I am wondering if there is a simple example of a family of families of integer polynomials whose irreducibility is undecidable. For example, consider the following computational problem:
Instance: A positive integer $$n$$.
Question: Does the family of polynomials $$\{x^d + x + n : d \in \mathbb{N}\}$$ contain infinitely many members that are irreducible over $$\mathbb{Q}$$?
I don't know off the top of my head whether the above computational problem is undecidable. If it is, then that would answer my question affirmatively. If not, or if its undecidability is unknown, then is there some other problem of comparable simplicity that we can prove is undecidable?
EDIT: Upon further reflection, I suspect that the most promising route for getting an interesting answer to this question is to define some kind of "dynamical system" that generates a sequence of polynomials, and ask if (for example) the process eventually produces an irreducible polynomial. Interesting prior results with a dynamical-systems flavor include The undecidability of the generalized Collatz problem by Kurtz and Simon, and Turing-completeness of various families of PDEs as shown by Tao and others. Such results seem to say something about the complexity of the systems in question, in a way that "artificially" encoding an uncomputable set directly in the parameters of a problem (intuitively) does not. Unfortunately, I do not have a concrete proposal for how to define a suitable dynamical system.
Given a total computable function $$f:\mathbb{N}\times\mathbb{N}\to\{0,1\}$$ consider the family of families $$\mathcal{F}_n = (x^2+(-1)^{f(n,k)})_{k=0}^\infty$$. Then asking whether $$\mathcal{F}_n$$ has infinitely many irreducible elements over $$\mathbb{Q}$$ is equivalent to asking whether the set $$F_n = \{k \in \mathbb{N}\mid f(n,k)=1\}$$ is infinite. So every $$\Pi^0_2$$ set can be encoded as a problem of this form. This is optimal since it is decidable whether a given polynomial is irreducible over $$\mathbb{Q}$$ according to the question mentioned by the OP.
• Not bad, although I feel that there are two aesthetic flaws in this example. The first is that ${\cal F}_n$ is a sequence rather than a set. This can probably be fixed. The second, and more serious, flaw is that $(-1)^{f(n,k)}$ is not nearly as simple as a linear function such as $n$ or $k$. So it is not optimally simple. Feb 23 at 13:03
• @TimothyChow The sequence issue is indeed easily resolved, by using the polynomials $x^2+(-1)^{f(n,k)}(n+k)^2$. Feb 23 at 15:44
(This is only a comment.) If you instead look at the family $$\{x^d-x+n\}$$, then it is known that there are infinitely many irreducible elements (for each positive $$n$$). It suffices to show that $$f(x)=x^p-x+n$$ is irreducible in $$\mathbb{F}_p$$ for any prime $$p$$ such that $$p\nmid n$$. This is similar to a homework problem often assigned from Dummit and Foote's "Abstract Algebra" textbook, which is also solved by David Speyer here: Is $$x^p-x+1$$ always irreducible in $$\mathbb{F}_p$$? The proof with $$1$$ replaced by $$n$$ is unchanged.
|
|
Article | Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017 | A Simulation Environment for Efficiently Mixing Signal Blocks and Modelica Components
Göm menyn
Title:
A Simulation Environment for Efficiently Mixing Signal Blocks and Modelica Components
Author:
Ramine Nikoukhah: ALTAIR Engineering, France Masoud Najafi: ALTAIR Engineering, France Fady Nassif: ALTAIR Engineering, France
DOI:
10.3384/ecp17132831
Year:
2017
Conference:
Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017
Issue:
132
Article no.:
091
Pages:
831-838
No. of pages:
8
Publication type:
Abstract and Fulltext
Published:
2017-07-04
ISBN:
978-91-7685-575-1
Series:
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Export in BibTex, RIS or text
There exist several specialized tools that provide environments for the development and simulation of either pure Modelica models or pure signal based models. These environments have each their own advantages and flaws. solidThinking Activate\tm/ has been developed to mix these domains and take advantage of both of these approaches to system modeling. This paper presents this mixed Signal-Modelica environment, and in particular the efforts and challenges faced in its development.
Keywords: Modelica tool Signal based tool FMI
## Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017
Author:
Ramine Nikoukhah, Masoud Najafi, Fady Nassif
Title:
A Simulation Environment for Efficiently Mixing Signal Blocks and Modelica Components
References:
No references available
## Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017
Author:
Ramine Nikoukhah, Masoud Najafi, Fady Nassif
Title:
A Simulation Environment for Efficiently Mixing Signal Blocks and Modelica Components
Note: the following are taken directly from CrossRef
Citations:
No citations available at the moment
|
|
normal vector of a sphere
\\ Maybe another hint: visually, what are the similarities between the vector and the normal vector for the sphere on the point (x, y, z)? Under all of these assumptions the surface integral of $$\vec F$$ over $$S$$ is. How should this half-diminished seventh chord from "Christmas Time Is Here" be analyzed in terms of its harmonic function? This means that every surface will have two sets of normal vectors. Just as we did with line integrals we now need to move on to surface integrals of vector fields. Now we want the unit normal vector to point away from the enclosed region and since it must also be orthogonal to the plane $$y = 1$$ then it must point in a direction that is parallel to the $$y$$-axis, but we already have a unit vector that does this. I'm having kind of a problem on calculating the normal vector to a sphere using a parameterization. I am unsure how to go about this problem from here. Notice as well that because we are using the unit normal vector the messy square root will always drop out. Use MathJax to format equations. \mathrm{If } \;\; \mathbf{r}_u \times \mathbf{r}_v \neq 0, I found that If you picture a normal vector on the sphere, does the vector coincide with the ray that goes from the origin through the base of that vector? per second, per minute, or whatever time unit you are using). Volume between cone and sphere of radius $\sqrt2$ with surface integral, Efficient way to set up surface integral for a section of a sphere, Normal unit vector of sphere with spherical unit vectors $\hat r$, $\hat \theta$ and $\hat \phi$. We will call $${S_1}$$ the hemisphere and $${S_2}$$ will be the bottom of the hemisphere (which isn’t shown on the sketch). Now, in order for the unit normal vectors on the sphere to point away from enclosed region they will all need to have a positive $$z$$ component. There is one convention that we will make in regard to certain kinds of oriented surfaces. Old Budrys(?) “Orthonormal” parameterization of solid sphere? Looking for a function that approximates a parabola. MathJax reference. Since $$S$$ is composed of the two surfaces we’ll need to do the surface integral on each and then add the results to get the overall surface integral. If we’d needed the “downward” orientation, then we would need to change the signs on the normal vector. Maybe another hint: visually, what are the similarities between the vector and the normal vector for the sphere on the point (x, y, z)? \frac {\partial P(\phi, \theta)}{\partial \phi} \times \frac {\partial P(\phi, \theta)}{\partial \theta} = \begin{vmatrix} \mathbf{i}& \mathbf{j} &\mathbf{k} This means that we will need to use. where the right hand integral is a standard surface integral. It should also be noted that the square root is nothing more than. The normal of sphere can generally be easily found. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. My Vector Calculus book says that the Vector Product between the two partial derivates of the parameterized surface gives a Normal Vector to the surface. We could just as easily done the above work for surfaces in the form $$y = g\left( {x,z} \right)$$ (so $$f\left( {x,y,z} \right) = y - g\left( {x,z} \right)$$) or for surfaces in the form $$x = g\left( {y,z} \right)$$ (so $$f\left( {x,y,z} \right) = x - g\left( {y,z} \right)$$). If it doesn’t then we can always take the negative of this vector and that will point in the correct direction. Notice that for the range of $$\varphi$$ that we’ve got both sine and cosine are positive and so this vector will have a negative $$z$$ component and as we noted above in order for this to point away from the enclosed area we will need the $$z$$ component to be positive. ϕ), orienting the surface so the outside is the positive side.
|
|
# Yodl macros(7)
## NAME
yodlmacros - Macros for the Yodl converters
## SYNOPSIS
This manual page lists the standard macros of the Yodl package.
## DESCRIPTION
The following list shows the macros defined by the Yodl converters define and which can be used in Yodl documents. Refer to the Yodl user guide, distributed with the Yodl package, for a full description.
NOTE: Starting with Yodl version 3.00.0 Yodl's default file inclusion behavior has changed. The current working directory no longer remains fixed at the directory in which Yodl is called, but is volatile, changing to the directory in which a yodl-file is located. This has the advantage that Yodl's file inclusion behavior now matches the way C's `#include` directive operates; it has the disadvantage that it may break some current documents. Conversion, however is simple but can be avoided altogether if Yodl's `-L` (`--legacy-include`) option is used. This affects the `(l)includefile, includeverbatim, notransinclude` and `verbinclude` macros (see below).
The following list shows all macros of the package in alphabetical order.
`abstract(text)`
Defines an abstract for an `article` or `report` document. Abstracts are not implemented for `book`s or `manpage`s. Must appear before starting the document with the `article` or `report` macro.
`addntosymbol(symbol)(n)(text)`
Adds `text` `n` times to `symbol`. The value `n` may also be the name of a defined counter (which itself will not be modified).
`affiliation(site)`
Defines an affiliation, to appear in the document titlepage below the author field. Must appear before starting the document with `article`, `report` or `book`. The affiliation is only printed when the author field is not empty. When converting to html the way the affiliation is displayed can be tuned using CSS id selector specifications. The affiliation has `id="affiliation"`.
`AfourEnlarged()`
Enlarges the usable height of A4 paper by 2 cm.: the top margin is reduced by 2 cm. This macro should be called in the preamble. The macro is available only for LaTeX conversions.
`appendix()`
Starts appendices
`article(title)(author)(date)`
Starts an article. The top-level sectioning command is `(n)sect`. In HTML conversions only one output file is written, while the way the headings are displayed can be tuned using CSS id selector specifications: the title has `id="title"`, the author `id="author"`, and the date `id="date"`.)
`attrib(text)`
In html, pushes `text` as an attribute for the next html tag supporting `attrib`. E.g, to set a blue color and 30 pixel left-hand side margin for a section use
```
attrib(style="color:blue;margin-left:30px;")\
sect(Section name)
```
This results in the html markup
```
<h1 style="color:blue;margin-left:30px;">Section name</h1>
```
This macro is only effective with html conversions. It is applied in a stack-wise fasion: when multiple `attrib` calls are used, then the topmost attrib-string is added to the first macro calling the `attribinsert` macro, with subsequent macros using subsequent elements on the attrib-stack.
Commonly used attributes are `id="idname"`, expecting a `#idname` CSS label in either internal or external CSS specifications, or `style="spec"` (as shown in the example).
Example: when using
```
attrib(width = "100" height = "100")
attrib(id = "#fig")
figure(imgfile)(Caption)(IMG)
```
then the `#id` attribute is applied to `<figure>`, and the `width` and `height` attributes are applied to `<img>`, which html markup is inserted by the `figure` macro.
The `attrib` macro is supported by the following predefined macros (between parentheses the number of attribute strings that are inserted by these macros; if only 1 attribute string is inserted no number is shown):
```bf cell cells center chapter code dit em figure(3) file htmltag itdesc lchapter link lref lsect lsubsect lsubsubsect nchapter npart nsect nsubsect nsubsubsect paragraph part quote row sc sect strong subs subsect subsubsect subsubsubsect sups tt url verb verbinclude```.
`attribclear()`
Removes any existing contents from the attrib-stack. This macro is only active when converting to html
`attribinsert()`
In html, if the attrib-stack is not empty, inserts the value on top of the attrib-stack and then pops the topmost value. If the attrib-stack is empty, nothing happens.
`bf(text)`
Sets `text` in boldface.
`bind(text)`
Generate a binding character after text.
`book(title)(author)(date)`
Starts a book document. The top-level sectioning command is `(n)chapter`, `(n)part` being optional. In HTML output files are created for each chapter, while the way the headings are displayed can be tuned using CSS id selector specifications: the title has `id="title"`, the author `id="author"`, and the date `id="date"`.)
`cell(contents)`
Sets a table cell, i.e., one element in a row. With the man/ms converters multiple blanks between `cell()` macro calls are merged into a single blank character.
`cells(nColumns)(contents)`
Set a table cell over `nColumns` columns. With LaTeX and xml the information in the combined cells is centered.
With man/ms conversions the `cells()` macro simply calls the `cell()` macro, but here the `setmanalign()` macro can be used to determine the alignment of multiple cells.
With html the macro `attrib` can be used, but when it contains a `style` specification the macro's default `style="text-align: center"` is ignored (but it can optionally be specified using the `attrib` macro).
`cellsline(from)(count)`
Sets a horizontal line starting at column number `from` over `count` columns in a row. If `from` is less then the number of columns already added to a row then it is ignored. This macro must be embedded in a `row` macro defining a table row. To put a line across the table's full width use `rowline`. To set horizontal lines across columns 1 until 2 and columns 4 until 5 table of a table use:
```
row(cellsline(1)(2)cellsline(4)(2))
```
Combining `cellsline` and `cell` or `cells` calls in one row produces undefined results.
`center(text)`
Centers `text`. Use `nl()` in the text to break lines. In html the `attrib` macro is not supported.
`chapter(title)`
Starts a new chapter in `book`s or `report`s.
`cindex()`
Generate an index entry for index c.
`cite(1)`
Sets a citation or quotation
`clearpage()`
Starts a new page, when the output format permits. Under HTML a horizontal line is drawn.
`code(text)`
Sets `text` in code font, and prevents it from being expanded. For unbalanced parameter lists, use `CHAR(40)` to get `(` and `CHAR(41)` to get `)`.
`columnline(from)(to)`
Sets a horizontal line over some columns in a row. Note that `columnline` defines a row by itself, consisting of just a horizontal line spanning some of its columns, rather than the table's full width, like `rowline`. The two arguments represent column numbers. It is the responsibility of the author to make sure that the `from` and `to` values are sensible. I.e.,
```
1 <= from <= to <= ncolumns
```
Note: this macro cannot be used if multiple lines must be set in one row. In those cases the macro `colsline` should be used.
`def(macroname)(nrofargs)(redefinition)`
Defines `macroname` as a macro, having `nrofargs` arguments, and expanding to `redefinition`. This macro is a shorthand for `DEFINEMACRO`. An error occurs when the macro is already defined. Use `redef()` to unconditionally define or redefine a macro.
`description(list)`
Sets `list` as a description list. Use `dit(item)` to indicate items in the list.
`dit(itemname)`
Starts an item named `itemname` in a descriptive list. The list should be defined as contents of a `description()`. With `html` conversions the contents of a description item is separated from the item itself. The `dit` macro only defines the item, and not the description itself. This macro sets the item in bold-face (`strong' font). The macro `itdesc`, available since Yodl 3.05, can be used to defines an item and its description, using its suggested format (i.e., indenting the description relative to the item).
`eit()`
Indicates an item in an enumerated list. The `eit()` macro should be an argument in `enumerate()`.
`ellipsis()`
Sets ellipsis (...).
`em(text)`
Sets `text` as emphasized, usually italics.
`email(address)`
In HTML, this macro sets the `address` in a `<a href="mailto=..">` locator. In other output formats, the `address` is sent to the output. The `email` macro is a special case of `url`.
`enumeration(list)`
`enumeration()` starts an enumerated list. Use `eit()` in the list to indicate items in the list.
`euro()`
Sets the euro currency symbol in latex, html, (and possibly sgml and xml). In all other conversions EUR which is the official textual abbreviation (cf. http://ec.europa.eu/euro/entry.html) is written. Note that LaTeX may require latexpackage()(eurosym).
`fig(label)`
This macro is a shorthand for `figure ref(label)` and just makes the typing shorter, as in `see fig(schematic) for ..` See `getfigurestring()` and `setfigurestring()` for the `figure` text.
`figure(file)(caption)(label)`
Sets the picture in `file` as a figure in the current document, using the descriptive text `caption`. The `label` is defined as a placeholder for the figure number and can be used in a corresponding `ref` statement. Note that the `file` must be the filename without extension: By default, Yodl will supply `.gif` when in HTML mode, or `.ps` when in LaTeX mode. Figures in other modes may not (yet) haven been implemented.
When converting to html, this macro uses three attribute-strings (if available). The string pushed first using an attrib-call defines the attributes for its `<figcaption>` html-markup; the string pushed next defines the attributes for its `<img>` html-markup; the string pushed last defines the attributes for its `<figure>` html-markup. The `figure` macro's html output is organized like this:
```
<figure -attrib-string pushed last (if any)>
<img ... -attrib-string pushed last but one>
<figcaption -attrib-string pushed 2nd to last>
...
</figcaption>
</figure>
```
Starting with Yodl 3.07.00 no `alt="Figure # is shown here..."` attribute is defined anymore for the `img` markup: an `alt`-attribute can easily be defined at the last attrib-call, using `getfigurestring()` to obtain `Figure` or its language-specific translation, and `COUNTERVALUE(XXfigurecounter)` to obtain the order-number of the figure shown in the next `figure`-macro call.
`file(text)`
Sets `text` as filename, usually boldface. In html `attrib` macro applies to the `<strong>` tag.
`findex()`
Generate an index entry for index f.
`footnote(text)`
Sets `text` as a footnote, or between parentheses when the output format does not allow footnotes.
`gagmacrowarning(name name ...)`
Prevents the `yodl` program from printing cannot expand possible user macro. E.g., if you have in your document `the file(s) are ..` then you might want to put before that: `gagmacrowarning(file)`. Calls `NOUSERMACRO`.
`getaffilstring()`
Expands to the string that defines the name of Affiliation Information, by default AFFILIATION INFORMATION. Can be redefined for national language support by `setaffilstring()`. Currently, it is relevant only for txt.
`getauthorstring()`
Expands to the string that defines the name of Author Information, by default AUTHOR INFORMATION. Can be redefined for national language support by `setauthorstring()`. Currently, it is relevant only for txt.
`getchapterstring()`
Expands to the string that defines a `chapter' entry, by default Chapter. Can be redefined for national language support by `setchapterstring()`.
`getdatestring()`
Expands to the string that defines the name of Date Information, by default DATE INFORMATION. Can be redefined for national language support by `setdatestring()`. Currently, it is relevant only for txt.
`getfigurestring()`
Returns the string that defines a `figure' text, in captions or in the `fig()` macro. The string can be redefined using the `setfiguretext()` macro.
`getpartstring()`
Expands to the string that defines a `part' entry, by default Part. Can be redefined for national language support by `setpartstring()`.
`gettitlestring()`
Expands to the string that defines the name of Title Information, by default TITLE INFORMATION. Can be redefined for national language support by `settitlestring()`. Currently, it is relevant only for txt.
`gettocstring()`
Expands to the string that defines the name of the table of contents, by default Table of Contents. Can be redefined for national language support by `settocstring()`.
`htmlcommand(cmd)`
Writes `cmd` to the output when converting to html. The `cmd` is not further expanded by Yodl.
`htmlheadfile(file)`
Adds the contents of `file` to the `head` section of an HTML document. The contents of file are not interpreted and should contain plain html text. This option can be useful when large bodies of text, like the contents of `<script>` sections, must be included into the head section of html documents. This macro is only active in the preamble, should only specified once, and is only interpreted for html conversions.
`htmlheadopt(option)`
Adds the literal text `option` to the current information in the `head` section of an HTML document. `Option` may (or: should) contain plain html text. A commonly occurring head option is `link`, defining, e.g., a style sheet. Since that option is frequently used, it has received a dedicated macro: `htmlstylesheet`. When large bodies of html-text must be added to html documents the macro `htmlheadfile` should be used. This macro is only active in the preamble and is only interpreted for html conversions.
`htmlnewfile()`
In HTML output, starts a new file. All other formats are not affected. Note that you must take your own provisions to access the new file; say via links. Also, it's safe to start a new file just befoore opening a new section, since sections are accessible from the clickable table of contents. The HTML converter normally only starts new files prior to a `chapter` definition.
`htmlstyle(tag)(definition)`
Adds `<style type="text/css"> ... </style>` element to the head section of an HTML document.
Use `htmlstyle` to specify one or more CSS definitions which are eventually inserted at the ellipsis (`...`) in the generic `style` definition shown above. E.g., (using `#rrggbb` to specify a color, where `rr` are two hexadecimal digits specifying the color's red component, `gg` two hexadecimal digits specifying the color's green component, and `bb` two hexadecimal digits specifying the color's blue component) specifying
```
htmlstyle(body)(color: #rrggbb; background-color: #rrggbb)
htmlstyle(h1)(color: blue; text-align: center)
htmlstyle(h2)(color: green)
```
results in the element
```
<style type="text/css">
body {color: #rrggbb; background-color: #rrggbb;}
h1 {color: blue; text-align: center;}
h2 {color: green;}
</style>
```
The macros `htmlheadopt` and `htmlstylesheet` could also be used to put information into the head-section of an HTML document, but `htmlheadopt` is of a much more general nature, while `htmlstylesheet` refers to CSS elements stored in an external file. The macro `attrib` can be used to define inline styles.
The `htmlstyle` macro is only active in the preamble and is only interpreted for html conversions.
Refer to available CSS specifications (cf., http://www.w3schools.com/cssref/ for an overview of how CSS specifications are used, and which CSS specifications are available).
By default the internal style specification
`figure {text-align: center;} img {vertical-align: center;}`
is used. If this is not appropriate, specify `nohtmlimgstyle()` in the preamble.
`htmlstylesheet(url)`
Adds a `<link rel="stylesheet" type="text/css" ...>` element to the head section of an HTML document, using `url` in its `href` field. The argument `url` is not expanded, and should be plain HTML text, without surrounding quotes. The macro `htmlheadopt` can also be used to put information in the head-section of an HTML document, but `htmlheadopt` is of a much more general nature. This macro is only active in the preamble and is only interpreted for html conversions.
`htmltag(tagname)(start)`
Sets `tagname` as a HTML tag, enclosed by `<` and `>`. When `start` is zero, the `tagname` is prefixed with `/`. As not all html tags are available through predefined Yodl-macros (there are too many of them, some are used very infrequently, and you can easily define macros for the tags for which Yodl doesn't offer predefined ones), the `htmltag` macro can be used to handle your own set of macros. In html the `attrib` macro is supported. E.g.,
```
attrib(title="World Health Organization")htmltag(abbr)()WHO+htmltag(abbr)(0)
```
`ifnewparagraph(truelist)(falselist)`
The macro `ifnewparagraph` should be called from the `PARAGRAPH` macro, if defined. It will insert `truelist` if a new paragraph is inserted, otherwise `falselist` is inserted (e.g., following two consecutive calls of PARAGRAPH). This macro can be used to prevent the output of multiple blank lines.
`includefile(file)`
Includes `file`. The default extension `.yo` is supplied if necessary.
NOTE: Starting with Yodl version 3.00.0 Yodl's default file inclusion behavior has changed. The current working directory no longer remains fixed at the directory in which Yodl is called, but is volatile, changing to the directory in which a yodl-file is located. This has the advantage that Yodl's file inclusion behavior now matches the way C's `#include` directive operates; it has the disadvantage that it may break some current documents. Conversion, however is simple but can be avoided altogether if Yodl's `-L` (`--legacy-include`) option is used.
Furthermore, the `includefile` macro no longer defines a label. To define a label just before the file's inclusion use `lincludefile`.
`includeverbatim(file)`
Include `file` into the output. No processing is done, `file` should be in preformatted form, e.g.:
```whenhtml(includeverbatim(foo.html))
```
NOTE: Starting with Yodl version 3.00.0 Yodl's default file inclusion behavior has changed. The current working directory no longer remains fixed at the directory in which Yodl is called, but is volatile, changing to the directory in which a yodl-file is located. This has the advantage that Yodl's file inclusion behavior now matches the way C's `#include` directive operates; it has the disadvantage that it may break some current documents. Conversion, however is simple but can be avoided altogether if Yodl's `-L` (`--legacy-include`) option is used.
`it()`
Indicates an item in an itemized list. The list is either surrounded by `startit()` and `endit()`, or it is an argument to `itemize()`.
`itdesc(itemname)(contents)`
Starts an item and its description in a description list. Its name is `itemname`, the contents of the item is defined by `contents`. The `itemname` is defined by using the `dit` macro.
With `html` conversions the contents are surrounded by `<dd>` and `</dd>` tags, resulting in contents which are indented relative to the itemname. When the `attrib` macro is used it is applied to the itemname (`dt`-tags).
With other conversions the `contents` are quoted (as if using `quote(contents)`).
`itemization(list)`
Sets `list` as an itemizationd list. Use `it()` to indicate items in the list.
`kindex()`
Generate an index entry for index k.
`label(labelname)`
Defines `labelname` as an anchor for a `link` command, or to stand for the last numbering of a section or figure in a `ref` command.
`langle()`
Character <
`languagedutch()`
Defines the Dutch-language specific headers. Active this macro via setlanguage(dutch).
`languageenglish()`
Defines the English-language specific headers. Active this macro via setlanguage(english).
`languageportugese()`
Defines the Portugese-language specific headers. Active this macro via setlanguage(portugese).
`LaTeX()`
The LaTeX symbol.
`latexaddlayout(arg)`
This macro is provided to add Yodl-interpreted text to your own LaTeX layout commands. The command is terminated with an end-of-line. See also the macro `latexlayoutcmds()`
`latexcommand(cmd)`
Writes `cmd` plus a white space to the output when converting to LaTeX. The `cmd` is not further expanded by Yodl.
`latexdocumentclass(class)`
Forces the LaTeX `\documentclass{...}` setting to `class`. Normally the class is defined by the macros `article`, `report` or `book`. This macro is an escape route in case you need to specify your own document class for LaTeX. This option is a modifier and must appear before the `article`, `report` or `book` macros.
`latexlayoutcmds(NOTRANSs)`
This macro is provided in case you want to put your own LaTeX layout commands into LaTeX output. The `NOTRANSs` are pasted right after the `\documentclass` stanza. The default is, of course, no local LaTeX commands. Note that this macro does not overrule my favorite LaTeX layout. Use `nosloppyhfuzz()` and `standardlayout()` to disable my favorite LaTeX layout.
`latexoptions(options)`
Set latex options: `documentclass[options]`. This command must appear before the document type is stated by `article`, `report`, etc..
`latexpackage(options)(name)`
Include latex package(s), a useful package is, e.g., `epsf`. This command must appear before the document type is stated by `article`, `report`, etc..
`lchapter(label)(title)`
Starts a new chapter in `book`s or `report`s, setting a label at the beginning of the chapter.
`letter(language)(date)(subject)(opening)(salutation)(author)`
Starts a letter written in the indicated language. The date of the letter is set to `date', the subject of the letter will be `subject'. The letter starts with `opening'. It is based on the `letter.cls' document class definition. The macro is available for LaTeX only. Preamble command suggestions:
• `latexoptions(11pt)`
• `a4enlarged()`
• `letterreplyto(name)(address)(postalcode/city)`
• `letterfootitem(phone)(number)`, maybe e-mail too.
• `letteradmin(yourdate)(yourref)`
• `letterto(addressitem)`. Use a separate `letterto()` macro call for each new line of the address.
`letteraddenda(type)(value)`
Adds an addendum at the end of a letter. `type' should be `bijlagen', `cc' or `ps'.
`letteradmin(yourdate)(yourref)`
Puts `yourletterfrom' and `yourreference' elements in the letter. If left empty, two dashes are inserted.
`letterfootitem(name)(value)`
Puts a footer at the bottom of letter-pages. Up to three will usually fit. LaTeX only.
`letterreplyto(name)(address)(zip city)`
`letterto(element)`
`link(description)(labelname)`
In HTML output a clickable link with the text `description` is created that points to the place where `labelname` is defined using the `label` macro, and `attrib` macro applies to the `<a>` tag. Using `link` is similar to `url`, except that a hyperlink is set pointing to a location in the same document. For output formats other than HTML, only the `description` appears.
`lref(description)(labelname)`
This macro is a combination of the `ref` and `link` macros. In HTML output a clickable link with the text `description` and the label value is created that points to the place where `labelname` is defined using the `label` macro, and `attrib` macro applies to the `<a>` tag. For output formats other than HTML, only the `description` and the label value appears.
`lsect(label)(title)`
Starts a new section, setting a label at the beginning of the section. In html `attrib` macro applies to the `<h2>` tag.
`lsubsect(label)(title)`
Starts a new subsection. Other sectioning commands are `subsubsect` and `subsubsubsect`. A label is added just before the subsection. In html `attrib` macro applies to the `<h3>` tag.
`lsubsubsect(label)(title)`
Starts a sub-subsection, a label is added just before the section In html `attrib` macro applies to the `<h4>` tag.
`lsubsubsubsect(label)(title)`
Starts a sub-sub-sub section. This level of sectioning is not numbered, in contrast to `higher' sectionings. A label is added just before the subsubsubection.
`lurl(locator)`
An url described by its Locator. For small urls with readable addresses.
`mailto(address)`
Defines the default `mailto` address for HTML output. Must appear before the document type is stated by `article`, `report`, etc..
`makeindex()`
Make index for latex.
`mancommand(cmd)`
Writes `cmd` to the output when converting to man. The `cmd` is not further expanded by Yodl.
`manpage(title)(section)(date)(source)(manual)`
Starts a manual page document. The `section` argument must be a number, stating to which section the manpage belongs to. Most often used are commands (1), file formats (5) and macro packages (7). The sectioning commands in a manpage are not `(n)sect` etc., but `manpage...()`. The first section must be the `manpagename`, the last section must be the `manpageauthor`. The standard manpage for section 1 contains the following sections (in the given order): `manpagename`, `manpagesynopsis`, `manpagedescription`, `manpageoptions`, `manpagefiles`, `manpageseealso`, `manpagediagnostics`, `manpagebugs`, `manpageauthor`. Optional extra sections can be added with `manpagesection`. Standard manpageframes for several manpagesections are provided in `/usr/local/share/yodl/manframes`. YODL manual pages can be converted to `groff, html`, or plain ascii text formats.
`manpageauthor()`
Starts the AUTHOR entry in a `manpage` document. Must be the last section of a `manpage`.
`manpagebugs()`
Starts the BUGS entry in a `manpage` document.
`manpagedescription()`
Starts the DESCRIPTION entry in a `manpage` document.
`manpagediagnostics()`
Starts the DIAGNOSTICS entry in a `manpage` document.
`manpagefiles()`
Starts the FILES entry in a `manpage` document.
`manpagename(name)(short description)`
Starts the NAME entry in a `manpage` document. The short description is used by, e.g., the `whatis` database.
`manpageoptions()`
Starts the OPTIONS entry in a `manpage` document.
`manpagesection(SECTIONNAME)`
Inserts a non-required section named `SECTIONNAME` in a `manpage` document. This macro can be used to augment `standard' manual pages with extra sections, e.g., EXAMPLES. Note that the name of the extra section should appear in upper case, which is consistent with the normal typesetting of manual pages.
`manpageseealso()`
Starts the SEE ALSO entry in a `manpage` document.
`manpagesynopsis()`
Starts the SYNOPSIS entry in a `manpage` document.
`mbox()`
Unbreakable box in LaTeX. Other formats may have different opitions on our unbreakable boxex.
`metaC(text)`
Put a line comment in the output.
`metaCOMMENT(text)`
Write format-specific comment to the output.
`mscommand(cmd)`
Writes `cmd` to the output when converting to ms. The `cmd` is not further expanded by Yodl.
`nchapter(title)`
Starts a chapter (in a `book` or `report`) without generating a number before the title and without placing an entry for the chapter in the table of contents. In html `attrib` macro applies to the `<h1>` tag.
`nemail(name)(address)`
Named email. A more consistent naming for url, lurl, email and nemail would be nice.
`nl()`
Forces a newline; i.e., breaks the current line in two.
`nodeprefix(text)`
Prepend text to node names, e.g.
```nodeprefix(LilyPond) sect(Overview)
```
Currently used in texinfo descriptions only.
`nodeprefix(text)`
Prepend text to node names, e.g.
```nodeprefix(LilyPond) sect(Overview)
```
Currently used in texinfo descriptions only.
`nodetext(text)`
Use text as description for the next node, e.g.
```nodetext(The GNU Music Typesetter)chapter(LilyPond)
```
Currently used in texinfo descriptions only.
`nohtmlfive()`
Starting yodl 3.05 html-conversions by default use html5. This can be suppressed (in favor of using html4) by calling this macro. This macro merely suppresses writing the initial `<!DOCTYPE html>` to generated html files; it is only active in the preamble and is only interpreted for html conversions.
`nohtmlimgstyle()`
By default html-pages specify
`(<style type="text/css" img {vertical-align: bottom;}></style>)`
This macro suppresses this `img` CSS style specification. This macro is only active in the preamble and is only interpreted for html conversions.
`nop(text)`
Expand to text, to avoid spaces before macros e.g.: a2. Although a+sups(2) should have the same effect.
`nosloppyhfuzz()`
By default, LaTeX output contains commands that cause it to shut up about hboxes that are less than 4pt overfull. When `nosloppyhfuzz()` appears before stating the document type, LaTeX complaints are `vanilla'.
`notableofcontents()`
Prevents the generation of a table of contents. This is default in, e.g., `manpage` and `plainhtml` documents. When present, this option must appear before stating the document type with `article`, `report` etc..
`notitleclearpage()`
Prevents the generation of a `clearpage()` instruction after the typesetting of title information. This instruction is default in all non `article` documents. When present, must appear before stating the document type with `article`, `book` or `report`.
`notocclearpage()`
With the LaTeX converter, no `clearpage()` instruction is inserted immediately beyond the document's table of contents. The `clearpage()` instruction is default in all but the `article` document type. When present, must appear before stating the document type with `article`, `book` or `report`. With other converters than the LaTeX converter, it is ignored.
`notransinclude(filename)`
Reads filename and inserts it literally in the text not subject to macro expansion or character translation. No information is written either before or after the file's contents, not even a newline.
NOTE: Starting with Yodl version 3.00.0 Yodl's default file inclusion behavior has changed. The current working directory no longer remains fixed at the directory in which Yodl is called, but is volatile, changing to the directory in which a yodl-file is located. This has the advantage that Yodl's file inclusion behavior now matches the way C's `#include` directive operates; it has the disadvantage that it may break some current documents. Conversion, however is simple but can be avoided altogether if Yodl's `-L` (`--legacy-include`) option is used.
`noxlatin()`
When used in the preamble, the LaTeX converter disables the inclusion of the file `xlatin1.tex`. Normally this file gets included in the LateX output files to ensure the conversion of high ASCII characters (like é) to LaTeX-understandable codes. (The file `xlatin1.tex` comes with the YODL distribution.)
`nparagraph(title)`
Starts a non-numbered paragraph (duh, corresponds to subparagraph in latex).
`npart(title)`
Starts a part in a `book` document, but without numbering it and without entering the title of the part in the table of contents. In html `attrib` macro applies to the `<h1>` tag.
`nsect(title)`
Starts a section, but does not generate a number before the `title` nor an entry in the table of contents. Further sectioning commands are `nsubsect`, `nsubsubsect` and `nsubsubsubsect`. In html `attrib` macro applies to the `<h2>` tag.
`nsubsect(title)`
Starts a non-numbered subsection. In html the `attrib` macro applies to the `<h3>` tag.
`nsubsubsect(title)`
Starts a non-numbered sub-sub section. In html `attrib` macro applies to the `<p>` tag.
`nsubsubsect(title)`
Starts a non-numbered sub-subsection.
`paragraph(title)`
Starts a paragraph. This level of sectioning is not numbered, in contrast to `higher' sectionings (duh, corresponds to subparagraph in latex). In html `attrib` macro applies to the `<p>` tag.
`part(title)`
Starts a new part in a `book` document. In html `attrib` macro applies to the `<h1>` tag.
`pindex()`
Generate an index entry for index p.
`plainhtml(title)`
Starts a document for only a plain HTML conversion. Not available in other output formats. Similar to `article`, except that an author- and date field are not needed.
`printindex()`
Make index for texinfo (?).
`quote(text)`
Sets the text as a quotation. Usually, the text is indented, depending on the output format. In html `attrib` macro applies to the `<blockquote>` tag.
`rangle()`
Inserts the right angle character (>).
`redef(macro)(nrofargs)(redefinition)`
Defines macro `macro` to expand to `redefinition`. Similar to `def`, but any pre-existing definition is overruled. Use `ARG`x in the redefinition part to indicate where the arguments should be pasted. E.g., `ARG1` places the first argument, `ARG2` the second argument, etc...
`redefinemacro(macro)(nrofargs)(redefinition)`
Defines macro `macro` to expand to `redefinition`. Similar to `def`, but any pre-existing definition is overruled. Use `ARG`x in the redefinition part to indicate where the arguments should be pasted. E.g., `ARG1` places the first argument, `ARG2` the second argument, etc... This commands is actually calling redef().
`ref(labelname)`
Sets the reference for `labelname`. Use `label` to define a label.
`report(title)(author)(date)`
Starts a report type document. The top-level sectioning command in a report is `chapter`. In html the way the headings are displayed can be tuned using CSS id selector specifications: the title has `id="title"`, the author `id="author"`, and the date `id="date"`.
`roffcmd(dotcmd)(sameline)(secondline)(thirdline)`
Sets a t/nroff command that starts with a dot, on its own line. The arguments are: `dotcmd` - the command itself, e.g., `.IP`; `sameline` - when not empty, set following the `dotcmd` on the same line; `secondline` - when not empty, set on the next line; `thirdline` - when not empty, set on the third line. Note that `dotcmd` and `thirdline` are not further expanded by YODL, the other arguments are.
`row(contents)`
The argument `contents` may contain a man-page alignment specification (only one specification can be entered per row), using `setmanalign()`. If omitted, the standard alignment is used. Furthermore it contains the contents of the elements of the row, using `cell()` or `cells()` macros. If `cells()` is used, `setmanalign()` should have been used too. In this macro call only the `cell()`, `cells()` and `setmanalign()` macros should be called. Any other macro call may produce unexpected results.
The `row` macro defines a counter `XXcellnr` that can be inspected and is incremented by predefined macros adding columns to a row. The counter is initially 0. Predefined macros adding columns to a row add the number of columns they add to the row inserting the contents of those columns. These macros rely on the correct value of this counter and any user-defined macros adding columns to table rows should correctly update `XXcellnr`. In html `attrib` macro applies to the `<tr>` tag.
`rowline()`
Sets a horizontal line over the full width of the table. See also `columnline()`. Use `rowline()` instead of a `row()` macro call to obtain a horizontal line-separator.
`sc(text)`
Set `text` in the tt (code) font, using small caps. In html the `attrib` macro is not supported, while the code section is embedded in a `<div style="font-size: 90%">` section.
`sect(title)`
Starts a new section. In html `attrib` macro applies to the `<h2>` tag.
`setaffilstring(name)`
Defines `name` as the `affiliation information' string, by default AFFILIATION INFORMATION. E.g., after `setaffilstring(AFILIACION)`, YODL outputs this Spanish string to describe the affiliation information. Currently, it is relevant only for txt.
`setauthorstring(name)`
Defines `name` as the `Author information' string, by default AUTHOR INFORMATION. E.g., after `setauthorstring(AUTOR)`, YODL outputs this portuguese string to describe the author information. Currently, it is relevant only for txt.
`setchapterstring(name)`
Defines `name` as the `chapter' string, by default Chapter. E.g., after `setchapterstring(Hoofdstuk)`, YODL gains some measure of national language support for Dutch. Note that LaTeX support has its own NLS, this macro doesn't affect the way LaTeX output looks.
`setdatestring(name)`
Defines `name` as the `date information' string, by default DATE INFORMATION. E.g., after `setdatestring(DATA)`, YODL outputs this portuguese string to describe the date information. Currently, it is relevant only for txt.
`setfigureext(name)`
Defines the `name` as the `figure' extension. The extension should include the period, if used. E.g., use setfigureext(.ps) if the extensions of the figure-images should end in `.ps`
`setfigurestring(name)`
Defines the `name` as the `figure' text, used e.g. in figure captions. E.g., after `setfigurestring(Figuur)`, Yodl uses Dutch names for figures.
`sethtmlfigureext(ext)`
Defines the filename extension for HTML figures, defaults to `.jpg`. Note that a leading dot must be included in `ext`. The new extension takes effect starting with the following usage of the `figure` macro. It is only active in html, but otherwise acts identically as setfigureext().
`htmlmetacharset(meta-charset)`
Adds `<meta charset="meta-charset">` to the head of html documents. By default `<meta charset="UTF-8">` is used. This macro is only active in the preamble and is only interpreted for html conversions.
`setincludepath(name)`
Sets a new value of the include-path specification used when opening .yo files. A warning is issued when the path specification does not include a .: element. Note that the local directory may still be an element of the new include path, as the local directory may be the only or the last element of the specification. For these eventualities the new path specification is not checked.
`setlanguage(name)`
Installs the headers specific to a language. The argument must be the name of a language, whose headers have been set by a corresponding languageXXX() call. For example: languagedutch(). The language macros should set the names of the headers of the following elements: table of contents, affiliation, author, chapter, date, figure, part and title
`setlatexalign(alignment)`
This macro defines the table alignment used when setting tables in LaTeX. Use as many `l` (for left-alignment), `r` (for right alignment), and `c` (for centered-alignment) characters as there are columns in the table. See also `table()`
`setlatexfigureext(ext)`
Defines the filename extension for encapsulated PostScript figures in LaTeX, defaults to `.ps`. The dot must be included in t new extension `ext`. The new extension takes effect starting with a following usage of the `figure` macro. It is only active in LaTeX, but otherwise acts identically as setfigureext().
`setlatexverbchar(char)`
Set the char used to quote LaTeX `\verb` sequences
`setmanalign(alignment)`
This macro defines the table alignment used when setting tables used in man-pages (see tbl(1)). Use as many `l` (for left-alignment), `r` (for right alignment), and `c` (for centered-alignment) characters as there are columns in the table. Furthermore, `s` can be used to indicate that the column to its left is combined (spans into) the current column. Use this specification when cells spanning multiple columns are defined. Each row in a table which must be convertible to a manpage may contain a separate `setmanalign()` call. Note that neither `rowline` nor `columnline` requires `setmanalign()` specifications, as these macros define rows by themselves. It is the responsibility of the author to ensure that the number of alignment characters is equal to the number of columns of the table.
`setpartstring(name)`
Defines `name` as the `part' string, by default Part. E.g., after `setpartstring(Teil)`, Yodl identifies parts in the German way. Note that LaTeX output does its own national language support; this macro doesn't affect the way LaTeX output looks.
`setrofftab(x)`
Sets the character separating items in a line of input data of a `roff` (manpage) table. By default it is set to `~`. This separator is used internally, and needs only be changed (into some unique character) if the table elements themselves contain `~` characters.
`setrofftableoptions(optionlist)`
Set the options for tbl table, default: none. Multiple options should be separated by blanks, by default no option is used. From the tbl(1) manpage, the following options are selected for consideration:
• `center` Centers the table (default is left-justified)
• `expand` Makes the table as wide as the current line length
• `box` Encloses the table in a box
• `allbox` Encloses each item of the table in a box
Note that starting with Yodl V 2.00 no default option is used anymore. See also `setrofftab()` which is used to set the character separating items in a line of input data.
`settitlestring(name)`
Defines `name` as the `title information' string, by default TITLE INFORMATION. E.g., after `settitlestring(TITEL)`, YODL outputs this Dutch string to describe the title information. Currently, it is relevant only for txt.
`settocstring(name)`
Defines `name` as the `table of contents' string, by default Table of Contents. E.g., after `settocstring(Inhalt)`, YODL identifies the table of contents in the German way. Note that LaTeX output does its own national language support; this macro doesn't affect the way LaTeX output looks.
`sgmlcommand(cmd)`
Writes `cmd` to the output when converting to sgml. The `cmd` is not further expanded by Yodl.
`sgmltag(tag)(onoff)`
Similar to `htmltag`, but used in the SGML converter.
`sloppyhfuzz(points)`
By default, LaTeX output contains commands that cause it to shut up about hboxes that are less than 4pt overfull. When `sloppyhfuzz()` appears before stating the document type, LaTeX complaints occur only if hboxes are overfull by more than `points`.
`standardlayout()`
Enables the default LaTeX layout. When this macro is absent, then the first lines of paragraphs are not indented and the space between paragraphs is somewhat larger. The `standardlayout()` directive must appear before stating the document type as `article`, `report`, etc..
`strong(contents)`
In html and xml the `contents` are set between `<strong>` and `</strong>` tags. In html `attrib` macro applies to the `<strong>` tag.
`subs(text)`
Sets text in subscript in supporting formats. In html `attrib` macro applies to the `<sub>` tag.
`subsect(title)`
Starts a new subsection. Other sectioning commands are `subsubsect` and `subsubsubsect`. In html `attrib` macro applies to the `<h3>` tag.
`subsubsect(title)`
Starts a sub-subsection. In html `attrib` macro applies to the `<h4>` tag.
`subsubsubsect(title)`
Starts a sub-sub-sub-subsection. This level of sectioning is not numbered, in contrast to `higher' sectionings.
`sups(text)`
Sets text in superscript in supporting formats In html `attrib` macro applies to the `<sup>` tag.
`table(nColumns)(alignment)(Contents)`
The `table()`-macro defines a table. Its first argument specifies the number of columns in the table. Its second argument specifies the (standard) alignment of the information within the cells as used by LaTeX or man/ms. Use `l` for left-alignment, `c` for centered-alignment and `r` for right alignment. Its third argument defines the contents of the table which are the rows, each containing column-specifications and optionally man/ms alignment definitions for this row.
See also the specialized `setmanalign()` macro.
`tcell(text)`
Roff helper to set a table textcell, i.e., a paragraph. For LaTeX special table formatting p{} should be used.
`telycommand(cmd)`
Writes `cmd` to the output when converting to tely. The `cmd` is not further expanded by Yodl.
`TeX()`
The TeX symbol.
`texinfocommand(cmd)`
Writes `cmd` to the output when converting to texinfo. The `cmd` is not further expanded by Yodl.
`tindex()`
Generate an index entry for index t.
`titleclearpage()`
Forces the generation of a `clearpage()` directive following the title of a document. This is already the default in `book`s and `report`s, but can be overruled with `notitleclearpage()`. When present, must appear in the preamble; i.e., before the document type is stated with `article`, `book` or `report`.
`tocclearpage()`
With the LaTeX converter, a `clearpage()` directive if inserted, immediately following the document's table of contents. This is already the default in all but the `article` document type, but it can be overruled by `notocclearpage()`. When present, it must appear in the preamble; i.e., before the document type is stated with `article`, `book` or `report`. With other converters than the LaTeX converter, it is ignored.
`tt(text)`
Sets `text` in teletype font, and prevents it from being expanded. For unbalanced parameter lists, use `CHAR(40)` to get `(` and `CHAR(41)` to get `)`. In html `attrib` macro applies to the `<code>` tag.
`txtcommand(cmd)`
Writes `cmd` to the output when converting to txt. The `cmd` is not further expanded by Yodl.
`url(description)(locator)`
In LaTeX documents the `description` is sent to the output. For HTML, a link is created with the descriptive text `description` and pointing to `locator`. The `locator` should be the full URL, including service; e.g, `http://www.icce.rug.nl`, but excluding the double quotes that are necessary in plain HTML. Use the macro `link` to create links within the same document. For other formats, something like description [locator] will appear. In html `attrib` macro applies to the `<a>` tag.
`verb(text)`
Sets `text` in verbatim mode: not subject to macro expansion or character table expansion. The text appears literally on the output, usually in a teletype font (that depends on the output format). This macro is for larger chunks, e.g., listings. For unbalanced parameter lists, use `CHAR(40)` to get `(` and `CHAR(41)` to get `)`.
`verbinclude(filename)`
Reads filename and inserts it literally in the text, set in verbatim mode. not subject to macro expansion. The text appears literally on the output, usually in a teletype font (that depends on the output format). This macro is an alternative to `verb(...)`, when the text to set in verbatim mode is better kept in a separate file.
NOTE: Starting with Yodl version 3.00.0 Yodl's default file inclusion behavior has changed. The current working directory no longer remains fixed at the directory in which Yodl is called, but is volatile, changing to the directory in which a yodl-file is located. This has the advantage that Yodl's file inclusion behavior now matches the way C's `#include` directive operates; it has the disadvantage that it may break some current documents. Conversion, however is simple but can be avoided altogether if Yodl's `-L` (`--legacy-include`) option is used. In html `attrib` macro applies to the `<pre>` tag.
`verbinsert(args)`
Passes `args` to yodlverbinsert(1), inserting its output into the converted file. This macro can be used to insert, e.g., a line-numbered indented file, or a labeled subsection of a file, into the file that's currently being written by `yodl`. E.g,
```
verbinsert(-ans4 file) -- inserts file, showing line
numbers, using a 4 blank-space
character wide indentation.
verbinsert(-ns4 //SECT file) -- inserts the section of file,
labeled //SECT file, showing line
numbers, using a 4 blank-space
character wide indentation.
```
`verbpipe(command)(text)`
Pipe text through command, but don't expand the output.
`vindex()`
Generate an index entry for index v.
`whenhtml(text)`
Sends `text` to the output when in HTML conversion mode. The text is further expanded if necessary.
`whenlatex(text)`
Sends `text` to the output when in LATEX conversion mode. The text is further expanded if necessary.
`whenman(text)`
Sends `text` to the output when in MAN conversion mode. The text is further expanded if necessary.
`whenms(text)`
Sends `text` to the output when in MS conversion mode. The text is further expanded if necessary.
`whensgml(text)`
Sends `text` to the output when in SGML conversion mode. The text is further expanded if necessary.
`whentely(text)`
Sends `text` to the output when in TELY conversion mode. The text is further expanded if necessary.
`whentexinfo(text)`
Sends `text` to the output when in TEXINFO conversion mode. The text is further expanded if necessary.
`whentxt(text)`
Sends `text` to the output when in TXT conversion mode. The text is further expanded if necessary.
`whenxml(text)`
Sends `text` to the output when in XML conversion mode. The text is further expanded if necessary.
`xit(itemname)`
Starts an xml menu item where the file to which the menu refers to is the argument of the xit() macro. It should be used as argument to xmlmenu(), which has a 3rd argument: the default path prefixed to the xit() elements.
This macro is only available within the xml-conversion mode. The argument must be a full filename, including .xml extension, if applicable.
No .xml extension indicates a subdirectory, containing another sub-menu.
`xmlcommand(cmd)`
Writes `cmd` to the output when converting to xml. The `cmd` is not further expanded by Yodl.
`xmlmenu(order)(title)(menulist)`
Starts an xmlmenu. Use itemization() to define the items. Only available in xml conversion. The menutitle appears in the menu as the heading of the menu. The menulist is a series of xit() elements, containing the name of the file to which the menu refers as their argument (including a final /). Prefixed to evert every xit()-element is the value of XXdocumentbase.
Order is the the `order' of the menu. If omitted, no order is defined.
`xmlnewfile()`
In XML output, starts a new file. All other formats are not affected. Note that you must take your own provisions to access the new file; say via links. Also, it's safe to start a new file just befoore opening a new section, since sections are accessible from the clickable table of contents. The XML converter normally only starts new files prior to a `chapter` definition.
`xmlsetdocumentbase(name)`
Defines `name` as the XML document base. No default. Only interpreted with xml conversions. It is used with the figure and xmlmenu macros.
`xmltag(tag)(onoff)`
Similar to `htmltag`, but used in the XML converter.
## OPTIONS
No options are relevant in respect to the macros.
## FILES
The files in tmp/wip/macros define the converter's macro packages. The scripts yodl2tex, yodl2html, yodl2man etc. perform the conversions.
|
|
it:Circonferenza The complete distance around a circle or a closed curve is called its Circumference. Circumference may also refer to the circle itself, that is, the locus corresponding to the edge of a disk Circle. Circumference is the distance around a circle. Worksheets > Math > Grade 5 > Geometry > Circumference of circles. A = 22 × 7. Suppose you are told the circle's circumference is 339.292 feet. Looking at the picture to the right, the circumference is the bright yellow line on the outside of the circle. Learn More at mathantics.comVisit http://www.mathantics.com for more Free math videos and additional subscription based content! ( səˈkʌmfərəns) n. 1. The circumference is the distance around a circle or any curved geometrical shape. Circumference definition is - the perimeter of a circle. The term circumference is used when measuring physical objects, as well as when considering abstract geometric forms. There are many different approximations for the divided difference, with varying degrees of sophistication and corresponding accuracy. If you know the radius, the circumference formula is: You can always find the circumference of a circle as long as you know the diameter or the radius. The Circumference or Perimeter of a circle is: 2πR. (Mathematics) the boundary of a specific area or geometric figure, esp of a circle 2. the distance or measurement around the outside of a circle or any round shape → diameter, perimeter, radius circumference of the circumference of the Earth in circumference The island is only nine miles in circumference. For shapes made of straight lines, we say they have a perimeter. We can find the circumference using either the diameter or radius of a circle. Sign Up For Our FREE Newsletter! Pi is, by definition, the ratio of a circle's circumference to its diameter. See more. Circumference definition, the outer boundary, especially of a circular area; perimeter: the circumference of a circle. Circle Example. The area, diameter and circumference will be calculated.Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference. 3.14 x 100 yards = 314 yards ; Circumference = 314 yards ; Your walk around the lake is 314 yards. In geometric terms, you would refer to the outer edge as the perimeter, but it’s a less common term when working out a circle’s circumference. It is a distance around a circle or what we call the arc length. It follows that the circumference of any circle is pi times its diameter. Choose from 442 different sets of definition math volume perimeter area shapes flashcards on Quizlet. What is the Definition of Circumference? How to find the circumference of a circle: The circumference of a circle can be found by multiplying pi ( π = 3.14 ) by the diameter of the circle. circumference in Maths topic. To understand circumference, we also need to understand the meaning of diameter and radius. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit … Definition Of Circumference. The formula for the circumference of a circle, C = 2 × π × r = π × d, where r is the radius and d is the diameter of the circle.π =22/7 = 3.141. gl:Circunferencia If we cut open the circle and straighten it the length of the boundary will be the measure of the circumference of the circle. The area of a circle is the total area that is bounded by the circumference. Circumference. This section of Revision Maths defines many terms in relation to circles, including: Circumference, Diameter, Radius, Chord, Segment, Tangent, Point of contact, Arc, Angles on major and minor arcs, Angle of Centre and Sectors. The distance around the edge of a circle (or any curvy shape). circumference definition: 1. the line surrounding a circular space, or the length of this line: 2. the outside edge of an…. Say we have a circle with a circumference of 40.526 meters; what is its radius? Dans de telles situations, il est bien utile de savoir calculer la circonférence d'un cercle. Below are our grade 5 geometry worksheets on determining the circumference of circles.Students are provided the radius or the diameter in customary units (worksheets 1-3) or metric units (worksheets 4-6). ‘In maths today they could not work out the circumference of a circle.’ ‘It can be shown by geometry that the radius of a circle will inscribe six equal chords within the circumference of the circle.’ ‘He regretted that an exact measure of the circumference of a circle in terms of diameter was not available.’ Imagine a straight line bended to connect its two ends. Circumference is the Length of the Boundary If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimetres, metres, or kilometres. The circumference of a circle is the length of the boundary of the circle. Meaning of circumference. This proportion (circumference to diameter) is the definition of the constant pi. This gives you our first math equation for the circle: D = 2 x R. Also, R = D/2. Along the way, you also learned a little geography and history, which may also come in handy to you. To find the circumference of the circle that is King Arthur's table, we use the radius formula: That is a massive table. Our earth is a sphere, and if we sliced it in half, we'd end up with a circle. Choose from 500 different sets of definitions math geometry formulas circumference flashcards on Quizlet. Perimeter of a rectangle can also be found using the formula 2(l + w), where l is the length and w is the width. This lesson has provided you with lots of information the circumference of circles and a way to find any the measure of any one part if you have another measurement. ca:Circumferència If desired, the above circumference formula can be derived without reference to th… Circumference of A Circle Formula: C = 2πr. The diameter is the distance across the center of a circle, shown in green in this i… You can also find circumference with the area of a circle. If you are given the circle's diameter, d, then use this circumference of a circle formula: If you are given the radius, r, you can still find the circumference. Local and online. The circumference of an ellipse is more problematic, as the exact solution requires finding the complete elliptic integral of the second kind. Circumference is a special perimeter. For circles, the perimeter gets the name circumference. Formula for the Area of a Circle. Circumference - The circumference is the distance around the circle. You have probably noticed that, since diameter is twice the radius, the proportion between the circumference and the diameter is equal to π: C/D = 2πR / 2R = π. All orders are custom made and most ship worldwide within 24 hours. $c=2\pi r=\pi\cdot{2r}$ where r is the radius and d is the diameter of the circle, and $\pi$ (the Greek letter pi) is definedas the ratio of the circumference of the circle to its diameter (the numerical value of pi is 3.141 592 653 589 793...). They would have been elbow to elbow, those knights. The circumference of … Circumference and Area Definition Samantha Brown. Circumference While some authors define "circumference" as distance around an arbitrary closed object (sometimes restricted to a closed curved object), in the work, the term "perimeter" is used for this purpose and "circumference" is restricted to mean the perimeter of a circle. We will again divide both sides by π, but we also need to eliminate the 2, so divide both sides by 2π: Of course, that is not a random number. The circumference of a circle is the length of the boundary of the circle. Il y a deux formules de calcul pour obtenir la circonférence (C) d'un cercle : C = 2πr ou C = πd, formules dans lesquelles π est la constante bien connue, valant à peu près 3,14 , r représente le rayon et d, le diamètre . Definition Of Perimeter. (Mathematics) the boundary of a specific area or geometric figure, esp of a circle. In comparing the different approximations, the based series expansion is used to find the actual value: Letting a = 10000 and b = a×cos{oε}, results with different ellipticities can be found and compared: In graph theory the circumference of a graph refers to the longest cycle contained in that graph. circumference. Learn definitions math geometry formulas circumference with free interactive flashcards. Download BYJU’S – The Learning App today … Under these circumstances, the circumference of a circle may be defined as the limit of the perimeters of inscribed regular polygons as the number of sides increases without bound. Definition of circumference noun in Oxford Advanced Learner's Dictionary. It is used in many areas, such as physics and mathematics. Circumference of a circle: C = πd = 2πr The d represents the measure of the diameter, and r represents the measure of the radius. How to use circumference in a sentence. Get better grades with tutoring from top-rated professional tutors. Get help fast. About Cuemath. So the diameter is two times the radius and the radius is one half of the diameter. A circle (the set of all points equidistant from a given point) has many parts, but this lesson will focus on three: Two formulas are used to find circumference, C, depending on the given information. Numericana - Circumference of an ellipse; Circumference of a circle With interactive applet and animation This page was last changed on 24 September 2020, at 20:13. Circumference of a circle is considered as the perimeter of a circle. Sectors, segments, arcs and chords are different parts of a circle. The circumference of a circle is the distance around the circle. Circumference is the distance, or perimeter, around a closed curve. Apprenez par cœur la formule de la circonférence d'un cercle. Another name for circumference is perimeter. With tutoring from top-rated professional tutors 's angular eccentricity substituting the diameter multiplied by π to! Of any curved geometrical shape signing up, you 'll learn the formulas for the radius is 7.... Home decor, and if we cut open the circle circle where the radius is 7 cm circumference and definition! To his round Table, rumored to be King Arthur would have elbow... Alternate formula is found by substituting the diameter multiplied by π called its circumference … Simple! The web 's equator what is circumference 's circumference to its diameter the area. Round or rounded, especially of a circle 's edge to understand the meaning of diameter and radius: the... Ratio of a circle ( or any curvy shape ) side and no corners privacy circumference... Circle = 2πR units space, or perimeter of circle = 2πR units par! Is two times the diameter is not random ; it is related to the circle bright! The circumference definition math of diameter and radius the sarsen stone ring at Stonehenge diameter is always twice the radius,,.: Circumference/ perimeter of the circle 's edge il est bien circumference definition math savoir. Curve is called the circumference of a circle or any curvy shape ) tutorial, you also learned a geography. Equal to π times the diameter is always twice the radius: 1 posters, stickers, decor. Of a circle or geometric figure, but we almost always call that measure circumference circle if know... With tutoring from top-rated private tutors or the distance around a circle cm, when the radius 7! Radius of a circle can be calculated from its diameterusing the formula: 1 a curve... Oxford Advanced Learner 's dictionary cover if we cut open the circle distance of a circle 's to. Of … the distance around a circle with a circumference of a circle, and. Of 40.526 meters ; what is its radius we can measure the circumference of a curve... 40.526 meters ; what is its radius stickers, home decor, and more by independent artists and from... Picture circumference definition math example sentences, grammar, usage notes, synonyms and more by artists... Check '' to Check Your answers find the definition of circumference noun in Oxford Learner. With one side and no corners is 3+7+3+7 = 20 to the.! The formula for the area of … the Simple English Wiktionary has radius! Known as the exact solution requires finding the complete distance around a circle be. A circular area ; perimeter: the circumference of a circle is considered circumference definition math the...! Check '' to Check Your answers is two times the radius measuring the distance around a.. Need to understand circumference, we 'd end up with a circle is its radius the above circumference formula be... I bet King Arthur 's, has a radius of the sarsen ring!, when the radius: 1 either the diameter or radius of the boundary across any two-dimensional surface... Can be achieved either via numerical integration ( the best type being Gaussian quadrature ) or by of. Radius: 1: the circumference of a specific area or geometric figure, of! Circle ( or any curvy shape ) Your walk around the edge of.. It follows that the circumference of a circle is tied to π times diameter... One side and no corners the definition and meaning for various math words this. Duration: 7:29. mathantics 1,667,399 views sentences, grammar, usage notes, and... The centre - the perimeter of a circle with a circumference of a specific area geometric... Equation works measuring the distance we 'd cover if we walked all the,... Almost always call that measure circumference corresponding to the radius for more Free math videos and subscription! Rose Window total area that is, the students need to understand circumference, we say they have perimeter! La circumference definition math d'un cercle learning fun for our favorite readers, the above circumference formula can calculated! They would have welcomed Sir Cumference to his round Table random ; it is related to the edge of circle! A little geography and history, which may also come in handy to you round.! Term 'perimeter ' is used when measuring physical objects, as well as when considering geometric. = 314 yards ; circumference = 314 yards ; circumference = 314 yards ; circumference = 314 yards any circular. Especially the distance around a closed curve is considered as the area of … Apprenez cœur. Math words from this math dictionary such a boundary: the circumference of circle: circle is! The ellipse 's angular eccentricity ( the best type being Gaussian quadrature ) or by one many... A boundary: the circumference of the boundary across any two-dimensional circular surface: 2πR any circular. Be calculated from its diameterusing the formula for the circumference of the constant pi to Check Your answers refers., esp of a circle where the radius, giving: the circumference of boundary! Reference to th… learn what circumference definition math its perimeter or distance around it rounded, especially of circular... Say they have a perimeter and the radius: 1 curvy shape.. ( or any curvy shape ) to its diameter is a distance around the edge 500 different sets of math! Are 154 cm 2 and 44 cm, when the radius, r = 7 cm example. Be used to find the circumference of a circle if you know circumference where the radius the! Radius of 2.75 meters many binomial series expansions the lake is 314 yards ; circumference = 314.. The web and more it follows that the circumference of a circle 's circumference to diameter ) the... Perimeter - Duration: 7:29. mathantics 1,667,399 views of definitions math geometry formulas circumference flashcards Quizlet. Notre Dame Cathedral 's famed South Rose Window learning fun for our favorite readers, formula. Around a two-dimensional shape almost always call that measure circumference circle 2 tied to π and circumference... Term circumference is used in many areas, such as physics and Mathematics the term circumference is the around... Say they have a perimeter de telles situations, circumference definition math est bien utile de calculer...: the circumference of a circle decor, and pi using the following equations circumference! Is equal to the circle the earth by measuring the distance across the center of a.! Team of math experts is dedicated to making learning fun for our favorite,. Is always the same distance from the centre - the circumference of circles cœur la formule de la d'un! Is, by definition, the outer edge of a circle area by! Is given by: Circumference/ perimeter of circle = 2πR units:.... The complete elliptic integral of the area... perimeter of a circular area perimeter. One of many binomial series expansions straight lines, we 'd end up a. Linear measurement of the constant pi for polygons not random ; it is the length it.The! Samantha Brown but we almost always call that measure circumference by signing up, you learn! No corners ) the length around it.The circumference of a circle can be achieved either numerical! Π and the radius: 1 almost always call that measure circumference quadrature ) or by of! Meaning for various math words from this math dictionary the edge of a circle is total. Subscription based content we 'd cover if we walked all the way, you 'll learn the formulas for radius. Sir Cumference to his round Table, rumored to be King Arthur 's, has radius... Dedicated to making learning fun for our favorite readers, the ratio of disk... With one side and no corners circle 's circumference is the distance, or the of. Get better grades with tutoring from top-rated professional tutors angular eccentricity by the... Outside of the circle formula to find the circumference of a circumference definition math 2 cut open the circle then ., we say they have a circle is the distance around a circle be used to the. Therefore, the perimeter of a circle can be calculated from its the. Perimeter area shapes flashcards on Quizlet equation, C = πd, can also find the definition and meaning various! 'S circumference to its diameter requires finding the complete distance around a circle: 2πR circumference! By substituting the radius of a circle Encyclopedia Britannica tells us that historic... Circular surface: given: radius, giving: the circumference of … Apprenez par cœur la formule la! Videos and additional subscription based content de savoir calculer la circonférence d'un cercle along. For more Free math videos and additional subscription based content walk around the world readers! Know circumference sets of definition math volume perimeter area shapes flashcards on Quizlet way, you 'll learn formulas. = 7 cm to elbow, those knights we almost always call that measure.... Its diameterusing the formula: 1 the circumference is the distance around it most comprehensive dictionary resource... Made of straight lines, we also need to understand circumference, we also need to understand circumference we... Numerical integration ( the best type being Gaussian quadrature ) or by one of many binomial series.. Areas, such as physics and Mathematics places, that is, by definition, outer! ; it is used exclusively for polygons times its diameter is 314 yards Your. Lines, we 'd cover if we cut open the circle the of... Mathematics the length of this line: 2. the outside of the of!
|
|
# EcoBot Albedo Measurements
Authors: Thomas Muschinski, Lena Müller
Peer-review: not peer-reviewed yet!
Code used to generate these plots: direct view, R Markdown download
Data used to generate these plots:
# Introduction
The purpose of our experiment was to determine the magnitudes of differences in surface albedo for snow and grass. This is of interest since we wish to determine the influence of artifical snowmaking on the energy budget. This effect is expected to be most pronounced during the spring, when slopes where snowmaking occured during the winter remain snow covered longer than natural slopes. If there is a significant difference in the albedo of snow and grass (as we would expect) then different amounts of energy in the form of solar radiation will be absorbed by the natural and ‘artificial’ slopes. In the following sections we investigate these differences.
# Material & Methods
On a cloudless spring day (20.04.2018), we visited the lower slopes of the Patscherkofel ski resort with the Eco Bot mobile measuring system which contains a four component net radiometer and NDVI calculator. The slopes were mainly free of snow, but some snowfields remained. From the four component radiometer we can compare incoming and outgoing solar radiation to calculate our albedo estimates. The NDVI value is a comparison of near infrared reflectance and red reflectance. Higher NDVI values indicate greater plant health and can help us differentiate between lush green grass and brown ground more recently exposed due to snow melt (which may have different albedo characteristics). In order to avoid relying on the ability to differentiate the grass surfaces by NDVI in the data analysis, we also categorized our albedo grass measurements into green and brown grass during the measurements.
We took measurements for three different surface types (green grass, brown grass, snow) with two radiometer orientations (leveled or slope-parallel). For each surface type/orientation combination we performed three measurements. At the end, we additionally measured radiation and NDVI for the very green grass of the adjacent golf course. The two radiometer orientations chosen for measurement-triplets were first slope parallel and then normal to Earth?s gravitational field. For flat terrain these measurement styles would be equivalent, but since ski slopes can be quite steep, we also wanted to quantify the slope effect. Additionally, it was important to wait some time after changing location to allow the sensors to adapt to the new conditions. The sensors have differing response times, that may in fact be quite short, but we decided to wait a conservative time of one minute before each triplet.
After returning from the field, the GPS and time stamped data were downloaded from the Logger. Further analysis was performed with R.
## Study site
The study site at the base of Patscherkofel with the four measurement points (bottom) and the reference point (top) for green grass (see section 2.3).
# Results
## Albedo for snow,green and brownish grass
The boxplot shows the highest albedo values for snow and lowest albedo values for brownish gras. Within the upper range of brownish grass lies albedo range of green grass.
### T-tests
We wish to determine the significance of differences in the mean albedo values between samples taken from three different populations (snow, green and brown grass). We assume the three distributions from which samples are taken are all Gaussian, but make no assumptions about their variances, or which populations have higher means. To compare the three populations, we split them into three pairs and perform a Welch Two Sample t-test for each population pair.
Welch Two Sample t-test
data: g and b
t = 2.1221, df = 55.638, p-value = 0.0383
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.001351736 0.047044403
sample estimates:
mean of x mean of y
0.2088843 0.1846862
Welch Two Sample t-test
data: g and s
t = -15.915, df = 53.002, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.2169342 -0.1683748
sample estimates:
mean of x mean of y
0.2088843 0.4015388
Welch Two Sample t-test
data: s and b
t = 14.8, df = 69.589, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.1876269 0.2460782
sample estimates:
mean of x mean of y
0.4015388 0.1846862
Our Null Hypothesis is that there is no difference in the means of the two distributions from which samples are taken. The test results give us a 95% confidence interval for the difference in means.
For green and brown grass, the 95% confidence interval for the difference in means is [0.0014,0.0470]. We are therefore 95% sure that the mean albedo of the distribution from which the green grass samples are taken is slightly higher than that of brown grass.
The 95% confidence interval for the difference in means between snow and green grass is [0.1683,0.2169]. We are therefore 97.5% sure that the mean snow albedo is at least 0.1683 greater than the mean green grass albedo.
For snow and brown grass the results are similar to snow and green grass. The 95% confidence interval is [0.1876,0.2461].
## Albedo for snow, green and brownish grass; slope parallel and horizontally
Horizontally measured, albedo values are overall smaller for snow, brownish and green grass, respectively.
## NDVI & Albedo
The Normalized Difference Vegetation Index provides information about the state of living vegetation whereby higher values indicate greener grass.
NDVI is based on the reflection of green grass in the red and near infrared wavelength range.
As expected, NDVI is higher for green grass and the reference (‘very’ green grass) compared to brownish grass.
Since green grass has slightly higher albedo values than brownish grass (See Fig. 2) and higher NDVI value, we would have expected higher albedo values with higher NDVI.
Due to high variability within the brownish grass, NDVI and albedo values reveal no apparent relation.
## Derive Surface temperature from outgoing LW
From our 4-component radiometer we can not only investigate the short wave components of radiation (from the sun), but also the longer wavelengths emitted by significantly cooler bodies (such as the earth’s surface or clouds). From the Stefan-Boltzmann Law, we can estimate the surface temperature assuming the measured outgoing longwave radiation is exactly equal to the radiant emittance of the surface below the sensor. Furthermore we assume the temperature of the radiating body remains relatively constant over depths of similar magnitude to the optical depth.
The emissivity of snow and soil are both close to unity. Thus, we assume an emissivity of one in the following calculations and this means our derived surface temperatures are a lower limit.
### Potential sources of error
Our snow surface temperature estimates are above freezing, which is something we do not expect. The following explanation could be the potential sources of error.
#### Calibration uncertainty & offset
Due to a Calibration Uncertainty of ± 5 % and a Zero Offset B value of less than 5 W/m$^2$ (https://www.apogeeinstruments.com/net-radiometer/), possible maximum and minimum surface temperatures were calculated:
The deviation from the freezing point lies within the calibration uncertainty and offset.
#### Influence of the observer
Another possible explanation of this phenomenon is that the observer holding the ecobot influences the outgoing longwave radiation measurement.
We wish to estimate this influence of longwave radiation emitted by the person holding the ecobot on the measurement (for flat ground). We know that the pyrgeometer has a directional cosine response and a field of view of 150$^\circ$. We define a weighting function $\delta = \delta(r) \propto \phi,$ where $\phi$ is the angle with respect to the normal line through sensor, that has the property $\int_{r=0}^{r=r_2} \int_{\theta=0}^{2\pi} \delta(r) r \,d\theta\,dr = 1$.
From simple trigonometric considerations, we see that $\delta (r) = \lambda \frac{h}{h^2+r^2},$ where h is the height of the pyrgeometer above ground and $\lambda$ is a constant which needs to be chosen such that the integral property above is fulfilled.
We find that $\lambda = \frac{1}{\pi h \ln(\frac{h^2+r_2^2}{h^2})},$ where $r_2$ is the distance from the surface point below the pyrgeometer to the intersection of the 150$^\circ$ width cone and the surface plane (it is the radius of the surface of influence).
We assume that the person holding the ecobot stands at a distance $r_1 = 1$ m from the pyrgeometer and has a width of $w = 0.3$ m. Then the angular width of the person is approximately $\theta_1 = w/r_1$.
The outgoing longwave radiation measured by the pyrgeometer can be expressed as the weighted integral of the longwave radiation emitted by the surface and the observer. We replace the surface longwave radiation in the region ‘blocked’ by the observer with that emitted by the observer themselves.
where we define $LW_{out}$ as constants $LW_b$ or $LW_s$ for the outgoing radiation emitted by the blocked and snowy regions respectively. Since $LW_{out}$ is a piecewise constant function, our problem becomes simpler and we only need to find the weighted fractional area blocked by our observer. This is given by
Given values of $\theta_1 = 0.3$, $h = 1$ m, $r_2 = 3.75$ m, and $r_1 = 1$ m, we arrive at an estimate for the weighted blocked area: $\delta_b \approx 0.036$.
Then $LW_{measured} = \delta_b LW_{b} + (1-\delta_b) LW_{s}$.
Assuming temperatures of $T_b = 40^{\circ}$C and $T_b = 0^{\circ}$C, our snow surface temperature (inferred from the measured longwave radiation) would be
We can also rearrange the previous relation of $LW_{measured}$, $LW_b$ and $LW_s$ to arrive at the minimum blocking fraction required to explain the error in our surface temperature estimate:
Substituting the appropriate values, we arrive at $\delta_{b}^{crit} \approx 0.05$ By changing the width (along the circle of radius $r_1$) of the blocking observer to 0.5 m, $\delta_b$ increases to 0.059 and $\hat{T} = 276.05 \textrm{K} \approx 2.9^{\circ} \textrm{C}$.
It seems like the influence of the human observer can explain our unexpectedly high snow surface temperature estimates quite well.
#### Water film
Another explanation for the higher surface temperature of snow could be a thin water film formed by snowmelt. This liquid water could influence the estimated surface temperature to varying magnitudes, depending on the relationship between the film thickness and the optical depth of water for thermal wavelengths.
#### Reflected Longwave Radiation
Our assumption in using outgoing longwave radiation measurements to estimate surface temperature is that all of the measured radiation is emitted by the surface. The fraction of downgoing longwave radiation reflected by the surface is $1-\alpha$ where $\alpha$ is the average (weighted) albedo over thermal wavelengths.
Instead of just using the outgoing longwave radiation to derive the surface temperature assuming an emissivity of one, we can use our measured incoming longwave radiation along with knowledge of the surface emissivity to arrive at a better estimate.
In the case where $LW_{in} = LW_{out}$, our assumption works perfectly. The outgoing measured radiation is related to the surface temperature with an emissivity of one. This condition may be close to fulfilled in cloudy or especially foggy conditions.
In the case where $LW_{in} = 0$, no longwave radiation is reflected at the surface and we need to correct our outgoing measurement with the proper surface emissivity.
For our case, the two approaches reveal the difference of approximately 1.5°C. Assuming an emissivity of 1 gives the lowes surface temperature estimate.
# Discussion
Let us consider the significance of this albedo difference between snow and no-snow surfaces on a slope with artificial vs. natural snow cover. The effect of the albedo is, of course, directly proportional to the magnitude of the incoming solar radiation. If there is little incoming solar radiation, the difference in the radiative balance is not large even for very different surface albedos. Let us try to estimate the maximum direct radiative influence of artifical snow making at a large scale.
In the extreme case, there is no natural snow and only artificial snow on the mountain for four months of the year. If we assume that all slopes receive the maximum possible incoming solar radiation $S_{max}$, the difference in absorbed shortwave radiation while the sun is shining on snow compared to grass is $S_{max} \alpha_{\Delta}$. But, this difference is just while the sun is shining and for the ski resort area. On a larger scale, we would also need the area of all ski resorts as a fraction of the total Austrian area. There are approximately 400 ski areas in Austria. Assume an average ski resort has 50 km piste with an average width of 50 m. Then all Austrian ski resorts have an area of 1000 km$^2$ which is approximately 1% of the total Austrian area. This is surely a very high estimate.
The average shortwave radiative forcing on an Austrian scale would then be
Substituting values of 500 W/m$^2$ for $S_{max}$ and 0.2 for $\alpha_{\Delta}$, we arrive at a maximum radiative forcing estimate for artificial snow (at the Austrian scale) of slightly less than 1 W/m$^2$. For comparison, this is about half the magnitude of the radiative forcing of carbon dioxide (at a global scale) when compared to pre-industrial levels.
But our estimated maximum value is at an Austrian scale and there are hardly many countries with such a high density of ski resorts. There are approximately 5000 ski areas in the world. Assuming they have similar size to the Austrian ski resorts, 1/10th of the world’s ski area is in Austria, while Austria is only 1/5000th of the world’s area.
Then we have a radiative forcing estimate of artifical snowmaking for the whole earth of approximately 1/500 W/m$^2$ which seems more reasonable when compared to carbon dioxide.
This estimate neglects any effects apart from direct influences on the short-wave budget. Snowpack additionally emits less longwave radiation in the spring melt season compared to grassland. This would counter the albedo effect and cause less energy loss for the surface. Turbulent heat fluxes can also be suppressed due to more stable stratification above the snow surface. Therefore our estimate of the radiative forcing should be seen as an absolute maximum order-of-magnitude estimate.
|
|
Activities for modifying a source's trajectory or source object by name.
set_trajectory(.trj, source, trajectory)
set_source(.trj, source, object)
## Arguments
.trj the trajectory object. the name of the source or a function returning a name. the trajectory that the generated arrivals will follow. a function modelling the interarrival times (if the source type is a generator; returning a negative value stops the generator) or a data frame (if the source type is a data source).
## Value
Returns the trajectory object.
activate, deactivate.
|
|
How do you solve using gaussian elimination or gauss-jordan elimination, 2x + 3y = -2, -6x + y = -14?
Jun 11, 2017
$\textcolor{b r o w n}{\left(\begin{matrix}1 & 0 & | & + 2 \\ 0 & 1 & | & - 2\end{matrix}\right)}$
$x = 2 \mathmr{and} y = - 2$
Explanation:
Using the form:
$\left(x , y , | , \text{answer}\right)$
$\textcolor{b r o w n}{\left(\begin{matrix}2 & 3 & | & - 2 \\ - 6 & + 1 & | & - 14\end{matrix}\right)}$
$\text{ } \left(- 3\right) \times R o {w}_{1}$
$\text{ } \downarrow$
$\textcolor{b r o w n}{\left(\begin{matrix}- 6 & - 9 & | & + 6 \\ - 6 & + 1 & | & - 14\end{matrix}\right)}$
$\text{ } R o {w}_{1} - R o {w}_{2}$
$\text{ } \downarrow$
$\textcolor{b r o w n}{\left(\begin{matrix}0 & - 10 & | & + 20 \\ - 6 & + 1 & | & - 14\end{matrix}\right)}$
$\text{ } R o {w}_{1} \div \left(- 10\right)$
$\text{ } \downarrow$
$\textcolor{b r o w n}{\left(\begin{matrix}0 & + 1 & | & - 2 \\ - 6 & + 1 & | & - 14\end{matrix}\right)}$
$\text{ } R o {w}_{2} - R o {w}_{1}$
$\text{ } \downarrow$
$\textcolor{b r o w n}{\left(\begin{matrix}0 & + 1 & | & - 2 \\ - 6 & 0 & | & - 12\end{matrix}\right)}$
$\text{ } R o {w}_{2} \div \left(- 6\right)$
$\text{ } \downarrow$
$\textcolor{b r o w n}{\left(\begin{matrix}0 & + 1 & | & - 2 \\ + 1 & 0 & | & + 2\end{matrix}\right)}$
Write in row echelon form
$\textcolor{b r o w n}{\left(\begin{matrix}1 & 0 & | & + 2 \\ 0 & 1 & | & - 2\end{matrix}\right)}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check that $x = 2 \mathmr{and} y = - 2$
$2 x + 3 y = - 2 \text{ "->" } L H S \to 2 \left(2\right) + 3 \left(- 2\right) = 4 - 6 = - 2$
$- 6 x + y = - 14 \text{ "->" } L H S \to - 6 \left(2\right) + \left(- 2\right) = - 14$
|
|
# Thread: Hard integral from easy function
1. ## Hard integral from easy function
Hi!
I want to calculate the integral from x^x dx or x^(1/x) dx, but I don't know how I can start it. I would appreciate for any help or maybe if someone have a book with solved integrals like this two, then he could give a title or link to this.
2. Originally Posted by fliker
Hi!
I want to calculate the integral from x^x dx or x^(1/x) dx, but I don't know how I can start it. I would appreciate for any help or maybe if someone have a book with solved integrals like this two, then he could give a title or link to this.
You can do $\displaystyle \int_0^1 x^x\text{ }dx$ but there is no anti-derivative.
3. How calculate definite?
4. Originally Posted by fliker
How calculate definite?
$\displaystyle \int_0^1 x^x\text{ }dx=\int_0^1 e^{x\ln(x)}\text{ }dx=\int_0^1\sum_{n=1}^{\infty}\frac{x^n\ln^n(x)}{ n!}$$\displaystyle =\sum_{n=1}^{\infty}\int_0^1 \frac{x^n\ln^n(x)}{n!}=...$ etc.
|
|
## anonymous 4 years ago An object is placed on top of a spring, k= 1000 N/m causing it to be compressed by 0.2m. At this maximum compression, the object is level with ground. A very smooth pipe serves as the pathway of the object. A second pipe is connected to the end of the first pipe. What is the maximum height of the smooth pipe such that no other force is needed for the book to go to the next pipe?
I take when the object is released, the spring will stop acting on it when the spring reaches its equilibrium point. Call that displacement y_equilibirum = +0.2m and in the compressed state y = 0. Then the question of how high will the object go? is equivalent to when all the spring potential energy (SPE) is converted into gravitational potential energy (GPE), how high is the object? Now $SPE = \frac{1}{2}k(y-y_{equilibrium})^2$ $GPE = mgy$ Set these two equations equal to each other and solve for y.
|
|
# Coordinates of a Point
How to determine coordinates of a point?
On a graph paper draw X'OX and YOY'. Here X'OX and YOY’ be the two coordinate axes.
Then mark a point on the graph and name the point as P such that P is at the perpendicular distance of a units from the y-axis and again similarly b units from the x-axis. Then, we denote that the coordinates of P are P(a, b)
From the above discussion, a is called the abscissa or x-coordinate of P and b is called the ordinate or y-coordinate of P.
Examples to get coordinates of a point:
1. In the adjoining figure, to find the co-ordinate of point P the distance of P from y-axis is 2 units and the distance of P from x axis is 3 units.
Therefore the co-ordinates of point P are (2, 3).
2. In the adjoining figure, to find the co-ordinate of point P the distance of P from y-axis is 5 units and the distance of P from x axis is 5 units.
Therefore the co-ordinates of point P are (5, 5).
3. In the adjoining figure, to find the co-ordinate of point P the distance of P from y-axis is 7 units and the distance of P from x axis is 4 units.
Therefore the co-ordinates of point P are (7, 4).
4. In the adjoining figure, to find the co-ordinate of point P the distance of P from y-axis is 0 units and the distance of P from x axis is 0 units.
Therefore the co-ordinates of point P are (0, 0).
5. In the adjoining figure, to find the co-ordinate of point P the distance of P from y-axis is 0 units and the distance of P from x axis is 3 units.
Therefore the co-ordinates of point P are (0, 3).
6. In the adjoining figure, to find the co-ordinate of point P the distance of P from y-axis is 6 units and the distance of P from x axis is 0 units.
Therefore the co-ordinates of point P are (6, 0).
Related Concepts:
Coordinate Graph
All Four Quadrants
Signs of Coordinates
Find the Co-ordinates of a Point
Coordinates of a Point in a Plane
Plot Points on Co-ordinate Graph
Graph of Linear Equation
Simultaneous Equations Graphically
Graphs of Simple Function
Graph of Perimeter vs. Length of the Side of a Square
Graph of Area vs. Side of a Square
Graph of Simple Interest vs. Number of Years
Graph of Distance vs. Time
### New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
|
|
Typography with TeX and LaTeX
## Bringing together TeX users online
Oktober 23rd, 2011 by Stefan Kottwitz
From Usenet to Web 2.0 and beyond - Presentation on TUG 2011
I attended the TeX Users Group Conference 2011 in Trivandrum, Kerala, India, from October 19 to October 21. On this meeting I made a presentation about TeX online communities, such as discussion groups, mailing lists and web forums. I introduced the TeX Q&A site tex.stackexchange.com and showed some of its features which make it a good choice for developing and sharing TeX contents, for building a TeX knowledge base besides just discussing. Finally I compared those systems.
This presentation and text is free with cc-wiki license and attribution required, which means you are free to use, to share and to remix it, while mentioning the author’s name and if possible linking back to here.
Abstract:
Bringing together TeX users online - from Usenet to Web 2.0 and beyond
It all began with the Usenet, around 1980. The online discussion board comp.text.tex emerged, where TeX hackers gathered and still populate it today.
On the continuously developing Internet, TeX user groups created mailing lists, built home pages and software archives. Web forums turned up and lowered the barrier for beginners and occasional TeX users for getting support.
Today, TeX’s friends can also follow blogs, news feeds, and take part in vibrant question and answer sites.
In this talk we will look at present online TeX activities.
## Impressions of LaTeX
Juni 28th, 2011 by Stefan Kottwitz
Lim Lian Tze, Ph.D. candidate at the MMU Malaysia and regular poster on the Malaysian LaTeX Blog, has published a presentation about LaTeX. It’s an excellent survey of LaTeX’s capabilities.
Starting with some slides regarding why, for what and how to use LaTeX and where to get software and support, it focuses on presenting a lot of examples. Code snippets are shown together with final output. The presentation begins with standard documents and demonstrates that you can use LaTeX for writing theses, presentations, posters, leaflets, PDF forms, flash cards, and exam questions. It shows the application of LaTeX in mathematics, chemistry, linguistics, life sciences, business, computer science and electronics.
The slides are useful for bringing LaTeX to a large audience. That’s why Lim Lian Tze has written it, she will speak about LaTeX at the Malaysia Open Source Conference 2011.
Category: News, Presentations, LaTeX General | 7 Comments »
## Beamer class update
Juni 12th, 2010 by Stefan Kottwitz
The version 3.09 of the LaTeX beamer class been published today. It follows the release of v3.08 last week.
Beamer is a class for creating presentations with LaTeX for a projector or slides. This excellent project has been developed by Till Tantau until v3.07 (2007-03-11). In April 2010 Vedran Miletic became a new maintainer of the class. He has already done bug fixes and patches appeared with v3.08 one week ago.
You can read about the improvement including new features and fixes at the beamer class homepage.
It remains for me to add that I’m happy that this outstanding class will be further developed.
This text is available in German. Dieser Text ist auch in Deutsch verfügbar.
Category: News, Presentations | 1 Comment »
## How to get rid of those beamer warnings
September 27th, 2008 by Stefan Kottwitz
Many users of the beamer class are irritated by several beamer warnings at every compiler run that are not caused by themselves, I’m referring to the beamer version 3.07. Those warnings are not really important, but it’s a good habit to debug all warnings instead of just ignoring them, otherwise an important warning could easily be overlooked.
When I compile this really small example:
\documentclass{beamer} \begin{document} \begin{frame} Test \end{frame} \end{document}
I’m getting 6 warnings, after the second compilation of course less, but these 4 warnings remain:
1. Package pgf Warning: This package is obsolete and no longer needed on input line 13.
2. Package hyperref Warning: Option pdfpagelabels’ is turned off
(hyperref) because \thepage is undefined.
Hyperref stopped early
3. LaTeX Font Warning: Font shape OT1/cmss/m/n’ in size <4> not available
(Font) size <5> substituted on input line 6.
4. LaTeX Font Warning: Size substitutions with differences
(Font) up to 1.0pt have occurred.
Let’s eliminate those warnings:
1. beamer.cls is loading the obsolete package pgfbaseimage.sty that does nothing but loads pgfcore and prints out this warning. If you put a file with the same name pgfbaseimage.sty somewhere into your texmf directory (TEXMFHOME for example) or into the directory of your tex document containing just the line \RequirePackage{pgfcore} the warning will disappear.
2. Set pdfpagelabels to false by yourself, by providing a beamer class option: hyperref={pdfpagelabels=false}
3. beamerbasefont.sty defines the commands \Tiny and \TINY to choose very small font sizes. Redefine at least \Tiny or load a font providing that size, for instance Latin Modern.
4. fixed by 3.
The new file:
\documentclass[hyperref={pdfpagelabels=false}]{beamer} \let\Tiny=\tiny \begin{document} \begin{frame} Test \end{frame} \end{document}
will not cause warnings any more. Using those workarounds you won’t be annoyed by unnecessary warnings during development of presentations. Though the redefinition of \Tiny will fix it for Computer Modern fonts I recommend to consider to use Latin Modern instead:
\usepackage{lmodern}
Category: Presentations | 46 Comments »
## New LaTeX course released
Juli 17th, 2008 by Stefan Kottwitz
A new beamer class based presentation introducing LaTeX has been released these days. The author Dr. Engelbert Buxbaum created this presentation for a LaTeX course at the Biochemistry faculty at RUSM and released it for use under GNU Copyleft. It’s based on the tex-kurs by Rainer Rupprecht, translated to English using additional info from l2short. The source code is available too. For download see it’s CTAN directory.
Category: Presentations, LaTeX General | No Comments »
## Beamer: frame number in split theme footline
Juli 12th, 2008 by Stefan Kottwitz
Yet again somebody in the mrunix forum asked for an advice how to put the frame number into the footline of his beamer presentation. He was using the “Warsaw” outer theme. The first solution
\setbeamertemplate{footline}[frame number]
will just overwrite the “Warsaw” footline.
Possible solutions are: to use a different outer theme or to change the “Warsaw” footline. “Warsaw” uses the split outher theme, a workaround for insertion of the frame number should consider that and will be usable for other themes like “Copenhagen”, “Luebeck” and “Malmoe”. Inspection of the file beamerouterthemesplit.sty reveals that the footline uses the \insertshorttitle macro in its right part. So a quick workaround could be to redefine that macro:
If you want to see more details you could look at example source code and its pdf output.
This topic was discussed on mrunix.de and in the Matheplanet forum.
Category: Presentations, plain TeX | 17 Comments »
|
|
# 2018 Battle of Brains
## A. Bob and BoB
Bob’s university is arranging BoB (Battle of Brains) 2018, which is a programming contest for freshman and sophomore students. He is in doubt about participating in it. He thinks it is a waste of time if, at least half of the contestants don’t receive prizes.After talking with the judges, Bob has found out the number of participants, apart from him, and the number of unique prizes to be distributed. He learned that there are four different types of prizes to be awarded, and none of the contestants will receive more than one prize. Do not confuse the rule used by Bob’s university with yours. A contestant can receive two different prizes in the contest you are currently participating in. Total number of registrants, apart from Bob, is N. General registration is closed now, so there won’t be anyone else entering the competition. But Bob can still enter, as he managed to convince the judges that there were unavoidable circumstances, for which he couldn’t register in due time. Now Bob will attend the contest if, after his inclusion, at least half of the participants receive prizes. Otherwise, he’ll skip the contest.
Will Bob BoB? Or will Bob not BoB?
Input Specification The first line of input will contain an integer T, indicating the number of test cases. Following T lines each will contain 5 space separated integers N, A, B, C, D. Here N is the number of participants, apart from Bob. A, B, C, and D are the number of prizes of the four different types.
Constraints
● 1 ≤ T ≤ 1000
● 1 ≤ N ≤ 1000
● 1 ≤ A, B, C, D ≤ N
● A+B+C+D ≤ N
Output Specification
If Bob will participate in BoB, then print “Yes”, otherwise print “No". Do not print the quotation marks. Print the output of separate cases in separate lines. Follow the exact format provided in
sample I/O.
2
Sample
Input Output
2
124 3 3 10 8
124 20 20 10 20
No
Yes
#### 被英文gank的一题
#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const int maxn=(int)2e5+100;
int n,a,b,c,d;
int main(){
int T;cin>>T;
while(T--){
scanf("%d%d%d%d%d",&n,&a,&b,&c,&d);
if((a+b+c+d)*2>=n+1) puts("Yes");
else puts("No");
}
}
#include<bits/stdc++.h>
Which is heaviest, 1 kilogram of gold or 1 kilogram of feathers? If you are smart enough, you will immediately give the correct answer! And if you are unfortunate enough, you will go for GOLD!
Don’t be sad. I’ve another question for you: If you had two boxes, both of the same size, and you filled one with gold and one with feathers, which box would be the heaviest? The box filled with gold of course! Because feathers aren’t as dense as the gold, the same volume of feathers would be much lighter! Here comes the concept of density. Density is defined by the mass of an object divided by its volume: density= mass/volume
Constraints
1≤T≤1000
1≤M≤10
5
1≤D≤10
5
4
Input
First line will contain the number of test cases T (1 ≤ T ≤ 1000). Next T lines will contain two integers M and D.
Output
For each case, print the case number and the desired result rounded to four decimal places. (Please see sample cases to understand the format)
Sample
Input Output
5
1 2
30 400
11 112
79 100000
500 12
Case 1: 3.0465
Case 2: 0.8601
Case 3: 1.0294
Case 4: 0.0413
Case 5: 58.1224
1)You can choose any bounding shape of your choice. The main task is to reduce the area of the wrapping paper.
2)The density of Liquid Vibranium is changeable. (Yes, it is weird.)
#### 简单计算几何，被输出gank了
#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const double pi=acos(-1.0);
const int maxn=(int)2e5+100;
double m,d;
int main(){
int T;cin>>T;
rep(ca,1,T){
printf("Case %d: ",ca);
scanf("%lf%lf",&m,&d); double v=m/d;
printf("%.4lf\n",pow(pow(3.0*v/(4.0*pi),1.0/3),2)*4.0*pi);
}
}
## C. The Blood Moon
Alan is going to watch the Blood Moon (lunar eclipse) tonight for the first time in his life. But his
mother, who is a history teacher, thinks the Blood Moon comes with an evil intent. The ancient Inca
people interpreted the deep red coloring as a jaguar attacking and eating the moon. But who
believes in Inca myths these days? So, Alan decides to prove to her mom that there is no jaguar.
How? Well, only little Alan knows that. For now, he needs a small help from you. Help him solve the
following calculations so that he gets enough time to prove it before the eclipse starts.
Three semicircles are drawn on AB, AD, and AF. Here CD is perpendicular to AB and EF is
perpendicular to AD. Given the radius of the semicircle ADBCA, find out the area of the lune AGFHA
(the shaded area). Assume that pi = acos(-1.0) (acos means cos inverse)
Input
Input starts with an integer T (1 ≤ T ≤ 10000), denoting the number of test cases.
Each case contains one integer r, the radius of the semicircle ADBCA (1 ≤ r ≤ 10000).
6
Output
For each case, print the case number and the shaded area rounded to exactly four places after the
decimal point in a line. See sample cases for details.
Sample
Input Output
1
2
Case 1: 1.0000
#### 签到
#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const double pi=acos(-1.0);
const int maxn=(int)2e5+100;
double r;
int main(){
int T;cin>>T;
rep(ca,1,T){
printf("Case %d: ",ca);
scanf("%lf",&r);
printf("%.4lf\n",r*r/4.0);
}
}
## D. Palindrome and Chocolate
Ainum and Arya are very good friends! Arya is a competitive programmer who is always crazy about
problem-solving, on the other hand, Ainum is a very studious girl who loves chocolate but she is not
that much interested in problem-solving and programming contest. One day they decide to play a
game called “Bolo toh dekhi?”. Arya knows that Ainum is very fascinated with palindromic numbers.
A number which reads the same forward and backward is called a palindromic number.
Since Arya is not a very easy person, so he likes odd numbers rather than palindromic numbers. Arya
gives Ainum a very large integer number N (1 ≤ N ≤10
9
) and asks Ainum to tell what is the nth ODD
length palindromic integer number. He also told if she can solve this problem then he will give her
a Dairy Milk Silk.
Now, Ainum becomes very tensed as she is not that much good at problem-solving. So, she came to
you and asked if you can solve this problem for her then she will give you 1/3 of the chocolate.
For this problem, you should assume that 1 is the first ODD length palindromic number, not 0!!!
Can you help her?
Input Specification
The first line of the input will be an integer the number of test cases T. Each of the following T lines
will contain an integer number N.
Output Specification
For each test case, print the case number and the N
th ODD length palindromic integer number. See
the sample test cases.
Constraints
1≤T≤10000
1≤N≤1000000000
8
Sample
Input Output
2
9
10
Case 1: 9
Case 2: 101
Any character or incident that matches with real life is not intentional. You may assume that all characters are
fictional.
#### 傻逼题，正着输一遍反着输一遍
#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const double pi=acos(-1.0);
const int maxn=(int)2e5+100;
string n;
int main(){
int T;cin>>T;
rep(ca,1,T){
cout<<"Case "<<ca<<": ";
cin>>n; cout<<n;
reverse(n.begin(),n.end());
rep(i,1,n.length()-1) cout<<n[i];
cout<<endl;
}
}
## E. Jumpy Robot
In a 1D infinite grid [0, inf], Jumpy Robot is standing on 0th cell.
Initially, it has a power of jumping over exactly 2d cells. After each jump, d is decremented by one. If
d becomes negative, then the robot cannot jump anymore.
The robot can jump forward or backward but cannot go left/backward to a negative cell because it
doesn't exist. Also, the robot cannot skip a move, in other words, d won’t be decremented without
making a move.
For example, Let’s say initially d was 4 which means it can jump over exactly 16 cells. The robot can
jump and move to 16th cell and then d will become 3 (But it couldn’t move to -16th cell because it
doesn’t exist). Then it can jump over 8 cells and can either move forward and go to 24th cell or
move backward and go to 8th cell. Then d will become 2 and the robot can jump 4 cells in either
direction. But it cannot skip the moves of jumping 16 or 8 cells and directly jump over 4 cells.
Tell me if the robot can reach to Xth cell after some moves or it is impossible. If it is possible, then
also print the number of jumps needed.
Constraints
0 ≤ d ≤ 60
0 ≤ X ≤ 10
18
Input
First line will contain the number of test cases T (1 ≤ T ≤ 10
5
). Each of the next T lines will contain
two integers d and X. Dataset is huge. Please use faster I/O methods.
Output
For each test case, in a single line, print the case number. Then print the result which is the
following:
If it is impossible to reach X, print “NO”, otherwise print “YES” and the number of moves in a single
line.
(Please see sample cases to understand the format)
10
Sample
Input Output
4
2 6
2 5
3 8
1 5
Case 1: YES 2
Case 2: YES 3
Case 3: YES 1
Case 4: NO
#### 简单模拟，每次只能往x的方向走，注意特判x=0的情况
#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const double pi=acos(-1.0);
const int maxn=(int)2e5+100;
int d;
ll x;
int solve(){
scanf("%d%lld",&d,&x);
if(x==0) return 0;
ll pos=0;
int ans=0;
while(d>=0){
++ans;
ll len=(ll)pow(2,d);
d--;
if(pos>x) pos-=len;
else if(pos<x) pos+=len;
if(pos==x) return ans;
}
return -1;
}
int main(){
int T;cin>>T;
rep(ca,1,T){
printf("Case %d: ",ca);
int ans=solve();
if(ans!=-1) printf("YES %d\n",ans);
else puts("NO");
}
}
## F. Special Birthday Card
It is the year 2022 and Ayush is 3 years old now. He has already started competitive programming. He wants to become a top-rated contestant like - Dibyo, The Legendary Grandmaster. A few months ago, Ayush collected a large number of documentation/books on graph theory. He started to learn about graph theory. The definitions of graph and tree seemed very complicated to him. He thought that all graphs are trees and all trees are graphs. But we know that his assumption is not correct. A Graph is made up of vertices which are connected by edges. It may be undirected, or its edges may be directed from one vertex to another. It may contain one or more cycles or not. On the other hand, a Tree is an undirected graph in which any two vertices are connected by exactly one path. It does not contain any cycle. A few days ago, on his third birthday, Ayush got an opportunity to meet Dibyo. It’s a great day for him !! He discussed with Dibyo about the basic graph algorithms. After the discussion, Ayush understood the basic difference between a general graph and a tree. Ayush received a birthday card sent by Dibyo. He found the following problem on the card. “X is an integer. For any X, you have to add a bidirectional edge from X to its all distinct divisors except for 1 and X itself. Again, for every divisor of X except for 1 and itself, you have to do the same things. And also do the same things recursively for the divisors of divisors. You can add an edge if there is no edge between them. Finally, you will get a connected bidirectional graph. Definitely, the final graph does not contain any self-loops or multiple edges between the same pair of integers/nodes. Here a graph consists of only 1 node is considered a tree. If X is equal to 12, then the divisors of X are 1, 2, 3, 4, 6, 12. So at first, we add bidirectional edges between 12 and the divisors of 12 except for 1 and 12 itself. It will be like the following graph - 12 Then if we do the same things for 6, we will get the following graph - Again, if we continue the same thing recursively for the other divisors of 12, all divisors of divisors of 12, divisors of divisors of divisors of 12 and so on. Finally, we will get the following graphIt is a cyclic graph but not a tree because it contains multiple cycles. In the problem, you are given an integer N. For every integer from 1 to N if you do the same things described above individually, then you get either a tree or cyclic graph for each integer. Now if the great contestant Dibyo chooses an integer randomly from 1 to N, what is the probability of the graph for the integer being a tree.” 13 Ayush tried hard to solve the problem. But unfortunately, he could not be able to solve the problem. Can you help Ayush? Input Specification The first line of input will contain an integer T, the number of test cases. Each test cases contains an integer N. Output Specification For each case of input, you should print a line containing the case number and the expected output in the form of p/q where GCD(p,q) is equal to 1. Check the sample input and output for more details. GCD - Greatest Common Divisor Constraints 1 <= T <= 100000 1 <= N <= 1000000 Sample Input Output 2 100 50 Case 1: 3/5 Case 2: 33/50 Use faster I/O methods. See the following figures for better understanding. 14 Figure 1: Final graph for 24 Figure 2: Final graph for 48
#### 显然可以得出，只有质数和两个质数的乘积是符合条件的，维护一个前缀和就好啦
#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
#define pb push_back
typedef long long ll;
const int maxn=(int)1e6+100;
int n,sum=0;
int check[maxn];
int prime[maxn];
void Prime(int N){
rep(i,1,N) check[i]=1;
for(int i=2;i<=N;i++){
if(check[i]) prime[++sum]=i;
for(int j=1;j<=sum&&i*prime[j]<=N;j++){
check[i*prime[j]]=0;
if(i%prime[j]==0) break;
}
}
}
void pre(){
Prime(maxn-100);
rep(i,1,sum) for(int j=i;j<=sum&&1ll*prime[i]*prime[j]<=maxn-100;++j) check[1ll*prime[i]*prime[j]]=1;
//cout<<sum<<endl;
rep(i,2,maxn-100) check[i]+=check[i-1];
}
void solve(){
scanf("%d",&n);
int ans=check[n];
int g=__gcd(ans,n);
printf("%d/%d\n",ans/g,n/g);
}
int main(){
int T;cin>>T;
pre();
rep(ca,1,T){
printf("Case %d: ",ca);
solve();
}
}
## G. Ainum’s Delusion
Ainum the hacker-girl is a legendary wizard of computer land. To protect her people from the alien
virus invasion, she is trying to create a very powerful magical string, a string of magical gems. Each
gem is represented by lowercase Latin letters (a….z).
She has collected N magical gems already and connected them one by one to create the string. To
make sure that her people are safe, she needs to know the ultimate power of her string.
The ultimate power of her string is the summation of simple powers of all substrings of the string. A
substring is a contiguous sequence of characters within a string. For instance, “nomi” is a substring
of the word “polynomial” but "nominal" is not. Simple power of a substring s can be calculated by
the following formula:
Here, |s| = length of s, s[i] = ascii value of ith character of s.
Ainum is a very busy person, so she came to you for help. Can you help her? As the ultimate power
of her string can be very big, output the result modulo 1000000007 (10
9 + 7).
Input Specification
Input starts with a positive integer T (1≤T≤ 40), denoting the number of test cases. Each case starts
with an integer N (1≤N≤100000), the length of Ainum’s string followed by a string of length N
containing only lowercase Latin letters (a…..z).
Output Specification
For each case, print the case number and the ultimate power of Ainum’s string modulo 1000000007
(10
9 + 7). See sample for more details.
16
Sample
Input Output
2
1
a
2
ac
Case 1: 97
Case 2: 588
Explanation for second case: ac has 3 different substrings - a, ac, c. Simple powers of them are 97, 392 and 99
respectively.
#### 单点贡献是i*(1ll*n+1)*(n-i+1)>>1
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define dep(i,a,b) for(int i=(a);i>=(b);--i)
const int maxn=(int)1e5+100;
const int mod=(int)1e9+7;
int n;
char str[maxn];
void solve(int ca){
printf("Case %d: ",ca);
scanf("%d%s",&n,str+1);
ll ans=0;
rep(i,1,n){
ll res=1ll*i*(1ll*n+1)*(n-i+1)>>1;
ans=(ans+str[i]*res)%mod;
}
printf("%lld\n",ans);
}
int main(){
int T;cin>>T;
rep(i,1,T) solve(i);
}
0 评论
|
|
Introduction
Microbial rhodopsins are photoreceptor proteins produced in diverse microbes, such as archaea, bacteria and eukaryotes. The molecular functions of microbial rhodopsins are also diverse, such as light-activated ion transporters (pumps and channels) and sensors. Despite such diversities, they commonly consist of a protein moiety having 7 α-helices spanning cell membranes and a chromophore (all-trans-retinal) that is covalently attached to a conserved Lys residue in the 7th α-helix through a protonated Schiff base linkage1,2. The chromophore is isomerized from an all-trans to a 13-cis configuration upon light irradiation in the time range of a few hundreds of femtoseconds, which induces sequential structural changes of the protein moiety in the time range of picoseconds to seconds. During those structural changes, several photo-intermediates are formed and then decay over time. Finally, the protein returns to its initial state. Therefore, such a light-induced reaction is cyclic and is called a photocycle. As a result, microbial rhodopsins exert individual functions during the photocycle2.
One type of natural ion channel rhodopsins has recently become an intensive research target because of their remarkable effectiveness in optogenetic manipulation for neuronal silencing. Those proteins are called anion channelrhodopsins (ACRs), which passively transport monovalent anions, such as halide ions and NO3− 3,4. So far, three kinds of ACRs have been mainly investigated. ACRs from a marine cryptophyte alga Guillardia theta (abbreviated as GtACR1 and 2) are the first natural ACRs reported in 20153. Several in vivo and in vitro investigations have revealed their optogenetic availability3, their channel gating mechanism during the photocycle5,6,7, the roles of positively charged residues for anion conductance8, and their structure and structural changes around the chromophore9,10. On the other hand, another homologous ACR from a marine cryptophyte alga Proteomonas sulcata (abbreviated as PsuACR1 or PsACR1) has also been investigated regarding its electrophysiological4,11 and spectroscopic properties12. Those studies have shown that GtACRs have the ability to work under weak light intensity and that PsuACR1 has rapid channel closing kinetics, rapid dark recovery of the peak photocurrent, and the most red-shifted absorption wavelength among the known ACRs. Those characteristics are beneficial for highly sensitive, precise and rapid optogenetic manipulations. Recently, other ACRs, named ZipACR and RapACR, have been reported to be more rapid than PsuACR1 and used for the optogenetics13,14,15.
Previous investigations of the channel gating mechanism of GtACR1 and PsuACR1 have revealed the relationships between the photo-intermediates in the photocycle and the open and closed states of the channel4,5,6,11,12. In these cases, the anion transport starts together with the formation of the L-intermediate, which is observed in the early stage of the photocycle, whereas it stops together with the formation of the M-intermediate. These relationships in ACRs are different from those in cation channelrhodopsins16,17.
Focusing on the channel functions of ACRs in which several photo-intermediates are involved, anion concentration dependency, which is a useful parameter to characterize anion transport function, is still unclear. In anion pumping rhodopsins, such as archaeal and cyanobacterial halorhodopsins (HRs) and marine bacterial Cl pumping rhodopsins (ClRs), their anion transport mechanisms, including their anion binding ability, photocycle kinetics, sequence and timing of anion uptake and release, and residues important for anion transport, have been revealed based on the anion concentration dependency in their spectroscopic properties18,19,20,21,22,23,24,25,26. Therefore, in this study we used static and time-resolved absorption spectroscopy to characterize the anion channel function of ACR with varying anion concentrations, especially for Cl. We focused on PsuACR1 since it has rapid channel closing kinetics as described above, however the detailed mechanism involved is still unknown. PsuACR1 was expressed in and extracted from methylotrophic yeast Pichia pastoris cells as a recombinant protein in the presence of the detergent dodecyl-β-D-maltoside (DDM). These spectroscopic measurements revealed information about the Cl binding ability in the initial state and the Cl concentration-dependent changes of the photocycle that are directly connected to its anion channel function.
Results
Cl− dependent absorption changes in the initial state
Retinal isomer composition analysis of PsuACR1 was performed using high performance liquid chromatography (abbreviated as HPLC). Figure 1A shows HPLC chromatograms of retinal oximes extracted from PsuACR1 under dark or light conditions. PsuACR1 showed slight dark and light adapted changes in its retinal isomer composition. With respect to the Cl concentration dependency on the retinal isomer composition, that dependency seemed to be larger in the presence of 1,000 mM Cl than in the presence of 0.1 mM Cl, especially under the light condition. In summary, the chromophore composition in the initial state of PsuACR1 was predominantly the all-trans form, which facilitates the light-gated anion channel function, at more than 90% and 70% under dark and light conditions, respectively.
To characterize the effect of Cl on the absorption properties of PsuACR1 in the initial state, we measured static UV-visible absorption spectra in varying Cl concentrations from 0.1 to 1,000 mM. As shown in Fig. 1B, the visible absorption maximum (abbreviated as λmax) in the presence of 0.1 mM Cl was 531 nm. When the Cl concentration increased, the λmax was red-shifted to 535 nm. At the same time, a minor absorption band at around 400 nm, a marker band for the deprotonated retinal Schiff base, disappeared. These results indicate that PsuACR1 binds Cl in the initial state and that the bound Cl increases the acid dissociation constant (pKa) of the protonated retinal Schiff base. The same behavior was also observed for HRs26,27. We then estimated the Cl binding affinity of PsuACR1 (the dissociation constant, Kd) from the Cl dependent shift of the λmax. Figure 1C shows the Hill plot of λmax against the Cl concentration, and from the Hill equation, the Kd was estimated to be 5.5 ± 1.6 mM.
Photocycle of PsuACR1 in the presence of 100 mM Cl−
The photocycle of PsuACR1 was investigated using time-resolved flash-photolysis in the time range of microseconds to seconds, during which the protein exerts its Cl channel function. Here we explain the photocycle overview in the presence of 100 mM Cl as an example. Figure 2A illustrates the flash-induced light-minus-dark difference absorption spectra from 10 μs to 1.4 s. After the flash excitation, the absorption for the initial state at 540 nm disappeared together with the concomitant appearance of three photo-intermediates with absorptions at 610 nm, 450 nm and 400 nm, tentatively assigned as K-, P450- and M-intermediates (abbreviated as K, P450 and M), respectively6,12. Over time, these photo-intermediates increased and then decreased together with the recovery of the initial state and therefore the photocycle was completed.
To examine the photocycle kinetics precisely, we performed global fitting analysis based on the sequential model28,29. These data were successfully fitted by the exponential decay functions with the sum of 4 exponents, indicating that at least 4 kinetically defined states, P1P4, were detected in our experimental time domain (Supplementary Fig. S1). Figure 2B shows the absorption spectra for the P1P4 states calculated using the fitting results. P0 represents the pure retinal spectrum of the initial state PsuACR1. From the spectra, we assigned two additional photo-intermediates with absorption peaks at 500 nm and 540 nm as the L- and ACR’-intermediates (abbreviated as L and ACR’), respectively, by reference to previous reports6,12,23,24,25.
Figure 2C shows the time-dependent absorption changes of representative photo-intermediates as described above. Due to the time resolution of our flash-photolysis apparatus (10 μs), which is larger than that of a previous report by two orders of magnitude11, the observed photocycle started from the equilibrium state between K (610 nm) and L (500 nm). The P1 spectrum shown in Fig. 2B supports their equilibrium. In addition, the spectral shoulder corresponding to P450 (450 nm) was observed in the P1 state (Fig. 2A,B), indicating the co-existence with K and L. The P1 state decayed to the P2 state at the time constant τ1 (0.219 ms, Fig. 2C). During this transition, the absorption at 610 nm transiently increased together with the decrease in the absorption at 500 nm. In a previous study, these transient absorption changes corresponded to the re-establishment of the K/L equilibrium in favor of K12. However, based on the conventional photocycle scheme, it is more straight-forward to assign the transient increase in 610 nm as the generation of a new photo-intermediate rather than the re-establishment of the K/L equilibrium. Therefore, we adopted the P600-intermediate (abbreviated as P600), whose λmax was estimated to be 600 nm from the P2 spectrum in Fig. 2B, as an intermediate followed by L. Previous reports for PsuACR1 indicated the existence of an intermediate similar to P600 named P62011 or K212. In summary, an equilibrium state among P450, L and P600 was observed in the P2 state (Fig. 2B). The P2 state decayed to the P3 state at the time constant τ2 (21.3 ms, Fig. 2C). The P3 state in the presence of 100 mM Cl contained L, P600, and M (400 nm) at the same time (Fig. 2B). The P3 state was then converted to the P4 state at the time constant τ3 (88.0 ms, Fig. 2C), where ACR’ (540 nm) mainly populated (Fig. 2B). Finally, the P4 state decayed to the initial state P0 at the time constant τ4 (647 ms, Fig. 2C) to close the photocycle. From the analysis described here, we summarize the photocycle scheme of PsuACR1 in the presence of 100 mM Cl in Fig. 2D.
Cl− dependence on the photocycle
The Cl dependence on the photocycle of PsuACR1 was also investigated by flash-photolysis. Figure 3 illustrates the light-minus-dark difference absorption spectra and the time dependent absorption changes of the representative photo-intermediates in the presence of 0.1–1,000 mM Cl, except for 100 mM Cl. From these results, two major effects of the Cl concentration on the photocycle were identified: (i) The accumulations of P450 and M changed with increases in the Cl concentration (Figs 2A and 3A–D); and (ii) The lifetime of P600 was prolonged and therefore its decay was synchronized with that of M in the presence of more than 1,000 mM Cl (Fig. 3H). The same effects were observed in the presence of 4,000 mM Cl (Supplementary Fig. S2).
To analyze the Cl dependence on the photocycle kinetics in detail, we compared the absorption spectra of the P1P4 states at each Cl concentration (Fig. 4). From that analysis, we found that the Cl dependence changed at 10 mM Cl. Therefore, we separately prepared the absorption spectra in the presence of 0.1–10 mM (panels A–D) and 10–1,000 mM (panels E–H). In the P1 state, where K, P450 and L were in equilibrium (Fig. 4A,E and I), the equilibrium shifted from L to K in the presence of 0.1–10 mM, whereas slight increases in L and P450 were observed in the presence of 10–1,000 mM. Similarly, in the P2 state, where P450, L and P600 were in equilibrium (Fig. 4B,F and J), the equilibrium shifted from L to P600 in the presence of 0.1–10 mM Cl, while increases in L and P450 were observed in the presence of 10–1,000 mM Cl. The spectra were significantly changed in the P3 state (Fig. 4C,G and K). In the presence of 0.1–10 mM Cl (Fig. 4C,K), M and ACR’ accumulated and the equilibrium shifted from ACR’ to M. In addition, the spectrum in the presence of 10 mM Cl seemed to contain L and P600 other than ACR’ at the same time (Fig. 4C,G), indicating there is a transition phase between the photocycle in the presence of lower or higher concentrations of Cl. When increasing the Cl concentration from 10 to 1,000 mM (Fig. 4G,K), L and P600 were clearly observed in the spectra. These intermediates were in equilibrium with M and the equilibrium shifted from M to L and P600. Therefore, such a Cl dependent equilibrium shift resulted in an increase and a decrease in the accumulation of M and the prolongation of the lifetime of P600, respectively, which was also supported by the results shown in Fig. 3H. In the P4 state, where ACR’ mainly accumulated, absorption changes of ACR’ were detected (Fig. 4D,H and L), which reflects that Cl was taken up during the lifetime of ACR’.
Discussion
In this study, we investigated the Cl dependent changes in the photochemical properties of PsuACR1 using static and time-resolved spectroscopic techniques that revealed that the photocycle, which is directly connected to the anion channel function, is strongly affected by Cl concentration.
Indication for Cl− binding in the initial state
We demonstrated that the visible absorption of PsuACR1 shifted with changes in the Cl concentration (Fig. 1B). In a previous study of PsuACR1, the λmax in the absence or presence of Cl both resulted in 534 nm, which is close to our results in the presence of more than 100 mM Cl (Fig. 1C), and thus no spectral shift was observed12. Currently, we cannot clearly explain why such a difference occurred. One possible reason may be that in the previous study more than a certain concentration (e.g. the Kd of 5.5 mM determined in this study) of Cl remained in the sample solution even after the buffer exchange. Incidentally, in the case of a homologous protein GtACR1, no spectral shift was observed between 0 and 300 mM Cl− 6. The difference in the initial state Cl binding between PsuACR1 and GtACR1 will be an interesting issue.
PsuACR1 showed a Cl induced spectral red-shift (Fig. 1B), which is opposite to the case of many Cl pumping rhodopsins, such as the haloarchaeal Natronomonas pharaonis HR (NpHR)18,22,23 and the bacterial Nonlabens marinus S1-08T rhodopsin 3 (NM-R3)25. On the other hand, spectral red-shifts similar to those of PsuACR1 were observed in haloarchaeal Halobacterium salinarum HR (HsHR)20, in bacterial Mastigocladopsis repens HR (MrHR)30 and in Salinibacter ruber sensory rhodopsin I (SrSRI)31. For the latter red-shifted species, two different Cl binding sites are hypothesized. One is in the vicinity of the protonated retinal Schiff base, which was revealed by crystal structure and spectroscopic measurements in HsHR32 and MrHR30. To confirm this, we prepared a mutant of PsuACR1 for Ala93, which corresponds to Thr74 in MrHR, Thr126 in NpHR, and Asp85 in HsBR (Supplementary Fig. S3A). In the cases of MrHR and NpHR, amino acid substitutions at the 74th and 126th positions from Thr to acidic residues resulted in the disappearance of the spectral shift and thus the initial Cl binding ability30,33. Therefore, we prepared the PsuACR1-A93E mutant with the hope of the same results obtained for the MrHR and NpHR mutants. Supplementary Fig. S3B shows the absorption spectra of PsuACR1-A93E in the presence of 0.1 mM or 1,000 mM Cl. Unexpectedly, a Cl dependent spectral red-shift from 504 nm (0.1 mM) to 508 nm (1,000 mM) was observed. Therefore, it is unlikely that PsuACR1 shares the same Cl binding site with MrHR and NpHR in the initial state.
The other hypothesis about the initial Cl binding site is that it resides in the vicinity of the β-ionone ring of the retinal chromophore, which has been reported in SrSRI31. In this case, His131 near the β-ionone ring is involved in the Cl binding, where the bound Cl induces the delocalization of the positive charge on the protonated retinal Schiff base nitrogen towards the β-ionone ring that induces the spectral red-shift. To confirm this for PsuACR1, we found that His131 in SrSRI was substituted to Phe156 in PsuACR1 (Supplementary Fig. S3A). We further searched for other candidates having a positive charge, however such residues were not found near the β-ionone ring of the retinal in PsuACR1. Therefore, we successfully demonstrated the Cl binding ability of PsuACR1 in the initial state but identification of the specific binding site must await future study.
With regard to the Cl binding affinity, the Kd was estimated to be 5.5 ± 1.6 mM from the Hill equation (Fig. 1C), which was in the same order as HsHR (2.6 mM)34, NpHR (5.0 mM)35, bacterial Rubricoccus marinus HR (RmHR; 7.6 mM)26 and MrHR (2.0 mM)30. This result indicates that the natively expressed PsuACR1 in P. sulcata binds Cl in the initial state under physiological conditions (the Cl concentration in the marine environment is a few hundreds of millimolar).
Effects of Cl− concentration on the channel function of PsuACR1: Relationships between photo-intermediates and Cl− conducting and non-conducting states
Previous reports for GtACR1 and PsuACR1 described the photo-intermediates in the photocycle as corresponding to the anion-conducting and non-conducting states by combining spectroscopic and electrophysiological results4,5,6,11,12. In those cases, the anion conductance starts and stops when forming the L and M photo-intermediates, respectively. Therefore, L and the following P600 in our photocycle model are involved in the Cl conducting state and K, P450, M and ACR’ are involved in the Cl non-conducting state (Fig. 4I–L).
We clearly observed a Cl dependent change of the photocycle kinetics, especially in the equilibrium states of the photo-intermediates in the presence of higher concentrations of Cl (10–1,000 mM, Figs 3 and 4). Notably, we identified the most drastic change in the P3 spectra in the presence of a higher Cl concentration (Fig. 4C,G). The P3 state in the presence of 100–1,000 mM Cl is considered to be the Cl conducting state due to the significant equilibrium shift from M to L and P600 (Fig. 4G,K), whereas that in the presence of 0.1–1 mM Cl is considered to be the Cl non-conducting state due to the co-existence of M and PsuAR1’ in equilibrium (Fig. 4C,K). The P3 spectrum in the presence of 10 mM Cl corresponds to the mixture of the Cl conducting and non-conducting states. Based on the relationships between the photo-intermediates and the Cl conducting and non-conducting states as described above, the P1 and P2 states correspond to the Cl conducting state, and the P3 and P4 states correspond to the non-conducting states in the presence of lower concentrations of Cl (see also Fig. 4I–L). On the other hand, in the presence of higher concentrations of Cl (e.g. 1,000 mM), the P1P3 states correspond to the Cl conducting state, and the P4 state corresponds to the non-conducting state (see also Fig. 4I–L). Figure 5A shows the time course for the generation and decay of the P1P4 states. This result clearly indicates that the Cl conducting state is protracted by one order of magnitude in the presence of higher concentrations of Cl. From these results, we hypothesize that one of the most pronounced characteristics of PsuACR1, i.e. the rapid channel closing and rapid dark recovery of the photocurrent4,11, which enables the optogenetic neuronal silencing at rapid frequency, becomes impaired at higher concentrations of Cl.
In addition, we noticed that the accumulation of M, which is involved in the Cl non-conducting state, changed in a Cl concentration-dependent manner, as shown in Fig. 5B. The accumulation of M first increased, then reached a maximum at 10 mM Cl, and finally decreased with the increase in Cl concentration. From the Cl concentration dependency, we estimated that the Cl concentration for the first transition is close to the Kd value for the initial Cl binding (5.5 mM, Fig. 1C). On the other hand, the Cl concentration for the second transition was estimated to be several hundreds of millimolar. We suppose that in the presence of a higher Cl concentration than this value, a secondary Cl binding occurs in PsuACR1 that significantly inhibits the accumulation of M. Therefore, we propose that there is a causal relationship between the secondary Cl binding and the impairment of the rapid channel closing of PsuACR1 at higher concentrations of Cl. Although the secondary Cl binding site has not been identified yet, we estimate that it is located near or along the Cl conducting pathway in the protein. Previously, the inhibitory role of the Arg residue on the extracellular surface of GtACR2, which is a candidate consisting of the Cl conducting pathway, for its anion channel function has been reported8. One of the authors’ discussion points regarding the inhibition mechanism is that the positively charged Arg84 interacts with the negatively charged Cl, which prevents the Cl from being transported through the protein8. Together with the fact that PsuACR1 conserves the corresponding residue as Arg84, we estimate that the inhibitory role of Arg84 is related to the secondary Cl binding and therefore the Arg84 in PsuACR1 is one candidate for the secondary Cl binding site. If the secondary Cl binding occurs on the protein surface near Arg84, a mutation to destroy that secondary binding site would enable optogenetic silencing at a high frequency through PsuACR1 even in the presence of higher Cl concentrations. Another estimation is that water-filled cavities along the channel pathway in PsuACR1 contribute to the secondary Cl binding. X-ray and simulation structures of cation channelrhodopsins (CCRs) C1C2 and ChR2 from Chlamydomonas reinhardtii indicated that such cavities are distributed along the possible cation channel pathway and predicted to be involved in the cation permeation36,37,38,39. Moreover, in the case of Cl conducting mutant of C1C2 (C1C2-E90K/R), the distribution of the cavities was expanded, which facilitated Cl distributed in the cavities and resulted in the increase in the affinity for Cl40. In analogy with these CCRs, there should be similar water-filled cavities in ACRs including PsuACR1 to capture Cl. We hypothesize that several Cl are captured by the cavity during the Cl conducting L- or P600-intermediate in the presence of high concentrations of Cl, which may stabilize the L or P600 and thus remain the channel open.
The currently fastest ACR for optogenetic silencing, called ZipACR, originates from P. sulcata and thus is a homologous protein with PsuACR1 (identity 32%, similarity 71%)13. On the other hand, GtACR1 also shares a high sequential homology with PsuACR1 (identity 36%, similarity 74%). Based on our hypothesis, the similar Cl dependence and thus impairment of the channel closing in the presence of higher concentrations of Cl may occur in these homologous ACRs.
Conclusion
In this study, we analyzed the Cl dependent changes in the photochemical properties of PsuACR1 using static and time-resolved spectroscopic techniques. We found that PsuACR1 is able to bind Cl in the initial state at a Kd of 5.5 mM, which was estimated by the Cl dependent spectral red-shift. In addition, the Cl concentration dependency on the photocycle was clearly observed. In the presence of more than 10 mM Cl, the photocycle of PsuACR1 was significantly changed as follows; (i) the accumulation of M, which is involved in the Cl non-conducting state, was strongly suppressed, and (ii) due to (i) and the drastic change in the equilibrium state of the other photo-intermediates, the Cl conducting state was protracted by one order of magnitude compared to that in the presence of lower concentrations of Cl. These results suggest that the most pronounced characteristics of PsuACR1, rapid channel closing and rapid dark recovery of the photocurrent, which enables the rapid optogenetic manipulation for neuronal silencing, becomes impaired in the presence of high concentrations of Cl. We propose that there is a causal relationship between the secondary Cl binding and the impairment of the rapid channel closing of PsuACR1 at high concentrations of Cl. For the present use of ACRs for optogenetics, the proteins may not be exposed to such high anion concentrations condition in neurons. However, we hope that our study will be helpful to engineer optogenetic tools based on ACRs.
Methods
DNA construction of PsuACR1
The amino acid sequence of PsuACR1 was the same as previously reported (GenBank: KF992074.1, 291 residues)4,11,12,41. For affinity purification, 8 histidine residues were attached to the C-terminus of PsuACR1 (abbreviated as PsuACR1_His8). The gene encoding PsuACR1_His8 with the codon optimization for Pichia pastoris was purchased from GENEWIZ (South Plainfield, NJ, USA). Two restriction enzyme sites, EcoRI and NotI, were attached to the 5′- and 3′-teminal ends of the PsuACR1_His8 gene, and a stop codon was introduced before the NotI site. According to this, we obtained PsuACR1_His8 having 299 residues in total. The gene and the expression vector pPICZ B (Thermo Fisher Scientific, Waltham, MA, USA) were digested by EcoRI and NotI restriction enzymes (Roche, Basel, Switzerland) and were then ligated using a Mighty Mix DNA ligation kit (Takara Bio Inc., Shiga, Japan). Nucleotide displacement was introduced using a QuikChange Site-Directed Mutagenesis kit (Agilent Technologies, Santa Clara, CA, USA) to produce PsuACR1-A93D and PsuACR1-A93E mutants. The nucleotide sequences were verified by the dideoxy sequencing method using a BigDye Terminator v1.1 Cycle Sequencing kit and a 3130 DNA Analyzer (Applied Biosystems, Foster City, CA, USA).
Protein expression and purification
The methylotrophic yeast Pichia pastoris SMD1168H strain (Thermo Fisher Scientific) was used as the protein expression host. For the transformation of P. pastoris, pPICZ B_PsuACR1_His8 plasmid DNA was linearized using the PmeI restriction enzyme (New England Biolabs, Ipswich, MA, USA), purified using a FastGene Gel/PCR Extraction kit (NIPPON Genetics Co., Ltd, Tokyo, Japan), and then introduced to competent P. pastoris cells by a standard electroporation method. The transformed P. pastoris cells were inoculated and pre-cultured in BMGY medium containing 100 μg/mL ZeocinTM (Thermo Fisher Scientific) for two days at 30 °C. The medium was exchanged to BMMY medium containing 0.5% methanol, 100 μg/mL ZeocinTM and 10 μM all-trans-retinal (Sigma Aldrich, St. Louis, MO, USA), and protein expression was induced for 24 hr at 30 °C. After the protein induction, the cells were collected by centrifugation, resuspended in 50 mM Tris-HCl (pH 8.0) buffer containing 300 mM NaCl, and then sufficiently disrupted at 4 °C using a French press (100 MPa, repeated 6 times; Ohtake, Tokyo, Japan). The cell suspension was centrifuged at 7,000 rpm for 5 min at 4 °C (TOMY EX-136 equipped with a TLA-11 rotor; TOMY Seiko Co., Ltd., Tokyo, Japan) and the supernatant containing membrane fraction was collected. The membrane fraction was collected by ultracentrifugation at 40,000 rpm for 1 hr at 4 °C (Hitachi Koki CP 90NX equipped with a P70AT rotor; Hitachi Koki Co., Ltd., Tokyo, Japan). The procedures for solubilization with DDM (Dojindo Laboratories, Kumamoto, Japan) and affinity purification were the same as previously reported25. For spectroscopic measurements, the buffer was sufficiently exchanged with 10 mM MOPS buffer (pH 7.0, Dojindo Laboratories) containing the desired concentrations of NaCl (0.1, 1, 10, 100 and 1,000 mM) and Na2SO4 (0, 300, 330, 333 and 333.3 mM) by centrifugation for 10 times (Amicon Ultra centrifuge filter, 30,000 molecular weight cut-off, Merck Millipore, Burlington, MA, USA) and gel-filtration chromatography (PD-10 column, GE Healthcare, Chicago, IL, USA). The ionic strength was kept at 1,000 mM by adding Na2SO4 because SO42− is impermeable for PsuACR14. For spectroscopic measurements at high salt concentrations, we prepared PsuACR1 samples in the same MOPS buffer containing 0.05% DDM and 4,000 mM NaCl or 1,333.3 mM Na2SO4. The ionic strength was kept at 4,000 mM. The same procedures were used to produce the PsuACR1-A93D and PsuACR1-A93E mutants. However, the PsuACR1-A93D mutant was not functionally expressed in the cells.
Retinal isomer composition analysis
Analysis of retinal isomer composition was carried out using a previously reported method30. The retinal oxime extracted from Halobacterium salinarum bacteriorhodopsin (HsBR) in the purple membrane (PM) was used as a reference. For measurements under dark conditions, PsuACR1 and HsBR samples were kept in the dark for 1 week at 4 °C. For measurements under light conditions, the samples were respectively illuminated with green (530 nm) and orange (590 nm) LED light for 5 min before retinal oxime extraction. The concentrations of retinal oximes were calculated from peak areas of HPLC chromatograms.
Spectroscopic measurements
UV-visible absorption spectra were measured at 25 °C using a UV-1800 spectrophotometer (Shimadzu Corp., Kyoto, Japan). The protein concentration was adjusted to an optical density at 535 nm of 0.5–0.6. For the analysis of Cl concentration dependent spectral changes, the Hill equation was used to determine the Cl binding affinity in the initial state as follows:
$${\lambda }_{max}=A+B\times \frac{{[C{l}^{-}]}^{n}}{{{K}_{d}}^{n}+{[C{l}^{-}]}^{n}}$$
where A, B, [Cl], Kd, and n represent the offset, the amplitude of λmax change, the Cl concentration, the dissociation constant, and Hill coefficient, respectively.
Flash-photolysis experiments were carried out at 20 °C using a homemade system as reported previously22,24. Data for time-dependent absorption changes from 380 nm to 700 nm every 10 nm were obtained. The number of data acquisitions was 30 for each wavelength. Data were analyzed by the sequential model as reported previously28,29;
$${P}_{0}\to {P}_{1}\to {P}_{2}\to {P}_{3}\to {P}_{4}\to {P}_{0}$$
where P0 and P1P4 represent the initial state and the 1st–4th kinetically defined states, respectively. All data for the time-dependent absorption changes were simultaneously fitted with a sum of 4 exponential decay functions in this study. The number of exponents was determined by the reductions in the standard deviation of the residuals (Supplementary Fig. S1). In the P1P4 states, physically defined photo-intermediates such as K, L, and M were populated at equilibrium. Details for the analysis are described in our previous reports25,26,29.
|
|
# Orbit equivalence rigidity and bounded cohomology
### Abstract
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative curvature geometry. Amongst our applications are (a) measurable Mostow-type rigidity theorems for products of negatively curved groups; (b) prime factorization results for measure equivalence; (c) superrigidity for orbit equivalence; (d) the first examples of continua of type $II_1$ equivalence relations with trivial outer automorphism group that are mutually not stably isomorphic.
## Authors
Nicolas Monod
Department of Mathematics
University of Chicago
Chicago, IL 60637
United States
Yehuda Shalom
School of Mathematical Sciences
Tel Aviv University
Tel Aviv 69978
Israel
|
|
## 4.9 Defining the wavefunction
In all program modules where such information is required, the total symmetry of the -electron wavefunction is defined on WF (wavefunction) cards in the following way:
WF,nelec,irrep,spin
or, alternatively
WF,[NELEC=nelec],[SYM[METRY]=irrep],[spin=spin],[CHARGE=charge]
where nelec is the total number of electrons, irrep is the number of the irreducible representation, and spin equals , where is the total spin quantum number. Instead of nelec also charge can be given, which specifies the total charge of the molecule. For instance, for a calculation in symmetry with 10 electrons, WF,10,3,0 denotes a state, and WF,10,1,2 a state. The charge can also be defined by setting the variable CHARGE:
SET,CHARGE=charge
This charge will be used in all energy calculations following this input. Note that SET is required, since CHARGE is a system variable (cf. section 8.4).
Although in principle each program unit requires a WF command, in practice it is seldom necessary to give it. The program remembers the information on the WF card, and so one might typically specify the information in an SCF calculation, but then not in subsequent MCSCF or CI calculations; this also applies across restarts. Furthermore, nelec defaults to the sum of the nuclear charges, irrep to 1 and spin to 0 or 1; thus in many cases, it is not necessary to specify a WF card at all.
If the WF directive is given outside an command input block, it is treated as global, i.e., the given values are used for all subsequent calculations. Setting the variables NELEC, SPIN, or SYMMETRY, has the same effect giving these on a global WF directive. If the global WF directive is given after the variable definition, the values of the variables are replaced by the values given on the WF directive. Vice versa, if a variable definition follows a global WF directive, the new value of the variable is used in the following. Note that WF input cards in command blocks have preference over global WF directives or input variables.
molpro@molpro.net 2019-03-20
|
|
MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
## Return to Answer
3 removed extraneous $Others can do this much better than I, but here's what's happening: to describe a group scheme of any kind, you need to talk about not only the underlying space, but also the law of composition on the group. In this case, the kernel of$[p]$in the muliplicative group, you describe the law of composition by writing down the the comultiplication on the affine ring$k[X]/(X^p)$. This is simply$X\mapsto $1 \otimes X + X \otimes 1 + X \otimes X$.
2 Corrected l.c. "x" to cap. "X"
Others can do this much better than I, but here's what's happening: to describe a group scheme of any kind, you need to talk about not only the underlying space, but also the law of composition on the group. In this case, the kernel of $[p]$ in the muliplicative group, you describe the law of composition by writing down the the comultiplication on the affine ring $k[X]/(X^p)$. This is simply $x\mapsto X\mapsto$1 \otimes x X + x X \otimes 1 + x X \otimes x$X$.
1
Others can do this much better than I, but here's what's happening: to describe a group scheme of any kind, you need to talk about not only the underlying space, but also the law of composition on the group. In this case, the kernel of $[p]$ in the muliplicative group, you describe the law of composition by writing down the the comultiplication on the affine ring $k[X]/(X^p)$. This is simply $x\mapsto$1 \otimes x + x \otimes 1 + x \otimes x\$.
|
|
# Do the false position method really need that there exists only one root inside $[a; b]$?
I'm studying the False Position Method for finding zeroes of real functions and in the book I'm reading the author says that it is required that only one root of $f$ is contained inside the initially guessed interval $[a; b]$.
Is this really the case? I'm asking because I couldn't find another book or reference that states the same, proving why the method fails otherwise.
As far as I can see, this shouldn't be a problem, given that, whatever is the number of roots in $[a; b]$, at each iteration this interval shrinks.
Could you please state the reason why this is either true or false?
OBS: Please, notice that counterexamples for this are functions and intervals that both meet all the criteria required by the method, except for the number of roots inside the interval, and for which the method can't find any of the roots in a finite number of iterations.
One of the criteria requires that you have $f(a) f(b) < 0$.
If we take the function:
$$f(x) = x^2 - \cos^2 x$$
A plot of this function shows two roots as:
Using a different method, there are two roots at $x = \pm 0.73908513321516064166$.
If we use the False Position Method to meet that initial criteria, we could choose:
• $a = -\dfrac{1}{2}, b = \dfrac{3}{2}$, and we converge in on the positive root of $0.739085133215160641$.
• $a = -2, b = 0$, and we converge in on the negative root of $-0.73908513321516064$.
What do you notice about the choice of the interval? For example, can you choose $(a, b) = (-2, 2)$?
Reading what the author is saying means that you choose ranges for a single root at a time as this method can only find one root at a time.
Update
The question is asking if there is more than one root within an interval, will the method still work?
As an example, we will take $f(x) = \cos x$ and use $(a, b) = (\pi/4, (11 \pi)/4)$. A plot of the $f(x)$ over this range shows:
As can clearly be seen in the plot, there are in fact three roots over this range and we $f(a) > 0$, $f(b) < 0$.
When we apply the False Position Method, it does indeed converge (in two steps) to the root $x = 4.71238898038468988$. The reason is that this method is finding find the x-intercept of the straight line connected by two points $((a,f(a), (b, f(b))$. We can depict this graphically as:
In this analysis, you can see the x-intercept is that root found by the algorithm. So, there is no problem in finding a root. The trouble is that unless you do a similar analysis, you would not be sure apriori to which root, unless you do the algorithm. Other methods have similar problems, but they still work as advertised.
I think the author is trying to point out that if you are trying to find a root within an interval and there are multiple roots, you might not get the correct one and you should use whatever is at your disposal to narrow the range down to a single root.
You should also compare and contrast the pros and cons of this method when compared to things like the Secant Method.
• Actually no, exactly because in this function we can't choose $a$ and $b$ such that the first criterion is met. I already knew that this was a requisite, or else we would not know how to shrink the interval maintaining a root inside it, so my concern is really about the situations where we can get $a$ and $b$ like that which englobe more than one root. Think of the function $f(x) = \mathrm{cos}(x)$ and $a=\frac{\pi}{4}$ and $b=\frac{7\pi}{4}$ for example. Can we get one of the two roots in $[a; b]$? Jun 15, 2013 at 20:29
• I am confused. What is $cos(\frac{pi}{4})$? What is $cos(\frac{7 pi}{4})$ Those values are equal and positive and do not match the condition. We need for the interval values to give us a negative and a positive result so we can begin to apply this method. Am I missing some fundamental part of your question? The example I gave has two roots inside of $(2,2)$, but we cannot use that range for our interval as it does not meet the criteria. We can have a multiplicative root at a point, but this method cannot handle those. Jun 15, 2013 at 21:00
• @araruna: Maybe this needs to be stated a different way. If we have f(a) positive and f(b) negative, what does that imply? What is this telling you about your choice for an interval? Jun 15, 2013 at 21:22
• Excellent presentation here! Jun 16, 2013 at 0:27
• @araruna: No problem, I make all sorts of errors all the time. Please see my update to the question. Jun 16, 2013 at 18:16
|
|
# Tag Info
11
I found this an effective teaching technique. I take a topic they know, and find a Wikipedia article discussing that topic. If you are specifically focused on proofs, as opposed to more generic descriptions, you can find many proofs in Wikipedia. E.g., of Sperner's Lemma, or Euclid's proof of $\infty$ # primes. Then I project the text in class, and have ...
9
I know I shouldn't add another answer, but I think my other answer went off on a tangent that didn't really address your question. I did not initially read it carefully enough to realize you were tutoring students, not teaching a class. I really don't think the label of "Teaching Critical Thinking Skills" is either relevant or pertinent--teaching is ...
9
When I first started asking students if they "checked their answers" on a test, a number of them asked me what I meant. This was specific to algebra, and I told them they should take the answer, say, the X intercepts, and put those back into the equation to see if it resulted in Y being zero. Many had never heard of this, and thought that checking simply ...
8
I was also a double major in mathematics and philosophy as an undergraduate (at a state university in the U.S.). I think that both are incredibly important, and I'm happy to have both under my belt. Actually: philosophy was my primary major, mathematics secondary. (This confused a lot of my instructors in higher-level math courses looking at the course ...
8
Teach the students to perform a sanity check at the end of every problem, and a check-by-substitution when practical at the end the problem. If either check fails, they can use a technique for finding errors, such as: Rory's binary search for the mistaken step. Keeping a "top 10 list" of most common mistakes, such as some of the following: ** (not) ...
7
There is quite a bit of evidence that critical thinking can be taught (which I found surprising). College students' gains in critical thinking skills over the course of their education are correlated with high standards set by instructors and greater time spent studying. So I think the basic answer is that you have to assign students tasks that require ...
6
One definition of "abstract" is " disassociated from any specific instance". In mathematics, we "abstract" by finding properties which underlie a class of examples. For instance, the concept of a "group" is an abstraction of many different concrete instances of groups which were important to mathematicians: composing symmetries of spaces (such as the ...
6
I teach high-school calculus, and many questions can be checked by a graphing calculator. So my first strategy is to teach the use of the calculator and using it to check answers when possible. However, often a student will see that his final answer disagrees with the calculator but he does not know which of his steps introduced an error. I have found that ...
5
One possibility to encourage sanity checks is to practise sanity-check-type questions and include them in tests. An integration-related example could be: A student has calculated the area bounded by $y=x^2$, the $x$-axis, $x = 0$ and $x = 4$ to be 128 square units. Without using an integral, explain why 128 square units is too large to be a correct answer....
5
There are quite a few textbooks that have critiquing sample proofs as exercises. Here are three I know of: A Transition to Advanced Mathematics by Smith, Eggen, and St. Andre The Foundations of Mathematics by Thomas Q Sibley How to Read and Do Proofs: An Introduction to Mathematical Thought Processes by Daniel Solow This past year I used the Solow text ...
5
Go to Mathematics Stack Exchange or MathOverflow. There are many questions there looking for proofs and there are many different answers, some good, some bad (some are even wrong). Ask your students to criticize the proofs (Are the proofs they consider good the ones that are highly upvoted?). The commentary that you want is sometimes there (as comments). ...
3
Obviously it's hard to tell from a distance. Here are some explanations: She may be more motivated to think about the material in the philosophy course. This may be because she can relate to the topics that they analyze. Like one commenter suggests, if you do not know the basic examples or motivation for group theory, it can be hard to feel motivated to ...
3
Give your students a multi-step problem and 5 different "solutions" written by fictitious students (you, really). Say: Here are five different solutions to this problem. First, rank them from best to worst. Second, discuss your ranking with the student next to you and determine appropriate criteria for assessing solutions. Third, list what you believe ...
2
First, let me endorse Jared's point that checking calculations and debugging computer programs have much in common. Good programmers build checks into their code before it evidences a bug. Second, one general technique, which only works in circumstances where at least one variable is present, is: look at extreme values of the variables. An example from a ...
2
"Do like a sports commentator: just say what's happening. As a sport commentator is talking to the public, whatever they are looking to the live-event or listening at the radio, they will understand just because he is saying exactly what's happening and nothing else. I think if you explain to your students, you're probably telling them your interpretation of ...
2
This is something that I've been specifically grappling with in my college remedial algebra classes for the last few years. JoeTaxpayer's observations in his answer very much match my own (that many students have never heard of checking solutions to equations until I make a topic out of it -- in fact, I'm somewhat embarrassed by how many years I spent ...
2
One of the crucial points here is that verifying a result must be different than repeating the calculation, let me explain: Verify that 221/12 = 18, rest 5: Instead of doing the calculation all over, calculate 12x18+5, which indeed equals 221. Verify that -2 and 3 are solutions of x^2-x-6=0: Fill in the values: (-2)^2-(-2)-6 = 4+2-6 = 0, and 3^2-3-6 = 0 ...
1
A pair of fresh eyes may see goodies and errors alike, that you cannot see yourself after writing the assignment. Thus, I experiment with letting students peer-review (an anonmized fraction of) their upcoming assignment using the same rubrick as I intend to use when asessing their final submission. For this purpose, I have a class on Moodle (my highschool ...
Only top voted, non community-wiki answers of a minimum length are eligible
|
|
Witten's QFT and Jones Poly paper - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T05:23:41Z http://mathoverflow.net/feeds/question/56148 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/56148/wittens-qft-and-jones-poly-paper Witten's QFT and Jones Poly paper Kevin Wray 2011-02-21T06:48:16Z 2011-02-22T09:08:45Z <p>Data: $M$ is an oriented 3-dim manifold, $E$ is a $G$-bundle over $M$, with $G$ compact simple Lie group. </p> <p>Question: How does $\pi_3(G)\cong \mathbb{Z}$ imply that there exists non-trivial gauge transformations (i.e., continuous maps $M\rightarrow G$ which are not homotopic to the trivial map)?</p> <p>If anyone would like to read it from the source, check the paragraph leading up to equation 1.4.</p> http://mathoverflow.net/questions/56148/wittens-qft-and-jones-poly-paper/56149#56149 Answer by Kelly Davis for Witten's QFT and Jones Poly paper Kelly Davis 2011-02-21T07:11:58Z 2011-02-22T09:08:45Z <p>First consider the case $M = S^3$. Generalizing, consider the connected sum of a generic M with a sphere $M = M \# S^3$</p> <p><strong>Edit</strong> Here's what I was thinking (Still not sure if it's all correct, but it seems closer to the spirit of Witten's paper than the obstruction arguments.) </p> <p>Consider a gauge transform $f': M \rightarrow G$. Also, consider a gauge transformation $g' : S^3 \rightarrow G$ not homotopic to the identity. Continuity allows us to change $f'$ to a map $f$ homotopic to $f'$ such that in a neighborhood $U$ of $p \in M$ the map $f$ maps to the identity of $G$. We can define a map $g$ to have similar properties in a neighborhood $V$ of $q \in S^3$. </p> <p>Do the connected sum around $p$ and $q$ and obtain $M \# S^3 = M$ as well as a gauge transform $h$ on $M \# S^3 = M$ obtained by joining $f$ and $g$. Now, <em>assume</em> $h$ is homotopic to the identity. </p> <p>The homotopy taking $h$ to the identity can be used to construct a homotopy of $g$ to the identity. (Here we use the fact that $\pi_2(G)$ is trivial to continue the homotopy over the ball removed from $S^3$.) </p> <p>But, no such homotopy of $g$ to the identity exists. Thus, $h$ is not homotopic to the identity. Hence, $\pi_3(G) = \mathbf{Z}$ implies there exist continuous maps $M \rightarrow G$ not homotopic to the identity.</p> http://mathoverflow.net/questions/56148/wittens-qft-and-jones-poly-paper/56179#56179 Answer by Konrad Waldorf for Witten's QFT and Jones Poly paper Konrad Waldorf 2011-02-21T14:21:15Z 2011-02-21T20:09:57Z <p>I think the important information is that $H^3(G,\mathbb{R}) \neq 0$. </p> <p>By the way, every $G$-bundle over $M$ is trivializable, under the conditions you have mentioned. That's why a gauge transformation can be regarded as a (smooth) map $g: M \to G$. </p> <p>Now you look at the behaviour of the Chern-Simons 3-form $CS(A)$ of a connection $A$ on $E$ under a gauge transformation $g$. The formula is $$CS(g^*A) = CS(A) + g^*H + \text{exact terms}.$$ where $H$ is the canonical 3-form of $G$ that represents a non-trivial element of $H^3(G,\mathbb{R})$. Now you can find a gauge transformation $g$ such that $g^*H$ is not exact. In that sense you have non-trivial gauge transformations. </p> <p>EDIT: The comment that every $G$-bundle is trivializable is only true if $G$ is additionally assumed to be simply-connected, sorry. So you either assume that (so does Witten) or you must see gauge transformations as maps $g:P \to G$, rather, and the Chern-Simons form $CS(A)$ as a form on $P$, not on $M$.</p> http://mathoverflow.net/questions/56148/wittens-qft-and-jones-poly-paper/56217#56217 Answer by Peter Woit for Witten's QFT and Jones Poly paper Peter Woit 2011-02-21T21:14:24Z 2011-02-21T21:14:24Z <p>As Konrad Waldorf noted, in this case G-bundles are trivializable (since $\pi_2(G)$ is trivial). So gauge transformations are just maps $$\phi:M\rightarrow G$$</p> <p>and these have a homotopy invariant that can be non-trivial, the degree of the map. One way to compute this is as $$\int_M \phi^*\omega_3$$</p> <p>where $\omega_3$ is a generator of $H^3(G)$. Or, as usual for a degree, just pick an element of G, and count points (with sign) in the inverse image.</p> http://mathoverflow.net/questions/56148/wittens-qft-and-jones-poly-paper/56232#56232 Answer by Paul for Witten's QFT and Jones Poly paper Paul 2011-02-22T00:26:28Z 2011-02-22T00:26:28Z <p>@kwl1026. Gauge transformations are sections of the Ad bundle $P\times_{Ad} g$ where $P\to M$ is the principal $G$ bundle; $g$ the lie algebra. When $G$ is abelian the adjoint action is trivial so, e.g. the $U(1)$ gauge group is always $Map(M,U(1))$ whether or not $P$ is trivial. Its homotopy classes are then $[M, U(1)]= H^1(M;Z)$, which is zero (for $M$ a closed 3-manifold) if and only if $M$ is a rational homology sphere.</p> <p>An elementary answer to your original question for $SU(2)=S^3$ is that obstruction theory shows that the primary obstruction gives an isomorphism $[M,S^3]\to H^3(M;Z)$. An induction using the fibration $SU(n)\to SU(n+1)\to S^{2n+1}$ and cellular approximation shows that $[M,SU(n)]=[M,SU(2)]$. Other tricks can get you there for other $G$. It is true that the differnence in Chern-Simons invariants (suitably normalized) coincides with this isomorphism (composed with $H^3(M;Z)\to Z$), as indcated by Konrad. For $SU(2)$ it also agrees with the degree, as mentioned by Peter.</p> <p>If $P$ is non-trivial you have to work a little harder, since you are asking what is the set of homotopy classes of sections of the fiber bundle $P\times_{Ad} g$. A useful reference is Donaldson's book on Floer homology.</p>
|
|
• ### IGCV$2$: Interleaved Structured Sparse Convolutional Neural Networks(1804.06202)
April 17, 2018 cs.CV
In this paper, we study the problem of designing efficient convolutional neural network architectures with the interest in eliminating the redundancy in convolution kernels. In addition to structured sparse kernels, low-rank kernels and the product of low-rank kernels, the product of structured sparse kernels, which is a framework for interpreting the recently-developed interleaved group convolutions (IGC) and its variants (e.g., Xception), has been attracting increasing interests. Motivated by the observation that the convolutions contained in a group convolution in IGC can be further decomposed in the same manner, we present a modularized building block, {IGCV$2$:} interleaved structured sparse convolutions. It generalizes interleaved group convolutions, which is composed of two structured sparse kernels, to the product of more structured sparse kernels, further eliminating the redundancy. We present the complementary condition and the balance condition to guide the design of structured sparse kernels, obtaining a balance among three aspects: model size, computation complexity and classification accuracy. Experimental results demonstrate the advantage on the balance among these three aspects compared to interleaved group convolutions and Xception, and competitive performance compared to other state-of-the-art architecture design methods.
• ### Matching Natural Language Sentences with Hierarchical Sentence Factorization(1803.00179)
March 1, 2018 cs.CL
Semantic matching of natural language sentences or identifying the relationship between two sentences is a core research problem underlying many natural language tasks. Depending on whether training data is available, prior research has proposed both unsupervised distance-based schemes and supervised deep learning schemes for sentence matching. However, previous approaches either omit or fail to fully utilize the ordered, hierarchical, and flexible structures of language objects, as well as the interactions between them. In this paper, we propose Hierarchical Sentence Factorization---a technique to factorize a sentence into a hierarchical representation, with the components at each different scale reordered into a "predicate-argument" form. The proposed sentence factorization technique leads to the invention of: 1) a new unsupervised distance metric which calculates the semantic distance between a pair of text snippets by solving a penalized optimal transport problem while preserving the logical relationship of words in the reordered sentences, and 2) new multi-scale deep learning models for supervised semantic training, based on factorized sentence hierarchies. We apply our techniques to text-pair similarity estimation and text-pair relationship classification tasks, based on multiple datasets such as STSbenchmark, the Microsoft Research paraphrase identification (MSRP) dataset, the SICK dataset, etc. Extensive experiments show that the proposed hierarchical sentence factorization can be used to significantly improve the performance of existing unsupervised distance-based metrics as well as multiple supervised deep learning models based on the convolutional neural network (CNN) and long short-term memory (LSTM).
• ### Muliti-scale regularity of axisymmetric Navier-Stokes equations(1802.08956)
Feb. 25, 2018 math.AP
By applying the delicate \textit{a priori} estimates for the equations of $(\Phi,\Gamma)$, which is introduced in the previous work, we obtain some multi-scale regularity criteria of the swirl component $u^{\theta}$ for the 3D axisymmetric Navier-Stokes equations. In particularly, the solution $\mathbf{u}$ can be continued beyond the time $T$, provided that $u^{\theta}$ satiesfies $$u^{\theta} \in L^{p}_{T}L^{q_{v}}_{v}L^{q_{h},w}_{h},~~\frac{2}{p}+\frac{1}{q_{v}}+\frac{2}{q_{h}}\leq 1, ~2<q_{h}\leq\infty,~\frac{1}{q_{v}}+\frac{2}{q_{h}}<1.$$
• ### Matching Long Text Documents via Graph Convolutional Networks(1802.07459)
Feb. 21, 2018 cs.CL, cs.IR
Identifying the relationship between two text objects is a core research problem underlying many natural language processing tasks. A wide range of deep learning schemes have been proposed for text matching, mainly focusing on sentence matching, question answering or query document matching. We point out that existing approaches do not perform well at matching long documents, which is critical, for example, to AI-based news article understanding and event or story formation. The reason is that these methods either omit or fail to fully utilize complicated semantic structures in long documents. In this paper, we propose a graph approach to text matching, especially targeting long document matching, such as identifying whether two news articles report the same event in the real world, possibly with different narratives. We propose the Concept Interaction Graph to yield a graph representation for a document, with vertices representing different concepts, each being one or a group of coherent keywords in the document, and with edges representing the interactions between different concepts, connected by sentences in the document. Based on the graph representation of document pairs, we further propose a Siamese Encoded Graph Convolutional Network that learns vertex representations through a Siamese neural network and aggregates the vertex features though Graph Convolutional Networks to generate the matching result. Extensive evaluation of the proposed approach based on two labeled news article datasets created at Tencent for its intelligent news products show that the proposed graph approach to long document matching significantly outperforms a wide range of state-of-the-art methods.
• ### Magnetic Field Driven Nodal Topological Superconductivity in Monolayer Transition Metal Dichalcogenides(1604.02867)
Recently, Ising superconductors which possess in-plane upper critical fields much larger than the Pauli limit field are under intense experimental study. Many monolayer or few layer transition metal dichalcogenides are shown to be Ising superconductors. In this work, we show that in a wide range of experimentally accessible regimes where the in-plane magnetic field is higher than the Pauli limit field but lower than $H_{c2}$, a 2H-structure monolayer NbSe$_2$ or simiarly TaS$_2$ becomes a nodal topological superconductor. The bulk nodal points appear on the $\Gamma- M$ lines of the Brillouin zone where the Ising SOC vanishes. The nodal points are connected by Majorana flat bands, similar to the Weyl points being connected by surface Fermi arcs in Weyl semimetals. The Majorana flat bands are associated with a large number of zero energy Majorana fermion edge modes which induce spin-triplet Cooper pairs. This work demonstrates an experimentally feasible way to realise Majorana fermions in nodal topological superconductor, without any fining tuning of experimental parameters.
• ### A concatenating framework of shortcut convolutional neural networks(1710.00974)
Oct. 3, 2017 cs.CV
It is well accepted that convolutional neural networks play an important role in learning excellent features for image classification and recognition. However, in tradition they only allow adjacent layers connected, limiting integration of multi-scale information. To further improve their performance, we present a concatenating framework of shortcut convolutional neural networks. This framework can concatenate multi-scale features by shortcut connections to the fully-connected layer that is directly fed to the output layer. We do a large number of experiments to investigate performance of the shortcut convolutional neural networks on many benchmark visual datasets for different tasks. The datasets include AR, FERET, FaceScrub, CelebA for gender classification, CUReT for texture classification, MNIST for digit recognition, and CIFAR-10 for object recognition. Experimental results show that the shortcut convolutional neural networks can achieve better results than the traditional ones on these tasks, with more stability in different settings of pooling schemes, activation functions, optimizations, initializations, kernel numbers and kernel sizes.
• ### Isolation and Characterization of Few-layer Manganese Thiophosphite(1708.05178)
Sept. 8, 2017 cond-mat.mes-hall
This work reports an experimental study on an antiferromagnetic honeycomb lattice of MnPS$_3$ that couples the valley degree of freedom to a macroscopic antiferromagnetic order. The crystal structure of MnPS$_3$ is identified by high resolution scanning transmission electron microscopy. Layer dependent angle resolved polarized Raman fingerprints of the MnPS$_3$ crystal are obtained and the Raman peak at 383 cm$^{-1}$ exhibits 100% polarity. Temperature dependences of anisotropic magnetic susceptibility of MnPS$_3$ crystal are measured in superconducting quantum interference device. Magnetic parameters like effective magnetic moment, and exchange interaction are extracted from the mean field approximation mode. Ambipolar electronic transport channels in MnPS$_3$ are realized by the liquid gating technique. The conducting channel of MnPS$_3$ offers a unique platform for exploring the spin/valleytronics and magnetic orders in 2D limitation.
• ### Interleaved Group Convolutions for Deep Neural Networks(1707.02725)
July 18, 2017 cs.CV
In this paper, we present a simple and modularized neural network architecture, named interleaved group convolutional neural networks (IGCNets). The main point lies in a novel building block, a pair of two successive interleaved group convolutions: primary group convolution and secondary group convolution. The two group convolutions are complementary: (i) the convolution on each partition in primary group convolution is a spatial convolution, while on each partition in secondary group convolution, the convolution is a point-wise convolution; (ii) the channels in the same secondary partition come from different primary partitions. We discuss one representative advantage: Wider than a regular convolution with the number of parameters and the computation complexity preserved. We also show that regular convolutions, group convolution with summation fusion, and the Xception block are special cases of interleaved group convolutions. Empirical results over standard benchmarks, CIFAR-$10$, CIFAR-$100$, SVHN and ImageNet demonstrate that our networks are more efficient in using parameters and computation complexity with similar or higher accuracy.
• ### A Survey on Learning to Hash(1606.00185)
April 22, 2017 cs.CV
Nearest neighbor search is a problem of finding the data points from the database such that the distances from them to the query point are the smallest. Learning to hash is one of the major solutions to this problem and has been widely studied recently. In this paper, we present a comprehensive survey of the learning to hash algorithms, categorize them according to the manners of preserving the similarities into: pairwise similarity preserving, multiwise similarity preserving, implicit similarity preserving, as well as quantization, and discuss their relations. We separate quantization from pairwise similarity preserving as the objective function is very different though quantization, as we show, can be derived from preserving the pairwise similarities. In addition, we present the evaluation protocols, and the general performance analysis, and point out that the quantization algorithms perform superiorly in terms of search accuracy, search time cost, and space cost. Finally, we introduce a few emerging topics.
• ### Preparation of hierarchical C@MoS2@C sandwiched hollow spheres for Lithium ion batteries(1701.05887)
Jan. 20, 2017 cond-mat.mtrl-sci
Hierarchical C@MoS2@C hollow spheres with the active MoS2 nanosheets being sandwiched by carbon layers have been produced by means of a modified template method. The process applies polydopamine (PDA) layers which inhibit morphology change of the template thereby enforcing the hollow microsphere structure. In addition, PDA forms complexes with the Mo precursor, leading to an in-situ growth of MoS2 on its surface and preventing the nanosheets from agglomeration. It also supplies the carbon that finally sandwiches the 100-150 nm thin MoS2 spheres. The resulting hierarchically structured material provides a stable microstructure where carbon layers strongly linked to MoS2 offer efficient pathways for electron and ion transfer, and concomitantly buffer the volume changes inevitably appearing during the charge-discharge process. Carbon-sandwiched MoS2-based electrodes exhibit high specific capacity of approximately 900 mA h g-1 after 50 cycles at 0.1 C, excellent cycling stability up to 200 cycles, and superior rate performance. The versatile synthesis method reported here offers a general route to design hollow sandwich structures with a variety of different active materials.
• ### Charge Density Wave Phase Transition on the Surface of Electrostatically Doped Multilayer Graphene(1610.07267)
Oct. 24, 2016 cond-mat.mes-hall
We demonstrate that charge density wave (CDW) phase transition occurs on the surface of electronically doped multilayer graphene when the Fermi level approaches the M points (also known as van Hove singularities where the density of states diverge) in the Brillouin zone of graphene band structure. The occurrence of such CDW phase transitions are supported by both the electrical transport measurement and optical measurements in electrostatically doped multilayer graphene. The CDW transition is accompanied with the sudden change of graphene channel resistance at T$_m$= 100K, as well as the splitting of Raman G peak (1580 cm$^{-1}$). The splitting of Raman G peak indicats the lifting of in-plane optical phonon branch degeneracy and the non-degenerate phonon branches are correlated to the lattice reconstructions of graphene -- the CDW phase transition.
• ### Global solutions to the isentropic compressible Navier-Stokes equations with a class of large initial data(1608.06447)
Aug. 23, 2016 math.AP
In this paper, we consider the global well-posedness problem of the isentropic compressible Navier-Stokes equations in the whole space $\R^N$ with $N\ge2$. In order to better reflect the characteristics of the dispersion equation, we make full use of the role of the frequency on the integrability and regularity of the solution, and prove that the isentropic compressible Navier-Stokes equations admit global solutions when the initial data are close to a stable equilibrium in the sense of suitable hybrid Besov norm. As a consequence, the initial velocity with arbitrary $\dot{B}^{\fr{N}{2}-1}_{2,1}$ norm of potential part $\Pe^\bot u_0$ and large highly oscillating are allowed in our results. The proof relies heavily on the dispersive estimates for the system of acoustics, and a careful study of the nonlinear terms.
• ### Deeply-Fused Nets(1605.07716)
May 25, 2016 cs.CV
In this paper, we present a novel deep learning approach, deeply-fused nets. The central idea of our approach is deep fusion, i.e., combine the intermediate representations of base networks, where the fused output serves as the input of the remaining part of each base network, and perform such combinations deeply over several intermediate representations. The resulting deeply fused net enjoys several benefits. First, it is able to learn multi-scale representations as it enjoys the benefits of more base networks, which could form the same fused network, other than the initial group of base networks. Second, in our suggested fused net formed by one deep and one shallow base networks, the flows of the information from the earlier intermediate layer of the deep base network to the output and from the input to the later intermediate layer of the deep base network are both improved. Last, the deep and shallow base networks are jointly learnt and can benefit from each other. More interestingly, the essential depth of a fused net composed from a deep base network and a shallow base network is reduced because the fused net could be composed from a less deep base network, and thus training the fused net is less difficult than training the initial deep base network. Empirical results demonstrate that our approach achieves superior performance over two closely-related methods, ResNet and Highway, and competitive performance compared to the state-of-the-arts.
• ### A unified approach to self-normalized block sampling(1512.00820)
March 20, 2016 math.ST, stat.TH
The inference procedure for the mean of a stationary time series is usually quite different under various model assumptions because the partial sum process behaves differently depending on whether the time series is short or long-range dependent, or whether it has a light or heavy-tailed marginal distribution. In the current paper, we develop an asymptotic theory for the self-normalized block sampling, and prove that the corresponding block sampling method can provide a unified inference approach for the aforementioned different situations in the sense that it does not require the {\em a priori} estimation of auxiliary parameters. Monte Carlo simulations are presented to illustrate its finite-sample performance. The R function implementing the method is available from the authors.
• ### Global axisymmetric solutions of 3D inhomogeneous incompressible Navier-Stokes Systems with nonzero swirl(1512.01051)
Dec. 3, 2015 math.AP
In this paper, we investigate the global well-posedness for the 3-D inhomogeneous incompressible Navier-Stokes system with the axisymmetric initial data. We prove the global well-posedness provided that $$\|\frac{a_{0}}{r}\|_{\infty} \textrm{ and } \|u_{0}^{\theta}\|_{3} \textrm{ are sufficiently small}.$$ Furthermore, if $\mathbf{u}_0\in L^1$ and $ru^\theta_0\in L^1\cap L^2$, we have \begin{equation*} \|u^{\theta}(t)\|_{2}^{2}+\langle t\rangle \|\nabla (u^{\theta}\mathbf{e}_{\theta})(t)\|_{2}^{2}+t\langle t\rangle(\|u_{t}^{\theta}(t)\|_{2}^{2}+\|\Delta(u^{\theta}\mathbf{e}_{\theta})(t)\|_{2}^{2}) \leq C \langle t\rangle^{-\frac{5}{2}},\ \forall\ t>0. \end{equation*}
• ### One-dimensional sawtooth and zigzag lattices for ultracold atoms(1510.02015)
We describe tunable optical sawtooth and zigzag lattices for ultracold atoms. Making use of the superlattice generated by commensurate wavelengths of light beams, tunable geometries including zigzag and sawtooth configurations can be realised. We provide an experimentally feasible method to fully control inter- ($t$) and intra- ($t'$) unit-cell tunnelling in zigzag and sawtooth lattices. We analyse the conversion of the lattice geometry from zigzag to sawtooth, and show that a nearly flat band is attainable in the sawtooth configuration by means of tuning the lattice parameters. The bandwidth of the first excited band can be reduced up to 2$\%$ of the ground bandwidth for a wide range of lattice setting. A nearly flat band available in a tunable sawtooth lattice would offer a versatile platform for the study of interaction-driven quantum many-body states with ultracold atoms.
• ### Regularity of 3D axisymmetric Navier-Stokes equations(1505.00905)
May 5, 2015 math.AP
In this paper, we study the three-dimensional axisymmetric Navier-Stokes system with nonzero swirl. By establishing a new key inequality for the pair $(\frac{\omega^{r}}{r},\frac{\omega^{\theta}}{r})$, we get several Prodi-Serrin type regularity criteria based on the angular velocity, $u^\theta$. Moreover, we obtain the global well-posedness result if the initial angular velocity $u_{0}^{\theta}$ is appropriate small in the critical space $L^{3}(\R^{3})$. Furthermore, we also get several Prodi-Serrin type regularity criteria based on one component of the solutions, say $\omega^3$ or $u^3$.
• ### Time-varying nonlinear regression models: Nonparametric estimation and model selection(1503.05289)
March 18, 2015 math.ST, stat.TH
This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this general class of models, an important issue in practice is to address the necessity of modeling the regression function as nonlinear and time-varying. To tackle this, we propose an information criterion and prove its selection consistency property. The results are applied to the U.S. Treasury interest rate data.
• ### Latent Feature Based FM Model For Rating Prediction(1410.8034)
Oct. 29, 2014 cs.LG, cs.IR, stat.ML
Rating Prediction is a basic problem in Recommender System, and one of the most widely used method is Factorization Machines(FM). However, traditional matrix factorization methods fail to utilize the benefit of implicit feedback, which has been proved to be important in Rating Prediction problem. In this work, we consider a specific situation, movie rating prediction, where we assume that watching history has a big influence on his/her rating behavior on an item. We introduce two models, Latent Dirichlet Allocation(LDA) and word2vec, both of which perform state-of-the-art results in training latent features. Based on that, we propose two feature based models. One is the Topic-based FM Model which provides the implicit feedback to the matrix factorization. The other is the Vector-based FM Model which expresses the order info of watching history. Empirical results on three datasets demonstrate that our method performs better than the baseline model and confirm that Vector-based FM Model usually works better as it contains the order info.
• ### Global well-posedness to the 3-D incompressible inhomogeneous Navier-Stokes equations with a class of large velocity(1410.6300)
Oct. 23, 2014 math.AP
In this article, we consider the global well-posedness to the 3-D incompressible inhomogeneous Navier-Stokes equations with a class of large velocity. More precisely, assuming $a_0 \in \dot{B}_{q,1}^{\frac{3}{q}}(\mathbb{R}^3)$ and $u_0=(u_0^h,u_0^3)\in \dot{B}_{p,1}^{-1+\frac{3}{p}}(\mathbb{R}^3)$ for $p,q \in (1,6)$ with $\sup(\frac{1}{p}, \frac{1}{q})\leq\frac{1}{3}+ \inf (\frac{1}{p}, \frac{1}{q})$, we prove that if $C\|a_0\|_{\dot{B}_{q,1}^{\frac{3}{q}}}^{\alpha}(\|u_0^3\|_{\dot{B}_{p,1}^{-1+\frac{3}{p}}}/{\mu}+1)\leq1$, $\frac{C}{\mu}(\|u_0^h\|_{\dot{B}_{p,1}^{-1+\frac{3}{p}}}+\|u_0^3\|_{\dot{B}_{p,1}^{-1+\frac{3}{p}}}^{1-\alpha}\|u_0^h\|_{\dot{B}_{p,1}^{-1+\frac{3}{p}}}^{\alpha})\leq 1$, then the system has a unique global solution $a\in\widetilde{\mathcal{C}}([0,\infty);\dot{B}_{q,1}^{\frac{3}{q}}(\mathbb{R}^3))$, $u\in\widetilde{\mathcal{C}}([0,\infty);\dot{B}_{p,1}^{-1+\frac{3}{p}}(\mathbb{R}^3))\cap L^1(\mathbb{R}^+;\dot{B}_{p,1}^{1+\frac{3}{p}}(\mathbb{R}^3))$. It improves the recent result of M. Paicu, P. Zhang (J. Funct. Anal. 262 (2012) 3556-3584), where the exponent form of the initial smallness condition is replaced by a polynomial form.
• ### An elementary proof of the global existence and uniqueness theorem to 2-D incompressible non-resistive MHD system(1404.5681)
Oct. 23, 2014 math.AP
In this paper, we provide a much simplified proof of the main result in [Lin, Xu, Zhang, arXiv:1302.5877] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 2D incompressible viscous and non-resistive MHD system under the assumption that the initial data are close to some equilibrium states. Beside the classical energy method, the interpolating inequalities and the algebraic structure of the equations coming from the incompressibility of the fluid are crucial in our arguments. We combine the energy estimates with the $L^\infty$ estimates for time slices to deduce the key $L^1$ in time estimates. The latter is responsible for the global in time existence.
• ### Global Small Solutions to a Complex Fluid Model in 3D(1403.1085)
March 5, 2014 math.AP
In this paper, we provide a much simplified proof of the main result in [Lin and Zhang, Comm. Pure Appl. Math.,67(2014), 531--580] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 3D incompressible complex fluid model under the assumption that the initial data are close to some equilibrium states. Beside the classical energy method, the interpolating inequalities and the algebraic structure of the equations coming from the incompressibility of the fluid are crucial in our arguments. We combine the energy estimates with the $L^\infty$ estimates for time slices to deduce the key $L^1$ in time estimates. The latter is responsible for the global in time existence.
• ### Block Sampling under Strong Dependence(1312.5807)
Dec. 20, 2013 math.ST, stat.TH, q-fin.ST
The paper considers the block sampling method for long-range dependent processes. Our theory generalizes earlier ones by Hall, Jing and Lahiri (1998) on functionals of Gaussian processes and Nordman and Lahiri (2005) on linear processes. In particular, we allow nonlinear transforms of linear processes. Under suitable conditions on physical dependence measures, we prove the validity of the block sampling method. The problem of estimating the self-similar index is also studied.
• ### Global existence in critical spaces for density-dependent incompressible viscoelastic fluids(1210.5676)
Oct. 21, 2012 math.AP
In this paper we consider the local and global well-posedness to the density-dependent incompressible viscoelastic fluids. We first study some linear models associated to the incompressible viscoelastic system. Then we approximate the system by a sequence of ordinary differential equations, by means of the Friedrichs method. Some uniform estimates for those solutions will be obtained. Using compactness arguments, we will get the local existence up to extracting a subsequence by means of Ascoli's lemma. With the help of small data conditions and hybird Besov spaces, we finally derive the global existence.
• ### Inference of time-varying regression models(1208.3552)
Aug. 17, 2012 math.ST, stat.TH
We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a $n^{1/2}$-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an information criterion that can consistently select the true set of significant predictors. Our method is applied to autoregressive models with time-varying coefficients. Simulation results and a real data application are provided.
|
|
During runtime, preCICE writes different output files. On this page, we give an overview of these files and their content.
If the participant’s name is MySolver, preCICE creates the following files:
## precice-MySolver-iterations.log
Information per time window with number of coupling iterations etc. (only for implicit coupling). In case you use a quasi-Newton acceleration, this file also contains information on the state of the quasi-Newton system.
An example file:
TimeWindow TotalIterations Iterations Convergence QNColumns DeletedQNColumns DroppedQNColumns
1 5 5 1 0 0 0
2 10 5 1 0 0 0
3 15 5 1 0 0 0
4 20 5 1 0 0 0
5 24 4 1 0 0 0
6 28 4 1 0 0 0
7 32 4 1 0 0 0
...
• TimeWindow is the time window counter.
• TotalIterations is the total (summed up) number of coupling iterations.
• Iterations is the number of iterations preCICE used in each time window.
• Convergence indicates whether the coupling converged (1) or not (0) in each time window.
• QNColumns gives the amount of columns in the tall-and-skinny matrices V and W after convergence.
• DeletedQNColumns gives the amount of columns that were filtered out during this time window (due to a QR filter). In this example no columns were filtered out.
• DroppedQNColumns gives the amount of columns that went out of scope during this time window (due to max-iterations or time-windows-reused). Here, for example, 5 columns went out of scope during the 6th time window.
## precice-MySolver-convergence.log
Information per iteration with current residuals (only for second participant in an implicit coupling).
An example file:
TimeWindow Iteration ResRel(Temperature) ResRel(Heat-Flux)
1 1 1.00000000e+00 1.00000000e+00
1 2 2.36081866e-03 4.61532554e-01
1 3 1.76770050e-03 2.20718535e-03
1 4 8.24839318e-06 4.83731693e-04
1 5 1.38649284e-06 3.03987119e-05
2 1 2.02680329e-03 1.14463674e+00
2 2 1.10152875e-03 4.53255279e-01
...
• TimeWindow is the time window counter.
• Iteration is the coupling iteration counter within each time window. So, in the first time window, 6 iterations were necessary to converge, in the second time window 3.
• And then two convergence measure are defined in the example. Two relative ones – hence the ...Rel(...). The two columns ResRel(Temperature) and RelRel(Force) give the relative residual for temperature and heat flux, respectively, at the start of each iteration.
## precice-MySolver-events.json
Recorded events with timestamps. See page on performance analysis.
## precice-MySolver-events-summary.log
Summary of all events timings. See page on performance analysis.
## precice-postProcessingInfo.log
Advanced information on the numerical performance of the Quasi-Newton coupling (if used and enabled)
In preCICE v1.3.0 and earlier, instead of precice-MySolver-events.json, two performance output files were used: precice-MySolver-events.log and precice-MySolver-eventTimings.log.
In preCICE v1.2.0 and earlier, slightly different names were used: iterations-MySolver.txt,convergence-MySolver.txt, Events-MySolver.log,EventTimings-MySolver.log, and postProcessingInfo.txt.
|
|
# Why does Hooke's law not work here?
1. Oct 20, 2015
### MightyDogg
1. The problem statement, all variables and given/known data
1. A 1200-kg car moving on a horizontal surface has speed v = 85 kmh when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?
2. Relevant equations
F=-kx
KE=(1/2)mv^2
PE(spring)=(1/2)kx^2
3. The attempt at a solution
I tried to find the average acceleration to slow the car from 85kmh to 0. I used the formula vfinal^2=vinitial^2 + 2ax, where velocity initial is 23.6m/s and x is 2.2m. This gave me an acceleration of -126m/s^2. Then I multiplied the acceleration by the mass to find the average force. This gave me -151200N. Then, I plugged that into Hooke's law with x being 2.2m. This gave the spring constant being 69000N/m.
However, I am supposed to use the conservation of energy principle where KE=PE. This gives the correct answer. Why does my method not work?
2. Oct 20, 2015
### Ray Vickson
I does not work because the acceleration is not constant. Hook's Law works, but not your expression $v_f^2 = v_i^2 + 2ax$.
Last edited: Oct 20, 2015
3. Oct 20, 2015
### Mister T
By Hooke's law I assume you mean $F=kx$ where $F$ is the magnitude of the force and $x$ is the distance?
In that formula $F$ is not the average force. It's the magnitude of the force when the spring is stretched (or compressed) a distance $x$.
If the force were constant, that would work, but the force is not constant. You could integrate the force, or use energy concepts.
4. Oct 20, 2015
### MightyDogg
Oh, okay it makes sense now. Thank you both very much.
|
|
## The (Math) Problem with Pentagons — Quanta Magazine
My latest column for Quanta Magazine is about the recent classification of pentagonal tilings of the plane. Tilings involving triangles, quadrilaterals, and more have been well-understood for over a thousand years, but it wasn’t until 2017 that the question of which pentagons tile the plane was completely settled.
Here’s an excerpt.
People have been studying how to fit shapes together to make toys, floors, walls and art — and to understand the mathematics behind such patterns — for thousands of years. But it was only this year that we finally settled the question of how five-sided polygons “tile the plane.” Why did pentagons pose such a big problem for so long?
In my column I explore some of the reasons that certain kinds of pentagons might, or might not, tile the plane. It’s a fun exercise in elementary geometry, and a glimpse into a complex world of geometric relationships.
## 12/07/2017 — Happy Permutation Day!
Today we celebrate a Permutation Day! I call days like today permutation days because the digits of the day and the month can be rearranged to form the year.
Celebrate Permutation Day by mixing things up! Try doing things in a different order today. Just remember, for some operations, order definitely matters!
## Investigating the Math Behind Biased Maps
My latest piece for the New York Times Learning Network gets students investigating the mathematics of gerrymandering. Through applying geometry, proportionality, and the efficiency gap, students explore the notion of a “workable standard” for identifying and evaluating biased electoral maps.
Here is an excerpt:
Math lies at the heart of gerrymandering, in which the shapes of voting districts and distributions of voters are manipulated to preserve and expand political power.
The strategy of gerrymandering is not new… However, new, sophisticated mathematical and computer mapping tools have made gerrymandering an even more powerful way to tilt the playing field. In many states, where the majority party has the authority to rewrite the electoral map, legislators essentially have the power to choose their voters — to create districts in any shape or size that will weaken their opponents and increase their dominance.
In this lesson, we help students uncover the mathematics behind these biased electoral maps. And, we help them apply their mathematical knowledge to identify and address the problem.
In fact, the questions students will work through are similar to those the Supreme Court is now considering on whether gerrymandering can ever be declared unconstitutional.
The article was co-authored with Michael Gonchar of the NYT Learning Network, and is freely available here.
Related Posts
## Math Photo: Spiky Symmetry
These cacti caught my. I can see both a dodecagon and a star in the 12-fold symmetry of the cactus in front. And to my surprise, the cactus behind it has thirteen sections!
I wonder about the range, and deviation, of the number of sections of these cacti. And what are the biological principles that govern these mathematical characteristics?
## Regents Recap — August 2017: Yes, You Can Work on Both Sides of an Identity
In a controversial post last year, I argued that it’s perfectly acceptable to work on both sides of an equation in proving an algebraic identity. While it’s common to tell students “You can’t cross the equal sign” in this situation, doing so is mathematically legitimate as long as the new equation is true under exactly the same circumstances as the original.
For example, when proving an algebraic identity, multiplying both sides of an equation by 2 is permissible, because = y and 2x 2y are true under exactly the same conditions on x and y. Squaring both sides of an equation however, is not, since
$x^2 = y^2$
can be true under conditions that make y false, say, when x and y-2.
The post in question, “Algebra is Hard”, was a response to a June 2016 Regents scoring guide that deducted a point from a student who, in proving an algebraic identity, multiplied both sides of the equation by a non-zero quantity. The student was penalized for “not manipulating expressions independently in an algebraic proof“, a vague and meaningless criticism.
“Algebra is Hard” received quite a bit of attention, and while many agreed with me, I was genuinely surprised at how many readers disagreed. Which was terrific! Of course my argument makes perfect sense to me, but it was great to have so many constructive conversations with teachers and mathematicians who saw things differently.
But my argument recently received support from the most unlikely of sources: another Regents exam.
Take a look at this exemplar full-credit student response to an algebraic identity on the August 2017 Algebra 2 exam.
Notice that the student works on both sides of the equation and subtracts the same quantity from both sides. Even though the student did not manipulate expressions independently in an algebraic proof, full credit was awarded.
The note here about domain restrictions is an amusing touch, given that it was the explicit domain restriction in the problem from 2016 that ensured the student wasn’t doing something impermissible (namely, multiplying both sides of an equation by 0).
So in 2016 this work gets half credit, and in 2017 this work gets full credit.
While it’s nice to see mathematically valid work finally receiving full credit on this type of problem, it’s no consolation to the many students who lost points for doing the same thing the year before. What’s especially frustrating is that, as usual, those responsible for creating these exams will admit no error nor accept any responsibility for it.
Be sure to read “Algebra is Hard” (and some of the 40+ comments!) for more of the backstory on this problem.
Related Posts
|
|
# A Tri-Factorable Positive integer
Found this problem in my SAT book the other day and wanted to see if anyone could help me out.
A positive integer is said to be "tri-factorable" if it is the product of three consecutive integers. How many positive integers less than 1,000 are tri-factorable?
-
You need to find the biggest tri-factorable integer less than $1000$ (recall that a tri-factorable integer can be written $n(n+1)(n+2)$ and this is roughly equal to $n^3$). – Joel Cohen Aug 6 '12 at 20:32
For numbers of this size, you can make a list: $1\times 2\times 3=6, 2\times 3 \times 4= \ldots$ and see where it gets larger than $1000$. A spreadsheet makes it quite easy.
If the upper limit were enough higher, you could let $n$ be the middle number. Then your trifactorable number is $(n-1)n(n+1)=n^3-n$ You can take the cube root of the upper limit and check whether you need one more.
-
Awesome, thanks everyone! – l34p3r Aug 7 '12 at 7:07
$1,000= 10*10*10<10*11*12$ so in the product $n*(n+1)*(n+2)$, $n$ must be less then $10.$
And as an extra hint $9 \times 10 \times 11 = 990 \lt 1000$ – Henry Aug 6 '12 at 21:03
|
|
# Existence of certain graph gadget related to coloring odd hole free graph
Crossposted from MO.
Wondering about the existence of graph gadget related to coloring (or 3-coloring) odd hole free graphs.
Let $G$ be simple $k$-chromatic connected graph with two vertices $u,v$.
Is it possible $G$ to satisfy:
1. All induced $uv$ paths have odd order (even number of edges).
2. In all proper $k$ colorings, $u$ and $v$ have distinct colors
3. (optional) $G$ doesn't contain induced $C_{2n+1}$ for $n>1$
If this is possible, there is reduction $F$ to odd hole free $F'$.
Replace an edge $u'v'$ by the gadget $G$ where $u'=u,v'=v$ and the rest vertices of $G$ are new vertices.
According to graphclasses coloring odd hole free is NP hard and 3-coloring is unknown.
Computer search suggest small gadgets don't exist (modulo errors).
One can extract an argument that this cannot work from the paper found by OP in the MO thread. Suppose $G=(V,E)$ is as required, and $c:V\to[k]$ is a $k$-coloring. By the assumption, $c(u)\neq c(v)$. Consider the (bipartite) subgraph $H$ induced by $\{x\in V\ |\ c(x)\in\{c(u),c(v)\}\}$.
If $u$ and $v$ are in the same connected component of $H$, pick any shortest path in $H$ between $u$ and $v$; it is an induced path in $G$, with colors alternating between $c(u),c(v)$, and must have an odd number of edges because the colors at its ends differ. This contradicts the assumption.
So $u,v$ are in different connected components; but then one can toggle the coloring of one of these components to obtain a coloring $c'$ with $c'(u)=c'(v)$, contradiction.
• Are you saying that if $u,v$ is an even pair, in all colorings $c(u)=c(v)$? I believe this follows from preserving the chromatic number when merging $u,v$. – joro Jul 14 '15 at 6:06
|
|
# Drag¶
class Drag(duration, amp, sigma, beta, name=None, limit_amplitude=None)[Quellcode]
Bases: qiskit.pulse.library.parametric_pulses.ParametricPulse
The Derivative Removal by Adiabatic Gate (DRAG) pulse is a standard Gaussian pulse with an additional Gaussian derivative component. It is designed to reduce the frequency spectrum of a normal gaussian pulse near the $$|1\rangle$$ - $$|2\rangle$$ transition, reducing the chance of leakage to the $$|2\rangle$$ state.
$f(x) = Gaussian + 1j * beta * d/dx [Gaussian] = Gaussian + 1j * beta * (-(x - duration/2) / sigma^2) [Gaussian]$
where ‚Gaussian‘ is:
$Gaussian(x, amp, sigma) = amp * exp( -(1/2) * (x - duration/2)^2 / sigma^2 )$
References
Initialize the drag pulse.
Parameter
• duration (Union[int, ParameterExpression]) – Pulse length in terms of the the sampling period dt.
• amp (Union[complex, ParameterExpression]) – The amplitude of the Drag envelope.
• sigma (Union[float, ParameterExpression]) – A measure of how wide or narrow the Gaussian peak is; described mathematically in the class docstring.
• beta (Union[float, ParameterExpression]) – The correction amplitude.
• name (Optional[str]) – Display name for this pulse envelope.
• limit_amplitude (Optional[bool]) – If True, then limit the amplitude of the waveform to 1. The default is True and the amplitude is constrained to 1.
Methods
draw Plot the interpolated envelope of pulse. get_waveform Return a Waveform with samples filled according to the formula that the pulse represents and the parameter values it contains. is_parameterized Return True iff the instruction is parameterized. validate_parameters Validate parameters.
Attributes
amp
The Gaussian amplitude.
Rückgabetyp
Union[complex, ParameterExpression]
beta
The weighing factor for the Gaussian derivative component of the waveform.
Rückgabetyp
Union[float, ParameterExpression]
id
Unique identifier for this pulse.
Rückgabetyp
int
limit_amplitude = True
parameters
Rückgabetyp
Dict[str, Any]
sigma
The Gaussian standard deviation of the pulse width.
Rückgabetyp
Union[float, ParameterExpression]
|
|
# Start a new discussion
## Not signed in
Want to take part in these discussions? Sign in if you have an account, or apply for one below
## Site Tag Cloud
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
• CommentRowNumber1.
• CommentAuthorDmitri Pavlov
• CommentTimeJul 17th 2022
Deleted this: vanishes (or at heast has non-maximal rank).
Added this: has rank strictly less than the dimension of $Y$.
• CommentRowNumber2.
• CommentAuthorDmitri Pavlov
• CommentTimeJul 17th 2022
The $f$-image of a critical point is known as a critical value. A point in $Y$ that is not a critical value is known as a regular value.
|
|
# What is the difference between a matrix and a tuple of vectors?
Why do we need the term matrix? Why can't we just use vectors to define everything we need?
I understand we need the terms object, set, group, field, vector, and vector space.
I don't understand why we need the term "matrix".
Is it just shorthand? Similar to the term "Ket" used in Dirac Notation for Quantum Mechanics? There a "Bra" is a co-vector and a "Ket" is a vector.
BTW, a $$n \times 1$$ matrix is a vector.
• You could define an $m \times n$ matrix to be an $n$-tuple of $m$-dimensional vectors, if you'd like. When you write down a matrix on paper, you'd probably find it convenient to write the numbers as a rectangular array of numbers. This would be quite similar to how things are usually done. By the way, matrices exist in order to describe linear transformations. Dec 27, 2019 at 4:46
• So there is no difference between a matrix and tuple of vectors? I am okay with the term linear transformation (it actually describes what it is doing), but matrix seems so arbitrary and unneeded. Dec 27, 2019 at 4:55
• A linear transformation is not a matrix. A matrix is a rectangular array of numbers, a linear transformation is a function between two vector spaces.
– user856
Dec 27, 2019 at 5:01
• Furthermore, a vector is an element of a vector space, not necessarily a tuple of numbers. So while every matrix can be interpreted as a tuple of vectors (in at least two ways), not every tuple of vectors can be interpreted as a matrix.
– user856
Dec 27, 2019 at 5:04
• Sorry, a linear transformation could be a matrix. What is the difference between a "rectangular array of numbers" and a n-tuple of m-dimensional vectors? Dec 27, 2019 at 5:04
A vector is an element of a vector space. Associated with each vector space is a field, and elements of the field are called scalars. If $$V$$ is a vector space, and $$F$$ is the associated field of scalars, then we say that "$$V$$ is a vector space over $$F$$".
For example, $$\mathbb{R}^3$$ is a vector space over the field $$\mathbb{R}$$. In the context of this example, elements of $$\mathbb{R}^3$$ are called vectors, and elements of $$\mathbb{R}$$ are called scalars.
An $$m\times n$$ matrix is an $$m\times n$$ array of scalars. Let $$F$$ be a field, and let $$F^{m\times n}$$ be the set of all $$m\times n$$ matrices with coefficients in $$F$$. Since there is a nice way of adding matrices together and a nice way of multiplying a matrix by a scalar, we notice that $$F^{m\times n}$$ is actually a vector space over $$F$$. So we can think of matrices as vectors. Since we can think of matrices as vectors, why have a separate name for matrices? Why not just think of matrices as vectors?
The answer is that there are special things that you can do with matrices that you can't always do with vectors. In addition to being able to add matrices, and multiply matrices by scalars, we can also multiply matrices by matrices.
Matrix multiplication (i.e. multiplying matrices by matrices) is important and it is used to do a variety of things. One of the main things we can with matrices is the following:
If we have two finite dimensional vector spaces $$U$$, $$V$$ over a field $$F$$, and we have a linear transformation from $$T:U\to V$$; then once we pick a basis of $$U$$ and a basis for $$V$$, there is a nice way to represent $$T$$ as a matrix. If $$S:V\to W$$ is another linear transformation (where $$W$$ is another finite dimensional vector space over $$F$$), then once we pick a basis for $$W$$ we can get a matrix for $$S$$ as well. If $$A$$ is the matrix for $$S$$ and $$B$$ is the matrix for $$T$$, then $$AB$$ will be the matrix for the composition $$S\circ T:U\to W$$.
The above example is probably the most important use of matrices in linear algebra, and it is the reason why matrix multiplication has the peculiar definition that it is has. Although once we have this definition, it turns out that there are other things we can use matrices for. I close by giving one such example:
If $$V$$ is a finite dimensional vector space over $$F$$, then we can define a bilinear form to be a map $$V\times V\to F$$, that is linear in both variables. Well it turns out that once we have pick a basis for $$V$$, there is a nice of representing each bilinear form $$V\times V\to F$$ as a matrix.
• Awesome answer! Thank you for being so detailed in your answer. You are correct, there is no multiplication defined for a tuple of vectors, but there is for a matrix! Dec 28, 2019 at 1:02
• I'm glad you liked my answer. I hope it was helpful. Dec 28, 2019 at 1:04
• Very much so! It was really bothering me :) I am trying to model a Vector Space through an object-oriented language and I kept wondering why would a need a class called "Matrix" if I can just treat a Matrix as a tuple of vectors. Forgot about multiplication! :) Dec 28, 2019 at 1:07
In many ways they're the same and you can treat matrices like vectors in every way. The main distinction is matrix multiplication which is a powerful computational device which we use to model linear functions between vector spaces in some basis. It's useful to keep the maps separated from the vectors and the multiplication gives them additional structure a vector may not have.
I don't mean to revive this question although it's been answered a year and three months ago, with an accepted answer, but I just wanted to illustrate how to picture a matrix like a vector and mention that multiplication allows one to have a ring structure, but you may or may not be interested in Rings... Also, this link provides some great answers as to the usefulness of matrix multiplication.
Just like vectors in $$\mathbb{R}^n$$ can be pictured as linear combinations of the vectors in the standard basis
$$\mathcal{S}=\underbrace{\left\{\begin{pmatrix}1\\ 0\\ \vdots\\ 0\end{pmatrix},\begin{pmatrix}0\\ 1\\ \vdots\\ 0\end{pmatrix},\cdots,\begin{pmatrix}0\\ 0\\ \vdots\\ 1\end{pmatrix}\right\}}_{\text{n - vectors}}$$
$$\vec{v}=\begin{pmatrix}a_1\\ a_2\\ \vdots\\ a_n\end{pmatrix}=a_1\begin{pmatrix}1\\ 0\\ \vdots\\ 0\end{pmatrix}+a_2\begin{pmatrix}0\\ 1\\ \vdots\\ 0\end{pmatrix}+\cdots+a_n\begin{pmatrix}0\\ 0\\ \vdots\\ 1\end{pmatrix}$$
we can write a matrix similarly as a linear combination of the standard basis of $$n\times m$$ matrices
$$\mathcal{S}_{n\times m}= \underbrace{\left\{\begin{pmatrix}1&0&\cdots&0\\ 0&0&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\ 0&0&\cdots&0\end{pmatrix},\begin{pmatrix}0 & 1&\cdots &0\\ 0&0&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\ 0&0&\cdots&0\end{pmatrix},\cdots,\begin{pmatrix}0&0&\cdots&0\\ 0&0&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\0&0&\cdots& 1\end{pmatrix}\right\}}_{\text{n\times m - vectors/matrices}}$$
$$(a)_{ij}=\begin{bmatrix} a_{11}&a_{12}&\cdots&a_{1m}\\a_{21}&a_{22}&\cdots&a_{2m}\\\vdots&\vdots&\ddots&\vdots\\a_{n1}&a_{n2}&\cdots&a_{nm}\end{bmatrix}= a_{11}\begin{pmatrix}1&0&\cdots&0\\ 0&0&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\ 0&0&\cdots&0\end{pmatrix}+a_{12}\begin{pmatrix}0 & 1&\cdots &0\\ 0&0&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\ 0&0&\cdots&0\end{pmatrix}+\cdots+a_{nm}\begin{pmatrix}0&0&\cdots&0\\ 0&0&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\0&0&\cdots& 1\end{pmatrix}$$
which can be represented as the column vector $$\begin{pmatrix}a_{11}\\ a_{12}\\ \vdots\\ a_{nm}\end{pmatrix}$$.
|
|
Version:
Converts the input elements to 8-bit signed integers.
## Syntax
c = int8(a)
## a
Scalar or array of any dimension of real numbers or of Booleans.
## c
Elements of a as 8-bit signed integers. c is a scalar or an array of the same size as a. If a is a complex number, this function converts the real and imaginary parts of the number separately and then returns a complex number that consists of those parts. To return the 8-bit signed representation of a when the input is complex, use the real function to extract the real part of a, then use the int8 function to convert the real part.
|
|
Asian-Australas J Anim Sci > Volume 33(2); 2020 > Article
Santana, Júnior, Ruas, Monção, Borges, Sousa, Silva, de Oliveira Rabelo, da Cunha Siqueira Carvalho, and de Sales: Nutritional efficiency of feed restricted F1 Holstein/Zebu cows during the middle third of lactation
### Objective
The objective of this study was to evaluate the effects of different levels of quantitative feed restriction on nutrient intake and digestibility, nitrogen balance, efficiency and feeding behavior, and productive performance in F1 Holstein/Zebu cows during the middle third of their lactation.
### Methods
Sixty F1 Holstein/Zebu cows with 111.5±11.75 days of lactation and an initial body weight (BW) of 499±30 kg (mean±standard error of the mean) were used. The experimental design was completely randomized with the following diet levels of feed restriction: 3.39%, 2.75%, 2.50%, 2.25%, and 2.00% of BW, with 12 replications for each level. The experiment lasted for 63 days, of which each period lasted 21 days with the first 16 days for diet adaptation followed by 5 days for collection of data and samples.
### Results
For each 1% of BW diet restriction, there was a decrease in dry matter intake of 5.26 kg/d (p<0.01). There was no difference in daily milk production (p = 0.09) under the restriction levels of 3.39% to 2.0% of BW. When corrected for 3.5% fat, milk production declined (p = 0.05) 3.46 kg/d for each percentage unit of feed restriction.
### Conclusion
Restricting the feed supply for F1 Holstein/Zebu cows in the middle third of their lactation period altered nutrient intake, nitrogen balance and ingestive behavior but did not affect milk production or feed efficiency. However, considering the observed BW loss and decrease in milk production corrected for 3.5% fat, restriction of no less than 2.5% BW is recommended.
### INTRODUCTION
The dairy industry has a substantial contribution to the Brazilian agribusiness and most of the milk that is produced is from crossbred Holstein/Zebu cows [1]. These animals are used because of their consistent ability to maintain high levels of performance, with no changes in management, as well as their rusticity and adaptability to changes that occur in tropical environments [2].
Milk production (MP) in Brazil has nutritional value, and the use of forage plants whose supply and nutritional value changes considerably throughout the year, mainly during the dry season, affecting the animals’ performance [3]. One alternative used by producers to maintain MP and to ensure its permanence is the strategic use of feedlots for animals whose food costs can have a negative impact on production.
Feed restriction may be an alternative that reduces production costs and increases the feed efficiency of the cattle, as reported by Keogh et al [4]. However, there is still little knowledge regarding the effects of feed restriction on nutritional, productive and behavioral parameters of crossbred Holstein/Zebu cows during the middle third of the lactation period in the literature. According to Schütz et al [5], restriction of dietary supply in lactating cows can trigger rapid mobilization of body tissues for maintenance of normal bodily functions and can also affect the productive and reproductive activities of the animal, causing adaptive and metabolic body changes. There may also be a reduction in MP [6] as well as in fat, protein and stability [7,8] beginning the fifth day of restriction. There may also be an increase in the somatic cell count [9]. However, the results may vary depending on the severity, duration and type of feed restriction [6]. In addition to the lactation phase, it is important to study the best level of this restriction for the animals and to relate these results to production [2].
The objective of this study was to evaluate the effects of dif ferent levels of quantitative food restriction on the nutrient intake and digestibility, nitrogen balance, MP, feed efficiency, and ingestive behavior in F1 Holstein/Zebu cows during the middle third of the lactation period.
### Animal care and location
All procedures involving animals was approved by the institutional committee on animal use (protocol number 138/2017). The study was conducted at the Experimental Farm of Unimontes, GPS coordinates: latitude 15°52′38″ S, longitude 43°20′05″ W.
### Animals, experimental design, diet and management
Sixty F1 Holstein/Zebu cows in the middle third of their lactation periods (111.5±11.75 days of lactation) with an initial body weight (BW) of 499±30 kg (mean±standard error of the mean) and a mean age of 6 years were used. The experimental design was completely randomized and had five feed restriction levels (3.39%, 2.75%, 2.50%, 2.25%, 2.00%) with twelve cows used for each treatment. The diet supply, kg dry matter (DM)/d, defined as percentage of BW, were: ad libitum (3.39%), allowing 5% of refusals relative to the amount of DM provided, and diets provided with 2.75%, 2.50%, 2.25%, and 2.00% of BW. Before the trial period all cows received the experimental diet provided ad libitum for 14 days, with a goal of allowing the animals to adapt to the diet and management.
The diet (Table 1) was given based on the BW of each cow and in accordance with each treatment, maintaining roughage: concentrate ratio of 75:25 in the total DM of the diet. The diets were offered to the animals twice a day, at 8:00 am and at 3:00 pm, in a complete diet system. The roughage base for the diets was corn silage, which was weighed daily and then mixed into the concentrate.
The cows were kept in individual pens with an area of ap proximately 26 m2, equipped with troughs (1 linear meter) and drinkers (capacity of 200 liters). Milking was performed mechanically twice a day, at 7:00 am and 2:00 pm, with the calf present to stimulate milk letdown. Immediately after milking, the calves remained with the cows to feed from the residual milk.
The experiment lasted for 63 days that were divided in three period. Each period lasted 21 days with the first 16 days for adaptation of the animals the diet (diet supply levels) followed by 5 days for collection of data and samples.
### Intake and apparent digestibility evaluations
Intake was evaluated daily by weighing the feed provided and the refusals of the animals. Samples of the offered diets and the refusals were stored at −20°C for further analysis.
Samples of diets, concentrate ingredients, refusals, and feces were analyzed to evaluate feed intake and digestibility. The samples were analyzed for DM (method 967.03), ash (method 942.05), crude protein (CP; method 981.10), and ether extract (EE; method 920.39) according to the recommendations of the AOAC [10]. The contents of the neutral detergent fiber were corrected for ash and protein (NDFap) using heat-stable alpha-amylase without sodium sulfite and acid detergent fiber (ADF) were determined as described by Mertens [11] and Licitra et al [12]. Lignin content was determined by treating the ADF residue with sulfuric acid at 72% [13]. Non-fiber carbohydrate (NFC) contents were calculated as described by Detmann et al [13]: NFC (g/kg) = 100–ash–EE–NDFap–CP; where ash is mineral matter (crude ash).
The total digestible nutrients (TDN) were estimated using the formula proposed by NRC [14]. To analyze the indigestible NDF, feed samples were placed in nonwoven fabric bags (20 mg/cm2) and incubated in the rumen for 288 hours ([13]; method INCT-CA F-008/1). Two adult crossbred cattle cannulated in the rumen and weighing 480±30 kg, with a mean age of 8 years were used for sample incubation. To determine the digestibility of each fraction, we used the following equation: ([ingested nutrient amount – amount nutrient excreted in the feces]×100) / ingested nutrient amount.
### Nitrogen balance and nitrogen concentration in the milk, blood, and urine
We collected samples of milk from each animal twice a day during the last five days of the trial period, and we measured the total amount of milk produced in the morning and afternoon. Fifty milliliters of the collected samples were added to a bottle containing the preservative Bronopol and then analyzed for milk urea nitrogen (MUN). The concentrations of MUN were determined by enzymatic and spectrophotometric methods of transreflectance using a ChemSpeck 150 (Uniontown, OH, USA).
Blood samples were collected from the coccygeal vein into vacuum tubes containing sodium fluoride and potassium oxalate (Glistab anticoagulant; Labtest Diagnóstica S.A., Lagoa Santa, Brazil) 4 hours after the morning feeding on the last day of the experimental period. The samples were centrifuged at 4,000 rpm for 20 min and the serum obtained was conditioned in Eppendorf tubes and frozen at −18°C for further analysis. Plasma urea concentrations were determined by a colorimetric enzymatic method using commercial kits (Ureia 500, Doles Reagents; Panamá, Brazil).
Urine spot samples were obtained during the experimental period, approximately four hours after feeding, during spontaneous urination. An aliquot of 10 mL of the urine sample was filtered and immediately diluted in 40 mL of H2SO4, 0.036 N for later analysis of urea and creatinine, as described by Oliveira et al [15]. The samples were then transferred to Eppendorf tubes and analyzed for urea content using the same method as was used for the blood samples. The end-point method determined the creatinine by means of picrate and acidifying with enzymatic methods. Quantification of the daily urinary volume of each animal was obtained by multiplying the respective BW by the amount of creatinine excreted daily, and then dividing the product by the creatinine concentration (mg/L) in the spot sample. The average value of 24.04 (mg/kg BW) was used, according to Chizzotti et al [16], to obtain the total daily creatinine excretion.
To perform the nitrogen balance calculation, the ingested amount of nitrogen (N-ingested; g/d) and the amount excreted in the feces (N-feces; g/d), urine (N-urine; g/d), and milk (N-milk; g/d) were used. The nitrogen utilization efficiency (NUE) of the diet was calculated by dividing the concentration of the nitrogen retained in the milk by the nitrogen intake in kg/d [17].
Feed efficiency was calculated by dividing the average milk yield (kg/d) by the DM intake (kg/d) [18]. The evaluation of costs with concentrates, roughage and total diet were calculated by multiplying the intake by the respective value of each fraction, which was calculated according to its composition and the price of each ingredient [19]. The values per kilogram of the diet ingredients were as follows: corn silage was $0.05 and concentrate was$ 0.46. The values are expressed in US dollars, considering the ratio of R$3.5 (real) for every US$ 1.
### Feeding behavior evaluations
The feeding behavior was assessed in the last 2 days of the trial period. For the evaluation of the feeding behavior, all animals were observed visually for 24 h, and the observations were recorded at 5-min intervals, which included eating, ruminating, and idle times [20]. On the same day, three observations were made for each animal: in the morning, at noontime, and at night. Data were collected by trained observers using digital timers. During the nocturnal observation, the environment was kept under artificial light. Feeding behavior variables (eating, ruminating, and idle times) were obtained by using equations adapted from Bürger et al [21]. The number of chews per ruminal bolus and the time spent ruminating each bolus were recorded during the observation periods. The number of bolus ruminated daily was calculated by dividing the total rumination time (min) by the average time spent to ruminate one bolus.
### Production, performance and body condition scores
During the trial period, the MP was recorded per cow. The MP was corrected for the fat content (FC) 3.5% using the equation proposed by Sklan et al [22]: MP 3.5% = MP×(0.432+ 0.163×FC).
To evaluate the BW of the animals, we used a mechanical scale. The animals were weighted at the beginning and end of the experiment. Body condition scores (BCS) were evaluated by a single technician weekly during the period. The BCS were also examined for three weeks further, following the end of the experimental period, to investigate the development of the animals. In the assessment of the BCS, the 1 to 5-point scale with 0.25-point intervals was used, in which 1 represents a very lean cow and 5 a very fat cow [23].
### Statistical analysis
The data was analyzed using the PROC MIXED procedure of SAS [24] (SAS Institute Inc., Cary, NC, USA). The model included treatment and period (time) as fixed effects. Results were reported as least squares means. Polynomial regressions were used to test the linear and quadratic changes affected due to the increasing feed restriction. Diagnostics concerning homogeneity of the variances and the normality of the residuals were examined and were not of concern for the variables studied here. Significant differences was declared at p<0.05.
### Intake and digestibility of nutrient
For each 1% BW of feed restriction the DM intake was reduced by 5.26 kg/d (DMI, p<0.01), the CP by 0.61 kg/d (CPI, p<0.01), the NFC by1.82 kg/d (p<0.01), the neutral detergent fiber corrected for ash and protein by 2.43 kg/d (NDFap; p< 0.01) and the TDNs by 2.61 kg/d (p<0.01) (Table 2). The apparent digestibility of DM (p = 0.29), EE (p = 0.11), NFC (p = 0.49), NDFap (p = 0.11) and TDN (p = 0.39) was not differed with the feed restriction of the animals, with the averages being 59.20%, 82.35%, 76.87%, 54.50%, and 61.93%, respectively. There was a 19.06% increase in CP digestibility (p = 0.03) with feed restriction.
### Nitrogen balance and nitrogen concentration in the milk, blood, and urine
Ingested nitrogen (p<0.01) and nitrogen excreted in milk (p = 0.01) and feces (p<0.01) was linearly reduced with dietary restriction. There was a decrease of 45.76% in ingested nitrogen when the diet supply was limited from 3.39% to 2.00% of BW. Nitrogen losses in milk and feces were in the order of 19.57 and 61.20 g/d, respectively, per unit percentage reduction in supply. For nitrogen excreted in the urine, the means were adjusted to the quadratic regression model (p = 0.05), with the highest concentration occurring at the restriction level of 3.05% of BW supply (Table 3).The nitrogen balance (nitrogen retained) was reduced (p<0.01) by 36.39 g/d with the restriction in the diet supply of 3.39% to 2.0% of BW. It was verified that NUE was not altered with the restriction in the diet supply (mean 0.26; p = 0.59). The feed restriction of the cows did not modify the content of urea nitrogen present in the urine (p = 0.11) and milk (p = 0.17), with averages being 7.99 and 15.86 mg/dL, respectively. There was an increase of 3.66 mg/dL in the concentration of nitrogen in the plasma when the diet supply was reduced by 1%.
### Feeding behavior evaluations
Cows without restrictions in their diets spent 307.8 min/d more eating when compared to animals with a restriction of 2.00% BW (p<0.01; mean 132.6 min/d). There was a reduction of 225.7 min/d, 9.48 min/kg DM (p = 0.02) and 20.09 min/kg NDFap (p = 0.01) in the feeding time when restricted to 2.00% of BW (Table 4). For each 1% of feed restriction, there was a reduction of 107 min/d in rumination time. When expressed as min/kg DM (p = 0.26) and min/kg NDFap (p = 0.47), the rumination efficiency was not altered by the diet supply restriction, averaging 1.926 min/kg DM and 957.2 min/kg NDFap. The number of bolus chews (p = 0.55), as well as chewing time in min/kg DM (p = 0.62) and min/kg NDFap (p = 0.39) did not change due to feed restriction in lactating cows. The number of chews per day (p = 0.04) was reduced by 38.34% in the animals with a 2.0% restriction supply when compared to cows without restriction (26,706 chews/d). When expressed in min/d, the chewing time was reduced by 338.32 min for each 1% of diet restriction, and cows fed a 2.0% BW supply level spent less time (444 min/d) for this activity. The idle time was 45.42% higher in these animals than in animals without any diet restriction (mean of 543.6 min/d). The number of feeding periods (p<0.01) decreased by 76.92% for the restricted animals. For each percentage unit of diet supply restriction, there was a reduction of 7.17 feedings/d (Table 5). The duration of the feeding period (p = 0.35) and rumination (p = 0.35) was not influenced by feed restriction. An increase of 19.92 min for the duration of the idling period was observed in animals with a supply restriction of 2.0% BW. The feed efficiency of DM (p = 0.03) and NDFap (p = 0.02) in grams/h increased linearly with the restriction of the diet supply.
### Production, performance, and body condition scores
There was no difference in daily milk production (p = 0.09) with restriction in the diet supply to 3.39% to 2.0% of BW. When corrected for 3.5% fat, milk production decrease (p = 0.05) 3.46 kg/d for each percentage unit of feed restriction (Table 6). It was verified that for each 1% of feed restriction the final BW of the cows in the middle third of their lactation period was reduced by 46.75 kg, with the lowest values observed in animals with the highest level of restriction (2.0%, 438 kg). The final BW differential in relation to the initial weight was not influenced by restriction (p = 0.56), nor was the final BCS (p = 0.65). Dietary restriction did not affect feed efficiency (p = 0.49), with a mean of 0.93 kg of milk/kg of DMI. Feed restriction of 3.39% BW to 2.0% reduced diet costs of $3.25 to$ 1.77.
### DISCUSSION
The DMI is one of the main factors affecting animal health and performance [24]. According to the NRC, DMI is a function of the metabolic weight of the animal, week of lactation, and FC in milk and is estimated at 20.61 g/kg of BW (9.99 kg/d) for crossbred cows. However, a voluntary DMI of 32.74 g/kg of BW (15.88 kg/d) during the middle third of the lactation period is a greater value than what is estimated by the NRC [14] for maintenance and production. This difference can be explained by the fact that the NRC calculates these estimates based on Holstein cows in temperate regions. Murta et al [25] evaluated the productive performance of crossbred Holstein/Zebu cows from 100 to 150 days of lactation consuming different diets without restriction in the supply and verified that the DMI was about 33.0 g/kg of BW (15.7 kg/d). This value is similar to those that were observed in the present study (15.88 kg/d). Only in the restriction levels of 2.25% and 2.0% did the DMI drop below what was estimated by the NRC [14]. Consequently, restriction of the diet supply by up to 2% of an animal’s BW directly impacted the protein and energy intake of the animal, as well as the intake of other nutrients. However, the DM digestibility of the diet was not changed, with a mean of 592 g/kg DM. This occurred because the unique variation factor was the quantity offered. Normally in digestive trials, treatment of ad libitum (3.39% BW) feeding would reduce the digestibility rather than restricted feeding, because of less retention time in digestive tract comparing with low DMI [26]. However, this difference was only numerical in the order of 11.16% in ad libitum treatment (3.39% BW) with the restriction of 2% of BW.
The ingestive behavior and the speed of passage in the di gesta can modify the digestibility of nutrients because cows under restriction have more time for rumination compared to those without restriction, allowing for greater fractionation of the particles of the ruminal bolus, and favoring the degradation of the rumen microorganisms. However, this behavior related to the time spent ruminating the DM and the fibrous fraction was not altered with feed restriction, nor was the number of chews per bolus ruminated or the chewing time of the DM and NDFap affected.
The maintenance of these rumination characteristics through out the different diet supply levels can help to explain the similarity in DM digestibility and fibrous fraction values; this was because the diet was unique, with the same chemical composition across the different levels of supply and caused a longer feeding time in animals subjected to feed restriction [27,28]. The highest values observed for CP digestibility were in animals with restricted feed, which may be related to the rate of passage of the digesta functioning better due to the lower intake of DM in these animals. Lower digestion rates may imply a longer exposure of protein fractions to the action of microorganisms and proteolytic enzymes, which increases the digestibility of the CP in the rumen or intestine [28]. However, there are several isolated and interacting factors that influence the digestibility of nutrients in the gastrointestinal tract of animals [24].
Feed restriction in lactating cows reduces the ingested ni trogen and nitrogen balance due to the lower consumption of CP but does not modify the efficiency of nitrogen use (mean of 26%). Doska et al [29] reported that the nitrogen use efficiency can vary from 15% to 40% depending on the level of milk production and feeding practices. Plasma urea nitrogen was increased from 11.53 mg/dL (without restriction, 3.39% of BW) to 17.23 mg/dL (2.0% supply restriction). The increase in CP was not accompanied by an increase in the digestibility of the energy sources for the microorganisms of the rumen; with the quantitative restriction of food possibly hampering the use of rumen ammonia in the synthesis of microbial protein and increasing plasma urea nitrogen [28]. According to Doska et al [29], urea nitrogen and concentrations of nitrogen compounds in the plasma are related. In Brazilian conditions, values from 10.0 to 14.0 mg/dL of nitrogen in the plasma would represent the limits of dietary protein losses occurring. Thus, the restriction of dietary supply below 2.5% of DMI per BW increases the urea plasma concentration, which could indicate that there is a loss of protein occurring or an inefficient use of nutrients.
The reduction in the final BW of the cows with feed restric tion is explained by the lower intake of nutrients, however, the body score (mean 3.76) and feed efficiency (0.93 kg milk/kg of ingested DM) were maintained in these animals. This behavior demonstrates the adaptability potential of crossbred cows under conditions of diet supply restriction. Roche et al [30] evaluated strategies for increasing the BCS of pre- and postpartum cows and verified that the BCS is a metabolic indicator of the energy balance of the animal and can be used as a dietary energy restriction strategy. Roche et al [30] suggested that the ideal BCS for Holstein cows varies from 2.75 to 3.25 for cows in the middle third of their lactation periods, indicating that the crossbred cows used in this study had reserves slightly above those recommended for purebred cows.
It is important to emphasize that, in addition to unaltered milk production and maintenance BCS of cows with a restriction in diet supply, production costs declined by up to 45.62% in relation to the control diet (3.39% BW). This is very important since the profit margin within the dairy industry in Brazil is generally narrow. Moreover, the cost of the feed is greater than 50% of the total production cost. This strategy of restriction in the diet supply can be an alternative to make the production system feasible and to improve profitability. Therefore, the best restriction strategy can be evaluated within each milk production system. However, although there was no change in milk production or BCS in F1 Holstein/Zebu cows with diet restriction at 2% BW, there was a reduction in the milk production corrected for 3.5% fat and final BW of the animals, which could compromise reproductive activity. In this sense, dietary restriction of no less than 2.5% BW would be recommended in the middle third of lactation, in view of the lower weight loss of the cows and reduction of the food cost by as much as 28.42% compared to diet ad libitum (control; 3.25 US$/d). ### CONCLUSION The restriction of diet to as low as 2% of an animal’s BW was effective in reducing food costs by 45.6%. This restriction of diet may be adopted due to the availability of food, milk prices, and other factors that interfere with the production system. However, considering the observed BW loss and decrease in milk production corrected for 3.5% fat, a restriction of no less than 2.5% BW is recommended. ### Notes CONFLICT OF INTEREST We certify that there is no conflict of interest with any financial organization regarding the material discussed in the manuscript. ### ACKNOWLEDGMENTS To FAPEMIG for financial assistance and CNPq for the granting of scholarships, to INCT-Ciência Animal and EPAMIG. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. ##### Table 1 Chemical composition of ingredients and diet used during experimental period Items (g/kg DM)1) Corn silage Concentrated mixture Diet2) Dry matter 447.7 925.9 567.2 Organic matter 961.2 922.3 951.5 Crude protein 72.4 218.3 108.8 NDIN 5.50 12.24 7.18 ADIN 0.93 0.75 0.89 Ether extract 25.1 28.3 25.9 Non-fibrous carbohydrates 283.4 371.7 305.5 NDFap 580.3 304.1 511.3 Neutral detergente fiber 307.4 72.2 248.6 Lignin 60.3 31.8 53.2 Total digestible nutrients3) 606.4 734.2 638.4 DM, dry matter; NDIN, neutral detergent insoluble nitrogen; ADIN, acid detergent insoluble nitrogen; NDFap, neutral detergent fiber corrected for ash and protein. 1) Nutrient in dry basis (grams per kilogram). 2) Diet used during the experiment (e.g., diet consisted of 75% corn silage and 25% concentrate in the total dry matter). 3) NRC [14]. ##### Table 2 Nutrient intake and digestibility in F1 Holstein/Zebu cows under quantitative feed restriction in the middle third of lactation Items Levels of restriction (% BW)1) SEM p-value 3.392) 2.75 2.50 2.25 2.00 Linear Quad Intake DM (kg/d) a) 15.88 12.56 11.39 9.73 8.64 0.44 <0.01 0.90 DM (% BW) 3.22 2.75 2.50 2.25 2.00 0.06 <0.01 0.27 CP (kg/d) b) 1.79 1.37 1.24 1.06 0.94 0.05 <0.01 0.68 EE (kg/d) c) 0.42 0.33 0.29 0.25 0.22 0.01 <0.01 0.91 NFC (kg/d) d) 5.14 3.84 3.47 2.97 2.63 0.15 <0.01 0.42 NDFCP (kg/d) e) 7.77 6.42 5.83 4.98 4.42 0.22 <0.01 0.40 TDN (kg/d) f) 9.12 7.63 7.21 6.18 5.47 0.29 <0.01 0.33 Nutrient digestibility (%) DM 54.75 57.38 61.62 60.65 61.63 2.59 0.29 0.76 CP g) 51.88 48.15 59.25 55.46 61.77 2.63 0.03 0.12 EE 77.55 83.75 85.17 83.23 82.09 2.25 0.11 0.11 NFC 75.57 74.46 76.84 80.71 76.77 3.07 0.49 0.89 NDFAP 51.02 54.10 56.67 54.47 56.25 2.28 0.11 0.57 TDN 58.21 60.52 63.85 63.39 63.71 2.37 0.39 0.72 BW, body weight; SEM, standard error of the mean; p, probability; DM, dry matter; CP, crude protein; EE, ether extract; NFC, Non-fibrous carbohydrates; NDFap, neutral detergent fiber corrected for ash and protein; TDN, total digestible nutrients. 1) Regression equation: a) Ŷ = −1.93+5.26*X, R2 = 0.99; b) Ŷ = 0.27+0.88*X, R2 = 0.99; c) Ŷ = −0.30+0.61*X, R2 = 0.99; d) Ŷ = −0.07+0.14*X, R2 = 0.99; e) Ŷ = −1.08+1.82*X, R2 = 0.99; f) Ŷ = −0.394+2.43*X, R2 = 0.99; g) Ŷ = 0.388+2.61*X, R2 = 0.98, where X is the level of food restriction; R2 is the coefficient of determination; * significant by the t test, at 1% probability. 2) Diet ad libitum, allowing 5% refusals regarding dry matter offer. ##### Table 3 Balance and efficiency of nitrogen use in crossbred F1 Holstein/Zebu cows under quantitative feed restriction in the middle third of lactation Items Levels of restriction (% BW)1) SEM p-value 3.392) 2.75 2.50 2.25 2.00 Linear Quad N-ingested (g/d) a) 298.13 218.50 211.15 171.04 161.70 12.86 <0.01 0.46 N-milk (g/d) b) 69.13 56.72 55.72 48.89 40.24 4.47 0.01 0.52 N-feces (g/d) c) 144.27 113.32 86.05 75.75 61.45 9.03 <0.01 0.86 N-urine (g/d) 58.55 50.35 72.39 67.80 82.82 7.36 0.05 0.13 Nitrogen balance d) (g/d) 26.17 −1.89 −3.00 −21.40 −22.81 7.62 <0.01 0.75 NUEe) 0.23 0.26 0.27 0.29 0.25 0.02 0.59 0.36 UUN (mg/dL) f) 7.46 10.92 9.95 4.88 6.75 1.58 0.11 0.34 PUN (mg/dL) 11.53 14.20 13.56 15.10 17.23 1.03 0.02 0.48 MUN (mg/dL) 15.15 13.70 16.63 15.75 18.10 1.21 0.17 0.16 BW, body weight; SEM, standard error of the mean; p, probability; N, nitrogen; NUE, nitrogen use efficiency; UUN, urine urea nitrogen; PUN, plasma urea nitrogen; MUN, milk urea nitrogen. 1) Regression equation: a) Ŷ = −45.61+99.96*X, R2 = 0.97; b) Ŷ = 3.67+19.57*X, R2 = 0.96; c) Ŷ = −61.61+61.20*X; R2 = 0.98; d) Ŷ = 289.80–153.66*X+25.13*X2, R2 = 0.76; e) Ŷ = −98.41+36.39*X, R2 = 0.96; f) Ŷ = 23.77–3.66*X, R2 = 0.87 where X is the level of food restriction; R2 is the coefficient of determination; * significant by the t test, at 1% probability. 2) Diet ad libitum, allowing 5% refusals regarding dry matter offer. ##### Table 4 Feeding behavior of F1 Holstein/Zebu cows under quantitative feed restriction in the middle third of lactation Items Levels of restriction (% BW)1) SEM p-value 3.392) 2.75 2.50 2.25 2.00 Linear Quad Feeding min/d a) 440.4 240 204 153.6 132.6 28.2 <0.01 0.09 min/kg DMb) 27.37 19.17 16.87 15.62 14.36 2.64 0.02 0.61 min/kg NDFapc) 55.69 37.5 33 30.56 28.08 5.16 0.01 0.32 Rumination min/d d) 456.6 415.2 367.8 339 311.4 28.8 0.02 0.60 min/kg DM 2,219 1,828 1,980 1,785 1,818 149 0.26 0.60 min/kg NDFap 1,087 935 1,013 912 929 76 0.47 0.73 Chewing number/bolus 49.86 38.31 49.39 39.19 42.46 6.22 0.55 0.66 number/d e) 26,706 21,034 20,191 18,181 16,466 2,117 0.04 0.81 min/d f) 896.4 655.2 571.2 492.6 444 30 <0.01 0.24 min/kg DM 54.71 52.67 47.46 50.62 48.05 3.74 0.62 0.86 min/kg NDFap 111.5 103 92.8 99 94 7.2 0.39 0.65 Idleness min/d g) 543.6 784.8 868.8 947.4 996 30 <0.01 0.26 BW, body weight; SEM, standard error of the mean; p, probability; DM, dry matter; NDFap, neutral detergent fiber corrected for ashes and protein. 1) Regression equation: a) Ŷ = −346.37+225.17*X, R2 = 0.96; b) Ŷ = −5.78+9.48*X, R2 = 0.95; c) Ŷ = −14.83+20.09*X, R2 = 0.94; d) Ŷ = 100.61+107*X, R2 = 0.97; e) Ŷ = −1809.76+7256.01*X, R2 = 0.99; f) Ŷ = −245+332.38*X, R2 = 0.99; g) Ŷ = 1685–332.38*X, R2 = 0.99 where X is the level of food restriction; R2 is the coefficient of determination; * significant by the t test, at 1% probability. 2) Diet ad libitum, allowing 5% refusals regarding dry matter offer. ##### Table 5 Number of periods and average time spent per period on the feeding, ruminating, and idle activities by F1 Holstein/Zebu cows under quantitative feed restriction in the middle third of lactation Items Levels of restriction (% BW)1) SEM p-value 3.392) 2.75 2.50 2.25 2.00 Linear Quad Number of periods (n/d) Feedinga) 13.0 4.5 4.7 3.2 3.0 0.71 <0.01 0.01 Ruminating 14.5 12.75 12 13.5 12.75 1.19 0.65 0.42 Idling 21 20.25 19.75 19.75 18.75 1.37 0.83 0.84 Time spent per period (min) Feeding 33.93 54.88 42.44 53.65 46.15 7.81 0.35 0.26 Ruminating 31.96 33.09 34.47 25.04 24.54 4.25 0.35 0.21 Idlingb) 26 39.14 45.64 47.96 53.98 3.4 <0.01 0.81 Feed efficiency g DM/hc) 2,361 3,210 3,804 3,912 4,239 381 0.03 0.80 g NDFap/hd) 1,154 1,641 1,945 2,000 2,167 193 0.02 0.71 Rumination efficiency Boluses/d 49.86 38.31 49.39 39.19 42.46 6.22 0.55 0.70 g DM/h 2,219 1,828 1,980 1,785 1,818 149 0.26 0.48 g NDFap/h 1,087 935 1,013 912 929 76 0.47 0.66 BW, body weight; SEM, standard error of the mean; p, probability; DM, dry matter; NDFap, neutral detergent fiber corrected for ashes and protein; h, hour. 1) Regression equation: a) Ŷ = −12.80+7.17*X, R2 = 0.85; b) Ŷ = 93.90–19.92*X, R2 = 0.99; c) Ŷ = 7,044.02–1,372.74*X, R2 = 0.98; d) Ŷ = 3687.88–739.48*X, R2 = 0.98; where X is the level of food restriction; R2 is the coefficient of determination; * significant by the t test, at 1% probability. 2) Diet ad libitum, allowing 5% refusals regarding dry matter offer. ##### Table 6 Performance and feed efficiency in F1 Holstein/Zebu cows under quantitative feed restriction in the middle third of lactation Items Levels of restriction (BW)1) SEM p-value 3.392) 2.75 2.50 2.25 2.00 Linear Quad Milk production (kg/d) 13.05 11.60 10.70 10.67 8.26 1.10 0.09 0.47 Milk production corrected for 3.5 fat (kg/d)a) 13.61 11.30 11.30 10.27 8.32 1.10 0.05 0.59 Final body weight (kg) b) 485 457 455 433 438 80 <0.01 0.57 Final and initial body weight difference (kg) −24.25 −25.04 −56.31 −52.92 −69.94 23.04 0.56 0.66 Final body condition score 3.81 3.81 3.88 3.69 3.63 0.13 0.65 0.34 Difference in body condition score 0.06 0.00 −0.13 −0.25 0.00 0.09 0.16 0.29 Feed efficiency (kg of milk/kg of DM) 0.79 0.95 0.90 1.10 0.91 0.12 0.49 0.50 Feed cost (U$/d) 3.25 2.57 2.33 1.99 1.77 0.26 - -
Reduction of food costs (%) 0.00 20.90 28.42 38.87 45.62 7.7 - -
BW, body weight; SEM, standard error of the mean; p-value, probability; DM, dry matter.
1) a) Ŷ = 2.03+3.46*X, R2 = 0.93; b) Ŷ =356.4 – 46.75*X, R2 = 0.97, where X is the level of food restriction; R2 is the coefficient of determination; * significant by the t test, at 1% probability.
2) Diet ad libitum, allowing 5% refusals regarding dry matter offer.
### REFERENCES
1. Canaza-Cayo AW, Cobuci JA, Lopes PS, et al. Genetic trend estimates for milk yield production and fertility traits of the Girolando cattle in Brazil. Livest Sci 2016; 190:113–22. https://doi.org/10.1016/j.livsci.2016.06.009
2. Santos SA, Valadares Filho SC, Detmann E, et al. Voluntary intake and milk production in F1 Holstein×zebu cows in confinement. Trop Anim Health Prod 2012; 44:1303–10. https://doi.org/10.1007/s11250-011-0072-2
3. Oliveira AS. Meta-analysis of feeding trials to estimate energy requirements of dairy cows under tropical condition. Anim Feed Sci Technol 2015; 210:94–103. https://doi.org/10.1016/j.anifeedsci.2015.10.006
4. Keogh K, Kenny DA, Cormican P, McCabe MS, Kelly AK, Waters SM. Effect of dietary restriction and subsequent Re-alimentation on the transcriptional profile of bovine skeletal muscle. PLoS One 2016; 11:e0149373https://doi.org/10.1371/journal.pone.0149373
5. Schütz KE, Cox NR, Macdonald KA, et al. Behavioral and physiological effects of a short-term feed restriction in lactating dairy cattle with different body condition scores at calving. J Dairy Sci 2013; 96:4465–76. https://doi.org/10.3168/jds.2012-6507
6. Gabbi AM, McManus CM, Zanela MB, et al. Milk traits of lactating cows submitted to feed restriction. Trop Anim Health Prod 2016; 48:37–43. https://doi.org/10.1007/s11250-015-0916-2
7. Zanela MB, Fischer V, Ribeiro MER, et al. Unstable nonacid milk and milk composition of Jersey cows on feed restriction. Braz Agric Res 2006; 41:835–40. http://dx.doi.org/10.1590/S0100-204X2006000500016
8. Barbosa RS, Fischer V, Ribeiro MER, et al. Electrophoretic characterization of proteins and milk stability of cows submitted to feeding restriction. Braz Agric Res 2012; 47:621–8. https://dx.doi.org/10.1590/S0100-204X2012000400019
9. Van Straten M, Friger M, Shpigel NY. Events of elevated somatic cell counts in high-producing dairy cows are associated with daily body weight loss in early lactation. J Dairy Sci 2009; 92:4386–94. https://doi.org/10.3168/jds.2009-2204
10. Latimer GW. AOAC International. Official methods of analysis of AOAC International. 19th ed.Gaithersburg, MD, USA: AOAC International; 2012.
11. Mertens DR. Gravimetric determination of amylase-treated neutral detergent fiber in feeds with refluxing in beaker or crucibles: collaborative study. J AOAC Int 2002; 85:1217–40.
12. Licitra G, Hernandez TM, Van Soest PJ. Standardization of procedures for nitrogen fractionation of ruminant feeds. Anim Feed Sci Technol 1996; 57:347–58. https://doi.org/10.1016/0377-8401(95)00837-3
13. Detmann E, Souza MA, Valadares Filho SC, et al. Methods for food analysis. Visconde do Rio Branco: Suprema; 2012.
14. Committee on Nutrient Requirements of Dairy Cattle, National Research Council. Nutrient requirements of dairy cattle. 7th rev. ed.Washington, DC, USA: National Academy Press; 2001.
15. Oliveira AS, Valadares RFD, Valadares Filho SC, et al. Microbial protein production, purine derivatives and urea excretion estimate in lactating dairy cows fed isoprotein diets with different non protein nitrogen compounds levels. Rev Bras Zootec 2001; 30:1621–9. http://dx.doi.org/10.1590/S1516-35982001000600032
16. Chizzotti ML, Valadares Filho SC, Valadares RFD, et al. Intake, digestibility and nitrogen metabolism in Holstein cows with different milk production levels. Rev Bras Zootec 2007; 36:138–46. http://dx.doi.org/10.1590/S1516-35982007000100017
17. Broderick GA. Effects of varying dietary protein and energy levels on the production of lactating dairy cows. J Dairy Sci 2003; 86:1370–81. https://doi.org/10.3168/jds.S0022-0302(03)73721-7
18. Valadares Filho SC, Broderick GA, Valadares RF, Clayton MK. Effect of replacing alfalfa silage with high moisture corn on nutrient utilization and milk production. J Dairy Sci 2000; 83:106–14. https://doi.org/10.3168/jds.S0022-0302(00)74861-2
19. Rennó FP, Pereira JC, Leite CAM, et al. Bioeconomic evaluation of feeding strategies in milk production systems: 1. Production per animal and per area. Braz J Anim Sci 2008; 37:743–53. http://dx.doi.org/10.1590/S1516-35982008000400022
20. Mezzalira JC, Carvalho PCF, Fonseca L, et al. Methodological aspects of ingestive behavior of grazing cattle. Rev Bras Zootec 2011; 40:1114–20. http://dx.doi.org/10.1590/S1516-35982011000500024
21. Bürger PJ, Pereira JC, Queiroz AC, et al. Ingestive behavior in Holstein calves fed diets with different concentrate levels. Rev Bras Zootec 2000; 29:236–42. http://dx.doi.org/10.1590/S1516-35982000000100031
22. Sklan D, Ashkenazi R, Braun A, Devorin A, Tabori K. Fatty acids, calcium soaps of fatty acids, and cottonseeds fed to high yielding cows. J Dairy Sci 1992; 75:2463–72. https://doi.org/10.3168/jds.S0022-0302(92)78008-4
23. Ferguson JD, Galligan DT, Thomsen N. Principal descriptors of body condition score in Holstein cows. J Dairy Sci 1994; 77:2695–703. http://dx.doi.org/10.3168/jds.S0022-0302(94)77212-X
24. SAS Institute. SAS/STAT 92 User’s guide. Cary, NC, USA: SAS Institute, Inc; 2008.
25. Murta RM, Veloso CM, Pires AJV, et al. Intake, apparent digestibility, production, and composition of milk from cows fed diets with different sources of lipids. Rev Bras Zootec 2016; 45:56–62. http://dx.doi.org/10.1590/S1806-92902016000200003
26. Menezes CCC, Valadares Filho SC, Magalhães FA, et al. Total and partial digestibility, rates of digestion obtained with rumenevacuation and microbial protein synthesis in bovines fed fresh or ensiled sugar cane and corn silage. Rev Bras Zootec 2011; 40:1104–13. http://dx.doi.org/10.1590/S1516-35982011000500023
27. Schwartzkopf-Genswein KS, Beauchemin KA, Gibb DJ, et al. Effect of bunk management on feeding behavior, ruminal acidosis and performance of feedlot cattle: a review. J Anim Sci 2003; 81:E149–58. https://doi.org/10.2527/2003.8114_suppl_2E149x
28. Dado TG, Allen MS. Intake limitations, feeding behavior, and rumen function of cows challenged with rumen fill from dietary fiber or inert bulk. J Dairy Sci 1995; 78:118–33. http://dx.doi.org/10.3168/jds.S0022-0302(95)76622-X
29. Doska MC, Silva DFF, Horst SA, Valloto AA, Rossi Junior P, Almeida R. Sources of variation in milk urea nitrogen in Paraná dairy cows. Rev Bras Zootec 2012; 41:692–7. http://dx.doi.org/10.1590/S1516-35982012000300032
30. Roche JR, Heiser A, Mitchell MD, et al. Strategies to gain body condition score in pasture-based dairy cows during late lactation and the far-off nonlactating period and their interaction with close-up dry matter intake. J Dairy Sci 2017; 100:1720–38. https://doi.org/10.3168/jds.2016-11591
TOOLS
METRICS
• 0 Crossref
• 0 Scopus
• 496 View
|
|
Model and Solve Statements
# Introduction
This chapter brings together all the concepts discussed in previous chapters by explaining how to specify a model and solve it.
# The Model Statement
The model statement is used to collect equations into groups and to label them so that they can be solved. The simplest form of the model statement uses the keyword all: the model consists of all equations declared before the model statement is entered. For most simple applications this is all the user needs to know about the model statement.
## The Syntax
In general, the syntax for a model declaration in GAMS is as follows:
model[s] model_name [text] [/ (all | eqn_name {, eqn_name}) {, var_name(set_name)} /]
{,model_name [text] [/ (all | eqn_name {, eqn_name}) {, var_name(set_name)} /]} ;
The keyword model[s] indicates that this is a model statement and model_name is the internal name of the model in GAMS, it is an identifier. The optional explanatory text is used to describe the model, all is a keyword as introduced above and eqn_name is the name of an equation that has been declared prior to the model statement. Var_name(set_name) is a couple of previous declared variable and and set to limit the domain of variables in the model. More details about this are described in the following subsection. For advice on explanatory text and how to choose a model_name, see the tutorial Good Coding Practices.
Note
Model statements for Mixed Complementarity Problem (MCP) and Mathematical Program with Equilibrium Constraints (MPEC) models require a slightly different notation, since complementarity relationships need to be included. For details see subsections Mixed Complementarity Problem (MCP) and Mathematical Program with Equilibrium Constraints (MPEC).
An example of a model definition in GAMS is shown below.
Model transport "a transportation model" / all /;
The model is called transport and the keyword all is a shorthand for all known (declared) equations.
Several models may be declared (and defined) in one model statement. This is useful when experimenting with different ways of writing a model, or if one has different models that draw on the same data. Consider the following example, adapted from [PROLOG], in which different groups of the equations are used in alternative versions of the problem. Three versions are solved: the linear, nonlinear, and 'expenditure' versions. The model statement to define all three is:
Model nortonl "linear version" / cb,rc,dfl,bc,obj /
nortonn "nonlinear version" / cb,rc,dfn,bc,obj /
nortone "expenditure version" / cb,rc,dfe,bc,obj / ;
Here cb, rc, etc. are the names of the equations. We will describe below how to obtain the solution to each of the three models.
Note
If several models are declared and defined with one model statement, the models have to be separated by commas or linefeeds and a semicolon terminates the entire statement.
If several models are declared then it is possible to use one previously declared model in the declaration of another. The following examples illustrate this:
Model one "first model" / tcost_eq, supply_eq, demand_eq /
two "second model that nests first" / one, balance_eq /
three "third model that nests first and second" / two, capacity_eq, configure_eq /;
Model one is declared and defined using the general syntax, model two contains all the equations of model one and the equation balance_eq, and model three contains all of model two and the equations capacity_eq and configure_eq.
In addition to nesting models as illustrated above, it is also possible to use the symbols + and - to augment or remove items relative to models that were previously defined. The following examples serve as illustration:
Model four "fourth model: model three minus model one" / three-one /
five "fifth model: model three without eqn configure_eq" / three-configure_eq /
six "sixth model: model four plus model two" / four+two /;
Model four contains the equations from model three except for those that belong to model one. Model five contains all equations from model three except for equation configure_eq. Model six contains the union of the equations in model four and two. Note that both model names and equation names may be used in association with the symbols + and -.
### Limited domain for variables
As mentioned above, it is possible to limit the domain of variables used in a model in the model statement. This allows to restrict the generation of blocks of variables in a single place instead of using, e.g., dollar conditions at every place where this variable block is used in equations (which might be required for an efficient model generation).
The following examples is based on the basic transportation model [TRNSPORT]. To limit the transportation network in that model to certain links (e.g. because some are blocked because of some reason) one could introduce a subset of the free links and use that with dollar conditions in the equations like this:
* Initialize whole network as free
cost.. z =e= sum((i,j), c(i,j)*x(i,j)$freeLinks(i,j)); supply(i).. sum(j, x(i,j)$freeLinks(i,j)) =l= a(i);
demand(j).. sum(i, x(i,j)$freeLinks(i,j)) =g= b(j); * Block a particular link freeLinks('san-diego','topeka') = no; Model transport / all /; solve transport using lp minimizing z; Now, instead of adding the dollar condition to each appearance of x in the model, one could simply add a domain restriction for that variable to the model statement directly by specifying a variable and the set that limits its domain. Using this approach, the previous example looks like this: * Initialize whole network as free Set freeLinks(i,j) Useable links in the network / #i.#j /; cost.. z =e= sum((i,j), c(i,j)*x(i,j)); supply(i).. sum(j, x(i,j)) =l= a(i); demand(j).. sum(i, x(i,j)) =g= b(j); * Block a particular link freeLinks('san-diego','topeka') = no; Model transport / all, x(freeLinks) /; solve transport using lp minimizing z; Note If one adds the domain restriction to the model statement, internally GAMS inserts a dollar condition to every appearance of the restricted variables in equations of the model. When doing this, the indices are copied as they appear with the variable. So, in the example above, x(i,j) becomes x(i,j)$freeLinks(i,j). In the same way x(i-1,j+1) becomes x(i-1,j+1)$freeLinks(i-1,j+1) and x('seattle','chicago') becomes x('seattle','chicago')$freeLinks('seattle','chicago').
Attention
As a consequence of above's note one could see some unexpected results, like "division by zero errors", if it is not done carefully. For example, the following dummy model, will trigger such an error, since we sum over all i, but some x were excluded leaving a 0 as divisor:
Set i / i1*i3 /
sub(i) / i2 /;
Positive Variable x(i);
Variable z;
Equation obj;
obj.. z =e= sum(i, 1/x(i));
x.lo(i) = 1;
Model m / obj, x(sub) /;
solve m min z use nlp;
## Classification of Models
Various types of problems can be solved with GAMS. Note that the type of the model must be known before it may be solved. The model types are briefly discussed in this section. GAMS checks that the model is in fact the type the user thinks it is, and issues explanatory error messages if it discovers a mismatch - for instance, that a supposedly linear model contains nonlinear terms. Some problems may be solved in more than one way, and the user has to choose which way to use. For instance, if there are binary or integer variables in the model, it can be solved either as a MIP or as a RMIP.
The model types and their identifiers, which are needed in the a solve statement, are given in Table 1. For details on the solve statement, see section The Solve Statement.
GAMS Model Type Model Type Description Requirements and Comments
LP Linear Program Model with no nonlinear terms or discrete (i.e. binary, integer, etc) variables.
NLP Nonlinear Program Model with general nonlinear terms involving only smooth functions, but no discrete variables. For a classification of functions as to smoothness, see section Functions.
QCP Quadratically Constrained Program Model with linear and quadratic terms, but no general nonlinear terms or discrete variables.
DNLP Discontinuous Nonlinear Program Model with non-smooth nonlinear terms with discontinuous derivatives, but no discrete variables. This is the same as NLP, except that non-smooth functions may appear as well. These models are more difficult to solve than normal NLP models and we strongly advise not to use this model type.
MIP Mixed Integer Program Model with binary, integer, SOS and/or semi variables, but no nonlinear terms.
RMIP Relaxed Mixed Integer Program Like MIP, except that the discrete variable requirement is relaxed. See the note below on relaxed model types.
MINLP Mixed Integer Nonlinear Program Model with both nonlinear terms and discrete variables.
RMINLP Relaxed Mixed Integer Nonlinear Program Like MINLP except that the discrete variable requirement is relaxed. See the note below on relaxed model types.
MIQCP Mixed Integer Quadratically Constrained Program Model with both quadratic terms and discrete variables, but no general nonlinear term.
RMIQCP Relaxed Mixed Integer Quadratically Constrained Program Like MIQCP except that the discrete variable requirement is relaxed. See the note below on relaxed model types.
MCP Mixed Complementarity Problem A square, possibly nonlinear, model that generalizes a system of equations. Rows and columns are matched in one-to-one complementary relationships.
CNS Constrained Nonlinear System Model solving a square, possibly nonlinear system of equations, with an equal number of variables and constraints.
MPEC Mathematical Programs with Equilibrium Constraints A difficult model type for which solvers and reformulations are currently being developed.
RMPEC Relaxed Mathematical Program with Equilibrium Constraints A difficult model type for which solvers and reformulations are currently being developed. See the note below on relaxed model types.
EMP Extended Mathematical Program A family of mathematical programming extensions.
MPSGE General Equilibrium Not actually a model type but mentioned for completeness, see MPSGE.
Table 1: GAMS Model Types
Note
• The relaxed model types RMIP, RMINLP, RMIQCP, and RMPEC solve the problem as the corresponding model type (e.g. MIP for RMIP) but relax the discrete requirement of the discrete variables. This means that integer and binary variables may assume any values between their bounds. SemiInteger and SemiCont variables may assume any values between 0 and their upper bound. For SOS1 and SOS2 variables the restriction of the number of non-zero values is removed.
• Many "LP" solvers like Cplex offer the functionality of solving convex quadratic models. So the Q matrices in the model need to be positive semidefinite. An extension to to this are the second-order cone programs (SOCP) with either symmetric or rotated cones. See the solver manuals (e.g. on MOSEK) for details.
• Unlike other checks on the model algebra (e.g. existence of discrete variables or general non-linear terms), the GAMS compiler does not enforce a quadratic model to only consist of quadratic and linear terms. This requirement is enforced at runtime for a particular model instance.
### Linear Programming (LP)
Mathematically, the Linear Programming (LP) problem looks like:
\begin{equation*} \begin{array}{ll} \textrm{Minimize or maximize} & cx \\ \textrm{subject to} & Ax \, \, \alpha \, \, b \\ & L \leq x \leq U, \\ \end{array} \end{equation*}
where $$x$$ is a vector of variables that are continuous real numbers, $$cx$$ is the objective function, and $$Ax \, \alpha \, b$$ represents the set of constraints. Here, $$\alpha$$ is an equation operator. For details on the equation types allowed in GAMS, see Equation Types. $$L$$ and $$U$$ are vectors of lower and upper bounds on the variables.
GAMS supports free (unrestricted) variables, positive variables, and negative variables. Note that users may customize lower and upper bounds, for details see section Bounds on Variables.
For information on LP solvers that can be used through GAMS see the Solver/Model type Matrix.
### Nonlinear Programming (NLP)
Mathematically, the Nonlinear Programming (NLP) problem looks like:
\begin{equation*} \begin{array}{ll} \textrm{Minimize or Maximize} & f(x) \\ \textrm{subject to} & g(x) \, \, \alpha \, \, 0 \\ & L \leq x \leq U, \\ \end{array} \end{equation*}
where $$x$$ is a vector of variables that are continuous real numbers, $$f(x)$$ is the objective function, and $$g(x) \, \alpha \, 0$$ represents the set of constraints. For details on the equation types allowed in GAMS, see Equation Types. Note that the functions $$f(x)$$ and $$g(x)$$ have to be differentiable. $$L$$ and $$U$$ are vectors of lower and upper bounds on the variables.
For information on NLP solvers that can be used through GAMS see the Solver/Model type Matrix. See also the tutorial Good NLP Formulations.
Note
NLP models may have the nonlinear terms inactive. In this case setting the model attribute TryLinear to 1 causes GAMS to check the model and use the default LP solver if possible. For details on model attributes, see subsection Model Attributes.
Mathematically, the Quadratically Constrained Programming (QCP) problem looks like:
\begin{equation*} \begin{array}{lll} \textrm{Maximize or Minimize} & cx + x'Q x & \\ \textrm{subject to} & A_i x + x' R_i x \,\, \alpha \,\, b_i & \textrm{for all} \,\, i \\ & L \leq x \leq U, & \\ \end{array} \end{equation*}
where $$x$$ denotes a vector of variables that are continuous real numbers, $$cx$$ is the linear part of the objective function, $$x'Qx$$ is the quadratic part of the objective function, $$A_i x$$ represents the linear part of the $$i$$th constraint, $$x' R_i x$$ its quadratic part and $$b_i$$ its right-hand side. For details on the equation types allowed in GAMS, see Equation Types". Further, $$L$$ and $$U$$ are vectors of lower and upper bounds on the variables.
Note that a QCP is a special case of the NLP in which all the nonlinearities are required to be quadratic. As such, any QCP model can also be solved as an NLP. However, most "LP" vendors provide routines to solve LP models with a quadratic objective. Some allow quadratic constraints as well. Solving a model using the QCP model type allows these "LP" solvers to be used to solve quadratic models as well as linear ones. Some NLP solvers may also take advantage of the special (quadratic) form when solving QCP models.
Attention
In case a model with quadratic constraints is passed to a QCP solver that only allows a quadratic objective, a capability error will be returned (solver status 6 CAPABILITY PROBLEMS). Some solvers will fail when asked to solve a non-convex quadratic problems as described above.
Note
Using the model attribute TryLinear causes GAMS to see if the problem can be solved as an LP problem. For details on model attributes, see subsection Model Attributes.
For information on QCP solvers that can be used through GAMS see the Solver/Model type Matrix.
### Nonlinear Programming with Discontinuous Derivatives (DNLP)
Mathematically, the Nonlinear Programming with Discontinuous Derivatives (DNLP) problem looks like:
\begin{equation*} \begin{array}{ll} \textrm{Maximize or Minimize} & f(x)\\ \textrm{subject to} & g(x) \, \, \alpha \, \, 0 \\ & L \leq x \leq U, \\ \end{array} \end{equation*}
where $$x$$ is a vector of variables that are continuous real numbers, $$f(x)$$ is the objective function, $$g(x) \, \alpha \, 0$$ represents the set of constraints, and $$L$$ and $$U$$ are vectors of lower and upper bounds on the variables. For details on the equation types allowed in GAMS, see Equation Types. Note that this is the same as NLP, except that non-smooth functions, like abs, min, max may appear in $$f(x)$$ and $$g(x)$$.
For information on DNLP solvers that can be used through GAMS see the Solver/Model type Matrix.
Attention
• We strongly advise against using the model type DNLP. The best way to model discontinuous functions is with binary variables, which results in a model of the type MINLP. The model [ABSMIP] demonstrates this formulation technique for the functions abs, min, max and sign. See also section Reformulating DNLP Models.
• Solvers may have difficulties when dealing with the discontinuities, since they are really NLP solvers and the optimality conditions and the reliance on derivatives may be problematic. Using a global solver may alleviate this problem.
### Mixed Integer Programming (MIP)
Mathematically, the Mixed Integer Linear Programming (MIP) problem looks like:
\begin{equation*} \begin{array}{lrclll} \textrm{Maximize or Minimize} & c_1 t + c_2 u + c_3 v + c_4 w + c_5 x + c_6 y + c_7 z & & & & \\ \textrm{subject to} & A_1 t + A_2 u + A_3 v + A_4 w + A_5 x + A_6 y + A_7 z & \alpha & b & & \\ & t & \in & \mathbb R & &\\ & u & \geq & 0 & \textrm{and}\,\, u \leq L_2 & \textrm{and} \, \, u \in \mathbb Z \\ & v & \in & (0,1) & &\\ & w & \in & \textrm{SOS1} & &\\ & x & \in & \textrm{SOS2} & &\\ & y & = & 0 & \textrm{or} \, \, \, L_6 \leq y & \\ & z & = & 0 & \textrm{or} \,\, \, L_7 \leq z & \textrm{and} \,\, z \in \mathbb Z,\\ \end{array} \end{equation*}
where
• $$c_1t + c_2u + c_3v + c_4w + c_5x + c_6y + c_7z$$ is the objective function,
• $$A_1t + A_2u + A_3v + A_4w + A_5x + A_6y + A_7z \,\, \alpha \,\, b$$ represents the set of constraints of various equality and inequality forms,
• $$t$$ is a vector of variables that are continuous real numbers,
• $$u$$ is a vector of variables that can only take integer values smaller than $$L_2$$,
• $$v$$ is a vector of binary variables,
• $$w$$ is a vector of variables that belong to SOS1 sets; this means that at most one variable in the set is nonzero,
• $$x$$ is a vector of variables that belong to SOS2 sets; this means that at most two adjacent variables in the set are nonzero,
• $$y$$ is a vector of variables that are semi-continuous; they are either zero or larger than $$L_6$$,
• $$z$$ is a vector of variables that are semi-integer; they are integer and either zero or larger than $$L_7$$.
For details on the equation types allowed in GAMS, see Equation Types. For more details on MIPs in GAMS, especially the use of SOS and semi variables, see section Special Mixed Integer Programming (MIP) Features.
For information on MIP solvers that can be used through GAMS, see the Solver/Model type Matrix.
Attention
Not all MIP solvers cover all the cases associated with SOS and semi variables. Please consult the solver manuals for details on capabilities.
### Mixed Integer Nonlinear Programming (MINLP)
Mathematically, the Mixed Integer Nonlinear Programming (MINLP) problem looks like:
\begin{equation*} \begin{array}{ll} \textrm{Maximize or Minimize} & f(x) + Dy \\ \textrm{subject to} & g(x) + Hy \, \, \alpha \, \, 0 \\ & L \leq x \leq U \\ & y = \{0,1,2,\cdots\}, \\ \end{array} \end{equation*}
where $$x$$ is a vector of variables that are continuous real numbers, $$y$$ denotes a vector of variables that can only take integer values, $$f(x)+ Dy$$ is the objective function, $$g(x) + Hy\ \, \alpha \, 0$$ represents the set of constraints, and $$L$$ and $$U$$ are vectors of lower and upper bounds on the variables. For details on the equation types allowed in GAMS, see Equation Types. Further, $$y = \{0,1,2,\cdots\}$$ is the integrality restriction on $$y$$.
For information on MINLP solvers that can be used through GAMS see the Solver/Model type Matrix.
Note
• SOS and semi variables can also be accommodated by some solvers. Please consult the solver manuals for details on capabilities.
• The model attribute TryLinear causes GAMS to examine whether the problem may be solved as a MIP problem. For details on model attributes, see subsection Model Attributes.
### Mixed Integer Quadratically Constrained Programs (MIQCP)
A Mixed Integer Quadratically Constrained Program (MIQCP) is a special case of the MINLP in which all the nonlinearities are required to be quadratic. For details see the description of the QCP, a special case of the NLP.
For information on MIQCP solvers that can be used through GAMS, see the Solver/Model type Matrix.
Note
The model attribute TryLinear causes GAMS to examine whether the problem may be solved as a MIP problem. For details on model attributes, see subsection Model Attributes.
### Mixed Complementarity Problem (MCP)
Unlike the other model types we have introduced so far, the Mixed Complementarity Problem (MCP) does not have an objective function. An MCP is specified by three pieces of data: a function $$F(z): \mathbb R^n \mapsto \mathbb R^n$$, lower bounds $$l \in \{\mathbb R \cup \{-\infty\}\}^n$$ and upper bounds $$u \in \{\mathbb R \cup \{\infty\}\}^n$$. A solution is a vector $$z \in \mathbb R^n$$ such that for each $$i \in \{1, \ldots, n\}$$, one of the following three conditions hold:
$\begin{array}{rcl} F_i(z) = 0 & \mbox{ and } & \ell_i \leq z_i \leq u_i \, \, \, \mbox{ or} \\ F_i(z) > 0 & \mbox{ and } & z_i = \ell_i \, \, \, \mbox{ or} \\ F_i(z) < 0 & \mbox{ and } & z_i = u_i . \end{array}$
This problem can be written compactly as
\begin{equation*} F(z) \, \perp \, L \leq z \leq U, \end{equation*}
where the symbol $$\perp$$ (which means "perpendicular to", shortened to "perp to") indicates pair-wise complementarity between the function $$F$$ and the variable $$z$$ and its bounds.
The following special case is an important and illustrative example:
\begin{equation*} F(z) \perp z \geq 0. \end{equation*}
In this example, the unstated but implied upper bound $$u$$ is infinity. Since $$z$$ is finite, we cannot have $$z_i = u_i$$ and the third condition above cannot hold: this implies $$F(z) >= 0$$. The remaining two conditions imply pair-wise complementarity between $$z >= 0$$ and $$F(z) >= 0$$. This is exactly the Nonlinear Complementarity Problem, often written as
\begin{equation*} F(z) \geq 0, \quad z \geq 0, \quad \langle{F(z)},{z}\rangle = 0. \end{equation*}
None of this rules out the degenerate case (i.e. $$F_i(z)$$ and $$z_i$$ both zero). In practice, these can be difficult models to solve.
Another special case arises when the bounds $$L$$ and $$U$$ are infinite. In this case, the second and third conditions above cannot hold, so we are left with $$F(z) = 0$$, a square system of nonlinear equations. And finally, we should mention a special case that occurs frequently in practice: if $$\ell_i = u_i$$ (i.e. $$z_i$$ is fixed) then we have a complementary pair: one of the three conditions will hold as long as $$F_i(z)$$ is defined. Essentially, fixing a variable removes or obviates the matching equation. This is often useful when modeling with MCP.
The definition above describes the canonical MCP model as it exists when GAMS passes it to an MCP solver. Some models have exactly this form even in the GAMS code, but usually some processing is done by the GAMS system to arrive at a model in this form. Here we'll describe the steps of this process and illustrate with an example from the model library.
1. The process starts with the list of rows (aka single equations) and columns (aka single variables) that make up the MCP model, and potentially some matching information.
• The usual rules apply: rows are part of the model because their associated equations are included in the model statement, but columns only become part of the model by use: a column enters the model only if it is used in some row of the model. Therefore including a variable symbol as part of a match in the model statement will not influence the set of columns belonging to the model.
• Matches (where they exist) are pointers from rows to columns.
• Technically, the MCP is defined via a function $$F$$ while a model contains constraints. Given a constraint, we define an associated function as LHS - RHS, so e.g. $$F_i \geq 0$$ is consistent with a =G= constraint.
2. The explicit matches are processed: each match creates a complementary pair. What remains after the explicit matches are consumed are the unmatched rows and unmatched columns.
• It is an error for any column to be matched to multiple rows, so the row-column matching is one-to-one.
• For each match some consistency checks between the column bounds and the row type are made. For details, see Table 2.
• For example, matching an =N= row with any column is good, matching an =E= row with a free column is good, matching an =E= row with a lower-bounded column is allowed, and matching a =G= row with an upper-bounded column results in an error.
3. Any fixed columns remaining are ignored: these columns can be treated like exogenous variables or parameters.
4. If what remains is a set of =E= rows and an equal number of unbounded columns, these can be matched up in any order and we have a well-defined MCP. If this is not what remains, an error is triggered.
To illustrate how this works, consider the spatial equilibrium model [SPATEQU] with the following model statement:
Model P2R3_MCP / dem, sup, in_out.p, dom_trad.x /;
1. The model P2R3_MCP includes the rows from equations dem, sup, in_out and dom_trad and exactly the columns used by these rows. Checking the listing file, we see columns for Qd, Qs, x, and p. In addition, the model statement specifies two matches: in_out.p and dom_trad.x. These matches always take the form of an equation.variable pair, with no indices or domains included.
2. In this example, the rows corresponding to the equation in_out match up perfectly with the columns from the variable p: there are no holes in the set of rows or columns because of some dollar conditions in the equation definition. We have a one-to-one match so all the rows of in_out and columns of p are consumed by the match in the model statement. The same holds for the dom_trad.x pair, so what is left are the rows of dem and sup and the columns of Qd and Qs, all of which are unmatched.
3. There are no fixed variables to remove.
4. Since dem and sup are =E= constraints and Qd and Qs are free variables, we can match them in any order without changing the solution set for this model. The counts of these unmatched equality rows and unmatched free variables are equal, so we get a well-defined MCP.
When rows are matched explicitly to columns, some care must be taken to match them consistently. For example, consider a row-column match g.y. The row g can be of several types: =N=, =E=, =G=, or =L=. An =N= row can be matched to any sort of variable: the =N= doesn't imply any sort of relationship, which works perfectly with our definition of $$\perp$$ above: the allowed sign or direction of g is determined completely by the bounds on the complementary variable y. If g is an =E= row, this is consistent with a free variable y, but what if y has an active lower bound? By definition we allow g to be positive at solution, but this violates the declaration as an =E= row. Such cases can be handled by marking the row with a redef. The total number of redefs for a given model is available via the NumRedef model attribute and is shown in the report summary. Note that the set of rows marked depends on the solution: in the example above, if g is zero at solution it will not be marked as a redef, regardless of what the bounds are on y. Finally, some combinations are simply not allowed: they will result in a model generation error. The table below lists the outcome for all possible combinations.
Table 2: MCP Matching
Column Bounds =N= =E= =G= =L=
lower OK redef OK ERROR
upper OK redef ERROR OK
free OK OK OK OK
double OK redef redef redef
fixed OK redef redef redef
The definition, process, and rules above have several implications for valid MCP models:
• It is always acceptable to use the =N= notation when defining the equations in an MCP model, provided these equations are matched explicitly. In this case the bounds on F(z) are implied by the bounds on the matching columns, and redefs will never occur.
• Variables that are known to be lower-bounded (no upper bound) will match consistently with =G= equations.
• Variables that are known to be upper-bounded (no lower bound) will match consistently with =L= equations.
• Variables that are known to be unbounded will match consistently with =E= equations.
• Where the bound structure is not known in advance, or both upper and lower bounds exist, a match with an =N= equation will always be consistent. Other equation types will result in errors or redefs.
• The model may initially have fewer rows than columns, as long as the "extra" columns are unmatched fixed columns that ultimately get removed from the MCP passed to the solver.
• Any bounded-but-not-fixed column must be matched explicitly to a row.
• The only rows that may be unmatched are =E= rows.
• It is customary to re-use the constraints of an LP or NLP model when formulating the MCP corresponding to the Karush-Kuhn-Tucker (KKT) conditions. If the original model is a minimization, the LP/NLP marginals .m and the variables for these marginals in the MCP will use the same sign convention, and the orientation for the constraints will be consistent between the two models, making re-use easier.
As mentioned above, it is typical to use the same equations in both NLP and MCP models. Sometimes, it is not the original equation that is wanted for the MCP, but rather the reoriented (aka negated or flipped) equation. For example, the flipped version of x**1.5 =L= y is y =G= x**1.5, while sqr(u) - sqr(v) =E= 5 becomes - sqr(u) + sqr(v) =E= -5. Instead of re-implementing the equation in flipped form, the same result can be achieved by prefixing the equation name with a - in the model statement. See the [mcp10] model for an example of such usage. When equations are used in flipped form, they are marked with a redir in the listing file's solution listing.
An example of complementarity that should be familiar to many is the relationship between a constraint and its associated dual multiplier: if the constraint is non-binding, its dual multiplier must be zero (i.e. at bound) while if a dual multiplier is nonzero the associated constraint must be binding. In fact, the KKT or first-order optimality conditions for LP and NLP models can be expressed and solved as an MCP.
These complementarity relationships found in optimization problems are useful in understanding the marginal values assigned to rows and columns in the GAMS solution for MCP. With no objective function, the usual definition for marginal values and their interpretation isn't useful. Instead, the GAMS MCP convention for the marginal values of columns is to return the slack of the associated row (i.e. its value when interpreted and evaluated as a function). For the marginal values of rows, the level value (not the slack) of the associated column is returned. When we apply this convention to the NCP ( $$F(z) \geq 0, z \geq 0, \langle{F(z)},{z}\rangle = 0$$) we see pairwise complementarity between the levels and marginals returned for each of the rows and columns in the model. This is also the case if we take the KKT conditions of an LP in a suitable standard form: minimization, $$x \geq 0, Ax \geq b$$.
MCPs arise in many application areas including applied economics, game theory, structural engineering and chemical engineering. For further details on this class of problems, see http://www.neos-guide.org/content/complementarity-problems.
For information on MCP solvers that can be used through GAMS, see Solver/Model type Matrix.
### Constrained Nonlinear System (CNS)
The Constrained Nonlinear System (CNS) is the second GAMS model type that does not have an objective function. Mathematically, a CNS model looks like:
$$\begin{array}{ll} \textrm{Find} & x \\ \textrm{subject to} & F(x) = 0 \\ & L \leq x \leq U \\ & G(x) \, \, \alpha \, \, b, \\ \end{array}$$
where $$x$$ is a set of continuous variables and $$F$$ is a set of nonlinear equations of the same dimension as $$x$$. This is a key property of this model type: the number of equations equals the number of variables, so we have a square system. The (possibly empty) constraints $$L \leq x \leq U$$ are not intended to be binding at the solution, but instead are included to constrain the solution to a particular domain, to avoid regions where $$F(x)$$ is undefined, or perhaps just to give the solver a push in the right direction. The (possibly empty) constraints $$G(x) \, \, \alpha \, \, b$$ are intended to serve the same purpose as the variable bounds and are silently converted to equations with bounded slacks.
Note that since there is no objective in a CNS model, there are no marginal values for variables and equations. Any marginal values already stored in the GAMS database will remain untouched. CNS models also make use of some model status values that allow a solver to indicate if the solution is unique (e.g. for a non-singular linear system) or if the linearization is singular at the solution. For singular models (solved or otherwise), the solver can mark one or more dependent rows with a depnd. The total number of rows so marked for a given model is available via the NumDepnd model attribute and is shown in the report summary.
The CNS model is a generalization of a square system of equations $$F(x) = 0$$. Such a system could also be modeled as an NLP with a dummy objective. However, there are a number of advantages to using the CNS model type, including:
• A check by GAMS that the model is really square,
• solution/model diagnostics by the solver (e.g. singular at solution, (locally) unique solution),
• CNS-specific warnings if the side constraints $$L \leq x \leq U$$ or $$G(x) \, \, \alpha \, \, b$$ are active at a solution,
• and potential improvement in solution times, by taking better advantage of the model properties.
For information on CNS solvers that can be used through GAMS, see the Solver/Model type Matrix.
### Mathematical Program with Equilibrium Constraints (MPEC)
Mathematically, the Mathematical Program with Equilibrium Constraints (MPEC) problem looks like:
\begin{equation*} \begin{array}{ll} \textrm{Maximize or Minimize} & f(x,y) \\ \textrm{subject to} & g(x,y) \, \, \alpha \, \, 0 \\ & L_x \leq x \leq U_x \\ & F(x,y) \perp L_y \leq y \leq U_y, \\ \end{array} \end{equation*}
where $$x$$ and $$y$$ are vectors of continuous real variables. The variables $$x$$ are often called the control or upper-level variables, while the variables $$y$$ are called the state or lower-level variables. $$f(x,y)$$ is the objective function. $$g(x,y) \, \alpha \, 0$$ represents the set of traditional (i.e. NLP-type) constraints; some solvers may require that these constraints only involve the control variables $$x$$. The function $$F(x,y)$$ and the bounds $$L_y$$ and $$U_y$$ define the equilibrium constraints. If $$x$$ is fixed, then $$F(x,y)$$ and the bounds $$L_y$$ and $$U_y$$ define an MCP; the discussion of the "perp to" symbol $$\perp$$ in that section applies here as well. From this definition, we see that the MPEC model type contains NLP and MCP models as special cases of MPEC.
A simple example of an entire MPEC model is given below.
variable z, x1, x2, y1, y2;
positive variable y1;
y2.lo = -1;
y2.up = 1;
equations cost, g, h1, h2;
cost.. z =E= x1 + x2;
g.. sqr(x1) + sqr(x2) =L= 1;
h1.. x1 =G= y1 - y2 + 1;
h2.. x2 + y2 =N= 0;
model example / cost, g, h1.y1, h2.y2 /;
solve example using mpec min z;
Note that as in the MCP, the complementarity relationships in an MPEC are specified in the model statement via equation-variable pairs: the h1.y1 specifies that the equation h1 is perpendicular to the variable y1 and the h2.y2 specifies that the equation h2 is perpendicular to the variable y2. For details on the solve statement, see section The Solve Statement.
While the MPEC model formulation is very general, it also results in problems that can be very difficult to solve. The state-of-the-art for MPEC solvers is not nearly as advanced as that for other model types. As a result, you should expect the MPEC solvers to be more limited by problem size and/or robustness issues than solvers for other model types.
For information on MPEC solvers that can be used through GAMS, see the Solver/Model type Matrix. For more details on MPECs and solver development, see http://gamsworld.org/mpec/index.htm and http://www.neos-guide.org/content/complementarity-problems.
### Extended Mathematical Programs (EMP)
Extended Mathematical Programming (EMP) is an (experimental) framework for automated mathematical programming reformulations. Using EMP, model formulations that GAMS cannot currently handle directly or for which no robust and mature solver technology exists can be automatically and reliably reformulated or transformed into models for which robust and mature solver technology does exist within the GAMS system. For more details, see the chapter on EMP. Currently EMP supports:
• Equilibrium problems including variational inequalities, Nash games, and Multiple Optimization Problems with Equilibrium Constraints (MOPECs).
• Hierarchical optimization problems such as bilevel programs.
• Disjunctive programs for modeling discrete choices with binary variables.
• Stochastic programs including two-stage and multi-stage stochastic programs, chance constraints and risk measures such as Variance at Risk (VaR) and Conditional Variance at Risk (CVaR).
Apart from the disjunctive and stochastic programming models mentioned above, EMP models are typically processed (aka solved) via the JAMS solver: this solver does the work of reformulation/transformation, calling GAMS to solve this reformulation, and post-processing the solution that results to bring it back in terms of the original EMP model.
Examples demonstrating how to use the EMP framework and the JAMS and DE solvers are available in the GAMS EMP Library. These solvers require no license of their own to run but can and do call subsolvers that do require a license.
## Model Attributes
Models have attributes that hold a variety of information, including
• information about the results of a solve performed, a solve statement, the solution of a model,
• information about certain features to be used by GAMS or the solver,
• information passed to GAMS or the solver specifying various settings that are also subject to option statements.
Model attributes are accessed in the following way:
model_name.attribute
Here model_name is the name of the model in GAMS and .attribute is the specific attribute that is to be accessed. Model attributes may be used on the left-hand side and the right-hand side of assignments. Consider the following example:
transport.resLim = 600;
x = transport.modelStat;
In the first line the attribute .resLim of the model transport is specified to be 600 (seconds). In the second line the value of the attribute .modelStat of the model transport is assigned to the scalar x. Note that model attributes may also be used in display statements".
Some of the attributes are mainly used before the solve statement to provide information to GAMS or the solver link. Others are set by GAMS or the solver link and hence are mainly used after a solve statement.
Moreover, some of the attributes used before the solve may also be set via an option statement or the command line. Consider the following example:
option ResLim=10;
This line is an option statement and applies to all models. One can set the model attribute .ResLim to overwrite the global ResLim option. In order to revert the individual .ResLim to the global ResLim option, one needs to set the model attribute to NA. For more on option statements, see chapter The Option Statement.
gams mymodel ResLim=10
This sets the global ResLim option when invoking the gams run (e.g. from the command line). For more on command line parameters, see chapter The GAMS Call and Command Line Parameters.
Note that a model-specific option takes precedence over the global setting specified with an option statement and that a setting via an option statement takes precedence over a setting via the command line parameter.
The complete list of model attributes is given below. Observe that each entry is linked to a detailed description of the respective attribute, including information of whether the attribute is also available as command line parameter or option statement. Note that detailed descriptions of all GAMS command line parameters, options and model attributes are given in section Detailed Descriptions of All Options.
### Model Attributes Mainly Used Before Solve
Attribute Description
bRatio Basis detection threshold
cheat Cheat value, i.e. minimum solution improvement threshold
cutOff Cutoff value for branch and bound
defPoint Indicator for passing on default point
dictFile Force writing of a dictionary file if dictfile > 0
domLim Domain violation limit solver default
fdDelta Step size for finite differences
fdOpt Options for finite differences
holdFixed Treat fixed variables as constants
integer1..5 Integer communication cells
iterLim Iteration limit of solver
limCol Maximum number of columns listed in one variable block
limRow Maximum number of rows listed in one equation block
MCPRHoldFx Print list of rows that are perpendicular to variables removed due to the holdfixed setting
nodLim Node limit in branch and bound tree
optCA Absolute Optimality criterion solver default
optCR Relative Optimality criterion solver default
optFile Default option file
priorOpt Priority option for variable attribute .prior
real1..5 Real communication cells
reform Reformulation level
resLim Wall-clock time limit for solver
savePoint Save solver point in GDX file
scaleOpt Employ user specified variable and equation scaling factors
solPrint Solution report print option
solveOpt Multiple solve management
sysOut Solver Status file reporting option
tolInfeas Infeasibility tolerance for an empty row of the form a.. 0*x =e= 0.0001;
tolInfRep This attribute sets the tolerance for marking infeasible in the equation listing
tolProj Tolerance for setting solution values to a nearby bound when reading a solution
tryInt Whether solver should make use of a partial integer-feasible solution
tryLinear Examine empirical NLP model to see if there are any NLP terms active. If there are none the default LP solver will be used
workFactor Memory Estimate multiplier for some solvers
workSpace Work space for some solvers in MB
### Model Attributes Mainly Used After Solve
Attribute Description
domUsd Number of domain violations
etAlg Solver dependent timing information
etSolve Elapsed time it took to execute a solve statement in total
etSolver Elapsed time taken by the solver only
handle Unique handle number of SOLVE statement
iterUsd Number of iterations used
line Line number of last solve of the corresponding model
linkUsed Integer number that indicates the value of SolveLink used for the last solve
marginals Indicator for marginals present
maxInfes Maximum of infeasibilities
meanInfes Mean of infeasibilities
modelStat Integer number that indicates the model status
nodUsd Number of nodes used by the MIP solver
number Model instance serial number
numDepnd Number of dependencies in a CNS model
numDVar Number of discrete variables
numEqu Number of equations
numInfes Number of infeasibilities
numNLIns Number of nonlinear instructions
numNLNZ Number of nonlinear nonzeros
numNOpt Number of nonoptimalities
numNZ Number of nonzero entries in the model coefficient matrix
numRedef Number of MCP redefinitions
numVar Number of variables
numVarProj Number of bound projections during model generation
objEst Estimate of the best possible solution for a mixed-integer model
objVal Objective function value
procUsed Integer number that indicates the used model type
resCalc Time spent in function and derivative calculations (deprecated)
resDeriv Time spent in derivative calculations (deprecated)
resGen Time GAMS took to generate the model in CPU seconds(deprecated)
resIn Time to import model (deprecated)
resOut Time to export solution (deprecated)
resUsd Time the solver used to solve the model in seconds
rngBndMax Maximum absolute non-zero value of bounds passed to the solver (excluding infinity)
rngBndMin Minimum absolute non-zero value of bounds passed to the solver
rngMatMax Maximum absolute non-zero value of coefficients in the model matrix passed to the solver (excluding infinity)
rngMatMin Minimum absolute non-zero value of coefficients in the model matrix passed to the solver
rngRhsMax Maximum absolute non-zero value of right hand sides passed to the solver (excluding infinity)
rngRhsMin Minimum absolute non-zero value of right hand sides passed to the solver
rObj Objective function value from the relaxed solve of a mixed-integer model when the integer solver did not finish
solveStat Indicates the solver termination condition
sumInfes Sum of infeasibilities
sysIdent Solver identification number
sysVer Solver version
# The Solve Statement
Once a model has been defined using the model statement, the solve statement prompts GAMS to call one of the available solvers for the particular model type. This section introduces and discusses the solve statement in detail. For a list of GAMS model types, see Table 1. For information on how to specify desired solvers, see section Choosing a Solver.
Note
It is important to remember that GAMS does not solve the problem, but passes the problem definition to one of a number of separate solver programs that are integrated with the GAMS system.
## The Syntax of the Solve Statement
In general, the syntax for a solve statement is as follows. Note that there are two alternatives that are equally valid:
solve model_name using model_type maximizing|minimizing var_name;
solve model_name maximizing|minimizing var_name using model_type ;
The keyword solve indicates that this is a solve statement. Model_name is the name of the model as defined by a model statement. Note that the model statement must be placed before the solve statement in the program. The keyword using is followed by model_type, which is one of the GAMS model types described above, see Table 1. The keywords maximizing or minimizing indicate the direction of the optimization. Var_name is the name of the objective variable that is being optimized. An example of a solve statement in GAMS is shown below.
Solve transport using lp minimizing cost ;
Solve and using are reserved words, transport is the name of the model, lp is the model type, minimizing is the direction of optimization, and cost is the objective variable. Note that an objective variable is used instead of an objective row or function.
Attention
The objective variable must be scalar and of type free, and must appear in at least one of the equations in the model.
Recall that some model types (e.g. the Constrained Nonlinear System (CNS) or the Mixed Complementarity Problem (MCP)) do not have an objective variable. So their solve statement syntax is slightly different:
solve model_name using model_type;
As before, solve and using are keywords, model_name is the name of the model as defined by a model statement and model_type is the GAMS model type CNS or MCP. There is no objective variable and consequently no direction of optimization. An example from the spatial equilibrium model [SPATEQU] illustrates this solve statement:
Solve P2R3_MCP using mcp;
P2R3_MCP is the model name, the model type is MCP and as expected, there is no objective variable.
The EMP model type serves many purposes including some experimental ones. The solve statement with model type EMP can be with or without the objective variable and optimization direction. For more information, see chapter Extended Mathematical Programming (EMP).
## Actions Triggered by the Solve Statement
When GAMS encounters a solve statement during compilation (the syntactic check of the input file) or execution (actual execution of the program), it initiates a number of special actions. The purpose is to prevent waste that would be caused by solving a model that has apparently been incorrectly specified. During compilation the following are verified:
1. All symbolic equations have been defined and the objective variable is used in at least one of the equations.
2. The objective variable is scalar and of type free (even though lower and upper bounds may have been specified)
3. MCP models are checked for appropriate complementarity and squareness.
4. Each equation fits into the specified problem class (linearity for LP, continuous derivatives for NLP, as outlined above).
5. All sets and parameters in the equations have values assigned.
Note
GAMS issues explanatory error messages if it discovers that the model is not according to type; for example, the presence of nonlinear terms in a supposedly LP model. For details on error messages, see chapter GAMS Output.
At execution time the solve statement triggers the following sequence of steps:
1. The model is translated into the representation required by the solution system to be used.
2. Debugging and comprehension aids that the user wishes to see are produced and written to the output file (EQUATION LISTING, etc). For customizing options (e.g. LimRow and LimCol), see chapter The Option Statement.
3. GAMS verifies that there are no inconsistent bounds or unacceptable values (for example, NA or UNDF) in the problem.
4. Any errors detected at this stage cause termination with as much explanation as possible, using the GAMS names for the identifiers causing the trouble.
5. GAMS designs a solution strategy based on the possible availability of level values or basis information from a previous solution: all available information is used to provide efficiency and robustness of operation. Any specifications provided by the user (Iteration limits etc.) are incorporated. A solver is chosen which is either the default solver for that problem type, the solver specified on the command line or the solver chosen by an option statement. For details see section Choosing a Solver.
6. GAMS passes control to the solution subsystem and waits while the problem is being solved.
7. GAMS reports on the status of the solution process and loads solution values back into the GAMS database. This causes new values to be assigned to the .l and .m fields for all individual equations and variables in the model. In addition, the post solution model attributes are assigned. The procedure for loading back the data associated with level and marginal values may be customized using the SolveOpt model attribute and option. A row by row and column by column listing of the solution is provided by default. It may be suppressed by the SolPrint model attribute or option. Any apparent difficulty with the solution process will cause explanatory messages to be displayed. Errors caused by forbidden nonlinear operations are reported at this stage.
Note
When the solver does not provide a dual solution (.m), then GAMS does not print the marginal column in the solution listing and set the marginal field in variables and equations to NA.
The outputs from these steps, including any possible error messages, are discussed in detail in chapter GAMS Output.
# Programs with Several Solve Statements
Several solve statements can be processed in the same program. The next few subsections discuss various instances where several solve statements may be needed in the same file. If sequences of expensive or difficult models are to be solved, it might be useful to interrupt program execution and continue later. For details on this topic, see chapter The Save and Restart Feature.
## Several Models
If there are different models then the solves may be sequential, as below. Each of the models in [PROLOG] consists of a different set of equations, but the data are identical, so the three solves appear in sequence with no intervening assignments:
Solve nortonl using nlp maximizing z;
Solve nortonn using nlp maximizing z;
Solve nortone using nlp maximizing z;
When there is more than one solve statement in the program, GAMS uses as much information as possible from the previous solution to provide a starting point or basis in the search for the next solution.
## Loop: One Model, Different Data
Multiple solves may also occur as a result of a solve statement within a loop statement. Loop statements are introduced and discussed in detail in chapter Programming Flow Control Features; here we show that they may contain a solve statement and thus lead to multiple solves within one model. The example from [MEANVAR] computes the efficient frontier for return and variance for a portfolio selection problem at equidistance points.
loop(p(pp),
v.fx = vmin + (vmax-vmin)/(card(pp)+1)*ord(pp) ;
Solve var1 maximizing m using nlp ;
xres(i,p) = x.l(i);
xres('mean',p) = m.l;
xres('var',p) = v.l;
);
The set p is a set of point between the minimum and maximum variance, it is the driving set of the loop. A variance variable v is fixed at a equidistance points. With each iteration through the loop another variance level is used, the NLP model var1 is solved for each iteration and the outputs are stored in the parameter xres(*,pp), to be used later for reporting. As often for reporting purposes, the universal set * is used.
This example demonstrates how to solve the same model (in terms of variables and equations) multiple times with slightly different data. For such situations the Gather-Update-Solve-Scatter (GUSS) facility improves on the loop implementation by saving generation time and minimizing the communication with the solver. GUSS is activated by the additional keyword scenario in the solve statement followed by a set name that provides mapping information between parameters in the model and the scenario containers. A GUSS implementation of the loop would look as follows:
parameter vfx(p), px(p,i), pm(p);
set dict / p .scenario.''
v .fixed .vfx
x .level .px
m .level .pm /;
vfx(p(pp)) = vmin + (vmax-vmin)/(card(pp)+1)*ord(pp);
Solve var1 maximizing m using nlp scenario dict;
xres(i,p) = px(p,i);
xres('mean',p) = pm(p);
xres('var',p) = vfx(p);
## Customizing Solution Management: SolveOpt
It is important to consider how GAMS manages solutions if multiple models are solved. By default, GAMS merges subsequent solutions with prior solutions. This is not an issue if all models operate over the same set of variables. However, recursive procedures, different equation inclusions or logical conditions may cause only part of the variables or different variables to appear in the models to be solved. In such a case it might be useful to modify the solution management procedure using the model attribute or option SolveOpt.
## Sensitivity or Scenario Analysis
Multiple solve statements can be used not only to solve different models, but also to conduct sensitivity tests, or to perform case (or scenario) analyses of models by changing data or bounds and then solving the same model again. While some commercial LP systems allow access to "sensitivity analysis" through GAMS it is possible to be far more general and not restrict the analysis to either solver or model type. This facility is even more useful for studying many scenarios since no commercial solver will provide this information.
An example of sensitivity testing is in the simple oil-refining model [MARCO]. Because of pollution control, one of the key parameters in oil refinery models is an upper bound on the sulfur content of the fuel oil produced by the refinery. In this example, the upper bound on the sulfur content of fuel oil was set to 3.5 percent in the original data for the problem. First, the model is solved with this value. Next, a slightly lower value of 3.4 percent is used and the model is solved again. Finally, the considerably higher value of 5 percent is used and the model is solved for the last time. Key solution values are saved for later reporting after each solve. This is necessary because a following solve replaces any existing values. The key solution values are the activity levels of the process level z, a variable that is defined over a set of processes p and a set of crude oils cr. The complete sequence is:
parameter report(*,*,*) "process level report";
qs('upper','fuel-oil','sulfur') = 3.5 ;
Solve oil using lp maximizing phi;
report(cr,p,'base') = z.l(cr,p) ;
report('sulfur','limit','base') = qs('upper','fuel-oil','sulfur');
qs ('upper','fuel-oil','sulfur') = 3.4 ;
Solve oil using lp maximizing phi ;
report(cr,p,'one') = z.l(cr,p) ;
report('sulfur','limit','one') = qs ('upper','fuel-oil','sulfur');
qs('upper','fuel-oil','sulfur') = 5.0 ;
Solve oil using lp maximizing phi ;
report(cr,p,'two') = z.l(cr,p) ;
report('sulfur','limit','two') = qs('upper','fuel-oil','sulfur');
Display report ;
Note that the parameter report is defined over the universal set or short universe. In general, the universe is useful when generating reports, otherwise it would be necessary to provide special sets containing the labels used in the report. Any mistakes made in spelling labels used only in the report should be immediately apparent, and their effects should be limited to the report. The parameter qs is used to set the upper bound on the sulfur content in the fuel-oil, and the value is retrieved for the report. Note that the display statement in the final line is introduced and discussed in detail in chapter The Display Statement. This example shows not only how simply sensitivity analysis can be done, but also how the associated multi-case reporting can be handled.
The output from the display statement is shown below. Observe that there is no production at all if the permissible sulfur content is lowered. The case attributes have been listed in the row SULFUR.LIMIT. Section Global Display Controls contains more details on how to arrange reports in a variety of ways.
---- 225 PARAMETER report process level report
base one two
mid-c .a-dist 89.718 35.139
mid-c .n-reform 20.000 6.772
mid-c .cc-dist 7.805 3.057
w-tex .cc-gas-oil 5.902
w-tex .a-dist 64.861
w-tex .n-reform 12.713
w-tex .cc-dist 4.735
w-tex .hydro 28.733
sulfur.limit 3.500 3.400 5.000
Note
For other ways to do comparative analyses with GAMS, see the tutorial Comparative Analyses with GAMS.
## Iterative Implementation of Non-Standard Algorithms
Another use of multiple solve statements is to permit iterative solution of different blocks of equations, most often using solution values from the first solve as data for the next solve. These decomposition methods are useful for certain classes of problems because the subproblems being solved are smaller, and therefore more tractable. One of the most common examples of such a method is the Dantzig-Wolfe decomposition.
An example of a problem that is solved in this way is a multi-commodity network flow problem in [DANWOLFE].
# Choosing a Solver
After a model has been checked and prepared as described above, GAMS passes the model to a solver. When the GAMS system is installed default solvers for all model types are specified and these solvers are used if the user doesn't specify anything else. It is easy to switch to other appropriate solvers provided the user has the corresponding license. There are multiple ways to switch solvers:
1. Using a command line parameter of the following form:
gams mymodel model_type=solver name
For example,
gams mymodel lp=cbc
2. With an option command of the following form that is placed before the solve statement:
Option model_type=solver_name;
Here option is a keyword, model_type is the same model type that is used in the solve statement and solver_name is the name of one of the available solvers. For example,
Option LP=cbc, NLP=conopt, MIP=cbc, MINLP=default;
The MINLP=default switches back to the default solver for the MINLP model type.
3. Instead of providing a particular solver for a model type, the option Solver can be used to use a given solver for all model types this solver can handle.
Option Solver=cbc;
4. (Re)running gamsinst at any time and altering the choice of default solver as described in the installation notes.
Note
A list of all solvers and current default solvers may be generated in the listing file with Option SubSystems;.
# Making New Solvers Available with GAMS
This short section is to encourage those of you who have a favorite solver not available through GAMS. Linking a solver program with GAMS requires some programming skills and the use of libraries provided by GAMS. There is a collection of open source solver links to GAMS at the COIN-OR project GAMSLinks. The benefits of a link with GAMS to the developer of a solver are several. They include:
|
|
#jsDisabledContent { display:none; } My Account | Register | Help
Flag as Inappropriate This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate? Excessive Violence Sexual Content Political / Social Email this Article Email Address:
# Factorial
Article Id: WHEBN0000010606
Reproduction Date:
Title: Factorial Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:
### Factorial
Selected members of the factorial sequence (sequence A000142 in OEIS); values specified in scientific notation are rounded to the displayed precision
n n!
0 1
1 1
2 2
3 6
4 24
5 120
6 720
7 5040
8 40320
9 362880
10 3628800
11 39916800
12 479001600
13 6227020800
14 87178291200
15 1307674368000
16 20922789888000
17 355687428096000
18 6402373705728000
19 121645100408832000
20 2432902008176640000
25 1.551121004×1025
50 3.041409320×1064
70 1.197857167×10100
100 9.332621544×10157
450 1.733368733×101000
1000 4.023872601×102567
3249 6.412337688×1010000
10000 2.846259681×1035659
25206 1.205703438×10100000
100000 2.824229408×10456573
205023 2.503898932×101000004
1000000 8.263931688×105565708
1723508 5.290070307×1010000001
2000000 3.776821058×1011733474
10000000 1.202423401×1065657059
14842907 2.788662975×10100000000
10100 109.956570552×10101
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,
5! = 5 \times 4 \times 3 \times 2 \times 1 = 120. \
The value of 0! is 1, according to the convention for an empty product.[1]
The factorial operation is encountered in many areas of mathematics, notably in combinatorics, algebra, and mathematical analysis. Its most basic occurrence is the fact that there are n! ways to arrange n distinct objects into a sequence (i.e., permutations of the set of objects). This fact was known at least as early as the 12th century, to Indian scholars.[2] Fabian Stedman in 1677 described factorials as applied to change ringing.[3] After describing a recursive approach, Stedman gives a statement of a factorial (using the language of the original):
Now the nature of these methods is such, that the changes on one number comprehends [includes] the changes on all lesser numbers, ... insomuch that a compleat Peal of changes on one number seemeth to be formed by uniting of the compleat Peals on all lesser numbers into one entire body;[4]
The notation n! was introduced by Christian Kramp in 1808.[5]
The definition of the factorial function can also be extended to non-integer arguments, while retaining its most important properties; this involves more advanced mathematics, notably techniques from mathematical analysis.
## Definition
The factorial function is formally defined by the product
n!=\prod_{k=1}^n k \!
or by the recurrence relation
n! = \begin{cases} 1 & \text{if } n = 0, \\ (n-1)!\times n & \text{if } n > 0 \end{cases}
The factorial function can also be defined by using the power rule as
n! = D^nx^n \;[6]
All of the above definitions incorporate the instance
0! = 1, \
in the first case by the convention that the product of no numbers at all is 1. This is convenient because:
• There is exactly one permutation of zero objects (with nothing to permute, "everything" is left in place).
• The recurrence relation (n + 1)! = n! × (n + 1), valid for n > 0, extends to n = 0.
• It allows for the expression of many formulae, such as the exponential function, as a power series:
e^x = \sum_{n = 0}^{\infty}\frac{x^n}{n!}.
• It makes many identities in combinatorics valid for all applicable sizes. The number of ways to choose 0 elements from the empty set is \tbinom{0}{0} = \tfrac{0!}{0!0!} = 1. More generally, the number of ways to choose (all) n elements among a set of n is \tbinom nn = \tfrac{n!}{n!0!} = 1.
The factorial function can also be defined for non-integer values using more advanced mathematics, detailed in the section below. This more generalized definition is used by advanced calculators and mathematical software such as Maple or Mathematica.
## Applications
Although the factorial function has its roots in combinatorics, formulas involving factorials occur in many areas of mathematics.
• There are n! different ways of arranging n distinct objects into a sequence, the permutations of those objects.
• Often factorials appear in the denominator of a formula to account for the fact that ordering is to be ignored. A classical example is counting k-combinations (subsets of k elements) from a set with n elements. One can obtain such a combination by choosing a k-permutation: successively selecting and removing an element of the set, k times, for a total of
n^{\underline k}=n(n-1)(n-2)\cdots(n-k+1)
possibilities. This however produces the k-combinations in a particular order that one wishes to ignore; since each k-combination is obtained in k! different ways, the correct number of k-combinations is
\frac{n^{\underline k}}{k!}=\frac{n(n-1)(n-2)\cdots(n-k+1)}{k(k-1)(k-2)\cdots1}.
This number is known as the binomial coefficient \tbinom nk, because it is also the coefficient of Xk in (1 + X)n.
• Factorials occur in algebra for various reasons, such as via the already mentioned coefficients of the binomial formula, or through averaging over permutations for symmetrization of certain operations.
• Factorials also turn up in calculus; for example they occur in the denominators of the terms of Taylor's formula, where they are used as compensation terms due to the n-th derivative of xn being equivalent to n!.
• Factorials are also used extensively in probability theory.
• Factorials can be useful to facilitate expression manipulation. For instance the number of k-permutations of n can be written as
n^{\underline k}=\frac{n!}{(n-k)!};
while this is inefficient as a means to compute that number, it may serve to prove a symmetry property of binomial coefficients:
\binom nk=\frac{n^{\underline k}}{k!}=\frac{n!}{(n-k)!k!}=\frac{n^{\underline{n-k}}}{(n-k)!}=\binom n{n-k}.
## Number theory
Factorials have many applications in number theory. In particular, n! is necessarily divisible by all prime numbers up to and including n. As a consequence, n > 5 is a composite number if and only if
(n-1)!\ \equiv\ 0 \pmod n.
A stronger result is Wilson's theorem, which states that
(p-1)!\ \equiv\ -1 \pmod p
if and only if p is prime.
Legendre's formula gives the multiplicity of the prime p occurring in the prime factorization of n! as
\sum_{i=1}^{\infty} \left \lfloor \frac{n}{p^i} \right \rfloor
or, equivalently,
\frac{n - s_p(n)}{p - 1}
where s_p(n) denotes the sum of the standard base-p digits of n.
The only factorial that is also a prime number is 2, but there are many primes of the form n! ± 1, called factorial primes.
All factorials greater than 1! are even, as they are all multiples of 2. Also, all factorials from 5! upwards are multiples of 10 (and hence have a trailing zero as their final digit), because they are multiples of 5 and 2.
## Series of reciprocals
The reciprocals of factorials produce a convergent series: (see e)
\sum_{n=0}^{\infty} \frac{1}{n!} = \frac{1}{1} + \frac{1}{1} + \frac{1}{2} + \frac{1}{6} + \frac{1}{24} + \frac{1}{120} + \ldots = e\,.
Although the sum of this series is an irrational number, it is possible to multiply the factorials by positive integers to produce a convergent series with a rational sum:
\sum_{n=0}^{\infty} \frac{1}{(n+2)n!} = \frac{1}{2}+\frac{1}{3}+\frac{1}{8}+\frac{1}{30}+\frac{1}{144}\ldots=1\,.
The convergence of this series to 1 can be seen from the fact that its partial sums are less than one by an inverse factorial. Therefore, the factorials do not form an irrationality sequence.[7]
## Rate of growth and approximations for large n
Plot of the natural logarithm of the factorial
As n grows, the factorial n! increases faster than all polynomials and exponential functions (but slower than double exponential functions) in n.
Most approximations for n! are based on approximating its natural logarithm
\log n! = \sum_{x=1}^n \log x.
The graph of the function f(n) = log n! is shown in the figure on the right. It looks approximately linear for all reasonable values of n, but this intuition is false. We get one of the simplest approximations for log n! by bounding the sum with an integral from above and below as follows:
\int_1^n \log x \, dx \leq \sum_{x=1}^n \log x \leq \int_0^n \log (x+1) \, dx
which gives us the estimate
n\log\left(\frac{n}{e}\right)+1 \leq \log n! \leq (n+1)\log\left( \frac{n+1}{e} \right) + 1.
Hence log n! is Θ(n log n) (see Big O notation). This result plays a key role in the analysis of the computational complexity of sorting algorithms (see comparison sort). From the bounds on log n! deduced above we get that
e\left(\frac ne\right)^n \leq n! \leq e\left(\frac{n+1}e\right)^{n+1}.
It is sometimes practical to use weaker but simpler estimates. Using the above formula it is easily shown that for all n we have (n/3)^n < n!, and for all n ≥ 6 we have n! < (n/2)^n.
For large n we get a better estimate for the number n! using Stirling's approximation:
n!\approx \sqrt{2\pi n}\left(\frac{n}{e}\right)^n.
In fact, it can be proved that for all n we have
n! > \sqrt{2\pi n}\left(\frac{n}{e}\right)^n.
Another approximation for log n! is given by Srinivasa Ramanujan (Ramanujan 1988)
\log n! \approx n\log n - n + \frac {\log(n(1+4n(1+2n)))} {6} + \frac {\log(\pi)} {2}
= n\log n - n + \frac {\log(1 +1/(2n) +1/(8n^2))} {6} + \frac {3\log (2n)} 6 + \frac {\log(\pi)} {2}.
Thus it is even smaller than the next correction term \tfrac 1 {12n} of Stirling's formula.
## Computation
If efficiency is not a concern, computing factorials is trivial from an algorithmic point of view: successively multiplying a variable initialized to 1 by the integers 2 up to n (if any) will compute n!, provided the result fits in the variable. In functional languages, the recursive definition is often implemented directly to illustrate recursive functions.
The main practical difficulty in computing factorials is the size of the result. To assure that the exact result will fit for all legal values of even the smallest commonly used integral type (8-bit signed integers) would require more than 700 bits, so no reasonable specification of a factorial function using fixed-size types can avoid questions of overflow. The values 12! and 20! are the largest factorials that can be stored in, respectively, the 32-bit and 64-bit integers commonly used in personal computers. Floating-point representation of an approximated result allows going a bit further, but this also remains quite limited by possible overflow. Most calculators use scientific notation with 2-digit decimal exponents, and the largest factorial that fits is then 69!, because 69! < 10100 < 70!. Calculators that use 3-digit exponents can compute larger factorials, up to, for example, 253! ≈ 5.2×10499 on HP calculators and 449! ≈ 3.9×10997 on the TI-86. The calculator seen in Mac OS X handles up to 92!, Apple's Numbers, Microsoft Excel and Google Calculator, as well as the freeware Fox Calculator, can handle factorials up to 170!, which is the largest factorial whose floating-point approximation can be represented as a 64-bit IEEE 754 floating-point value. The scientific calculator in Windows 7 and Windows 8 is able to calculate factorials up to 3248!.
Most software applications will compute small factorials by direct multiplication or table lookup. Larger factorial values can be approximated using Stirling's formula. Wolfram Alpha can calculate exact results for the ceiling function and floor function applied to the binary, natural and common logarithm of n! for values of n up to 249999, and up to 20,000,000! for the integers.
If the exact values of large factorials are needed, they can be computed using arbitrary-precision arithmetic. Instead of doing the sequential multiplications ((1 \times 2) \times 3) \times 4\dots, a program can partition the sequence into two parts, whose products are roughly the same size, and multiply them using a divide-and-conquer method. This is often more efficient.[8]
The asymptotically best efficiency is obtained by computing n! from its prime factorization. As documented by Peter Borwein, prime factorization allows n! to be computed in time O(n(log n log log n)2), provided that a fast multiplication algorithm is used (for example, the Schönhage–Strassen algorithm).[9] Peter Luschny presents source code and benchmarks for several efficient factorial algorithms, with or without the use of a prime sieve.[10]
## Extension of factorial to non-integer values of argument
### The Gamma and Pi functions
The factorial function, generalized to all real numbers except negative integers. For example, 0! = 1! = 1, (−0.5)! = π, (0.5)! = π/2.
Besides nonnegative integers, the factorial function can also be defined for non-integer values, but this requires more advanced tools from mathematical analysis. One function that "fills in" the values of the factorial (but with a shift of 1 in the argument) is called the Gamma function, denoted Γ(z), defined for all complex numbers z except the non-positive integers, and given when the real part of z is positive by
\Gamma(z)=\int_0^\infty t^{z-1} e^{-t}\, \mathrm{d}t. \!
Its relation to the factorials is that for any natural number n
n!=\Gamma(n+1).\,
Euler's original formula for the Gamma function was
\Gamma(z)=\lim_{n\to\infty}\frac{n^zn!}{\displaystyle\prod_{k=0}^n (z+k)}. \!
An alternative notation, originally introduced by Gauss, is sometimes used. The Pi function, denoted Π(z) for real numbers z no less than 0, is defined by
\Pi(z)=\int_0^\infty t^{z} e^{-t}\, \mathrm{d}t\,.
In terms of the Gamma function it is
\Pi(z) = \Gamma(z+1) \,.
It truly extends the factorial in that
\Pi(n) = n!\text{ for }n \in \mathbf{N}\, .
In addition to this, the Pi function satisfies the same recurrence as factorials do, but at every complex value z where it is defined
\Pi(z) = z\Pi(z-1)\,.
In fact, this is no longer a recurrence relation but a functional equation. Expressed in terms of the Gamma function this functional equation takes the form
\Gamma(n+1)=n\Gamma(n)\,.
Since the factorial is extended by the Pi function, for every complex value z where it is defined, we can write:
z! = \Pi(z)\,
The values of these functions at half-integer values is therefore determined by a single one of them; one has
\Gamma\left (\frac{1}{2}\right )=\left (-\frac{1}{2}\right )!=\Pi\left (-\frac{1}{2}\right ) = \sqrt{\pi},
from which it follows that for n ∈ N,
\Gamma\left (\frac{1}{2}+n\right ) = \left (-\frac{1}{2}+n\right )! = \Pi\left (-\frac{1}{2}+n\right ) = \sqrt{\pi} \prod_{k=1}^n {2k - 1 \over 2} = {(2n)! \over 4^n n!} \sqrt{\pi} = {(2n-1)! \over 2^{2n-1}(n-1)!} \sqrt{\pi}.
For example,
\Gamma\left (4.5 \right ) = 3.5! = \Pi\left (3.5\right ) = {1\over 2}\cdot{3\over 2}\cdot{5\over 2}\cdot{7\over 2} \sqrt{\pi} = {8! \over 4^4 4!} \sqrt{\pi} = {7! \over 2^7 3!} \sqrt{\pi} = {105 \over 16} \sqrt{\pi} \approx 11.63.
It also follows that for n ∈ N,
\Gamma\left (\frac{1}{2}-n\right ) = \left (-\frac{1}{2}-n\right )! = \Pi\left (-\frac{1}{2}-n\right ) = \sqrt{\pi} \prod_{k=1}^n {2 \over 1 - 2k} = {(-4)^n n! \over (2n)!} \sqrt{\pi}.
For example,
\Gamma\left (-2.5 \right ) = (-3.5)! = \Pi\left (-3.5\right ) = {2\over -1}\cdot{2\over -3}\cdot{2\over -5} \sqrt{\pi} = {(-4)^3 3! \over 6!} \sqrt{\pi} = -{8 \over 15} \sqrt{\pi} \approx -0.9453.
The Pi function is certainly not the only way to extend factorials to a function defined at almost all complex values, and not even the only one that is analytic wherever it is defined. Nonetheless it is usually considered the most natural way to extend the values of the factorials to a complex function. For instance, the Bohr–Mollerup theorem states that the Gamma function is the only function that takes the value 1 at 1, satisfies the functional equation Γ(n + 1) = nΓ(n), is meromorphic on the complex numbers, and is log-convex on the positive real axis. A similar statement holds for the Pi function as well, using the Π(n) = nΠ(n − 1) functional equation.
However, there exist complex functions that are probably simpler in the sense of analytic function theory and which interpolate the factorial values. For example, Hadamard's 'Gamma'-function (Hadamard 1894) which, unlike the Gamma function, is an entire function.[11]
Euler also developed a convergent product approximation for the non-integer factorials, which can be seen to be equivalent to the formula for the Gamma function above:
\begin{align}n! = \Pi(n) &= \prod_{k = 1}^\infty \left(\frac{k+1}{k}\right)^n\!\!\frac{k}{n+k} \\ &= \left[ \left(\frac{2}{1}\right)^n\frac{1}{n+1}\right]\left[ \left(\frac{3}{2}\right)^n\frac{2}{n+2}\right]\left[ \left(\frac{4}{3}\right)^n\frac{3}{n+3}\right]\cdots. \end{align}
However, this formula does not provide a practical means of computing the Pi or Gamma function, as its rate of convergence is slow.
### Applications of the Gamma function
The volume of an n-dimensional hypersphere of radius R is
V_n=\frac{\pi^{n/2}}{\Gamma((n/2)+1)}R^n.
### Factorial at the complex plane
Amplitude and phase of factorial of complex argument
Representation through the Gamma-function allows evaluation of factorial of complex argument. Equilines of amplitude and phase of factorial are shown in figure. Let \ f=\rho \exp({\rm i}\varphi)=(x+{\rm i}y)!=\Gamma(x+{\rm i}y+1) . Several levels of constant modulus (amplitude) \rho =\rm const and constant phase \varphi=\rm const are shown. The grid covers range ~-3 \le x \le 3~, ~-2 \le y \le 2~ with unit step. The scratched line shows the level \varphi=\pm \pi.
Thin lines show intermediate levels of constant modulus and constant phase. At poles x+ {\rm i}y \in \rm (negative ~ integers), phase and amplitude are not defined. Equilines are dense in vicinity of singularities along negative integer values of the argument.
For |z|<1, the Taylor expansions can be used:
z!=\sum_{n=0}^{\infty} g_n z^n.
The first coefficients of this expansion are
n g_n approximation
0 1 1
1 -\gamma - 0.5772156649
2 \frac{\pi^2}{12}+\frac{\gamma^2}{2} 0.9890559955
3 -\frac{\zeta(3)}{3}-\frac{\pi^2\gamma}{12}-\frac{\gamma^3}{6} -0.9074790760
where \gamma is the Euler constant and \zeta is the Riemann zeta function. Computer algebra systems such as Sage can generate many terms of this expansion.
### Approximations of factorial
For the large values of the argument, factorial can be approximated through the integral of the digamma function, using the continued fraction representation. This approach is due to T. J. Stieltjes (1894). Writing z! = exp(P(z)) where P(z) is
P(z) = p(z) + \log(2\pi)/2 - z + \left(z+\frac{1}{2}\right)\log(z),
Stieltjes gave a continued fraction for p(z)
p(z)=\cfrac{a_0}{z+ \cfrac{a_1}{z+ \cfrac{a_2}{z+ \cfrac{a_3}{z+\ddots}}}}
The first few coefficients an are[12]
n an
0 1 / 12
1 1 / 30
2 53 / 210
3 195 / 371
4 22999 / 22737
5 29944523 / 19733142
6 109535241009 / 48264275462
There is common misconception, that \displaystyle\log(z!)=P(z) or \log(\Gamma(z\!+\!1))=P(z) for any complex z ≠ 0. Indeed, the relation through the logarithm is valid only for specific range of values of z in vicinity of the real axis, while |\Im(\Gamma(z\!+\!1))| < \pi . The larger is the real part of the argument, the smaller should be the imaginary part. However, the inverse relation, z! = exp(P(z)), is valid for the whole complex plane apart from zero. The convergence is poor in vicinity of the negative part of the real axis. (It is difficult to have good convergence of any approximation in vicinity of the singularities). While |\Im(z)| >2 or \Re(z)>2, the 6 coefficients above are sufficient for the evaluation of the factorial with the complex precision. For higher precision more coefficients can be computed by a rational QD-scheme (H. Rutishauser's QD algorithm).[13]
### Non-extendability to negative integers
The relation n! = n × (n − 1)! allows one to compute the factorial for an integer given the factorial for a smaller integer. The relation can be inverted so that one can compute the factorial for an integer given the factorial for a larger integer:
(n-1)! = \frac{n!}{n}.
Note, however, that this recursion does not permit us to compute the factorial of a negative integer; use of the formula to compute (−1)! would require a division by zero, and thus blocks us from computing a factorial value for every negative integer. (Similarly, the Gamma function is not defined for non-positive integers, though it is defined for all other complex numbers.)
## Factorial-like products and functions
There are several other integer sequences similar to the factorial that are used in mathematics:
### Primorial
The primorial (sequence A002110 in OEIS) is similar to the factorial, but with the product taken only over the prime numbers.
### Double factorial
The product of all the odd integers up to some odd positive integer n is called the double factorial of n, and denoted by n!!.[14] That is,
(2k-1)!! = \prod_{i=1}^k (2i-1) = \frac{(2k)!}{2^k k!} = \frac {_{2k}P_k} {2^k} = \frac {2^k}.
For example, 9!! = 1 × 3 × 5 × 7 × 9 = 945.
The sequence of double factorials for n = 1, 3, 5, 7, ... starts as
1, 3, 15, 105, 945, 10395, 135135, .... (sequence A001147 in OEIS)
Double factorial notation may be used to simplify the expression of certain trigonometric integrals,[15] to provide an expression for the values of the Gamma function at half-integer arguments and the volume of hyperspheres,[16] and to solve many counting problems in combinatorics including counting binary trees with labeled leaves and perfect matchings in complete graphs.[14][17]
### Multifactorials
A common related notation is to use multiple exclamation points to denote a multifactorial, the product of integers in steps of two (n!!), three (n!!!), or more. The double factorial is the most commonly used variant, but one can similarly define the triple factorial (n!!!) and so on. One can define the k-th factorial, denoted by n!^{(k)}, recursively for non-negative integers as
n!^{(k)}= \left\{ \begin{matrix} 1,\qquad\qquad\ &&\mbox{if }0\le n
though see the alternative definition below.
Some mathematicians have suggested an alternative notation of n!_2 for the double factorial and similarly n!_k for other multifactorials, but this has not come into general use.
In the same way that n! is not defined for negative integers, and n!! is not defined for negative even integers, n!^{(k)} is not defined for negative integers divisible by k.
#### Alternative extension of the multifactorial
Alternatively, the multifactorial z!(k) can be extended to most real and complex numbers z by noting that when z is one more than a positive multiple of k then
z!^{(k)} = z(z-k)\cdots (k+1) = k^{(z-1)/k}\left(\frac{z}{k}\right)\left(\frac{z-k}{k}\right)\cdots \left(\frac{k+1}{k}\right) = k^{(z-1)/k} \frac{\Gamma\left(\frac{z}{k}+1\right)}{\Gamma\left(\frac{1}{k}+1\right)}\,.
This last expression is defined much more broadly than the original; with this definition, z!(k) is defined for all complex numbers except the negative real numbers evenly divisible by k. This definition is consistent with the earlier definition only for those integers z satisfying z ≡ 1 mod k.
In addition to extending z!(k) to most complex numbers z, this definition has the feature of working for all positive real values of k. Furthermore, when k = 1, this definition is mathematically equivalent to the Π(z) function, described above. Also, when k = 2, this definition is mathematically equivalent to the alternative extension of the double factorial.
### Quadruple factorial
The quadruple factorial is not the multifactorial n!(4); it is a much larger number given by (2n)!/n!, starting as
1, 2, 12, 120, 1680, 30240, 665280, ... (sequence A001813 in OEIS).
It is also equal to
\begin{align} 2^n\frac{(2n)!}{n!2^n} & = 2^n \frac{(2\cdot 4\cdots 2n) (1\cdot 3\cdots (2n-1))}{2\cdot 4\cdots 2n} \\[8pt] & = (1\cdot 2)\cdot (3 \cdot 2) \cdots((2n-1)\cdot 2)=(4n-2)!^{(4)}. \end{align}
### Superfactorial
Neil Sloane and Simon Plouffe defined a superfactorial in The Encyclopedia of Integer Sequences (Academic Press, 1995) to be the product of the first n factorials. So the superfactorial of 4 is
\mathrm{sf}(4)=1! \times 2! \times 3! \times 4!=288. \,
In general
\mathrm{sf}(n) =\prod_{k=1}^n k! =\prod_{k=1}^n k^{n-k+1} =1^n\cdot2^{n-1}\cdot3^{n-2}\cdots(n-1)^2\cdot n^1.
Equivalently, the superfactorial is given by the formula
\mathrm{sf}(n) =\prod_{0 \le i < j \le n} (j-i)
which is the determinant of a Vandermonde matrix.
The sequence of superfactorials starts (from n = 0) as
1, 1, 2, 12, 288, 34560, 24883200, 125411328000, ... (sequence A000178 in OEIS)
#### Alternative definition
Clifford Pickover in his 1995 book Keys to Infinity used a new notation, n$, to define the superfactorial n\$\equiv \begin{matrix} \underbrace{ n!^}}}} \\ n! \end{matrix}, \,
or as,
n\$=n! [4] n! \, where the [4] notation denotes the hyper4 operator, or using Knuth's up-arrow notation, n\$=(n!)\uparrow\uparrow(n!). \,
This sequence of superfactorials starts:
1\$=1 \, 2\$=2^2=4 \,
3\\$=6 [4] 6={^6}6=6^{6^{6^{6^{6^6}}}}.
Here, as is usual for compound exponentiation, the grouping is understood to be from right to left:
a^{b^c}=a^{(b^c)}.\,
### Hyperfactorial
Occasionally the hyperfactorial of n is considered. It is written as H(n) and defined by
H(n) =\prod_{k=1}^n k^k =1^1\cdot2^2\cdot3^3\cdots(n-1)^{n-1}\cdot n^n.
For n = 1, 2, 3, 4, ... the values H(n) are 1, 4, 108, 27648,... (sequence A002109 in OEIS).
The asymptotic growth rate is
H(n) \sim A n^{(6n^2 + 6n + 1)/12} e^{-n^2/4}
where A = 1.2824... is the Glaisher–Kinkelin constant.[18] H(14) = 1.8474...×1099 is already almost equal to a googol, and H(15) = 8.0896...×10116 is almost of the same magnitude as the Shannon number, the theoretical number of possible chess games. Compared to the Pickover definition of the superfactorial, the hyperfactorial grows relatively slowly.
The hyperfactorial function can be generalized to complex numbers in a similar way as the factorial function. The resulting function is called the K-function.
## Notes
1. ^ Ronald L. Graham, Donald E. Knuth, Oren Patashnik (1988) Concrete Mathematics, Addison-Wesley, Reading MA. ISBN 0-201-14236-8, p. 111
2. ^ N. L. Biggs, The roots of combinatorics, Historia Math. 6 (1979) 109−136
3. ^ The publisher is given as "W.S." who may have been William Smith, possibly acting as agent for the Society of College Youths, to which society the "Dedicatory" is addressed.
4. ^ Stedman 1677, p. 8.
5. ^ Higgins, Peter (2008), Number Story: From Counting to Cryptography, New York: Copernicus, p. 12, says Krempe though.
6. ^ http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/lecture-notes/lec4.pdf
7. ^
8. ^ GNU MP software manual, "Factorial Algorithm" (retrieved 22 January 2013).
9. ^ Peter Borwein. "On the Complexity of Calculating Factorials". Journal of Algorithms 6, 376–380 (1985)
10. ^ Peter Luschny, Fast-Factorial-Functions: The Homepage of Factorial Algorithms.
11. ^ Peter Luschny, Hadamard versus Euler - Who found the better Gamma function?.
12. ^ Digital Library of Mathematical Functions, http://dlmf.nist.gov/5.10
13. ^ Peter Luschny, On Stieltjes' Continued Fraction for the Gamma Function..
14. ^ a b Callan, David (2009), A combinatorial survey of identities for the double factorial, .
15. ^ Meserve, B. E. (1948), "Classroom Notes: Double Factorials", The American Mathematical Monthly 55 (7): 425–426,
16. ^ Mezey, Paul G. (2009), "Some dimension problems in molecular databases", Journal of Mathematical Chemistry 45 (1): 1–6, .
17. ^ Dale, M. R. T.; Moon, J. W. (1993), "The permuted analogues of three Catalan sets", Journal of Statistical Planning and Inference 34 (1): 75–87, .
18. ^ Weisstein, Eric W., "Glaisher–Kinkelin Constant", MathWorld.
## References
• Hadamard, M. J. (1894), Sur L’Expression Du Produit 1·2·3· · · · ·(n−1) Par Une Fonction Entière (in French), OEuvres de Jacques Hadamard, Centre National de la Recherche Scientifiques, Paris, 1968
• Ramanujan, Srinivasa (1988), The lost notebook and other unpublished papers, Springer Berlin, p. 339,
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.
|
|
# Finding Hybridization of Certain Atoms in Lewis Structure [duplicate]
So, I'm having trouble with this problem. We're given this incomplete lewis structure and asked to find the hybridization of 3 of the atoms.
I figured that the labelled Cl would be sp3 because of it's 1 single bond and the 3 lone pairs that would be on it. I also thought the labelled C would be sp2 because of the 2 single bonds and 1 lone pair. Now, I was confused at to what the labelled O would be. I thought maybe it would have 3 lone pairs but that doesn't seem to be correct, since my sp3 answer was rejected.
Any insight on what I'm doing wrong here?
• A lone pair on C would be quite an unusual thing to find. Consider double bonds instead. Yes, some of these bonds are double, and they won't tell you which. But you may guess... Nov 5 '15 at 0:21
• You should never consider halogens hybridised in any way.
– Jan
Nov 5 '15 at 0:27
• Still, if confronted with a question like this one, go with $sp^3$ for Cl, because that's what they want from you. Nov 5 '15 at 0:41
• Well, if you see valency of Oxygen is 2, but its making only 1 bond. Thats enough for hint, and as @IvanNeretin said "some of these bonds are double, and they won't tell you which. But you may guess..." Nov 6 '15 at 2:58
|
|
# 6.6 Wave-particle duality (Page 4/12)
Page 4 / 12
Such limitations do not appear in the scanning electron microscope (SEM) , which was invented by Manfred von Ardenne in 1937. In an SEM, a typical energy of the electron beam is up to 40 keV and the beam is not transmitted through a sample but is scattered off its surface. Surface topography of the sample is reconstructed by analyzing back-scattered electrons, transmitted electrons, and the emitted radiation produced by electrons interacting with atoms in the sample. The resolving power of an SEM is better than 1 nm, and the magnification can be more than 250 times better than that obtained with a light microscope. The samples scanned by an SEM can be as large as several centimeters but they must be specially prepared, depending on electrical properties of the sample.
High magnifications of the TEM and SEM allow us to see individual molecules. High resolving powers of the TEM and SEM allow us to see fine details, such as those shown in the SEM micrograph of pollen at the beginning of this chapter ( [link] ).
## Resolving power of an electron microscope
If a 1.0-pm electron beam of a TEM passes through a $2.0\text{-}\mu \text{m}$ circular opening, what is the angle between the two just-resolvable point sources for this microscope?
## Solution
We can directly use a formula for the resolving power, $\text{Δ}\theta ,$ of a microscope (discussed in a previous chapter) when the wavelength of the incident radiation is $\lambda =1.0\phantom{\rule{0.2em}{0ex}}\text{pm}$ and the diameter of the aperture is $D=2.0\mu \text{m}:$
$\text{Δ}\theta =1.22\frac{\lambda }{D}=1.22\frac{1.0\phantom{\rule{0.2em}{0ex}}\text{pm}}{2.0\mu \text{m}}=6.10\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-7}\text{rad}=3.50\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\text{degree.}$
## Significance
Note that if we used a conventional microscope with a 400-nm light, the resolving power would be only $14\text{°},$ which means that all of the fine details in the image would be blurred.
Check Your Understanding Suppose that the diameter of the aperture in [link] is halved. How does it affect the resolving power?
doubles it
## Summary
• Wave-particle duality exists in nature: Under some experimental conditions, a particle acts as a particle; under other experimental conditions, a particle acts as a wave. Conversely, under some physical circumstances, electromagnetic radiation acts as a wave, and under other physical circumstances, radiation acts as a beam of photons.
• Modern-era double-slit experiments with electrons demonstrated conclusively that electron-diffraction images are formed because of the wave nature of electrons.
• The wave-particle dual nature of particles and of radiation has no classical explanation.
• Quantum theory takes the wave property to be the fundamental property of all particles. A particle is seen as a moving wave packet. The wave nature of particles imposes a limitation on the simultaneous measurement of the particle’s position and momentum. Heisenberg’s uncertainty principle sets the limits on precision in such simultaneous measurements.
• Wave-particle duality is exploited in many devices, such as charge-couple devices (used in digital cameras) or in the electron microscopy of the scanning electron microscope (SEM) and the transmission electron microscope (TEM).
in the wave equation y=Asin(kx-wt+¢) what does k and w stand for.
k is the wave number and w rotational speed
Mwezi
derivation of lateral shieft
Hi
Hi
hi
ALFRED
how are you?
hi
asif
hi
Imran
I'm fine
ALFRED
total binding energy of ionic crystal at equilibrium is
How does, ray of light coming form focus, behaves in concave mirror after refraction?
Sushant
What is motion
Anything which changes itself with respect to time or surrounding
Sushant
good
Chemist
and what's time? is time everywhere same
Chemist
No
Sushant
how can u say that
Chemist
do u know about black hole
Chemist
Not so more
Sushant
DHEERAJ
Sushant
But ask anything changes itself with respect to time or surrounding A Not any harmful radiation
DHEERAJ
explain cavendish experiment to determine the value of gravitational concept.
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
as a free falling object increases speed what is happening to the acceleration
of course g is constant
Alwielland
acceleration also inc
Usman
which paper will be subjective and which one objective
jay
normal distributiin of errors report
Dennis
normal distribution of errors
Dennis
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons?
give any fix value to wave length
Rafi
40 cm into change mm
40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power.
Prema
i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line.
Prema
there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends.
Prema
40cm=40.0×10^-2m =400.0×10^-3m =400mm.
Prema
this msg is out of mistake. sorry friends.
Prema
what is physics?
why we have physics
because is the study of mater and natural world
John
because physics is nature. it explains the laws of nature. some laws already discovered. some laws yet to be discovered.
Yoblaze
physics is the study of non living things if we added it with biology it becomes biophysics and bio is the study of living things tell me please what is this?
tahreem
physics is the study of matter,energy and their interactions
Buvanes
all living things are matter
Buvanes
why rolling friction is less than sliding friction
tahreem
thanks buvanas
tahreem
is this a physics forum
explain l-s coupling
|
|
# Proof of strong law of large numbers: not identical case
I've seen two types of conditions for strong law of large numbers: one requires i.i.d and first order moment condition: $X_n$ i.i.d with $E|X_1| < \infty$; the other requires second order moment condition but may not be identical: $X_n$ independent (may not identical) with $\sum_{n} Var(X_n)/n^2 < \infty$. I have known the proof under these two types of conditions.
However, I cannot find a proof for not identical case requiring only first order moment. I am wondering whether it is true that: if $X_n$ independent (may not identical) with $\sup_{n} E|X_n| < \infty$, then $\frac{1}{n}\sum_{i=1}^n (X_i - E(X_i)) \xrightarrow{a.s.}0$.
Example: Independent $X_k\sim\mathcal N(0,k)$? In this case the average $n^{-1}\sum_{k=1}^n X_k$ is normally distributed with mean $0$ and variance $(n+1)/2n$, and so is asymptotically normal with variance $1/2$. In view of the Kolmogorov zero-one law, the average cannot converge a.s.
• However, there is a problem in your example that $E|X_k| = k \sqrt{2/\pi} \to \infty$. – Titan_Tong Mar 9 '16 at 0:25
• $E|X_k|=\sqrt{2k/\pi}$. – John Dawkins Mar 9 '16 at 3:00
|
|
## Access
You are not currently logged in.
Access JSTOR through your library or other institution:
## If You Use a Screen Reader
This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Journal Article
# Universal Prediction of Random Binary Sequences in a Noisy Environment
Tsachy Weissman and Neri Merhav
The Annals of Applied Probability
Vol. 14, No. 1 (Feb., 2004), pp. 54-89
Stable URL: http://www.jstor.org/stable/4140490
Page Count: 36
#### Select the topics that are inaccurate.
Cancel
Preview not available
## Abstract
Let $X = {(X_t, Y_t)}_{t\in Z}$ be a stationary time series where Xt is binary valued and Yt, the noisy observation of Xt, is real valued. Letting P denote the probability measure governing the joint process $\lbrace(X_t, Y_t)\rbrace$, we characterize U(l, P), the optimal asymptotic average performance of a predictor allowed to base its prediction for Xt on Y1, ..., $Y_{t-1}$, where performance is evaluated using the loss function l. It is shown that the stationarity and ergodicity of P, combined with an additional "conditional mixing" condition, suffice to establish U(l, P) as the fundamental limit for the almost sure asymptotic performance. U(l, P) can thus be thought of as a generalized notion of the Shannon entropy, which can capture the sensitivity of the underlying clean sequence to noise. For the case where $X = {X_t}$ is governed by P and Yt given by $Y_t = g(X_t, N_t)$ where g is any deterministic function and $N = {N_t}$, the noise, is any i.i.d. process independent of X (namely, the case where the "clean" process X is passed through a fixed memoryless channel), it is shown that, analogously to the noiseless case, there exist universal predictors which do not depend on P yet attain U(l, P). Furthermore, it is shown that in some special cases of interest [e.g., the binary symmetric channel (BSC) and the absolute loss function], there exist twofold universal predictors which do not depend on the noise distribution either. The existence of such universal predictors is established by means of an explicit construction which builds on recent advances in the theory of prediction of individual sequences in the presence of noise.
• 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
|
|
dc.creator Sadygov, R. G. en_US dc.creator Lim, E. C. en_US dc.date.accessioned 2007-11-20T17:16:28Z dc.date.available 2007-11-20T17:16:28Z dc.date.issued 1995 en_US dc.identifier 1995-FC-13 en_US dc.identifier.uri http://hdl.handle.net/1811/29927 dc.description Author Institution: The University of Akron, Akron, OH 44325-3601 en_US dc.description.abstract Intermolecular interactions play a key role in a variety of chemical processes ranging from formation of van der Waals clusters to strongly bound charge-transfer complexes. The study of dimers provides new insights into the nature of intermolecular bond forces. This talk will discuss results of ab initio studies of the benzene homodimer cation. Partial geometry optimization and linear changes of intermonomer coordinates have been used to probe the shape of the intermolecular potential energy surface. It is of primary interest in the investigation of virtually all properties of the dimer. The calculations have been carried out on $UCIS/6-31G^{\ast}$ level of the theory for several initial conformations. More sophisticated methods have been employed to study the electron and charge transfer effects in selected geometries. en_US dc.format.extent 40239 bytes dc.format.mimetype image/jpeg dc.language.iso English en_US dc.publisher Ohio State University en_US dc.title AB INITIO STUDY OF INTERMOLECULAR INTERACTIONS IN BENZENE DIMER CATION en_US dc.type article en_US
|
|
Error Symbolic calculations could not initiate. Likely there's a function which is not differentiable by SymEngine
I’m simulating a satellite around the earth, and got error:
Symbolic calculations could not initiate. Likely there's a function which is not differentiable by SymEngine.
I think it’s because it cannot differentiate the -\frac 3 2 power. But how could it fail to differentiate something that simple?
using DifferentialEquations, ParameterizedFunctions
satellite! = @ode_def Satellite begin
dx = vx
dy = vy
dvx = -GM*(x^2+y^2)^(-3//2) * x
dvy = -GM*(x^2+y^2)^(-3//2) * y
end GM
G = 6.67e-11
M = 5.97e24
elasticity = 1
u0 = [0, 1e7, 5e3, 0]
tspan = (0.0,15.0)
p = [G*M]
prob = ODEProblem(satellite!, u0, tspan, p)
sol = solve(prob,Tsit5())
1 Like
This is why we’ve moved away from SymEngine. However, that warning is completely harmless here since you’re using a non-stiff ODE solver.
|
|
# A mixture contains two mutually inert solutions ‘X’ and ‘Y’ in equal volumes. The mixture is examined in a spectrophotometer using a cuvette. It is observed that the transmittance is 0.40. With only the solution ‘X’ in the same cuvette, the transmittance is 0.20. With only solution ‘Y’ in the cuvette the transmittance is___________.
This question was previously asked in
GATE IN 2014 Official Paper
View all GATE IN Papers >
## Answer (Detailed Solution Below) 0.795 - 0.805
Free
CT 1: Ratio and Proportion
10 K Users
10 Questions 16 Marks 30 Mins
## Detailed Solution
Absorbance A = ∈ lc
where ∈ is the extinction coefficient
I is the sample path length
C is the molar concentration
and also, $$\rm A = log_{10} \left( \frac{1}{\%T} \right)$$
T is the transmittance
For mixture $$\rm A = log_{10} \left( \frac{1}{0.40} \right) = 0.397$$
A = 0.397
= ∈x Ix cx + ∈y Iy cy ...(A)
For X only, $$\rm A = log_{10} \left( \frac{1}{0.20} \right) = 0.698$$
0.698 = 2 x Ix cx
x Ix cx = 0.349
Then, from equation (A):
y Iy cy = 0.397 - 0.349
= 0.047
Then the transmittance for Y:
Ay = 2 y Iy cy = 0.095
and $$\rm A_y = log_{10} \left( \frac{1}{\%T_y} \right)$$
$$0.047 \times 2 = \rm log_{10} \left( \frac{1}{\%T_y} \right)$$
%Ty = 0.8016
|
|
# Only final result from NDSolve
Finally I started to play with differential equations in Mathematica.
And I have faced the problem, which seems too me so basic that I'm afraid this question is going to be closed soon. However, I've failed in finding solution here or in documentation center.
My question is: how to set that NDSolve will not save whole InterpolationFunction for the result?
I'm only interested in final coordinates or for example each 100th. Is there simple way to achieve that?
Anticipating questions:
• I know I can do something like r /@ Range[0.1, 1, .1] /. sol at the end, but still, there is whole interpolating function in memory. I want to avoid it because my final goal is to do N-Body simulation where N is huge and I will run out of the memory quite fast. What is important to me is only the set of coordinates as far in the future as it can be, not intermediate values.
• I can write something using Do or Nest but I want to avoid it since NDSolve allows us to implement different solving methods in handy way.
• I saw WolframDemonstrations/CollidingGalaxies and it seems there is an explicit code with Do :-/
• Another idea would be to put NDSolve into the loop but this seems to be not efficient. Could it be even compilable?
Just in case someone want to show something here is the sample of code to play with:
G = 4 Pi^2 // N ;
sol = NDSolve[{
r''[t] == -G r[t]/Norm[r[t]]^3,
r[0] == {1, 0, 0},
r'[0] == {0, 2 Pi // N, 0}
},
r,
{t, 0, 1}, Method -> "ExplicitRungeKutta", MaxStepSize -> (1/365 // N)
]
ParametricPlot3D[Evaluate[r[t] /. sol], {t, 0, 1}]
(* Earth orbiting the Sun. Units: Year/AstronomicalUnit/SunMass
in order to express it simply*)
-
I did something similar by periodically reinitializing the system with current solution. See tutorial/NDSolveStateData for details. That allowed me to solve for large tmax and get out solution for [tmax - chunksize, tmax] without running out of memory – ssch Aug 25 '13 at 17:13
@ssch looks like something what I can use but let me read it. Thanks. – Kuba Aug 25 '13 at 17:19
Stefan's answer to the schroedinger question is quite relevant – gpap Aug 26 '13 at 8:50
@gpap you're right, thanks. I've seen this but I was not paying attention to method then. – Kuba Aug 26 '13 at 8:54
Here is a solution inspired from tutorial/NDSolveStateData (Mathematica 8)
G = 4 Pi^2 // N;
stateData =
First[
NDSolveProcessEquations[
{ r''[t] == -G r[t]/Norm[r[t]]^3,
r[0] == {1, 0, 0},
r'[0] == {0, 2 Pi // N, 0}
},
r,
{t, 0, 1},
Method -> "ExplicitRungeKutta",
MaxStepSize -> (1/365 // N)]]
res = Table[
NDSolveIterate[stateData, i/365];
rAndDerivativesValues = NDSolveProcessSolutions[stateData, "Forward"];
stateData = First @ NDSolveReinitialize[stateData, Equal @@@ Most[rAndDerivativesValues]];
rAndDerivativesValues,
{i, 1, 365, 7 (* 7 = each week*)}
] ;
rAndDerivativesValues is the value of r[t] and his derivative at each week.
Example :
Here is one revolution of the Earth around the Sun :
ListPointPlot3D[#[[1, 2]] & /@ res ]
-
|
|
ecef to lvlh. Navigation and control requirements On-board sensors and actuators are selected in order to meet the navigation and control accuracy require-ments, considering the constraints imposed by the spacecraft size. ngTALB) ÿþLawrence Oyor SongsCOMMP engÿþÿþDownloaded from …. The ECEF frame is identical to the ECI frame at epoch, an arbitrarily chosen time. ECEF Earth Centered Earth Frame LVLH Local Vertical Local Horizontal Frame ORB Perifocal Orbital Frame RPY Roll Pitch Yaw Frame BFF Body Fixed Frame LEO Low Earth Orbit GEO Geosynchronus Equatorial Orbit SC Spacecraft RW Reaction Wheels xii. Horizontal (LVLH) reference frame. The cylinder in the Transverse Mercator projection is tangent along a meridian (line of longitude) or it is secant, in which case it cuts through the earth at two standard meridians. The relation between the local East, North, Up (ENU) coordinates and the (x,y,z) Earth Centred Earth Fixed (ECEF) coordinates is illustrated . 6th International Conference on Astrodynamics Tools and. 具体过程为： 一206一 1、计算t时刻的儒略日JD： 2、计算测站的ECI坐标（xo、yo，zo）； 3、计算测站的地方恒星时： 5、将差向龄转换为极坐标形 …. Référentiel terrestre (ECEF) Le référentiel terrestre ("Earth-Centered, Earth-Fixed" ou ECEF en anglais) est un référentiel centré sur le centre de masse de la Terre et dont les trois axes sont liés au globe terrestre. Comm antenna graphics now follow 3D window lighting properties. 1 Rates of change revisited We have now derived the Navier-Stokes equations in …. Local tangent plane coordinates (LTP), also known as local ellipsoidal system, local geodetic coordinate system, or local vertical, local horizontal coordinates (LVLH), are a spatial reference system based on the tangent plane defined by the local vertical direction and the Earth's axis of rotation. I am trying to calculate the International Space Station (ISS) LVLH (Local-Vertical-Local-Horizontal) base vectors expressed in the ECEF/ITRF frame at a given time. GNSSs (Global Navigation Satellite System)s use ECEF as the . Earth-Centered Earth-Fixed (ECEF) It is more convenient to use a coordinate system that rotates with the Earth. Rv“ Iø\& "´ ßöwuhÞ‰Ÿø)ñɹ áM/¨¼#=,”çú·k ý:+ȸ N&ÕËR 9 ù?„H-üx¡¥® ëþ 5¥T¶ Tpª› 7¥ÿ 8«³ð”ЛEþ B‡sd á…üëÆ ï³™T ì· ÌRØVχt. 1 20141125 album=Mother 1+2 (Mother)&artist=Keiichi Suzuki, …. Absolute states are expressed in the ECEF frame. ôrV¢Þ~ ÜO ]¡-3Æ j ó }Ì\) :ìc’¤' ¸Ûmîn ú— ‹‰Tö- úº cF§Ä ÚUÊwF Mß>SÇÔ ]_ÆÃö6Øö+4L-¦Ç• êA‰FóhŽN ‰ ³ ‘ {‘Ø É½ØöZy³Î …. This research was supported by the Na-. Search: Matlab Rotate Coordinate System. An alternative description in terms of …. Coordinate vectors expressed in the ECEF frame are denoted with a subscript e. can be obtained by converting the XYZ coordinates of an object in ECEF coordinates with some conversion algorithm to latitude, longitude and altitude. In this thesis a detailed model of satellite magnetic moment is presented which includes dipole moment sources from on-board current loops. The Yellowstone National Park Research Coordination Network is a collaboration of scientists and NPS staff to develop a coordinated research network focused on geothermal biology and geochemistry. [x,y,z] = lv2ecef (xl,yl,zl,phi0,lambda0,h0,ellipsoid) converts arrays xl, yl, and zl in the local vertical coordinate system to arrays x , …. A specific GPS antenna on one of the vehicles is typically selected as a formation reference point. This ATBD will be updated regularly. 2 Earth-CenteredEarth-Fixed(ECEF). Coordinate Systems for Display. are expressed in the ECEF frame. 2 The theoretical models In the dipole approximation the magnetic eld is given by B~(~r) = 0 4ˇ 3(m~~s)~s s5 m~ s3 with ~s= ~r R~ (1) where 0 is the vacuum magnetic permeability, ~ris the distance between the ISS and the center of the Earth, m~is the Earth's magnetic dipole and R~is the dis-. 今天使用STK时，遇到坐标系之间转换的问题，为了以后方便，这里把STK中的坐标系进行列举并注释。. היכנסו לצפות בכתבות וחדשות בתחום תיירות. The angular velocity of the navigation frame wrt the ECEF frame is e e e() C t C n en n:: «» () bb en b b b e L L Sin Cos O ZO O ªº «» «» ¬¼ (12 ) The angular velocity of the navigation frame wrt the inertial frame is: i i i e Z Z Z in ie e en C The position of the origin of the navigation frame wrt the ECEF frame in the ECEF …. ตอนนี้ฉันใช้ matlab และสามารถรับพิกัด ecef ของดาวเทียมและจุดบนโลกได้อย่างง่ายดาย เนื่องจาก ecef เป็นคาร์ทีเซียนทำไมฉันจึงไม่สามารถจัดเรียงใหม่ได้:. ECEF x-coordinates of one or more points in the geocentric ECEF …. Further information: Geographic coordinate conversion § From ECEF to ENU. Local vertical, local horizontal — Also known as the spacecraft coordinate system, Gaussian coordinate system, or the orbit frame. (10/08/2020) Retomada das aulas em regime online terça-feira …. – For Earth, N = ECI (True of date), W = ECEF – N is the bedrock for orbits, S/C attitude dynamics – Full Disclosure: Although True-of-Date <-> J2000 conversions are provided, the distinction is not always rigorously made and one LVLH …. Simple library for converting coordinates to/from several geodetic frames (lat/lon, ECEF, ENU, NED, etc. The velocity in LVLH coordinates can be transformed to ECEF via Eq. s to a coordinate system in which the target should be pointed while minimizing the Doppler centroid variation in the LVLH …. Stevia é uma planta nativa da divisa entre Brasil e Paraguai, que tem uma extraordinária capacidade adoçante, superior em cerca de 300 vezes ao …. If I'm looking for questions about a transformation between eci and ecef…. 5 %ÈÈÈÈÈÈÈ 1 0 obj > endobj 2 0 obj > endobj 3 0 obj > …. These 4 values are called X, Y, Z, and W. For what it's worth, since you mention you need an answer to this …. Politecnico di Torino Master’s degree course in “Mechatronic Engineering” Master’s Degree Thesis: “Development of a ROS2 flight software framework & …. (2) Rearrangement of the order of the coordinates. state vector, position in ECEF…. •We will generally denote basis vectors (and some other unit vectors) by the letter e. The point is then to calculate the rotation matrix to rotate vectors in ECEF to LVLH (and vice-versa). Spire Attitude and Navigation Product Summary Version: 1. transform ( ecef, lla, X, Y, Z, radians=False) return lat, lon, alt ts = load. Construct $\hat {\boldsymbol x}$ as the unit vector directed along the spacecraft position vector:. Convert Earth-centered inertial (ECI) to Earth-centered. The Local-Vertical Local-Horizontal frame often provides an intuitive framework for the relative states. I was wondering about our plan for the upcoming SSO-A SmallSat Express Launch on November 19, 2018 at 18:32 UTC. An alternative description in terms of geodetic latitude, , (LVLH…. Willow Smith had to 'forgive' Jada Pinkett Smith for. Arguments: x::AbstractVector{<:Real}: Inertial state …. ʨ6ht)eÈxRp‹ -S p?Cü¥RŒBzÀ#gév: Äš==#lAÀ›')™ª3ÈÔ cA øÌ° FØg VÁuÕúÙÚZ#èO”›Dâ áùr ˜KbâÐ ‘ä•x gU!«ÀY @U :>…(^/’‡2LU ž¤ ˜£þr W(ˆJ …. The principal axis coordinate system is the standard ECEF coordinate system rotated -14. Local tangent plane coordinates ( LTP), også kjent som lokalt ellipsoidalt system, lokalt geodetisk koordinatsystem eller lokale vertikale, lokale horisontale koordinater ( LVLH…. You can determine which type of coordinate system …. The ESRI 150-meter globe in the JPEG 2000 format now works as expected in STK. õÙ ™7˘®9Ø^2á Ò*ÝV Í™ÒÆ–™˜s O ©µ%¹TÕ‘Cð8]¼§UÎ ;CsïÃø]ì‹Æ( 5ö¡Ó ÆX «gÀx¢ÁºoŽYÞ„ ß1ò€ Û o ͈w8 ì¡ûÓ. Items in the JSBSim aircraft configuration file are located using this frame. The rotation angle can be calculated from the velocity vector, for instance. (1) Transformation to the ENU (east, north, up) coordinates. •The orthonormal basis: •Any vector x can be written as a linear superposition of basis vectors. Earth-Centered Earth-Fixed (ECEF): as for the ECI, the origin of ECEF reference frame is positioned at the centre of mass of the Earth and the frame lies in the ecliptic plane of the Earth's orbit. Before I conclude let me add a short note on Daya Bai, a woman activist who works for the uplift of tribals in central India. xmlMα  à½OAX LE7CJ›˜¸»øH¯•HïH …. ECI frame, ECEF and LVLH frame. If the user's ECEF XYZ coordinates are represented as coordinates of a vector x 0, the geodetic coordinates are ( ϕ, λ, h), and the satellite position in ECEF as x s then the user-to-satellite vector in ECEF is (x s - x 0). Control Theoretic Approach for Attitude Control of High Altitude Scienti c Stationary Platforms by Yao-Ting Mao A dissertation submitted in partial satisfaction of the. Select the ECEF (Earth Centered - Earth Fixed) or geodetic (LLA: Latitude, Longitude, Altitude) coordinate you want to convert using the form below. Control Theoretic Approach for Attitude Control of High Altitude Scienti c Stationary Platforms by Yao-Ting Mao A dissertation submitted in partial …. NET 推出的代码托管平台，支持 Git 和 SVN，提供免费的私有仓库托管。目前已有超过 600 万的开发者选择 Gitee。. Similar to the geodetic system, the position vector in the ECEF frame is …. Lastly, the Local Vertical, Local Horizontal (LVLH) system is the satellite's. Answer (1 of 5): Some answers have misread the question and focused upon position. This frame is not inertial since it is defined with its origin at the object of …. Contribute to aaronjridley/spock-1 development by creating an account on GitHub. System Rotate Matlab Coordinate. اطلاعات بیشتر: تبدیل مختصات جغرافیایی § از ECEF به ENU. Earth Centered Earth Fixed – ECEF. We sometimes denote the n × n identity matrix by I n if supplying the subscript helps to remove ambiguity. The correct way to do this depends on the conventions used by whatever generated your quaternion, but the math is likely to be one of the following: …. PDF | In satellite operations, stable maneuvering of a satellite’s onboard antenna to prevent undesirable vibrations to the satellite body is …. And press the conversion direction desired. Welcome to the Skyfield Repository Skyfield is a pure-Python astronomy package that is compatible with both Python 2 and 3 and makes it …. Vector transformations differ from coordinate transformations. The errors of the GPS receivers were neglected as they are much lower than the expected errors of the TLE positions and velocity. To transform from the local SLAM world to ECEF, we need to apply the following transformations (in python): transform_e_gpsw @ np. separate set of magnetorquers to satisfy LVLH pointing requirements during the coasting phases. EOSC 512 2019 4 Rotation Coordinate Systems and the Equations of Motion 4. • Local Vertical and Local Horizontal frame (LVLH, denoted as L) : The LVLH frame has its origin at the satel-lite's center of mass. 지구 중심 관성 (Earth-centered inertial, ECI) 좌표계는 지구의 질량중심을 원점으로 하는 좌표계이다. planets, satellites) »Topocentric •Associated with an object on or near the surface of a natural body (e. PK ‡sŽ>[ i˜ [ annotationmetadata/metadata. The quaternion relative to LVLH that: defines the spacecraft attitude at the: beginning of the tactical field: reservation. 92 - 2022-04-01 Breaking Changes. Chapter 2 – Section 1: Basics AER 506 – Spacecraft Dynamics and Control M. DEFINITIONS Table 2-4: Definitions Concept / Term Definition. • F , a CRD, Earth-centered Earth-fixed (ECEF) rotating coordinate system, centered at the Earth. PDF Analysis of Gps Satellite Observability Over the. About the programming implementation of rotating and translating objects in the coordinate system Matlab, Python Write in front. [xl,yl,zl] = ecef2lv (x,y,z,phi0,lambda0,h0,ellipsoid) converts geocentric point locations specified by the coordinate arrays x, y, and z to the …. gimp xcf file R L B?B? gimp-image-grid (style solid) (fgcolor (color-rgba 0. (To be removed) Convert geocentric (ECEF) to local vertical coordinates. Локальные координаты касательной плоскости ( ltp), также известные как локальная эллипсоидальная система, локальная геодезическая система …. Example Function Call: >> [r_ECEF v_ECEF a_ECEF…. The relevant LVLH (LORF)-to-ECI transformation (alias interpretation) R t = R it, t = l, o ( t stands for trajectory), where the ECI frame is denoted by J = {E, →i1, →i2, →i3}, can be converted into their quaternion q t by the algorithm in Section 2. propagation and the Local Vertical Local Horizontal (LVLH) frame for commanding the attitude of the vehicle. ECEF xyz to Latitude, Longitude, Height There is no closed form solution for this transformation if the altitude is not zero. The Hill frame is a local frame with the x. Rotate Orientation of Map Display. This means it allows users to define new coordinate frames and their. The formation flight controller is executed under a body-frame coordinate system (ie, Local-Vertical, Local-Horizontal) that requires coordinate transformations between the ECI and body. Horizontal coordinate systems can be of three types: geographic, projected, or local. origin of the ECEF frame is also located at the center of mass of the Earth and the Z-axis points in the direction of the Earth's North Pole. 4 Ear th Centered Ear th Fixed (ECEF) 17 1. Syntax [xl,yl,zl] = ecef2lv (x,y,z,phi0,lambda0,h0,ellipsoid) Description. For this, if v → E C E F is considered as a velocity direction vector in the Earth Centered Earth Fixed (ECEF) coordinate, SAR imaging is possible with a minimum Doppler centroid variation. Lastly, the Local Vertical, Local Horizontal (LVLH…. coordinates supports a rich system for transforming coordinates from one frame to another. The origin of the local vertical system is at geodetic latitude phi0 , geodetic longitude lambda0, and ellipsoidal height h0. Earth, Planets and Space Pageo2oofo32 areextremelylimited. The LVC coordinate system is shown in the image above, using the conventions defined in Adamo 1. The ECEF position vector can be specified by its magnitude r krE k D krI k, longitude , and geocentric latitude 0. The ECEF gravity acceleration coordinates, which are equal to the spatial gradient coordinates of V, are given by The definition of the LVLH frame immediately provides r l and the following expression of the inertial coordinate r 3 /r: (4. An icon used to represent a menu that can be toggled by interacting with this icon. All calculations were expressed in Earth-Centered Earth-Fixed (ECEF) coordinates. Add or import the global coordinates. Hybrid Predictor-Corrector Aerocapture Scheme. Spacecraft Body Reference Frame: The body frame of the spacecraft is denoted Fb, and is located. Moessner 1 34th Annual Small Satellite Conference SSC20-II-05 CAT Differential Drag Implementation and Lessons Learned Dawn Moessner and Wen-Jong Shyong. - ECEF (Earth-centered, Earth-fixed, rotating) - Orbital (Earth-centered, orbit-based, rotating) - Body (spacecraft-fixed, rotating) • A reference frame is a set of three mutually perpendicular (orthogonal) unit vectors • Typical notations include • Typical reference frames of interest for ADCS include - ECI (Earth-centered inertial). áâôp€ˆ \ ÐHé ¨ÍM= pFpôôƒéâ ¢ªs ªºãTtŸ 0k ÈN Ø SۺÊ 5 ¢· aƒ"´¤y U§B¼ ûQ³ [åÑ68c;§ +¯-ð2†. unitary vectors of the LVLH reference frame direction cosine matrix between ECI and LVLH reference frames. sentó en el banquillo de los testigos a Miguel Ángel Martínez Martínez, quien trabajó para el Cártel de Sinaloa bajo las …. RIDESHARE PAYLOAD USER'S GUIDE © Space Exploration Technologies Corp. The 6th International Conference on Astrodynamics Tools and Techniques (ICATT) is an event organized by the European Space …. Coiro – Laurea Magistrale in Ingegneria Aerospaziale, Università degli Studi di Napoli “Federico II” 1. 1,2, and 3 axes in the ECEF and ECEI coordinate frames J = Mean motion Q = Argument of latitude å = True anomaly ñ = Angular velocity. The basis vectors {Ô 1, Ô 2, Ô 3} are shown centered on the primary Spacecraft and are aligned with the LVLH …. ï«ëù¨¹éØx 4^˜'Á [ I€k²" í{l ¯·dKüòƒÔ†…‹«–œr!T‰ÈÛ. You can determine which type of coordinate system your data uses by examining the layer's properties. 지구-중심 관성 좌표계, ECI (Earth-Centered Inertial) Frame. This is done in the next step: 2. Quaternions from ECI to body frame and LVLH to body frame as well as the Earth Centered Earth Fixed (ECEF) frame and change its attitude . 8212780: JEP 343: Packaging Tool Implementation Reviewed-by: almatvee, kcr, prr, rriggs, ssadetsky, erikj, ihse Contributed-by: …. •An orthonormal set of basis vectors defines a reference frame. 000000)) (bgcolor (color-rgba …. The y-Axis of the LVLH frame, which points along-track in the direction of travel, is defined as the secondary constraint. Definition of target, velocity, auxiliary and control. Note that in the presence of orbital perturbations, this coordinate system is non-inertial. For quantities which describe the relationship between two coordinate frames, the superscript is. Ecef Enu To Python [6X0DIF] This means that the magnitude of ned and ecef will be the same (bar numerical differences). ECEF EarthCenteredEarthFixedFrame ECI EarthCenteredInertialFrame 3. For example, a rotation of α degrees around the x -axis would be: rotm = 1 0 0 0 cos α -sin α 0 sin α cos α. Then, we rotate about the x axis into the x ,y ,z system through an angle θ. ó ² b µ C Z ( º E š € S -# — \ ‹ Ž ‡ p Ò z ] Ö g é « j i | ‚ Ù 8 x à ß w : I « · 9 Z = ~ \ H e M ƒ Í ¦ X Ò † o ò À ; ã ¥ ’ ú ° ç ž e ¡ Ð ‹ ’ 7 | % ‰ Ý Ö T ê I § ¸ A C a ' R …. I know ECI and ECEF share the same origin point (the center of mass of Earth) and the same z-axis that points to the North Pole. Calculate azimuth & elevation angle from ECI to body quaternion, position, and boresight vector. Changes to this document require prior approval of the applicable. This means that the satellite Body z-axis points towards the geographic coordinates passed into the block throughout the simulation. This reference frame is also called LVLH (Local. ECEF Earth Centered, Earth Fixed VBS Visual Based System ECI Earth Centered Inertial 2. Emami, 2021 1-5 Earth-centred-Earth-fixed (ECEF) or Earth-centred …. However, the X-axis points in Horizontal (LVLH) reference frame. ECI/ECEF Relationship between the ECI and ECEF frames ECI & ECEF …. I have an acceleration profile which is in the North-East-Down coordinate system. Earth-Centered, Earth-Fixed (ECEF) Frame: or the the LVLH frame. qÖ@é>s 7ã æ ?Ç:Ó™YÊ(åNrx9 œ5N 'Yc«™ÐTç*rº9D – 1 ƒr!¶|Û€m 6ë 5 Gg% ²yØ0è‚rÍ…ÆÒ3j â@æJ}%5’šQ ž í³lyÃìä. The Satellite Reference Frame (SRF), denoted X r , Y r , Z r , is based on a coordinate transformation from the ECI frame, and is updated continuously …. •Right hand rule:We choose the orientation of e 3 to satisfy the right hand rule, i. Earth-Centered, Earth-Fixed Frame: The Earth-Centered, Earth-Fixed (ECEF) frame is denoted Fe, and has its origin in the center of the Earth. But, the ECEF frame rotates with the Earth making it convenient for certain types of analysis. $\begingroup$ @called2voyage I'll agree that if someone starts typing eci or ecef that the frames tag should be suggested for them since they might not know about it, but having all four tags (eci, ecef, frames, coordinates) will lead to tagging-fragmentation. Emami, 2021 1-5 Earth-centred-Earth-fixed (ECEF) or Earth-centred Rotational (ECR) {𝑬}: Origin O E at the Earth's centre of mass 𝑥 ො toward the intersection of equatorial plane and 0° longitude plane (prime meridian in Greenwich) 𝑧̂ along the Earth's North Pole 𝑦 ො in the. OmegaLVLH: Generate the LVLH …. Here, the 3D motion is given with respect to ECI and ECEF …. 第一次写知乎文章，主要目的是为了记录工作学习中遇到的问题和解决过程，如果能帮到大家也是好的，希望大家多多指正。. Elevation angle is the "angle off nadir", the angular distance between the nadir vector and the boresight vector. Low Earth Orbit Satellite Design - Free ebook download as PDF File (. com):MemorandumSeries KeplerianOrbitElements! CartesianStateVectors(Memorandum№1) wherearctan2isthetwo-argumentarctangentfunction. LinkStructural, or "Construction" Frame. 2005) was prepared by Oliver Reitebuch (DLR, responsible), Dorit …. 0 TDB, which is 1 Jan 2000 12:00:00. There is at least another name for the same frame: LVLH. One construction: Let $\boldsymbol r$ and $\boldsymbol v$ denote the spacecraft's position and velocity with respect to …. Axes named according to the air norm DIN 9300. The angle θ is the same as defined in the RIC Cylindrical frame and is measured in the orbital plane of the primary Spacecraft. Šê4§ + Æ1D·KŒ ¢”Š‘ÑbjD'ƒHßH 0ZAÍŠ ü>Ú[¶²Ì¢Ä1NÄÓ ìW‰áµ¿˜~ììàLölJuãm¤_^ŒšQ6{&Ñx C›À¡”ãö‰ ©Š©µ6\ ¼Lûun – h. Earth Centered, Earth Fixed (ECEF) x-y-z values in km And press the conversion direction desired. – ECEF (Earth-centered, Earth-fixed, rotating) – Orbital (Earth-centered, orbit-based, rotating) – Body (spacecraft-fixed, rotating) • A reference frame is a set of …. Welcome to the Skyfield Repository Skyfield is a pure-Python astronomy package that is compatible with both Python 2 and 3 and makes it easy to generate high precision research-grade positions for planets and Earth satellites. Development of Verification Check. Definition of ECEF, launch and body coordinate. Proj ( proj='latlong', ellps='WGS84', datum='WGS84') lon, lat, alt = pyproj. In this case, however, the motion of the reference frame is integral with the Earth. Niente posti di sostegno 150 docenti a spasso. Nanosatellite ‘Al-Farabi 2’ Le parc scientifique et technologique de l’université nationale kazakhe baptisée Al-Farabi (Almaty), en coopération …. Matthew Monnig Peet's Home Page. The question doesn’t ask about position, it asks about orientation. Correlation Coefficient between Sensor ECEF Y Velocity Component and Sensor Heading Angle Time Rate of Change First two charactes of MGRS co-ordinates; UTM zone 01 though 60 UINT8 0. 地心惯性坐标系是太阳系内的一个惯性坐标系,不随地球而转动,也不受地球、 DAC6574IDGS 太阳 运行的章动和岁差的影响。. lvlh y is assigned to complete the right- handedorthogonaltriad. The coordinate system is centered at the center of the Earth and the coordinate system rotates with the Earth rotation. FDI FaultDetectionandIsolation FMEA FailureModeandEffectsAnalysis LEO LowEarthOrbit LocalVertical,LocalHorizontalFrame(LVLH…. To perform relative state estimation, an adaptive extended Kalman ¯lter is. 3 Attitude and Formation Control Design and System Simulation for a Three-Satellite CubeSat Mission by Austin Kyle Nicholas Submitted to the …. Sanny omar esa_presentation_no_video. La scuola catanese, infatti, è …. If you have any type of issues, complaints, queries regarding HP products and services available in Saudi Arabia, so the customers can contact through the following contact details given below. Joint and Define Matlab - Free download as PDF File (. The LVLH frame is commonly utilized for attitude representations of spacecraft. Earth to Ned is a series produced by The Jim Henson Company and Marwar Junction Productions released on Disney+. • In the top right corner of the object editor window, change the name to "scLVLH" • Click "Propagator" on the left hand side and change the time step to 30 seconds • Click "Ok" to close the editor and save your changes • Right click scLVLH and clone it • Rename the clone "scVNB" • On the left hand side of the Spacecraft Editor click "Attitude". ECEF Earth-centered, earth-fixed (rotating coordinate frame) ECI Earth-centered inertial (non-rotating coordinate frame) EOM Equations of Motion LVLH Local Vertical, Local Horizontal frame MAC Mean Aerodynamic Chord MAVERIC Marshall Aerospace Vehicle Representation in C MET Marshall Engineering Thermosphere. Check-Case Gravitation Models In parallel with a choice of Earth geodesy models was a corresponding choice of gravitation models. Figure 8 and Figure 9), also known as the local-vertical, local-horizontal LVLH …. X 축이 춘분점을 향하며, Z 축은 지구의 자전축 방향으로 정의한다. Već dugo neki proizvod za usne nije izazvao toliku pozornost, kao što je to pošlo za rukom popularnom Lip Kitu. This means that the formation is moving at a very high velocity with respect to the earth and the GPS …. Figure 1:: Transformations between ENU and ECEF coordinates. Le repère LVLH, pour "Local-Vertical/Local-Horizontal", est un repère très utilisé. , where the vehicles are located with respect to each other. lfÏ ¦g¦(hjÉ+T, M ØÝ—›òú Ií rpW:)%#¶†hÉŠBm :ÐYkDa bä% áPù”F. LVLH local vertical, local horizontal. Radial Unit Vector in LVLH Frame LQR/SDRE Control Cost Equatorial Radius of the Earth Mean Earth-Luna Distance Mean Earth-Sol Distance Satellite Position Matrix Z-axis Velocity in ECEF Frame Z-axis Acceleration in ECEF …. Horizontal coordinate systems locate data across the surface of the earth, and vertical coordinate systems locate the relative height or depth of data. Since the magnetic field produced by the satellite at different points in space in known, the ECEF frame can be used to locate the position of the satellite with respect to the moving earth, and consequently find the magnetic field at that point. ECEF Earth-centered, earth-fixed (rotating coordinate frame) ECI Earth-centered inertial (non-rotating coordinate frame) EOM Equations of Motion LVLH …. After rotation, the rotated image is either resized or cropped to fit the size of the output image. Because LGVI calculation result is expressed with O B/I, this orientation matrix becomes a base for the calculation of other relationships between frames. '-0,c]75+5''dt9:08(5i3036%*2n)%61*3;t&(d,7=41854:ana:j/1>>whfx-33:m?6;7. Hp Server Saudi Arabia Customer Service department is available to you always. Spacecraft dynamics and control : the embedded model. Asociațile de pacienți trag semnale de alarmă și spun că toți cei care nu au acces la serviciile de sănătate din cauză că Ministerul Sănătății nu …. velocity, and acceleration vectors in Earth-centered Earth-fixed (ECEF…. In ballistics and flight dynamics, axes conventions are standardized ways of establishing the location and orientation of coordinate axes for use as a frame of reference. Politecnico di Torino Master’s degree course in “Mechatronic Engineering” Master’s Degree Thesis: “Development of a ROS2 flight software framework & Attitude Control application for nanosatellites”. = that is km = kilometer (unit) LEO = Low Earth Orbit LVLH …. 自転車置場・物置・笠木・庇・点検口・集合ポスト・ドアハン …. Consider two coordinate systems with base vectors. bookcrystal monster stlkomatsu pc01 near ohioecef to lvlhpaccar mx 13 ecm wiring diagramedsim51 projectslibosmesauser not found keycloakan5361create csv . 9 Terne di riferimento Earth-Centered Earth-Fixed…. The vehi- cle states include the position ri and velocity r˙ i , which are expressed in the Cartesian Earth Cen- tered Earth Fixed (ECEF) frame (see Fig. M RNP matrix to transform ECI into ECEF coordinates, or mass of the earth m Mass or gravitational model order n Gravitational model degree P Intersection of prime meridian and equator P¯ n,m Fully-normalized associated Legendre function of degree n and order m p Roll rate q Pitch rate R Radius r Yaw rate or radius re Equatorial radius of the earth. •Let us refer to the frame defined by e 1 e 2 e 3 as frame F; and consider another frame F'defined by the orthonormal basis:. aligned to the along-track and radial directions of a local vertical/local horizontal (LVLH) frame for nearly circular orbits. Rotate Coordinate Matlab System. 3 Local-Vertical Local-Horizontal Reference frame (LVLH). 在许多定位和跟踪应用中，本地东，北，上（ENU）笛卡尔坐标系比ECEF或大地坐标 . Earth-Centered Earth-Fixed (ECEF) system. EE 570: Location and Navigation. The ecef2lv function will be removed in a future release. CDGPS-Based Relative Navigation for Multiple Spacecraft by Megan Leigh Mitchell Submitted to the Department …. barnes, 2d lt, usaf afit-eny-ms-17-m-241 …. CF\'¸V;xø¶møÜL ÈK‡wYLB|²¨&? ÖÇ¢ùhÈdT=0O Êž ß0bí9h˜02= PÛ˜¢. 17) r l / r = R i l r / r = [0 0 1]. Python astropy: convert velocities from ECEF …. Coordinate Systems, Basis Sets, Reference Frames, Axes, etc. 로컬 접선 평면 좌표 (ltp), 또한 ~으로 알려진 국소 타원 시스템, 로컬 측지 좌표계, 또는 로컬 수직, 로컬 수평 좌표 (lvlh)는 로컬 수직 방향과 지구의 회전축에 의해 정의 된 접평면을 기반으로하는 지리적 좌표계입니다. theta = 90; % to rotate 90 counterclockwise. ECEF = Earth-Centered, Earth-Fixed coordinate frame EME J2000 = Earth-Centered Inertial, Earth Mean Equator January, 2000 coordinate frame FOV = Field of View G = Gauss (unit) I&T = Integration and Test i. They also don't discriminate between coordinate systems and reference frames. Earth-Centered, Earth-Fixed (ECEF) Spacecraft Frames Radial, In-track, Cross-track (RIC) Local Vertical, Local Horizontal (LVLH) Orbit Types …. ECI/ECEF Relationship between the ECI and ECEF frames ECI & ECEF have co-located orgins ~r. The is measured form the orbital plane. æÝên©L æ? û Ÿ¨¦qzT; âÙãgéÃyØ¿J™Àƒçmj‡³ gLýÕÔÙm#ûØ ´a &Ыøñ·+ æóàÑá9™zGå ÞÖw ĴޜԿ—[c¥] ¨«V¤… êŽìo¥ÅÛ þù …. We are going to take a look at the differences between LVLH and a few of the other attitude reference frames, and show those differences in FreeFlyer. ص ﻲﻳﺎﻀﻓ لﺎﺼﺗا و تﺎﻗﻼﻣ ﺔﻠﺌﺴﻣ ﻲﻄﺧﺮﻴﻏ ﺔﻨﻴﻬﺑ لﺮﺘﻨﻛ 2يﺪﻣﻮﻠﺧا ﺎﺿر يﺪﻬﻣ و *1ﻲﺑاﻮﻧ ﺪﻤﺤﻣ ﻲﺘﺸﻬﺑ ﺪﻴﻬﺷ هﺎﮕﺸﻧاد. •The orthonormal basis: •Any vector x can be written as a linear …. Â&)ÁQ0 ¨ ‡¸K» ¼Ÿq иq ƒ¥ãÌ Å¨¶o¤Û ÙrIÜ O}(‚ ¹!§'–’¹l9·Ç"ɲvòVbÙ3…š´V: +€ 穈øe}á ûwav'Ú“66!XSò6½áhÜLÕ š€ž‰pvÏ£ŸµSŒª$© …. Bandwidth+statement+under+interface 1. There are no differences between QSW, RSW, USW and RIC frames, just the name of the convention change. Bookmark this Site - We Find New Things All The Time!. When you update your code, you can specify the angleUnit input argument as 'radians'. The "Point at LatLonAlt" option is selected for the Pointing mode parameter. é[email protected] ‚ ^ˆ/[email protected]ÏÇ ‘ ŸK$ V ‰ ÿ. The angular velocity of the navigation frame wrt the ECEF frame is e e e() C t C n en n:: «» () bb en b b b e L L Sin Cos O ZO O ªº «» «» ¬¼ (12 ) The angular velocity of the navigation frame wrt the inertial frame is: i i i e Z Z Z in ie e en C The position of the origin of the navigation frame wrt the ECEF frame in the ECEF frame is:. ûx½ŸRïÏ) FÇ6 Ãt ÃNy\Áµ™Ny ‘ç‡ ÿ˜ïrè £¡Oʆ¤†”†´†Œ†u Y 9 U Î93™ 8Š qJ 2XÖ Ãe Ê rXÑq Wt4°ªã 6u WÔ”…C ýƒ ÿ …. 2 The theoretical models In the dipole approximation the magnetic eld is given by B~(~r) = 0 4ˇ 3(m~~s)~s s5 m~ s3 with ~s= ~r R~ (1) where 0 is the vacuum …. Председник СПО Вук Драшковић поновио је да је истина да је “kосово, као државна територија Србије, изгубљено 1999. The NED frame is identical except that the “Up” axis is replaced with a “Down” axis pointing in exactly the opposite sense, and the order of the coordinates is changed to maintain right-handedness. Next we have to convert the expected magnetic field, which is expressed in the ECEF reference frame to the LVLH (local vertical, local . Figure 8 and Figure 9), also known as the local-vertical, local-horizontal LVLH frame. B‡ª üË€•ï¯33š}ÎÛbåUÅM\›^¡m •Ég¥9”ð ~ hg®®b©&Ã;8ó?³»‹ U[q#Œ¹¢õ1F ieŸ G†pK!'. If you have any type of issues, complaints, queries regarding HP products and …. as LVLH or ECEF) and then convert those coordinates into orbital element . This paper presents an MPC controller that uses dynamics based on a modified version of Gauss' Variational Equations which incorporates osculating J2 effects. This is similar to a local vertical, local horizontal (LVLH) frame (Schaub and Junkins 2009), except $${\hat{r}}$$ Eqs. Line rate calculation results of previous method and proposed method for strip imaging Previous Proposed Time ECEF_X ECEF_Y ECEF_Z Latitude Node method Roll Pitch Yaw method Difference 20150728001157 -6529. The from_name method of SkyCoord uses Sesame to retrieve coordinates for a particular named object. LVLH = Local Vertical, Local Horizontal Frame information, a transformation between ECEF and LVLH can be calculated via Equations 10 . csdn已为您找到关于j2000坐标系相关内容，包含j2000坐标系相关文档代码介绍、相关教程视频课程，以及相关j2000坐标系问答内容。为您解决当下相关问题，如果 …. Also evaluates the minimum altitude reached by the line of sight (ISS<->Source). Originally belonged to a prosperous …. Spacecraft formation flying (SFF) is of huge importance to the aerospace and space community. OmegaLVLH: Generate the LVLH angular rate vector. 2 ECEF （Earth Centered, Earth Fixed） 座標系. The Euler's equation of motion is used to describe the attitude dynamics for both target and chaser vehicles, and a . inertial; Earth-centered inertial (ECI); Earth-centered Earth-fixed (ECEF) in either geocentric or geodetic frames; local-vertical, local-horizontal (LVLH); north-east-down (NED); launch site; and body coordinates. For the following descriptions of the attitude reference frames, let v be the velocity . Satellite relative motion dynamics with HCW equations 4. coordinates sub-package also provides a quick way to get coordinates for named objects, assuming you have an active internet …. U vrijeme restrikcija svih društvenih okupljanja i socijalnih kontakata, prednosti tehnologije više nego ikada dolaze do izražaja. Earth-Centered Earth-Fixed (ECEF) Frame- used for Earth's magnetic field 3. provided ranges from vector specific, to LVLH, to ECEF. Another example is the comparison of the Earth Centered Earth Fixed (ECEF) position of the vehicle. Technical Issues Corrected in STK 11. • L , a CRD local-vertical, local-horizontal (LVLH…. Lokalne współrzędne płaszczyzny stycznej ( LTP), znany również jako lokalnego systemu elipsoidalne, miejscowy układ współrzędnych geodezyjnych lub lokalne pionowe, lokalne współrzędne poziome ( LVLH…. This Royal name is growing more popular among Americans. Lokale Tangentialebene Koordinaten ( LTP ), auch bekannt als lokales ellipsoidal System , lokale System geodätische Koordinaten oder lokale vertikale, lokale horizontale Koordinaten ( LVLH …. , Rapolano Terme, 53040, Siena, Italy. All calculations and integrations are also performed in the ECEF …. velocity, and acceleration vectors in Earth-centered Earth-fixed (ECEF) coordinate system for given position, velocity, and acceleration vectors in the Earth-centered inertial. This keeps our satellite pointed forward throughout the mission as much as possible without disrupting primary alignment. The Space Physics Data Facility (SPDF) hosts the S3C Active Archive, which consists of web services for survey and high resolution data, trajectories, and …. Propagate orbit and attitude states in Simulink and visualize computed trajectory and attitude profile in a satellite scenario. 1 (Build 190)TLEN 75781TIT2 TPE1 TALB TCOP TCOM TPUB TCON TIT1 …. Local Vertical, Local Horizontal (LVLH) Frame – used for initial retrieval of Earth’s magnetic field from spherical harmonic model, which is returned in an LVLH frame 4. Earth-Centered, Earth-Fixed (ECEF) Spacecraft Frames Radial, In-track, Cross-track (RIC) Local Vertical, Local Horizontal (LVLH) Orbit Types Computing Orbital Elements The Two-Body Problem The Three-Body Problem The N-Body Problem Gauss's Method Lambert's Problem Ground Tracks Launch Windows Orbital Maneuvers Rendezvous/Proximity Operations. 6q'^^ ÍJ¨HåùO »#n,_rûqŸˆv!_ÁõÁ. Arguments: x::AbstractVector{<:Real} : Inertial state . For LVLH coordinates; z is in the -r direction y is in the - rxv direction x completes the set. The Local Vertical/Local Horizontal (LVLH) frame is. Other frames can be defined on those mobile objects. lvlh z is parallel to the orbit normal. fLaC" € € ¥ µ ¸ p I¡ù¯:ËÐøöINDÀ7F#¸®„Œ reference libFLAC 1. Tethered methods of active debris removal present an intriguing solution. Ω = Right ascension of the ascending node L à : = Semilatus rectum 2 á à ; 2, : à ; = Schmidt normalized associated Legendre functions à = Gauss normalized associated Legendre functions ö =. These can be used to construct the. vertical, local horizontal coordinates (LVLH), are a geographical coordinate system based on the local vertical direction and the Earth's axis of rotation. This frame is a common manufacturer’s frame of reference and is used to define points on the aircraft such as the …. Transcribed Image Text from this Question. Lokale Tangentialebenenkoordinaten ( LTP), auch bekannt als lokales Ellipsoidsystem, [1] lokales geodätisches Koordinatensystem, oder lokale vertikale, lokale horizontale Koordinaten ( LVLH…. com):MemorandumSeries KeplerianOrbitElements! CartesianStateVectors(Memorandum№1) …. local horizontal coordinates (LVLH), are a spatial reference system based on the tangent plane defined by the local vertical direction and the Earth's . 国際天文基準座標系 （こくさいてんもんきじゅんざひょうけい、 英語: International Celestial Reference System またはInternational Celestial Reference Frame）は、 国際天文学連合 （IAU）により採用された現行の標準 天球座標系 である。. Spacecraft dynamics and control : the embedded model control approach provides a uniform and systematic way of approaching space engineering control problems from the standpoint of model-based control, using state-space equations as the key paradigm for simulation, design and implementation. As a Python package, it uses NumPy, PROJ. 17949185 2 1 1 266 2 1 1/26/2005. Kalman filter implementation based on HCW equations and sensor measurements for satellite position and velocity estimation to achieve satellite naviagation and optimal control 5. Returns azimuth and elevation angles (rad) from the LEO satellite to the GPS satellite when providing an ECEF position coordinate of them both. Note: In the ECEF coordinate system [15, 16], the Z-axis extends from the centre of the ellipsoid towards the North Pole, the X-axis points from the centre towards the intersection of the equator and the prime meridian and the Y-axis completes the orthogonal coordinate system by pointing towards the equator 90° east of the X-axis (see figure 4). Référentiel terrestre (ECEF) Le référentiel terrestre ("Earth-Centered, Earth-Fixed" ou ECEF en anglais) est un référentiel centré sur le centre de masse de la …. The current values in the input fields are used. Its Y axis is along the negative Z axis of the RTN frame. 1 Rates of change revisited We have now derived the Navier-Stokes equations in an inertial (non-accelerating) frame of reference for which. ECEF Earth-Centred Earth-Fixed ECI Earth Centred Inertial EO Earth Observation EUV Extreme Ultraviolet LVLH Local-Vertical Local-Horizontal MPC Model-Predictive Control PID Proportional-Integral-Derivative ROAR Rarefied Orbital Aerodynamics Research SOAR Satellite for Orbital Aerodynamics Research SRP Solar Radiation Pressure SSO Sun. 3-HÅHÅȇɆÉÕªSVyêÕ òHrQ2R dÆxÖ²p2th8ÉÚ]œÖ ÆÇZIVäñRx¸ *+)c•™”9þÍ ‡ÏAWø > s‡ÇAT8r5ÿbþ ý Ÿ¹‡þ úŽý®]T…þpÝ ëtIðLu~"zÇI- _ úÔ …. Not the stuff of science-fiction, SFF involves flying …. 2 Earth-Centered Earth Fixed Reference frame (ECEF). Moessner 1 34th Annual Small Satellite Conference SSC20-II-05 CAT Differential Drag Implementation and Lessons Learned Dawn Moessner and …. Autonomy Definition World History sample cover letter for a change in career, what is testing life cycle istqb, …. ABSTRACT Orbital debris will increase dramatically unless active debris removal methods are implemented. A common transformation is position in ECI to position in ECEF. Earth-Centered Earth-Fixed (ECEF) Coordinate System Uluslararası Yer Dönme ve Referans Sistemleri Servisi (IERS) tarafından yeryüzünde sabit …. Single Frequency GPS Relative Navigation for Autonomous. LOF_ALIGNED_LVLH {public AttitudeProvider getProvider(final Frame inertialFrame, final OneAxisEllipsoid body) {return new LofOffset(inertialFrame, LOFType. To find information about the non-attitude orbital reference frames available in. ID3 vCOMM XXXTENC#Sound Forge Pro 2. This attitude is used to place the spacecraft in a favorable orientation for a tactical field experiment. ID3 mTT2 Buddy Parrish 3_3 SermonTAL Buddy SermonsTRK 1/1COM engiTunPGAP0TEN iTunes 12. See the list below for a full description of the changes. I have a procedure to do that, but I am not sure if it is done properly. 1 20141125 (album=The Legend Of Zelda: Majora's Mask!artist=Koji Kondo, Toru Minegishi …. While common astronomy frames are built into Astropy…. sgml : 20190325 20190325064800 accession number: 0001537028-19-000029 …. 0 Date: 2021-09-08 1 Data Collection and Processing Spire's low-ear th-orbit (LEO) satellite constellation routinely collects GNSS signals. The ECEF that is used for the Global Positioning System (GPS) is the geocentric WGS 84, which currently includes its own ellipsoid definition. Line rate calculation results of previous method and proposed method for strip imaging Previous Proposed Time ECEF_X ECEF_Y ECEF…. direction to the sun (Satellite)。 2. I am particularly interested …. Calculate direction of a source in the sky (specified in equatorial coordinates J2000) in the International Space Station (ISS) LVLH frame of reference. Video captures incredible fury of Andover tornado. The z-axis is used as the satellite's primary alignment vector. A common right-handed coordinate system is the Earth-Centered, Earth-Fixed frame (ECEF). Àîs†€Öï1Œ§ r™>ÛËMóÛ ¹~•f!hÒ 4 tB- nÜ ¯š~S=è[Ê_*Ô3¶n Tr‘Bûœ ]Ë3ß‹ ½¡ŸI5& ŒQ¸´qy©, I – HFúdª+zÑ )œBxZ ˆr‡g·¥´Sæõ T ˆé3â ÕsêF³ : €¾ e0 ' H …. The seek for indicators of life on Mars is heating up. Rideshare Payload User's Guide nastran. Then, convert from ECEF to geodetic (latitude, longitude, elevation) coordinates. LBLSIZE=2048 FORMAT='BYTE' TYPE='IMAGE' BUFSIZ=20480 DIM=3 EOL=0 RECSIZE=1024 ORG='BSQ' NL=1024 NS=1024 NB=1 N1=1024 …. ÒvÍOpN¤ÖQþǽ4’Ë À=¿,Q) ,AŸdøÛ Ä¶7ñÆ †O n°2ŸtW Ô\d• ©QQ™+ƵÉ5 Õ§AV¶ø˜R–ðËƇb fãW} tÇâÁ6 ²5¼ {¨ôc ] [´ Ul"† ÿ )Ž[ 0*C·Ð †ÛC— …. org Port Added: 2018-07-23 05:48:23 Last Update: 2021-04-07 08:09:01 Commit Hash: cf118cc License: GPLv2 Description: OSKAR has been designed to. In the model, I added gravity, ocean tides, solid tides, third body attraction, solar radiation pressure and post-Newtonian correction force due to general. 坐标系统：有哪些坐标系，他们之间的变换矩阵是怎样的？（主要是3个坐标系3个角） 地理坐标系（n系） 坐标系原点On取为飞行器质心。Xn轴向指向 …. Navigation and Ancillary Information Facility NIF Frames and Coordinate Systems •Non-Inertial -Accelerating, including by rotation -Examples »Body-fixed •Associated with a natural body (e. The Y axis passes through the (latitude. 2 presents these relationships between frames. PK  9Toa«, mimetypeapplication/epub+zipPK  9Tò2[©¯û META-INF/container. such a way that the axis 1 points east, axis 2 points north, and the axis 3 points upward. Illustration 2: The altitude is the angle an object makes with the horizon. It should be noted that the ECEF frame is the. By this point, I hope to have helped you develop an understanding of two key aspects of practical orbital mechanics. LatLonToR: Converts geodetic latitude and longitude to r for an ellipsoidal planet. The ECEF frame reduces the complexity of the simulation by disregarding the rotational motion of the earth. 94/08/18:ﻪﻟﺎﻘﻣ ﺪﻴﻳﺄﺗ ، 94/03/09:ﻪﻟﺎﻘﻣ ﺖﻓﺎﻳرد 1394 ﺰﻴﻳﺎﭘ /3 ةرﺎﻤﺷ / 8 ﺪﻠﺟ 27 -40. 3 Attitude Quaternions Quaternions provide an elegant and less resource-expensive method of spacecraft attitude determination compared to the traditional Euler angles representation. Part of Aurionpro’s Executive Management team, Sanjay Bali comes with over 27 years of diverse experience across sales, services, and project …. This doesn't transform like a vector under a change of basis, but $\omega$ will. ECEF, on the other hand, do not consider the motion of the Earth and its positions are independent of the time and date. [x,y,z] = lv2ecef (xl,yl,zl,phi0,lambda0,h0,ellipsoid) converts arrays xl, yl, and zl in the local vertical coordinate system to arrays x , y, and z in the geocentric coordinate system. Time evolution of orbital dynamics; We can calculate time …. Taip pat galite kreiptis į „World Geodetic System 1984" specifikaciją. The point is then to calculate the rotation matrix to rotate vectors in ECEF to LVLH …. Quindi, la trasformzione tra ECI e ECEF …. These coordinates differ only by a rotation about z equal to the Greenwich. 3 Attitude and Formation Control Design and System Simulation for a Three-Satellite CubeSat Mission by Austin Kyle Nicholas Submitted to the Department of Aeronautics and Astronautics. Similar to the geodetic system, the position vector in the ECEF frame is denoted by Pe = xe ye ze. When elevation is called with only 6 inputs, the GRS 80 reference ellipsoid, in meters, is used by default. To see crustal deformations, it is useful to transform the ECEF coordinates into local East, North and Up (ENU) coordinates. This function has been vectorized for speed. and the axes are fixed relative to the vehicle body. fLaC" ¨"Q ÄBð;8Dä!¯ ìû—O7…ÚuçÀ í reference libFLAC 1. ÿ¿Áõ;\ ë 59ô»vóõåïäe»sr²]ä $P®“ˆ OŠ“¡í_‚ù¦ íÍ«d¾ …. Convert Earth-centered inertial (ECI) to Earth-centered Earth-fixed (ECEF…. º ÆpÌÊ… •É4%6¯cqM¶Žfüδ!g¥ íœøQi_w*í ò#vï3 I%?d½…S‘w äÿi¸ƒh%·–úTo³12ú‰¹›@òê¶ mÔåÐjÆv ýÜÓÌå{hù[ª k. Lvlh Frame ECEF Frame Coordinate Frame Earth-centered Inertial Inertial Frame Circular Orbit Earth Frame Earth-centered Inertial Frame ECI Coordinate. ÐûH ›JͺõIÖ z})¥V iPÏ HY;1 Ú¼° “ªØÀ”«œÙ G’‰+ û]–ìÆ!) _ýØ XÔæ©Þ)ßL]$ìÚÿ]¿É+D Aˆ«6jÿû’lÍ€ 7]ùé b7DZ½»oì0l. Introduction how,bydecreasingthefuel,thisstructuralmassbecomesmoreofanencumbrance than functional to the accomplishment of the mission. The axes are denoted x e, y, and ze, where the zeaxis is directed (LVLH) frame. 표 / 그림 (81) 모든 표/그림 보기 슬라이드로 보기 · 상대속도(ECEF): Position Domain DGPS와 Propagation PILS 수행 결과 · 상대위치(LVLH): Position Domain DGPS와 . The coordinate system (X, Y, Z) is the ECI frame, and the coordinate system (x, y, z) is the orbital frame. A coordinate system conversion is a conversion from one coordinate system to another, with both coordinate systems based on the same geodetic datum. Notice that, the computed coordinates are given in the ECEF frame tied to the earth at the emission time. This is a variation of LTP coordinate systems. Local Vertical Local Horizontal (LVLH) (Figure 2. ftypisom isomiso2avc1mp41*freevideo served by mod_h264_streamingæEmoovlmvhd|%°€|%°€ è ™ @ W9trak\tkhd |%°€|%°€ ™ @ …. Convert Pseudo Earth Fixed Inertial Coordinates to ECEF Coordinates. 国際天文基準座標系 （こくさいてんもんきじゅんざひょうけい、 英語: International Celestial Reference System またはInternational Celestial Reference …. Local tangent plane coordinates (LTP), sometimes named local vertical, local horizontal coordinates (LVLH), are a geographical coordinate system based …. µš u¶Yó¥þiiýV¶ X|—Gå‰ååÙÁ6e –½ »£gRqËŽ*h”У¤]VDPŸë8Í91³ Äå’ߦ葛[email protected]Ö/ ÝX –¦qL d evžg_½üFbõœÂå g6Ùo] °ëo. This document is a Precipitation Processing System (PPS) Configuration Management (CM)-controlled document. Æ€¼…«\$;% wd"ÈZH s[ÔuÂÓ½9%é4íp[â&b qäÜý” í7FQkdaËíL‡&ôÞ ~ç¢ÚJ£ñê^g` ¤éǃ€ Zh Ô ‡§Y#“>| Á:>ºŠLE3E ª’™5t 7þ½opù. The Z-axis coincides with the nadir vector (i. RIDESHARE PAYLOAD USER’S GUIDE © Space Exploration Technologies Corp.
|
|
# Do You Remember LCM?
Number Theory Level 2
$\huge \color{red}{2}, \color{green}{-4}$
Find the least common multiple (L.C.M.) of the two numbers above.
×
|
|
# Interpretation of upper bound on the Wasserstein Distance
I am trying to interpret the 2-Wasserstein distance and the upper bound on it. Let's say I have 2-Wasserstein distance between two distributions to be $$x$$, and I have an upper bound on it which gives me $$100x$$. How do I interpret this upper bound i.e. is this too loose or how good is it?
For example, if the value of $$x$$ is $$0.01$$ then $$100x$$ would be $$1$$ but is $$1$$ a significant value? Is $$1$$ as bad as $$100$$ if we look on a relative scale?
I am not sure what is the best way to evaluate the upper bound and interpret it.
• Can you cite the "2-Wasserstein" distance". How are you getting an upper bound? May 5 '21 at 0:48
• I am looking for an interpretation of the upper bound in general, the derivation of the upper bound depends on the application, shouldn't be relevant here. May 5 '21 at 14:31
• How can this be answered in general? How good or bad an upper bound is depends on what you want to do with it. So to get answers you need to include the relevant context. E.g. what are you trying to accomplish and how does the Wasserstein distance relate to it.
– g g
May 7 '21 at 12:58
• If we take accuracy loss as a metric for example, then we can easily interpret that. An upper bound of 100x in the case when actually loss x=0.01% is pretty ok. We wouldn't need a context here because we know what good or bad is in absolute terms. Is it possible to have the same interpretation for the 2-Wasserstein distance? May 8 '21 at 20:11
• @Dushyant Sahoo In general this would depend on the variation of the random variables. For an example see my answer here: stats.stackexchange.com/a/295729/150025 and consider the case where the two variance-covariance matrices are not the same. In that hypothetical example, how significant the 100x upper bound would depend on the variance-covariance matrices of the two Gaussians. May 9 '21 at 17:23
|
|
# How to trace out qubits from a multipartite density matrix [duplicate]
I have a density made up of 4 qubits. Say system A is made up of the first and second qubits while system B is made up of qubits 3 and 4. I want to trace out 2nd and 3rd qubits.
Is there any reference available to trace out qubits from a multipartite density matrix?
|
|
The distance between two points $\displaystyle{ \textbf{x}=(x_1,x_2,\dots,x_n) }$ and $\displaystyle{ \textbf{y}=(y_1,y_2,\dots,y_n) }$ in the classical Euclidean sense is
$\displaystyle{ \| x - y \| = \sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2 + \dots + (x_n - y_n)^2} }$
However, other measures are possible. On a grid (say, the distance to get from place to place in New York City), the distance is the lateral distance, since you can't go on diagonals:
$\displaystyle{ \| x - y \| = |x_1 - y_1| + \dots + |x_n - y_n| }$
We can dream up scenarios in which we take the cube of each term, and the cube root overall, or any other power that we care to choose. We'll generalize, and define the $\displaystyle{ p }$-norm of a vector $\displaystyle{ \mathbf{x} }$ to be
$\displaystyle{ \|x\|_p = (|x_1|^p + \dots + |x_n|^p)^{\frac{1}{p}} }$
After you play with this for a while, you might ask, "what does the unit circle look like for some $\displaystyle{ p }$"? We'll explore this in two dimensions where it's easy to see. Nothing new happens in higher dimensions.
$\displaystyle{ p=2 }$ is our usual norm, and the unit circle is our usual circle. If we go to $\displaystyle{ p=1 }$, our grid norm above, then we are plotting the equation $\displaystyle{ |x_1| + |x_2| = 1 }$ which is just four line segments connecting the points (1,0), (0,1), (-1,0), and (0,-1). Here is a plot of the unit circles for $\displaystyle{ p=1,2,3,4 }$:
To see the more general behavior, note that we can take the norm of a fixed vector $\displaystyle{ x }$ as a function of $\displaystyle{ p }$. If we fix $\displaystyle{ x=(1,0) }$, or any of the other points on the axes, then the norm doesn't vary with $\displaystyle{ p }$. It's always 1. If we go at forty five degrees between the axes ($\displaystyle{ x=(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}) }$), then we have
$\displaystyle{ \begin{matrix} \|x\|_p & = & (\frac{1}{\sqrt{2}^p} + \frac{1}{\sqrt{2}^p})^{\frac{1}{p}} \\ & = & (2\frac{1}{2^{\frac{p}{2}}})^{\frac{1}{p}} \\ & = & (2^{1-\frac{p}{2}})^{\frac{1}{p}} \\ & = & 2^{(\frac{1}{p}-\frac{1}{2})} \end{matrix} }$
Here is a plot of the function:
Remember, we have here a fixed vector: its value goes down, so in order to get a length of 1, we have to put in a longer vector. The unit circle thus heads steadily towards a square.
The limiting case is the $\displaystyle{ \infty }$-norm, which is simply defined as $\displaystyle{ \|\mathbf{x}\|_\infty = \stackrel{max}{i=1,\dots,n} |x_i| }$, the largest component of the vector. A few moments thought show that the unit circle is simply the square centered at the origin with side length two, and all sides parallel to the axes.
Given these insights into the unit circle, we can actually use this to get another characteristic of a vector. How much does it lie on the axes? Are only two of its components in this basis important? Three?
To measure this, consider our vector $\displaystyle{ \mathbf{x} }$. Take
$\displaystyle{ -\frac{d\|\mathbf{x}\|_p}{dp}|_{p=1} }$
What is this horrible object? Consider a simple case, where $\displaystyle{ \mathbf{x} }$ has $\displaystyle{ k }$ components which are 1 and $\displaystyle{ n-k }$ components which are 0. Then
$\displaystyle{ \begin{matrix} - \frac{d\|\mathbf{x}\|_p}{dp} & = & -\frac{d}{dp} k^{\frac{1}{p}} \\ & = & \frac{1}{p} k^{\frac{1}{p}} \log k^{\frac{1}{p}} \end{matrix} }$
When we evaluate this at $\displaystyle{ p=1 }$, we get $\displaystyle{ -\frac{d\|\mathbf{x}\|_p}{dp}|_{p=1} = k\log k }$, which is at least monotonic in $\displaystyle{ k }$, and gives us an estimate of the number of components.
I was led to this weirdness by looking simple and suitable random variables to use in the Lockless-Ranganathan Formalism, to whit, how do you measure the amount of variation in a given nucleotide?
\end{document}
|
|
## Precalculus (6th Edition) Blitzer
We use mathematical induction as follows: Statement ${{S}_{1}}$ is; $3n=3$ Further simplifying on the right, we obtain $\frac{3n\left( n+1 \right)}{2}=3$. This true statement shows that ${{S}_{1}}$ is true. Suppose ${{S}_{k}}$ is true. Using ${{S}_{k}},{{S}_{k+1}}$ from the expression, ${{S}_{k}}=3+6+9+....+3k=\frac{3k\left( k+1 \right)}{2}$ Adding $3\left( k+1 \right)$ on both sides as given below: \begin{align} & 3+6+9+\ldots +3k+3\left( k+1 \right)=\frac{3k\left( k+1 \right)}{2}+3\left( k+1 \right) \\ & 3+6+9+\ldots +3k+3\left( k+1 \right)=\frac{3k\left( k+1 \right)+6\left( k+1 \right)}{2} \\ & 3+6+9+\ldots +3k+3\left( k+1 \right)=\frac{3{{k}^{2}}+3k+6k+6}{2} \\ & 3+6+9+\ldots +3k+3\left( k+1 \right)=\frac{3{{k}^{2}}+9k+6}{2} \end{align} Therefore, $3+6+9+\ldots +3k+3\left( k+1 \right)=\frac{3\left( k+1 \right)\left( k+2 \right)}{2}$ Thus, ${{S}_{k+1}}$ is true. The result ${{S}_{n}}=3+6+9+....+3n=\frac{3n\left( n+1 \right)}{2}$ holds true.
|
|
Calc. the MM from decay and half life
1. Jun 3, 2005
shoopa
howdy,
how can one determine molar mass when the half life and dacay rate (d/min) and mass of matter are known? im really puzzled. thanks for the help.
2. Jun 4, 2005
Gokul43201
Staff Emeritus
Please post the exact question and your thoughts. As of now, there's insufficient data.
3. Jun 4, 2005
Staff: Mentor
Gokul: if the decay is defined as counts/minute there is enough data to solve the question
Calculate number of atoms in the sample that shows known number of decays per minute. You know the number of atoms, you know number of moles. Ready.
4. Jun 4, 2005
GCT
It would be appropriate to post the exact form of the question.
5. Jun 4, 2005
Gokul43201
Staff Emeritus
True (if the decay rate and mass are the "initial decay rate" and the "initial mass").
|
|
# Question
A truth serum given to a suspect is known to be 90 percent reliable when the person is guilty and 99 percent reliable when the person is innocent. In other words, 10 percent of the guilty are judged innocent by the serum and 1 percent of the innocent are judged guilty. If the suspect was selected from a group of suspects of which only 5 percent are guilty of having committed a crime, and the serum indicates that the suspect is guilty of having committed a crime, what is the probability that the suspect is innocent?
Sales0
Views51
|
|
E. Subway Innovation
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Berland is going through tough times — the dirt price has dropped and that is a blow to the country's economy. Everybody knows that Berland is the top world dirt exporter!
The President of Berland was forced to leave only k of the currently existing n subway stations.
The subway stations are located on a straight line one after another, the trains consecutively visit the stations as they move. You can assume that the stations are on the Ox axis, the i-th station is at point with coordinate xi. In such case the distance between stations i and j is calculated by a simple formula |xi - xj|.
Currently, the Ministry of Transport is choosing which stations to close and which ones to leave. Obviously, the residents of the capital won't be too enthusiastic about the innovation, so it was decided to show the best side to the people. The Ministry of Transport wants to choose such k stations that minimize the average commute time in the subway!
Assuming that the train speed is constant (it is a fixed value), the average commute time in the subway is calculated as the sum of pairwise distances between stations, divided by the number of pairs (that is ) and divided by the speed of the train.
Help the Minister of Transport to solve this difficult problem. Write a program that, given the location of the stations selects such k stations that the average commute time in the subway is minimized.
Input
The first line of the input contains integer n (3 ≤ n ≤ 3·105) — the number of the stations before the innovation. The second line contains the coordinates of the stations x1, x2, ..., xn ( - 108 ≤ xi ≤ 108). The third line contains integer k (2 ≤ k ≤ n - 1) — the number of stations after the innovation.
The station coordinates are distinct and not necessarily sorted.
Output
Print a sequence of k distinct integers t1, t2, ..., tk (1 ≤ tj ≤ n) — the numbers of the stations that should be left after the innovation in arbitrary order. Assume that the stations are numbered 1 through n in the order they are given in the input. The number of stations you print must have the minimum possible average commute time among all possible ways to choose k stations. If there are multiple such ways, you are allowed to print any of them.
Examples
Input
31 100 1012
Output
2 3
Note
In the sample testcase the optimal answer is to destroy the first station (with x = 1). The average commute time will be equal to 1 in this way.
|
|
# Tag Info
0
With grid inside a new tcolorbox: \documentclass[a4paper]{article} % DINA4 (210 × 297 [mm]) \usepackage[%showframe=true, width=16cm, height=26cm, ]{geometry} \pagestyle{empty} \usepackage{tikz} \usetikzlibrary{calc} \usepackage[most]{tcolorbox} \begin{document} \begin{tcolorbox}[ height=6cm, sharp corners, after skip=0pt, enhanced, remember, finish={% \...
1
There are differences between how the width of a tcolorbox environment and a \draw grid are determined. In a tcolorbox environment, its total natural width is exactly \linewidth. Here the entire left and right rules are drawn within that width. In a \draw (0, 0) grid (1, 1);, its total width is "1cm + line width", because tikz draws a line with ...
1
Such irregular structure can be easily obtained with a tcbposter (also from tcolorbox package like tcbraster). Altough a poster is supposed to have a regular structure, it's possible to change height, width and placement for all boxes. It's even possible to define boxes which height is defined by the space between other boxes. Following code shows how to ...
3
The option specifying height of first row is named raster row 1, not row 1. Option tcb/raster row m is documented in documentation of tcolorbox, section 15.4. \documentclass{article} \usepackage[showframe=true]{geometry} \usepackage[most]{tcolorbox} \tcbset{ SymbolStyle/.style={boxrule=4pt,colframe=blue}, NoGaps/.style={boxsep=0pt, left=0pt, right=0pt, ...
1
The gap between box frame and box contents of a tcolorbox environment is controlled by options left, right, top, and bottom, respectively. They are shown in tcolorbox's documentation, sec. 2 and documented in sec. 4.7.4. With each of them set to 0pt, you get \documentclass{article} \usepackage[showframe=true, ]{geometry} \usepackage[most]{tcolorbox} \tcbset{...
0
Please control arc with the help of -- arc=0mm,outer arc=1mm, \begin{tcolorbox} [arc=0mm,outer arc=1mm, boxrule=0mm,toprule=0mm,bottomrule=0mm,left=1mm,right=1mm,leftrule=5pt, titlerule=0mm,toptitle=0mm,bottomtitle=0mm,top=0mm, colframe=blue!50!black,colback=blue!5!white,coltitle=blue!50!black, ] This is a tcolorbox! \...
4
You can replace the frame code so that only the left border is drawn, which removes the artefacts and allows you to have the sharp internal corners: \documentclass{article} \usepackage[skins]{tcolorbox} \newtcolorbox{blueleftbox}{% enhanced, boxrule=0pt, leftrule=5pt, sharp corners=west, frame code={ \fill[blue] ([xshift=5pt]frame.north ...
4
Among other solutions, you could use a \tcbposter with three boxes. For tcbposter look at section 20 in tcolorbox documentation. \documentclass{article} %%% \usepackage{geometry} \geometry{ paperheight=842pt, paperwidth=595pt, margin=0pt, } \setlength{\parindent}{0cm} \usepackage[most]{tcolorbox} \definecolor{theme}{HTML}{333d4f} \...
1
After reading the LuaTeX reference, I realize that it is possible to directly \input from Lua strings. The key is to override find_read_file and open_read_file callbacks, which allows us to write our own back-end for \input commands. For details, please see the code below. \documentclass{article} \usepackage[T1]{fontenc} \usepackage{verbatim} \usepackage{...
5
set attach boxed title to top left to get a boxed title on the top left. rule above the title and the custom title box is drawn in boxed title style={overlay={...}} rule above the frame and shade below the title is drawn in overlay unbroken={...} left rule is drawn by borderline west=... shadow is controled by drop fuzzy shadow \documentclass{article} \...
2
Straight from the book -- http://mirror.iopb.res.in/tex-archive/macros/latex/contrib/tcolorbox/tcolorbox.pdf \documentclass[11pt]{article} \usepackage{amsmath,amssymb} \usepackage{varioref} \usepackage{tcolorbox} \tcbuselibrary{skins} \usepackage{cleveref} \newtcolorbox{YetAnotherTheorem}[1]% {enhanced,arc=0mm,outer arc=0mm, boxrule=0mm,toprule=1mm,...
1
You can play with add to width and right or left dimensions to include the margin notes inside the tcolorbox frames. \documentclass{article} \usepackage{lipsum} \usepackage[most]{tcolorbox} \usepackage{lmodern} \usepackage{marginnote} \begin{document} \begin{tcolorbox}[add to width=3cm, right=3.4cm] \lipsum[2]\marginnote{this is a margin note} \lipsum[1] \...
2
Based on your MWE: \documentclass[border=3mm]{standalone} \usepackage{enumitem} \setlist[itemize]{nosep, leftmargin=*} \usepackage[most]{tcolorbox} \usetikzlibrary{arrows.meta, matrix, positioning} \usepackage[none]{hyphenat} \begin{document} \newtcolorbox{GreenBox}[2][]{% enhanced, colback = ...
12
Useful libraries The arrows.meta tikzlibrary, along with shadows.blur (for the rectangles and arrows) and shapes, can do things you were missing. Here's what I got Does this look somewhat close to what was desired ? Differences from the original Intentionally I kept these simple, rather than accurately mimicking the target : The box widths were made ...
4
Look at this. I hope it helps you. I put some comments to guide with instructions. Sorry for not using the tcolorbox as you requested. I found it easier the way below. IMHO, it may simplify your work. Edit: I rewrote the code to become cleaner. Hope this looks better now! \documentclass[10pt, border=20pt]{standalone} \usepackage[dvipsnames]{xcolor} \...
6
A tcbraster to start with: \documentclass[10pt]{standalone} \usepackage{enumitem} \setlist[itemize]{leftmargin=*, itemsep = 0em} \usepackage[none]{hyphenat} \usepackage{tikz} \usetikzlibrary{matrix, shapes, arrows, positioning} \usepackage[most]{tcolorbox} \begin{document} \tcbset{ innerbox/.style={enhanced, fonttitle=\bfseries, ...
1
You can setup the chars with the literate key of listings: \documentclass{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{pmboxdraw} \usepackage{newunicodechar} \newunicodechar{└}{\textSFii} \newunicodechar{├}{\textSFviii} \newunicodechar{─}{\textSFx} \usepackage{tcolorbox} %\tcbuselibrary{listingsutf8,breakable,skins} \...
3
Suprisingly, I have not encountered this situation before. As commented before, there seems to be to much shrinkable space inside the box. The break algorithm detects that the box cannot be broken further, but the resulting last box seems to be too large to fit on the page (not really true here). So, the bounding box for the last box part is made smaller to ...
0
I've not found a way to prevent the overlap from happening, but I have figured out how to know if it occurs (kind of). The idea is to call \pdfsavepos so that \pdflastypos knows the end of the tcolorbox and the beginning of what comes after. Then we can compare them and type out a warning if something is wrong. The only downside is that using the tcolorbox ...
4
tcolorbox with enhanced skin can be remember(ed) as to be referenced later on inside a tikzpicture. This way there's no need for a tcolorbox inside a TikZ node unless you need special positioning between boxes. Following code shows an example with OP's code. GreenBox definition has been changed to accept an optional parameter and making box title mandatory. \...
2
Second attempt It seems to be controlled by middle and boxsep. If we set them both to be zero the we get: It's not immediately clear to me that this is better than the previous manual adjustment. First, there is a faint hint of a yellow line above the subtitle line. Secondly, as explained on page 11 of the manual, boxsep is added all over the place, which ...
0
The frame hidden option accomplishes what you are asking. Take a look at the documentation of this option (screenshot here) See minimal working example below (screenshot here) \documentclass{article} \usepackage[skins, listings]{tcolorbox} \usepackage{lipsum, showframe} \begin{document} \lipsum[1][1-4] \begin{tcblisting}{ bicolor, colback = blue!10!white,...
1
You can change the order in the graphics pages key: \documentclass[a4paper]{article} \usepackage{geometry} \usepackage[final]{pdfpages} \usepackage{graphicx} \pagestyle{empty} \usepackage[skins,raster]{tcolorbox} \begin{document} \begin{tcbraster}[% raster columns=2, colframe = white, raster height=\textheight,raster equal skip=0pt,blank, ...
0
By default a tcbraster equally divides its total width (linewidth by default) between its columns. This is the reason for your wider than expected central box. You can force the width for a particular box with raster force size=false and some add to width on a particular box. But in this case you have to manually compute all widths in order to distribute the ...
2
Try this: \documentclass{article} \usepackage[many]{tcolorbox} \newtcbtheorem[number within=chapter]{TcbAlgorithm}{Algorithm}{ colback=blue!5, colframe=blue!5, coltitle=red, }{thm} \usepackage[noend]{algpseudocode} \usepackage{algorithm} \usepackage{xpatch} \xpatchcmd\algorithmic {\labelwidth 1.2em} {\labelwidth .7em} {}{\fail} \begin{document} ...
2
I change overlay={\bclampe} to overlay={ \node[inner sep=0pt, xshift=.85cm, anchor=center] at ($(frame.north west)!.5!(frame.south west)$) {\bclampe}; } where xshift=.85cm is half the value of leftrule=1.7cm. Full example \documentclass{article} \usepackage[tikz]{bclogo} \usepackage[most]{tcolorbox} \usepackage{varwidth} \usetikzlibrary{calc} \...
0
The simple answer is to use tcolorbox instead of \tcbox, as follows: \begin{tcolorbox} \begin{small} \begin{concmath} first line\\ % here a new line is expected in the box. second line. \end{concmath} \end{small} \end{tcolorbox}
2
Use option tikznode. It is documented near the end of tcolorbox documentation, sec. 4.12. For example, \documentclass{article} \usepackage{tcolorbox} \usepackage{tikz} \begin{document} \tcbox[tikznode]{% \small text \\ text } \end{document} Update With \tcbox[tikznode]{% \begin{small} \begin{concmath} first line\\ % ...
Top 50 recent answers are included
|
|
# American Institute of Mathematical Sciences
2008, 5(1): 20-33. doi: 10.3934/mbe.2008.5.20
## Global stability analysis for SEIS models with n latent classes
1 Department of Mathematics and Computer Science, University of Dschang, Cameroon 2 Department of Mathematics, University of Douala, Cameroon 3 University of Yaoundé I 4 Laboratoire de Mathématiques et Applications, UMR CNRS 7122, University of Metz and INRIA Lorraine, Metz
Received October 2006 Revised June 2007 Published January 2008
We compute the basic reproduction ratio of a SEIS model with n classes of latent individuals and bilinear incidence.The system exhibits the traditional behaviour. We prove that if R0 ≤1, then the disease-free equilibrium is globally asymptotically stable on the nonnegative orthant and if R0 > 1, an endemic equilibrium exists and is globally asymptotically stable on the positive orthant.
Citation: Napoleon Bame, Samuel Bowong, Josepha Mbang, Gauthier Sallet, Jean-Jules Tewa. Global stability analysis for SEIS models with n latent classes. Mathematical Biosciences & Engineering, 2008, 5 (1) : 20-33. doi: 10.3934/mbe.2008.5.20
[1] Qingming Gou, Wendi Wang. Global stability of two epidemic models. Discrete and Continuous Dynamical Systems - B, 2007, 8 (2) : 333-345. doi: 10.3934/dcdsb.2007.8.333 [2] Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya. Global stability for a class of discrete SIR epidemic models. Mathematical Biosciences & Engineering, 2010, 7 (2) : 347-361. doi: 10.3934/mbe.2010.7.347 [3] Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya. Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 61-74. doi: 10.3934/dcdsb.2011.15.61 [4] C. Connell McCluskey. Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence. Mathematical Biosciences & Engineering, 2010, 7 (4) : 837-850. doi: 10.3934/mbe.2010.7.837 [5] Wendi Wang. Epidemic models with nonlinear infection forces. Mathematical Biosciences & Engineering, 2006, 3 (1) : 267-279. doi: 10.3934/mbe.2006.3.267 [6] Jinliang Wang, Xianning Liu, Toshikazu Kuniya, Jingmei Pang. Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility. Discrete and Continuous Dynamical Systems - B, 2017, 22 (7) : 2795-2812. doi: 10.3934/dcdsb.2017151 [7] Yoshiaki Muroya, Toshikazu Kuniya, Yoichi Enatsu. Global stability of a delayed multi-group SIRS epidemic model with nonlinear incidence rates and relapse of infection. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3057-3091. doi: 10.3934/dcdsb.2015.20.3057 [8] Shouying Huang, Jifa Jiang. Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate. Mathematical Biosciences & Engineering, 2016, 13 (4) : 723-739. doi: 10.3934/mbe.2016016 [9] Yukihiko Nakata, Yoichi Enatsu, Yoshiaki Muroya. On the global stability of an SIRS epidemic model with distributed delays. Conference Publications, 2011, 2011 (Special) : 1119-1128. doi: 10.3934/proc.2011.2011.1119 [10] Attila Dénes, Gergely Röst. Global stability for SIR and SIRS models with nonlinear incidence and removal terms via Dulac functions. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1101-1117. doi: 10.3934/dcdsb.2016.21.1101 [11] Jianquan Li, Zhien Ma. Stability analysis for SIS epidemic models with vaccination and constant population size. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 635-642. doi: 10.3934/dcdsb.2004.4.635 [12] Jianquan Li, Zhien Ma, Fred Brauer. Global analysis of discrete-time SI and SIS epidemic models. Mathematical Biosciences & Engineering, 2007, 4 (4) : 699-710. doi: 10.3934/mbe.2007.4.699 [13] Kazuyuki Yagasaki. Optimal control of the SIR epidemic model based on dynamical systems theory. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2501-2513. doi: 10.3934/dcdsb.2021144 [14] Jing Hui, Lansun Chen. Impulsive vaccination of sir epidemic models with nonlinear incidence rates. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 595-605. doi: 10.3934/dcdsb.2004.4.595 [15] Jing-Jing Xiang, Juan Wang, Li-Ming Cai. Global stability of the dengue disease transmission models. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 2217-2232. doi: 10.3934/dcdsb.2015.20.2217 [16] Zhanyuan Hou. Geometric method for global stability of discrete population models. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3305-3334. doi: 10.3934/dcdsb.2020063 [17] Paul Georgescu, Hong Zhang, Daniel Maxin. The global stability of coexisting equilibria for three models of mutualism. Mathematical Biosciences & Engineering, 2016, 13 (1) : 101-118. doi: 10.3934/mbe.2016.13.101 [18] Xiaomei Feng, Zhidong Teng, Kai Wang, Fengqin Zhang. Backward bifurcation and global stability in an epidemic model with treatment and vaccination. Discrete and Continuous Dynamical Systems - B, 2014, 19 (4) : 999-1025. doi: 10.3934/dcdsb.2014.19.999 [19] Gang Huang, Edoardo Beretta, Yasuhiro Takeuchi. Global stability for epidemic model with constant latency and infectious periods. Mathematical Biosciences & Engineering, 2012, 9 (2) : 297-312. doi: 10.3934/mbe.2012.9.297 [20] Geni Gupur, Xue-Zhi Li. Global stability of an age-structured SIRS epidemic model with vaccination. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 643-652. doi: 10.3934/dcdsb.2004.4.643
2018 Impact Factor: 1.313
|
|
# American Institute of Mathematical Sciences
doi: 10.3934/mcrf.2020047
## A stackelberg game of backward stochastic differential equations with partial information
School of Mathematics, Shandong University, Jinan 250100, China
* Corresponding author: Jingtao Shi
Received December 2019 Revised June 2020 Published November 2020
Fund Project: This work is financially supported by National Key R & D Program of China (2018YFB1305400) and National Natural Science Foundations of China (11971266, 11831010, 11571205)
This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs) with partial information, where the information of the follower is a sub-$\sigma$-algebra of that of the leader. Necessary and sufficient conditions of the optimality for the follower and the leader are first given for the general problem, by the partial information stochastic maximum principles of BSDEs and forward-backward stochastic differential equations (FBSDEs), respectively. Then a linear-quadratic (LQ) Stackelberg game of BSDEs with partial information is investigated. The state estimate feedback representation for the optimal control of the follower is first given via two Riccati equations. Then the leader's problem is formulated as an optimal control problem of FBSDE. Four high-dimensional Riccati equations are introduced to represent the state estimate feedback for the optimal control of the leader. Theoretic results are applied to a pension fund management problem of two players in the financial market.
Citation: Yueyang Zheng, Jingtao Shi. A stackelberg game of backward stochastic differential equations with partial information. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2020047
##### References:
show all references
##### References:
[1] Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 471-487. doi: 10.3934/dcds.2020264 [2] Giuseppina Guatteri, Federica Masiero. Stochastic maximum principle for problems with delay with dependence on the past through general measures. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020048 [3] Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020110 [4] Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020317 [5] Fabio Camilli, Giulia Cavagnari, Raul De Maio, Benedetto Piccoli. Superposition principle and schemes for measure differential equations. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020050 [6] Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020444 [7] Hai Huang, Xianlong Fu. Optimal control problems for a neutral integro-differential system with infinite delay. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020107 [8] Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020347 [9] Sihem Guerarra. Maximum and minimum ranks and inertias of the Hermitian parts of the least rank solution of the matrix equation AXB = C. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 75-86. doi: 10.3934/naco.2020016 [10] Yuan Tan, Qingyuan Cao, Lan Li, Tianshi Hu, Min Su. A chance-constrained stochastic model predictive control problem with disturbance feedback. Journal of Industrial & Management Optimization, 2021, 17 (1) : 67-79. doi: 10.3934/jimo.2019099 [11] Fathalla A. Rihan, Hebatallah J. Alsakaji. Stochastic delay differential equations of three-species prey-predator system with cooperation among prey species. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020468 [12] Reza Chaharpashlou, Abdon Atangana, Reza Saadati. On the fuzzy stability results for fractional stochastic Volterra integral equation. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020432 [13] Nicolas Rougerie. On two properties of the Fisher information. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020049 [14] Peng Luo. Comparison theorem for diagonally quadratic BSDEs. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020374 [15] Leanne Dong. Random attractors for stochastic Navier-Stokes equation on a 2D rotating sphere with stable Lévy noise. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020352 [16] Andy Hammerlindl, Jana Rodriguez Hertz, Raúl Ures. Ergodicity and partial hyperbolicity on Seifert manifolds. Journal of Modern Dynamics, 2020, 16: 331-348. doi: 10.3934/jmd.2020012 [17] Shengxin Zhu, Tongxiang Gu, Xingping Liu. AIMS: Average information matrix splitting. Mathematical Foundations of Computing, 2020, 3 (4) : 301-308. doi: 10.3934/mfc.2020012 [18] Huu-Quang Nguyen, Ya-Chi Chu, Ruey-Lin Sheu. On the convexity for the range set of two quadratic functions. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020169 [19] Hua Qiu, Zheng-An Yao. The regularized Boussinesq equations with partial dissipations in dimension two. Electronic Research Archive, 2020, 28 (4) : 1375-1393. doi: 10.3934/era.2020073 [20] Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020051
2019 Impact Factor: 0.857
|
|
SEARCH HOME
Math Central Quandaries & Queries
Question from ken, a parent: [(90+36-4) ÷ 2] x 15 =
Hi Ken,
The key here is to start as far inside the brackets and parentheses as you can. You have an expression inside brackets "[...]" and the inside this is a pair of parentheses "(...)" so that is where you start.
$90 + 36 - 4 = 122$ so your expression reduces to $[122 \div 2] \times 15.$ Now you have brackets and inside the brackets is $122 \div 2 = 61.$ Finally you have $61 \times 15$ so the result is the answer to $[(90+36-4) \div 2] \times15.$
Penny
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
|
|
Properties
Label 48.2.k Level 48 Weight 2 Character orbit k Rep. character $$\chi_{48}(11,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 12 Newform subspaces 1 Sturm bound 16 Trace bound 0
Related objects
Defining parameters
Level: $$N$$ = $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 48.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$48$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$16$$ Trace bound: $$0$$
Dimensions
The following table gives the dimensions of various subspaces of $$M_{2}(48, [\chi])$$.
Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0
Trace form
$$12q - 2q^{3} - 4q^{4} - 8q^{6} - 8q^{7} + O(q^{10})$$ $$12q - 2q^{3} - 4q^{4} - 8q^{6} - 8q^{7} - 8q^{12} - 4q^{13} + 16q^{16} + 4q^{18} - 12q^{19} - 8q^{21} + 16q^{22} + 24q^{24} + 10q^{27} - 8q^{28} + 28q^{30} - 4q^{33} - 8q^{34} + 20q^{36} - 4q^{37} + 20q^{39} - 40q^{40} - 24q^{42} + 12q^{43} - 12q^{45} - 40q^{46} - 48q^{48} - 20q^{49} + 24q^{51} - 16q^{52} - 52q^{54} + 24q^{55} + 32q^{58} - 16q^{60} + 12q^{61} + 56q^{64} + 28q^{66} + 28q^{67} + 4q^{69} + 40q^{70} + 40q^{72} - 34q^{75} + 56q^{76} + 60q^{78} - 4q^{81} - 16q^{82} + 16q^{84} + 32q^{85} - 60q^{87} - 64q^{88} - 16q^{90} - 56q^{91} + 28q^{93} - 48q^{94} - 56q^{96} - 8q^{97} - 52q^{99} + O(q^{100})$$
Decomposition of $$S_{2}^{\mathrm{new}}(48, [\chi])$$ into newform subspaces
Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
48.2.k.a $$12$$ $$0.383$$ 12.0.$$\cdots$$.2 None $$0$$ $$-2$$ $$0$$ $$-8$$ $$q+\beta _{6}q^{2}-\beta _{10}q^{3}+(-\beta _{1}+\beta _{10}+\beta _{11})q^{4}+\cdots$$
Hecke Characteristic Polynomials
$p$ $F_p(T)$
$2$ $$1 + 2 T^{2} - 2 T^{4} - 16 T^{6} - 8 T^{8} + 32 T^{10} + 64 T^{12}$$
$3$ $$1 + 2 T + 2 T^{2} - 2 T^{3} - 5 T^{4} - 20 T^{5} - 28 T^{6} - 60 T^{7} - 45 T^{8} - 54 T^{9} + 162 T^{10} + 486 T^{11} + 729 T^{12}$$
$5$ $$1 - 30 T^{4} - 49 T^{8} + 12796 T^{12} - 30625 T^{16} - 11718750 T^{20} + 244140625 T^{24}$$
$7$ $$( 1 + 2 T + 15 T^{2} + 20 T^{3} + 105 T^{4} + 98 T^{5} + 343 T^{6} )^{4}$$
$11$ $$1 - 62 T^{4} + 11023 T^{8} - 2631620 T^{12} + 161387743 T^{16} - 13290250622 T^{20} + 3138428376721 T^{24}$$
$13$ $$( 1 + 2 T + 2 T^{2} - 6 T^{3} - 25 T^{4} + 412 T^{5} + 892 T^{6} + 5356 T^{7} - 4225 T^{8} - 13182 T^{9} + 57122 T^{10} + 742586 T^{11} + 4826809 T^{12} )^{2}$$
$17$ $$( 1 - 62 T^{2} + 1903 T^{4} - 38180 T^{6} + 549967 T^{8} - 5178302 T^{10} + 24137569 T^{12} )^{2}$$
$19$ $$( 1 + 6 T + 18 T^{2} + 82 T^{3} + 539 T^{4} + 2636 T^{5} + 9476 T^{6} + 50084 T^{7} + 194579 T^{8} + 562438 T^{9} + 2345778 T^{10} + 14856594 T^{11} + 47045881 T^{12} )^{2}$$
$23$ $$( 1 - 86 T^{2} + 3791 T^{4} - 105684 T^{6} + 2005439 T^{8} - 24066326 T^{10} + 148035889 T^{12} )^{2}$$
$29$ $$1 - 830 T^{4} + 2253679 T^{8} - 1165110596 T^{12} + 1593984336799 T^{16} - 415204522757630 T^{20} + 353814783205469041 T^{24}$$
$31$ $$( 1 - 150 T^{2} + 10019 T^{4} - 392444 T^{6} + 9628259 T^{8} - 138528150 T^{10} + 887503681 T^{12} )^{2}$$
$37$ $$( 1 + 2 T + 2 T^{2} - 54 T^{3} + 567 T^{4} + 8764 T^{5} + 17852 T^{6} + 324268 T^{7} + 776223 T^{8} - 2735262 T^{9} + 3748322 T^{10} + 138687914 T^{11} + 2565726409 T^{12} )^{2}$$
$41$ $$( 1 + 138 T^{2} + 7887 T^{4} + 320492 T^{6} + 13258047 T^{8} + 389955018 T^{10} + 4750104241 T^{12} )^{2}$$
$43$ $$( 1 - 6 T + 18 T^{2} - 226 T^{3} + 4235 T^{4} - 18188 T^{5} + 58436 T^{6} - 782084 T^{7} + 7830515 T^{8} - 17968582 T^{9} + 61538418 T^{10} - 882050658 T^{11} + 6321363049 T^{12} )^{2}$$
$47$ $$( 1 + 170 T^{2} + 15791 T^{4} + 908172 T^{6} + 34882319 T^{8} + 829545770 T^{10} + 10779215329 T^{12} )^{2}$$
$53$ $$1 + 7714 T^{4} + 19237903 T^{8} + 30633057916 T^{12} + 151796308101343 T^{16} + 480271251833238754 T^{20} +$$$$49\!\cdots\!41$$$$T^{24}$$
$59$ $$( 1 - 30 T + 450 T^{2} - 3458 T^{3} + 3915 T^{4} + 231740 T^{5} - 2735068 T^{6} + 13672660 T^{7} + 13628115 T^{8} - 710200582 T^{9} + 5452812450 T^{10} - 21447728970 T^{11} + 42180533641 T^{12} )( 1 + 30 T + 450 T^{2} + 3458 T^{3} + 3915 T^{4} - 231740 T^{5} - 2735068 T^{6} - 13672660 T^{7} + 13628115 T^{8} + 710200582 T^{9} + 5452812450 T^{10} + 21447728970 T^{11} + 42180533641 T^{12} )$$
$61$ $$( 1 - 6 T + 18 T^{2} - 430 T^{3} - 121 T^{4} + 30796 T^{5} - 90148 T^{6} + 1878556 T^{7} - 450241 T^{8} - 97601830 T^{9} + 249225138 T^{10} - 5067577806 T^{11} + 51520374361 T^{12} )^{2}$$
$67$ $$( 1 - 14 T + 98 T^{2} - 706 T^{3} + 9435 T^{4} - 112164 T^{5} + 894884 T^{6} - 7514988 T^{7} + 42353715 T^{8} - 212338678 T^{9} + 1974809858 T^{10} - 18901751498 T^{11} + 90458382169 T^{12} )^{2}$$
$71$ $$( 1 - 230 T^{2} + 30127 T^{4} - 2527028 T^{6} + 151870207 T^{8} - 5844686630 T^{10} + 128100283921 T^{12} )^{2}$$
$73$ $$( 1 - 166 T^{2} + 19007 T^{4} - 1414164 T^{6} + 101288303 T^{8} - 4714108006 T^{10} + 151334226289 T^{12} )^{2}$$
$79$ $$( 1 - 358 T^{2} + 58915 T^{4} - 5817628 T^{6} + 367688515 T^{8} - 13944128998 T^{10} + 243087455521 T^{12} )^{2}$$
$83$ $$1 - 1374 T^{4} + 18563631 T^{8} - 336062521604 T^{12} + 880998758923551 T^{16} - 3094649526959042334 T^{20} +$$$$10\!\cdots\!61$$$$T^{24}$$
$89$ $$( 1 + 322 T^{2} + 51919 T^{4} + 5548348 T^{6} + 411250399 T^{8} + 20203001602 T^{10} + 496981290961 T^{12} )^{2}$$
$97$ $$( 1 + 2 T + 163 T^{2} - 220 T^{3} + 15811 T^{4} + 18818 T^{5} + 912673 T^{6} )^{4}$$
|
|
Convert the following polar equations to rectangular equations. a. r=1/(4sinx-3sinx) b.r=4
Question
Equations
Convert the following polar equations to rectangular equations.
a. $$\displaystyle{r}=\frac{{1}}{{{4}{\sin{{x}}}-{3}{\sin{{x}}}}}$$
b.r=4
2020-11-03
Step 1
To Determine:
Convert the following polar equations to rectangular equations.
a.$$\displaystyle\frac{{1}}{{{4}{\sin{{x}}}-{3}{\sin{{x}}}}}$$
b. r =4
Step 2
Explanation:
a.
Given that,
$$\displaystyle{r}=\frac{{1}}{{{4}{\sin{{x}}}-{3}{\sin{{x}}}}}=\frac{{1}}{{{\sin{{x}}}}}$$
Multiply both the side r
$$\displaystyle{r}^{{2}}=\frac{{r}}{{{\sin{{x}}}}}$$
We know that,
$$\displaystyle{r}^{{2}}={x}^{{2}}+{y}^{{2}}$$
$$\displaystyle{x}^{{2}}+{y}^{{2}}=\frac{{r}}{{{\sin{{x}}}}}$$
and we know that,
$$\displaystyle{y}={r}{\sin{{x}}}$$
$$\displaystyle{r}=\frac{{y}}{{{\sin{{x}}}}}$$
Put the value of r
$$\displaystyle{x}^{{2}}+{y}^{{2}}=\frac{{y}}{{{\sin{{x}}}}}/{\left({\sin{{x}}}\right)}$$
$$\displaystyle{x}^{{2}}+{y}^{{2}}=\frac{{y}}{{{{\sin}^{{2}}{x}}}}$$
Relevant Questions
Convert the following polar equation into a cartesian equation. Specifically describe the graph of the equation in rectangular coordinates: $$\displaystyle{r}={5}{\sin{\theta}}$$
Convert polar equation to a rectangular equation. Then determine the graph’s slope and y-intercept.
$$r\sin(0-\frac{\pi}{4})=2$$
In converting r = 5 from a polar equation to a rectangular equation, describe what should be done to both sides of the equation and why this should be done.
Find two different sets of parametric equations for the rectangular equation y = 4/(x − 1)
Replace the Cartesian equation with equivalent polar equations.
$$x^{2}+xy+y^{2}=1$$
Replace the polar equation with equivalent Cartesian equations. $$\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$$
Rewrite the polar equation $$r=5\sin (θ)r=5\sin (θ)$$ as a Cartesian equation.
$$\displaystyle{x}^{{{2}}}-{y}^{{{2}}}={a}^{{{2}}}$$
Find all a,b,c $$\displaystyle\in{\mathbb{{{R}}}}$$ that satisfy both equations:
|
|
# How do you find the local extrema of g(x)=-x^4+2x^2?
Feb 3, 2018
#### Answer:
$- 1 , 0 , 1$ are the points of local extrema of this function.
#### Explanation:
$g \left(x\right) = - {x}^{4} + 2 {x}^{2}$
$\Rightarrow g ' \left(x\right) = - 4 {x}^{3} + 4 x$
To find the points of Extrema put $g ' \left(x\right) = 0$
$\Rightarrow - 4 {x}^{3} + 4 x = 0$
$\Rightarrow - 4 \left(x\right) \left(x - 1\right) \left(x + 1\right) = 0$
Thus the points of local extrema are:-
x = 0 ;
$x - 1 = 0 \Rightarrow x = 1$
and $x + 1 = 0 \Rightarrow x = - 1$
And the Graph of the Function is given below :-
|
|
### Author Topic: Day Section, Question 1 (Read 10701 times)
#### Victor Ivrii
• Elder Member
• Posts: 2563
• Karma: 0
##### Day Section, Question 1
« on: January 31, 2013, 01:29:59 PM »
Determine the values of $\alpha$ , if any, for which all solutions of the following ODE tend to zero as $t\to\infty$ as well as all values of $\alpha$ , if any, for which all nonzero solutions become unbounded as $t\to\infty$
$$y'' - (2\alpha-1)y'+\alpha(\alpha-1)y=0.$$
#### Brian Bi
• Full Member
• Posts: 31
• Karma: 13
##### Re: Day Section, Question 1
« Reply #1 on: January 31, 2013, 04:26:03 PM »
The characteristic equation
r^2 - (2\alpha-1)r + \alpha(\alpha-1) = 0
factors as $(r - \alpha)(r - (\alpha - 1))$, so the general solution to the ODE is given by
y = A e^{\alpha t} + B e^{(\alpha-1)t}
where $A, B \in \mathbb{R}$.
We consider the following cases:
• $\alpha < 0$: Both exponentials will be decaying, so each solution tends to zero as $t \to \infty$.
• $\alpha = 0$ or $\alpha = 1$: Each $y = c$ for constant $c$ is a solution, so there exist solutions that neither tend to zero nor become unbounded as $t \to \infty$.
• $0 < \alpha < 1$: One exponential is growing and the other decaying, so there exist nonzero solutions that tend to zero as well as solutions that tend to infinity.
• $\alpha > 1$: Both exponentials will be growing. The larger of the two, $Ae^{\alpha t}$, dominates as $t \to \infty$, so $y$ is unbounded unless $A = 0$. If $A$ vanishes identically, then all nonzero solutions $Be^{(\alpha-1)t}$ again become unbounded.
We conclude that the answer is: (i) $\alpha < 0$, and (ii) $\alpha > 1$.
#### Zhuolin Liu
• Newbie
• Posts: 1
• Karma: 0
##### Re: Day Section, Question 1
« Reply #2 on: February 01, 2013, 04:02:18 PM »
I wonder, isn't that when 0<α<1, e(α-1)t tend to 0 as t tend to infinity, and eαt tend to infinity? As a result, isn't that all nonzero solutions become unbounded as t tend to zero when α>0 instead of α>1?
#### Brian Bi
• Full Member
• Posts: 31
• Karma: 13
##### Re: Day Section, Question 1
« Reply #3 on: February 01, 2013, 05:43:49 PM »
I wonder, isn't that when 0<α<1, e(α-1)t tend to 0 as t tend to infinity, and eαt tend to infinity? As a result, isn't that all nonzero solutions become unbounded as t tend to zero when α>0 instead of α>1?
The coefficient on $e^{\alpha t}$ might be zero, so you can have solutions that are just $A e^{(\alpha-1)t}$. These will decay to zero as $t \to \infty$.
#### Victor Ivrii
If we have two characteristic roots $\lambda_2 >0>\lambda_1$ then almost all solutions (with $C_1\ne 0$ and $C_2\ne 0$) are unbounded as $t\to \pm \infty$, solutions $C_2e^{\lambda_2t}$ ($C_2\ne 0$) are unbounded as $t\to +\infty$ and tend to $0$ as $t\to-\infty$ and solutions $C_1e^{\lambda_1t}$ ($C_2\ne 0$) are unbounded as $t\to -\infty$ and tend to $0$ as $t\to +\infty$.
PS. I prefer to write $+\infty$ rather than $\infty$ to avoid any ambiguity.
|
|
# zbMATH — the first resource for mathematics
Bayesian analysis of linear models. (English) Zbl 0564.62020
Statistics: Textbooks and Monographs, Vol. 60. New York - Basel: Marcel Dekker, Inc. XII, 454 p. $59.75 (U.S. & Canada);$ 71.50; SFr. 179.00 (all other countries) (1985).
This book is intended for a graduate course. It is very much in the spirit of G. E. P. Box and G. C. Tiao, Bayesian inference in statistical analysis. (1973; Zbl 0271.62044), in giving scant attention to the loss function, being mainly concerned with finding the posterior distribution and its characteristics, such as moments. This reviewer is uncomfortable with efforts at Bayesian analysis without loss functions. Chapter titles give a good idea of the contents.
1. Bayesian inference for the general linear model. (Includes introduction to Bayesian analysis). 2. Linear statistical models and Bayesian inference. 3. The traditional linear models. 4. The mixed model.
5. Time series models. 6. Linear dynamic systems. 7. Structural change in linear models. 8. Multivariate linear models. 9. Looking ahead.
Reviewer: M.Fox
##### MSC:
62F15 Bayesian inference 62J10 Analysis of variance and covariance (ANOVA) 62-02 Research exposition (monographs, survey articles) pertaining to statistics 62F03 Parametric hypothesis testing 62F10 Point estimation 62M20 Inference from stochastic processes and prediction 62J05 Linear regression; mixed models 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
|
|
# Properties
Label 507.2.b.g Level $507$ Weight $2$ Character orbit 507.b Analytic conductor $4.048$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$507 = 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 507.b (of order $$2$$, degree $$1$$, not minimal)
## Newform invariants
Self dual: no Analytic conductor: $$4.04841538248$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.153664.1 Defining polynomial: $$x^{6} + 5 x^{4} + 6 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$
## $q$-expansion
Coefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\beta_1,\ldots,\beta_{5}$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.
$$f(q)$$ $$=$$ $$q + \beta_{1} q^{2} + q^{3} + \beta_{2} q^{4} + ( -\beta_{3} + \beta_{5} ) q^{5} + \beta_{1} q^{6} + ( \beta_{3} - 3 \beta_{5} ) q^{7} + ( \beta_{1} + \beta_{3} ) q^{8} + q^{9} +O(q^{10})$$ $$q + \beta_{1} q^{2} + q^{3} + \beta_{2} q^{4} + ( -\beta_{3} + \beta_{5} ) q^{5} + \beta_{1} q^{6} + ( \beta_{3} - 3 \beta_{5} ) q^{7} + ( \beta_{1} + \beta_{3} ) q^{8} + q^{9} + ( 1 - 2 \beta_{4} ) q^{10} + ( 3 \beta_{1} - 4 \beta_{3} - 2 \beta_{5} ) q^{11} + \beta_{2} q^{12} + ( -1 + 4 \beta_{4} ) q^{14} + ( -\beta_{3} + \beta_{5} ) q^{15} + ( -3 + 3 \beta_{2} + \beta_{4} ) q^{16} + ( 2 + \beta_{2} ) q^{17} + \beta_{1} q^{18} + ( 3 \beta_{1} + \beta_{3} + 3 \beta_{5} ) q^{19} -\beta_{1} q^{20} + ( \beta_{3} - 3 \beta_{5} ) q^{21} + ( -2 + 3 \beta_{2} - 2 \beta_{4} ) q^{22} + ( 2 - 5 \beta_{2} - 3 \beta_{4} ) q^{23} + ( \beta_{1} + \beta_{3} ) q^{24} + ( 2 \beta_{2} + 3 \beta_{4} ) q^{25} + q^{27} + ( 3 \beta_{1} - 2 \beta_{3} - 2 \beta_{5} ) q^{28} + ( -1 - 2 \beta_{2} - 3 \beta_{4} ) q^{29} + ( 1 - 2 \beta_{4} ) q^{30} + ( -5 \beta_{1} + 2 \beta_{3} + 5 \beta_{5} ) q^{31} + ( -3 \beta_{1} + 4 \beta_{3} + \beta_{5} ) q^{32} + ( 3 \beta_{1} - 4 \beta_{3} - 2 \beta_{5} ) q^{33} + ( \beta_{1} + \beta_{3} ) q^{34} + ( 9 - 4 \beta_{2} - 5 \beta_{4} ) q^{35} + \beta_{2} q^{36} + ( -\beta_{1} + \beta_{3} - 4 \beta_{5} ) q^{37} + ( -7 + 3 \beta_{2} - 2 \beta_{4} ) q^{38} + ( 4 - \beta_{2} - 4 \beta_{4} ) q^{40} + \beta_{1} q^{41} + ( -1 + 4 \beta_{4} ) q^{42} + ( 1 - 2 \beta_{2} + 2 \beta_{4} ) q^{43} + ( -\beta_{1} - 3 \beta_{3} - 6 \beta_{5} ) q^{44} + ( -\beta_{3} + \beta_{5} ) q^{45} + ( 4 \beta_{1} - 2 \beta_{3} - 3 \beta_{5} ) q^{46} + ( -9 \beta_{1} + 3 \beta_{3} + 7 \beta_{5} ) q^{47} + ( -3 + 3 \beta_{2} + \beta_{4} ) q^{48} + ( -10 + 6 \beta_{2} + 7 \beta_{4} ) q^{49} + ( \beta_{1} - \beta_{3} + 3 \beta_{5} ) q^{50} + ( 2 + \beta_{2} ) q^{51} + ( -6 + 2 \beta_{2} + 3 \beta_{4} ) q^{53} + \beta_{1} q^{54} + ( -5 + 2 \beta_{2} ) q^{55} + ( -6 + 3 \beta_{2} + 8 \beta_{4} ) q^{56} + ( 3 \beta_{1} + \beta_{3} + 3 \beta_{5} ) q^{57} + ( -2 \beta_{1} + \beta_{3} - 3 \beta_{5} ) q^{58} + ( -4 \beta_{1} + 6 \beta_{3} + 8 \beta_{5} ) q^{59} -\beta_{1} q^{60} + ( -4 - 3 \beta_{2} + 2 \beta_{4} ) q^{61} + ( 8 - 5 \beta_{2} - 3 \beta_{4} ) q^{62} + ( \beta_{3} - 3 \beta_{5} ) q^{63} + ( -4 + 3 \beta_{2} + 5 \beta_{4} ) q^{64} + ( -2 + 3 \beta_{2} - 2 \beta_{4} ) q^{66} + ( -4 \beta_{1} + 3 \beta_{3} + 4 \beta_{5} ) q^{67} + ( 1 + 3 \beta_{2} + \beta_{4} ) q^{68} + ( 2 - 5 \beta_{2} - 3 \beta_{4} ) q^{69} + ( 8 \beta_{1} + \beta_{3} - 5 \beta_{5} ) q^{70} + ( -5 \beta_{1} - 2 \beta_{3} - \beta_{5} ) q^{71} + ( \beta_{1} + \beta_{3} ) q^{72} + ( 2 \beta_{1} - \beta_{3} - 7 \beta_{5} ) q^{73} + ( 1 - \beta_{2} + 5 \beta_{4} ) q^{74} + ( 2 \beta_{2} + 3 \beta_{4} ) q^{75} + ( -6 \beta_{1} + 7 \beta_{3} + 4 \beta_{5} ) q^{76} + ( 9 - 10 \beta_{2} - 2 \beta_{4} ) q^{77} + ( -5 + 5 \beta_{2} + \beta_{4} ) q^{79} + ( -\beta_{1} + 3 \beta_{3} - 4 \beta_{5} ) q^{80} + q^{81} + ( -2 + \beta_{2} ) q^{82} + ( -\beta_{1} - 3 \beta_{3} - 6 \beta_{5} ) q^{83} + ( 3 \beta_{1} - 2 \beta_{3} - 2 \beta_{5} ) q^{84} + ( -\beta_{1} - 2 \beta_{3} + 2 \beta_{5} ) q^{85} + ( 5 \beta_{1} - 4 \beta_{3} + 2 \beta_{5} ) q^{86} + ( -1 - 2 \beta_{2} - 3 \beta_{4} ) q^{87} + ( 1 + 5 \beta_{2} - \beta_{4} ) q^{88} + ( -2 \beta_{1} - \beta_{3} + 2 \beta_{5} ) q^{89} + ( 1 - 2 \beta_{4} ) q^{90} + ( -2 - 6 \beta_{2} - 5 \beta_{4} ) q^{92} + ( -5 \beta_{1} + 2 \beta_{3} + 5 \beta_{5} ) q^{93} + ( 15 - 9 \beta_{2} - 4 \beta_{4} ) q^{94} + ( 2 \beta_{2} - 5 \beta_{4} ) q^{95} + ( -3 \beta_{1} + 4 \beta_{3} + \beta_{5} ) q^{96} + ( 4 \beta_{1} - 10 \beta_{3} - 3 \beta_{5} ) q^{97} + ( -9 \beta_{1} - \beta_{3} + 7 \beta_{5} ) q^{98} + ( 3 \beta_{1} - 4 \beta_{3} - 2 \beta_{5} ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6q + 6q^{3} + 2q^{4} + 6q^{9} + O(q^{10})$$ $$6q + 6q^{3} + 2q^{4} + 6q^{9} + 2q^{10} + 2q^{12} + 2q^{14} - 10q^{16} + 14q^{17} - 10q^{22} - 4q^{23} + 10q^{25} + 6q^{27} - 16q^{29} + 2q^{30} + 36q^{35} + 2q^{36} - 40q^{38} + 14q^{40} + 2q^{42} + 6q^{43} - 10q^{48} - 34q^{49} + 14q^{51} - 26q^{53} - 26q^{55} - 14q^{56} - 26q^{61} + 32q^{62} - 8q^{64} - 10q^{66} + 14q^{68} - 4q^{69} + 14q^{74} + 10q^{75} + 30q^{77} - 18q^{79} + 6q^{81} - 10q^{82} - 16q^{87} + 14q^{88} + 2q^{90} - 34q^{92} + 64q^{94} - 6q^{95} + O(q^{100})$$
Basis of coefficient ring in terms of a root $$\nu$$ of $$x^{6} + 5 x^{4} + 6 x^{2} + 1$$:
$$\beta_{0}$$ $$=$$ $$1$$ $$\beta_{1}$$ $$=$$ $$\nu$$ $$\beta_{2}$$ $$=$$ $$\nu^{2} + 2$$ $$\beta_{3}$$ $$=$$ $$\nu^{3} + 3 \nu$$ $$\beta_{4}$$ $$=$$ $$\nu^{4} + 3 \nu^{2} + 1$$ $$\beta_{5}$$ $$=$$ $$\nu^{5} + 4 \nu^{3} + 3 \nu$$
$$1$$ $$=$$ $$\beta_0$$ $$\nu$$ $$=$$ $$\beta_{1}$$ $$\nu^{2}$$ $$=$$ $$\beta_{2} - 2$$ $$\nu^{3}$$ $$=$$ $$\beta_{3} - 3 \beta_{1}$$ $$\nu^{4}$$ $$=$$ $$\beta_{4} - 3 \beta_{2} + 5$$ $$\nu^{5}$$ $$=$$ $$\beta_{5} - 4 \beta_{3} + 9 \beta_{1}$$
## Character values
We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$$.
$$n$$ $$170$$ $$340$$ $$\chi(n)$$ $$1$$ $$-1$$
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
337.1
− 1.80194i − 1.24698i − 0.445042i 0.445042i 1.24698i 1.80194i
1.80194i 1.00000 −1.24698 1.44504i 1.80194i 3.44504i 1.35690i 1.00000 −2.60388
337.2 1.24698i 1.00000 0.445042 2.80194i 1.24698i 4.80194i 3.04892i 1.00000 3.49396
337.3 0.445042i 1.00000 1.80194 0.246980i 0.445042i 1.75302i 1.69202i 1.00000 0.109916
337.4 0.445042i 1.00000 1.80194 0.246980i 0.445042i 1.75302i 1.69202i 1.00000 0.109916
337.5 1.24698i 1.00000 0.445042 2.80194i 1.24698i 4.80194i 3.04892i 1.00000 3.49396
337.6 1.80194i 1.00000 −1.24698 1.44504i 1.80194i 3.44504i 1.35690i 1.00000 −2.60388
$$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 337.6 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Inner twists
Char Parity Ord Mult Type
1.a even 1 1 trivial
13.b even 2 1 inner
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 507.2.b.g 6
3.b odd 2 1 1521.2.b.m 6
13.b even 2 1 inner 507.2.b.g 6
13.c even 3 2 507.2.j.h 12
13.d odd 4 1 507.2.a.j 3
13.d odd 4 1 507.2.a.k yes 3
13.e even 6 2 507.2.j.h 12
13.f odd 12 2 507.2.e.j 6
13.f odd 12 2 507.2.e.k 6
39.d odd 2 1 1521.2.b.m 6
39.f even 4 1 1521.2.a.p 3
39.f even 4 1 1521.2.a.q 3
52.f even 4 1 8112.2.a.by 3
52.f even 4 1 8112.2.a.cf 3
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
507.2.a.j 3 13.d odd 4 1
507.2.a.k yes 3 13.d odd 4 1
507.2.b.g 6 1.a even 1 1 trivial
507.2.b.g 6 13.b even 2 1 inner
507.2.e.j 6 13.f odd 12 2
507.2.e.k 6 13.f odd 12 2
507.2.j.h 12 13.c even 3 2
507.2.j.h 12 13.e even 6 2
1521.2.a.p 3 39.f even 4 1
1521.2.a.q 3 39.f even 4 1
1521.2.b.m 6 3.b odd 2 1
1521.2.b.m 6 39.d odd 2 1
8112.2.a.by 3 52.f even 4 1
8112.2.a.cf 3 52.f even 4 1
## Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(507, [\chi])$$:
$$T_{2}^{6} + 5 T_{2}^{4} + 6 T_{2}^{2} + 1$$ $$T_{5}^{6} + 10 T_{5}^{4} + 17 T_{5}^{2} + 1$$
## Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$1 + 6 T^{2} + 5 T^{4} + T^{6}$$
$3$ $$( -1 + T )^{6}$$
$5$ $$1 + 17 T^{2} + 10 T^{4} + T^{6}$$
$7$ $$841 + 381 T^{2} + 38 T^{4} + T^{6}$$
$11$ $$1849 + 986 T^{2} + 61 T^{4} + T^{6}$$
$13$ $$T^{6}$$
$17$ $$( -7 + 14 T - 7 T^{2} + T^{3} )^{2}$$
$19$ $$12769 + 2586 T^{2} + 101 T^{4} + T^{6}$$
$23$ $$( 83 - 43 T + 2 T^{2} + T^{3} )^{2}$$
$29$ $$( -43 + 5 T + 8 T^{2} + T^{3} )^{2}$$
$31$ $$38809 + 3681 T^{2} + 110 T^{4} + T^{6}$$
$37$ $$8281 + 1421 T^{2} + 70 T^{4} + T^{6}$$
$41$ $$1 + 6 T^{2} + 5 T^{4} + T^{6}$$
$43$ $$( -29 - 25 T - 3 T^{2} + T^{3} )^{2}$$
$47$ $$829921 + 30798 T^{2} + 321 T^{4} + T^{6}$$
$53$ $$( 29 + 40 T + 13 T^{2} + T^{3} )^{2}$$
$59$ $$3136 + 1568 T^{2} + 196 T^{4} + T^{6}$$
$61$ $$( -223 + 12 T + 13 T^{2} + T^{3} )^{2}$$
$67$ $$9409 + 1454 T^{2} + 69 T^{4} + T^{6}$$
$71$ $$212521 + 11773 T^{2} + 194 T^{4} + T^{6}$$
$73$ $$27889 + 4189 T^{2} + 122 T^{4} + T^{6}$$
$79$ $$( -169 - 22 T + 9 T^{2} + T^{3} )^{2}$$
$83$ $$1849 + 4401 T^{2} + 146 T^{4} + T^{6}$$
$89$ $$1 + 54 T^{2} + 41 T^{4} + T^{6}$$
$97$ $$1413721 + 40451 T^{2} + 363 T^{4} + T^{6}$$
|
|
# Product of areas
Author: karavpetr
Problem has been solved: 42 times
Русский язык | English Language
Diagonals of the convex quadrilateral divided it into 4 triangles. It turned out that the areas of all four triangles are integer numbers. Find the product of all digits $n$, such that the product of all four areas of triangles cannot end with $n$.
|
|
# How does the Lorentz group act on a 4-vector in the spinor-helicity formalism $p_{\alpha\dot{\alpha}}$?
+ 2 like - 0 dislike
549 views
Given a 4-vector $p^\mu$ the Lorentz group acts on it in the vector representation: $$\tag{1} p^\mu \longrightarrow (J_V[\Lambda])^\mu_{\,\,\nu} p^\nu\equiv \Lambda^\mu_{\,\,\nu} p^\nu.$$ However, I can always represent a 4-vector $p^\mu$ using left and right handed spinor indices, writing $$\tag{2} p_{\alpha \dot{\alpha}} \equiv \sigma^\mu_{\alpha \dot{\alpha}} p_\mu.$$ So the question is: in what representation does the Lorentz group act on $p_{\alpha \dot{\alpha}}$?
There are a lot of questions about this and related topics around physics.se, with a lot of excellent answers, so let me clear up more specifically what I am asking for.
I already know that the answer to this question is that the transformation law is $$\tag{3} p_{\alpha \dot{\alpha}} \rightarrow (A p A^\dagger)_{\alpha\dot{\alpha}}$$ with $A \in SL(2,\mathbb{C})$ (how is mentioned for example in this answer by Andrew McAddams). I also understand that $$\tag{4} \mathfrak{so}(1,3) \cong \mathfrak{sl}(2,\mathbb{C}),$$ (which is explained for example here by Edward Hughes, here by joshphysics, here by Qmechanic).
So what is missing? Not much really. Two things:
1. How do I obtain (3) and what is the specific form of $A$, i.e. its relation with the vector representation $\Lambda^\mu_{\,\,\nu}$? Defining the following $$(\tilde p) \equiv p^\mu, \qquad \Lambda \equiv \Lambda^\mu_{\,\,\nu},$$ $$\sigma \equiv \sigma_{\alpha \dot \alpha}, \qquad \hat p \equiv p_{\alpha \dot \alpha},$$ we can rewrite (1) and (2) in matrix form as $$\tag{5} \hat p \equiv \sigma \tilde p \rightarrow \sigma \Lambda \tilde p = ( \sigma \Lambda \sigma^{-1}) \hat p,$$ however, this disagrees with (3) which I know to be right, so what is wrong with my reasoning?
2. Why does the transformation law (3) has a form $$\tag{6} A \rightarrow U^{-1} A U,$$ while the usual vector transformation (1) has a form $V \rightarrow \Lambda V$? I suspect this comes from a similar reason to that explained here by Prahar, but I would appreciate a confirmation about this.
This post imported from StackExchange Physics at 2015-01-13 11:51 (UTC), posted by SE-user glance
This post imported from StackExchange Physics at 2015-01-13 11:51 (UTC), posted by SE-user Qmechanic
@Qmechanic I edited the question to better specify my problem
This post imported from StackExchange Physics at 2015-01-13 11:51 (UTC), posted by SE-user glance
The question (v2) seems closely related to physics.stackexchange.com/q/153736/2451
This post imported from StackExchange Physics at 2015-01-13 11:51 (UTC), posted by SE-user Qmechanic
@Qmechanic I already saw it and I agree. Unfortunately there are no answers there.
This post imported from StackExchange Physics at 2015-01-13 11:51 (UTC), posted by SE-user glance
+ 1 like - 0 dislike
Your equation (3) comes from the following steps. First, a dotted index transforms in the complex conjugate representation of an undotted index. For a tensor product, each index transforms according to its own representation. Thus $$p_{a\dot a} \mapsto A_{ab} \bar A_{\dot a \dot b} p_{b\dot b} = A_{ab} p_{b\dot b} A^\dagger_{\dot b \dot a}$$ where on the left side of the equal sign we have elementwise complex conjugation. Putting the conjugate matrix on the right we have to take a transpose to get order of indices right.
In reasoning about (4) and (5) you are neglecting the transformation of $\sigma^\mu_{a\dot a}$. The correct description of the relation $p_{a\dot a} = \sigma^\mu_{a\dot a} p_\mu$ is that the 4-vector representation is equivalent to the $(\frac 1 2,0)\otimes(0,\frac 1 2)$ representation, by means of the linear transformation $$\sigma^\mu_{a \dot a} : V\to (\frac12,0)\otimes(0,\frac12)$$ meaning that $\sigma^\mu_{a\dot a}$ belongs to the space $(\frac 1 2,0)\otimes (0,\frac12) \otimes V^*$, on which the (double cover of the) Lorentz group acts. In fact, it acts like $$\sigma^\mu_{a\dot a} \mapsto A_{a\dot b} \sigma^\nu_{b\dot b} A^\dagger_{\dot b \dot a} (\Lambda^{-1})_\nu^\mu$$ so that $A^\mu_{a \dot a} p_\mu$ indeed has the correct transformation law.
This post imported from StackExchange Physics at 2015-01-13 11:51 (UTC), posted by SE-user Robin Ekman
answered Jan 12, 2015 by (215 points)
Thank you very much, that definitely sorted it out. Just one thing: could you also provide some reference where I can find more on the subject (particulary where I can find an exposition of the transformation rules of $\sigma^\mu_{\,\,\alpha\dot \alpha}$ that you quoted)?
This post imported from StackExchange Physics at 2015-01-13 11:51 (UTC), posted by SE-user glance
That $\sigma^\mu_{a \dot a}$ transforms in that manner is really implicit in the indices it has, so I don't know if it's written out anywhere. My best guess is Penrose & Rindler, but I haven't checked.
This post imported from StackExchange Physics at 2015-01-13 11:51 (UTC), posted by SE-user Robin Ekman
Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor) Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOverfl$\varnothing$wThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.
|
|
# Fermionic and bosonic mass deformations of $\mathcal{N}$ = 4 SYM and their bulk supergravity dual
Journal of High Energy Physics, May 2016
We examine the AdS-CFT dual of arbitrary (non)supersymmetric fermionic mass deformations of $\mathcal{N}$ = 4 SYM, and investigate how the backreaction of the RR and NS-NS two-form potentials dual to the fermion masses contribute to Coulomb-branch potential of D3 branes, which we interpret as the bulk boson mass matrix. Using representation theory and supergravity arguments we show that the fermion masses completely determine the trace of this matrix, and that on the other hand its traceless components have to be turned on as non-normalizable modes. Our result resolves the tension between the belief that the AdS bulk dual of the trace of the boson mass matrix (which is not a chiral operator) is a stringy excitation with dimension of order (g s N )1/4 and the existence of non-stringy supergravity flows describing theories where this trace is nonzero, by showing that the stringy mode does not parameterize the sum of the squares of the boson masses but rather its departure from the trace of the square of the fermion mass matrix. Hence, asymptotically-AdS flows can only describe holographically theories where the sums of the squares of the bosonic and fermionic masses are equal, which is consistent with the weakly-coupled result that only such theories can have a conformal UV fixed point.
This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP05%282016%29149.pdf
Iosif Bena, Mariana Graña, Stanislav Kuperstein, Praxitelis Ntokos, Michela Petrini. Fermionic and bosonic mass deformations of $\mathcal{N}$ = 4 SYM and their bulk supergravity dual, Journal of High Energy Physics, 2016, 149, DOI: 10.1007/JHEP05(2016)149
|
|
# Properties
Label 175.2 Level 175 Weight 2 Dimension 959 Nonzero newspaces 12 Newforms 32 Sturm bound 4800 Trace bound 2
## Defining parameters
Level: $$N$$ = $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newforms: $$32$$ Sturm bound: $$4800$$ Trace bound: $$2$$
## Dimensions
The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(175))$$.
Total New Old
Modular forms 1368 1163 205
Cusp forms 1033 959 74
Eisenstein series 335 204 131
## Trace form
$$959q$$ $$\mathstrut -\mathstrut 25q^{2}$$ $$\mathstrut -\mathstrut 28q^{3}$$ $$\mathstrut -\mathstrut 37q^{4}$$ $$\mathstrut -\mathstrut 38q^{5}$$ $$\mathstrut -\mathstrut 60q^{6}$$ $$\mathstrut -\mathstrut 41q^{7}$$ $$\mathstrut -\mathstrut 97q^{8}$$ $$\mathstrut -\mathstrut 55q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$959q$$ $$\mathstrut -\mathstrut 25q^{2}$$ $$\mathstrut -\mathstrut 28q^{3}$$ $$\mathstrut -\mathstrut 37q^{4}$$ $$\mathstrut -\mathstrut 38q^{5}$$ $$\mathstrut -\mathstrut 60q^{6}$$ $$\mathstrut -\mathstrut 41q^{7}$$ $$\mathstrut -\mathstrut 97q^{8}$$ $$\mathstrut -\mathstrut 55q^{9}$$ $$\mathstrut -\mathstrut 58q^{10}$$ $$\mathstrut -\mathstrut 60q^{11}$$ $$\mathstrut -\mathstrut 100q^{12}$$ $$\mathstrut -\mathstrut 58q^{13}$$ $$\mathstrut -\mathstrut 71q^{14}$$ $$\mathstrut -\mathstrut 116q^{15}$$ $$\mathstrut -\mathstrut 85q^{16}$$ $$\mathstrut -\mathstrut 50q^{17}$$ $$\mathstrut -\mathstrut 83q^{18}$$ $$\mathstrut -\mathstrut 36q^{19}$$ $$\mathstrut -\mathstrut 28q^{20}$$ $$\mathstrut -\mathstrut 82q^{21}$$ $$\mathstrut -\mathstrut 80q^{22}$$ $$\mathstrut -\mathstrut 48q^{23}$$ $$\mathstrut +\mathstrut 40q^{24}$$ $$\mathstrut -\mathstrut 6q^{25}$$ $$\mathstrut -\mathstrut 102q^{26}$$ $$\mathstrut -\mathstrut 4q^{27}$$ $$\mathstrut +\mathstrut 25q^{28}$$ $$\mathstrut -\mathstrut 54q^{29}$$ $$\mathstrut +\mathstrut 4q^{30}$$ $$\mathstrut -\mathstrut 32q^{31}$$ $$\mathstrut +\mathstrut 9q^{32}$$ $$\mathstrut -\mathstrut 8q^{34}$$ $$\mathstrut -\mathstrut 32q^{35}$$ $$\mathstrut -\mathstrut 53q^{36}$$ $$\mathstrut -\mathstrut 48q^{37}$$ $$\mathstrut -\mathstrut 40q^{38}$$ $$\mathstrut +\mathstrut 16q^{39}$$ $$\mathstrut -\mathstrut 6q^{40}$$ $$\mathstrut -\mathstrut 62q^{41}$$ $$\mathstrut +\mathstrut 38q^{42}$$ $$\mathstrut -\mathstrut 56q^{43}$$ $$\mathstrut -\mathstrut 32q^{44}$$ $$\mathstrut +\mathstrut 38q^{45}$$ $$\mathstrut -\mathstrut 72q^{46}$$ $$\mathstrut -\mathstrut 56q^{47}$$ $$\mathstrut +\mathstrut 56q^{48}$$ $$\mathstrut -\mathstrut 105q^{49}$$ $$\mathstrut -\mathstrut 46q^{50}$$ $$\mathstrut -\mathstrut 160q^{51}$$ $$\mathstrut +\mathstrut 6q^{52}$$ $$\mathstrut -\mathstrut 88q^{53}$$ $$\mathstrut +\mathstrut 28q^{54}$$ $$\mathstrut -\mathstrut 44q^{55}$$ $$\mathstrut -\mathstrut 79q^{56}$$ $$\mathstrut -\mathstrut 36q^{57}$$ $$\mathstrut +\mathstrut 46q^{58}$$ $$\mathstrut +\mathstrut 92q^{60}$$ $$\mathstrut +\mathstrut 14q^{61}$$ $$\mathstrut +\mathstrut 132q^{62}$$ $$\mathstrut +\mathstrut 61q^{63}$$ $$\mathstrut +\mathstrut 75q^{64}$$ $$\mathstrut +\mathstrut 14q^{65}$$ $$\mathstrut +\mathstrut 48q^{66}$$ $$\mathstrut +\mathstrut 52q^{67}$$ $$\mathstrut +\mathstrut 158q^{68}$$ $$\mathstrut +\mathstrut 52q^{69}$$ $$\mathstrut +\mathstrut 102q^{70}$$ $$\mathstrut -\mathstrut 124q^{71}$$ $$\mathstrut +\mathstrut 147q^{72}$$ $$\mathstrut +\mathstrut 34q^{73}$$ $$\mathstrut +\mathstrut 126q^{74}$$ $$\mathstrut +\mathstrut 28q^{75}$$ $$\mathstrut +\mathstrut 28q^{76}$$ $$\mathstrut +\mathstrut 18q^{77}$$ $$\mathstrut -\mathstrut 8q^{78}$$ $$\mathstrut +\mathstrut 16q^{79}$$ $$\mathstrut +\mathstrut 98q^{80}$$ $$\mathstrut -\mathstrut 91q^{81}$$ $$\mathstrut +\mathstrut 86q^{82}$$ $$\mathstrut +\mathstrut 48q^{83}$$ $$\mathstrut +\mathstrut 90q^{84}$$ $$\mathstrut +\mathstrut 22q^{85}$$ $$\mathstrut -\mathstrut 36q^{86}$$ $$\mathstrut +\mathstrut 4q^{87}$$ $$\mathstrut +\mathstrut 180q^{88}$$ $$\mathstrut +\mathstrut 84q^{89}$$ $$\mathstrut +\mathstrut 170q^{90}$$ $$\mathstrut -\mathstrut 56q^{91}$$ $$\mathstrut +\mathstrut 12q^{92}$$ $$\mathstrut +\mathstrut 28q^{93}$$ $$\mathstrut +\mathstrut 64q^{94}$$ $$\mathstrut +\mathstrut 28q^{95}$$ $$\mathstrut -\mathstrut 4q^{96}$$ $$\mathstrut +\mathstrut 114q^{97}$$ $$\mathstrut +\mathstrut 125q^{98}$$ $$\mathstrut -\mathstrut 68q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$
## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.
Label $$\chi$$ Newforms Dimension $$\chi$$ degree
175.2.a $$\chi_{175}(1, \cdot)$$ 175.2.a.a 1 1
175.2.a.b 1
175.2.a.c 1
175.2.a.d 2
175.2.a.e 2
175.2.a.f 2
175.2.b $$\chi_{175}(99, \cdot)$$ 175.2.b.a 2 1
175.2.b.b 4
175.2.b.c 4
175.2.e $$\chi_{175}(51, \cdot)$$ 175.2.e.a 2 2
175.2.e.b 2
175.2.e.c 4
175.2.e.d 6
175.2.e.e 6
175.2.f $$\chi_{175}(118, \cdot)$$ 175.2.f.a 4 2
175.2.f.b 4
175.2.f.c 4
175.2.f.d 8
175.2.h $$\chi_{175}(36, \cdot)$$ 175.2.h.a 4 4
175.2.h.b 28
175.2.h.c 32
175.2.k $$\chi_{175}(74, \cdot)$$ 175.2.k.a 8 2
175.2.k.b 12
175.2.n $$\chi_{175}(29, \cdot)$$ 175.2.n.a 56 4
175.2.o $$\chi_{175}(68, \cdot)$$ 175.2.o.a 4 4
175.2.o.b 4
175.2.o.c 8
175.2.o.d 24
175.2.q $$\chi_{175}(11, \cdot)$$ 175.2.q.a 144 8
175.2.s $$\chi_{175}(13, \cdot)$$ 175.2.s.a 144 8
175.2.t $$\chi_{175}(4, \cdot)$$ 175.2.t.a 144 8
175.2.x $$\chi_{175}(3, \cdot)$$ 175.2.x.a 288 16
## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(175))$$ into lower level spaces
$$S_{2}^{\mathrm{old}}(\Gamma_1(175)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 2}$$
|
|
alpha.curve {CMC} R Documentation
## Step-by-step Cronbach-Mesbah Curve
### Description
The function calculates and plots the Cronbach-Mesbah Curve for a given data set.
### Usage
alpha.curve(x)
### Arguments
x an object of class data.frame or matrix with n subjects in the rows and k items in the columns.
### Details
There is a direct connection between the Cronbach alpha coefficient α (see alpha.cronbach) and the percentage of variance explained by the first component in the Principal Component Analysis (PCA) on k items. The PCA is usually based on the analysis of the roots of the correlation matrix R of k variables which, under the hypothesis of a parallel model (see Lord and Novick, 1968) is:
1 ρ ... ρ ρ 1 ... ρ R = ... ... ... ... ρ ρ ... 1
This matrix has only two different roots. The greater root is λ_1=1+ρ(k-1) and the other roots are λ_2=…=λ_k=1-ρ=(k-λ_1)/(k-1). Thus, using the Spearman-Brown formula, we can express the reliability of the sum of the k items as follows:
\tilde ρ=k / (k-1) * (1 - 1/ lambda_1).
This indicates that there is a monotonic relationship between \tildeρ, estimated by α, and the first root λ_1, which in practice is estimated using the observed correlation matrix and thus gives the percentage of variance of the first principal component. Then, α is considered as a measure of unidimensionality.
In particular, to assess the unidimensionality of a set of items, it is possible to plot a curve, called step-by-step Cronbach-Mesbah curve, which reports the number of items (from 2 to k) on the x-axis and the corresponding maximum α coefficient on the y-axis obtained through the following steps:
1. first of all the Cronbach coefficient α=\tilde α^0 is computed using all the k items.
2. One at a time, the i-th item (i=1,...,k) is left out and the Cronbach coefficient, denoted by α_{-i}, is computed using the remaining (k-1) items. All the coefficients are collected in a set given by
\tilde α^1=≤ft(α_{-1},...,α_{-j},…,α_{-k}\right)
where the apex refers to the number of item removed at each time. Then, the maximum of \tilde α^1 is detected and the corresponding item is taken out. For example, if α_{-j} is the maximum of \tilde α^1, the j-th item is removed definitely from the scale.
3. The procedure of step 2 is repeated conditionally on the item removed previously. Supposing that item j was removed, the remaining items are left out one at a time and the corresponding Cronbach coefficient is calculated. This gives rise to the following set of (k-1) coefficients
\tilde α^2=≤ft(α_{-(1,j)},...,α_{-(j-1,j)},α_{-(j+1,j)},...,α_{-(k,j)}\right).
The item corresponding to the maximum of \tilde α^2 is then removed definitely. For example, if α_{-1} is the maximum of \tilde α^2, the first item is removed definitely from the scale together with the j-th item removed at step 2.
This procedure is repeated until only 2 items remain. Note that at each step the removed item is the one which leaves the scale with its maximum α value. If we remove a poor item, the α coefficient will increase, whereas if we remove a good item α must decrease. More precisely, the Spearman-Brown formula shows that increasing the number of items leads to increase the reliability of the total score. Thus, a decrease of the Cronbach-Mesbah curve, after adding a variables, would suggest that the added variable do not constitute an unidimensional set with the other variables. On the other hand, if the step-by-step Cronbach-Mesbah curve increases monotonically, then all the items contribute to measure the same latent trait and the bank of items is characterized by unidimensionality.
### Value
The functions returns:
1) an object of class data.frame with 3 columns. The first column N.Item contains the number of item used for computing the Cronbach α coefficients. It contains the values between 2 and k corresponding, respectively, to the case when only 2 items or all the items are used. The second column, Alpha.Max, refers to the maximums of the Cronbach coefficients calculated at each step of the procedure, that is (max \tilde α^{k-2},...,max \tilde α^1,max \tilde α^0). Finally, the last column, Removed.Item, reports the name of the item removed at each step, that is (argmax \tilde α^{k-2},...,argmax \tilde α^1,argmax \tilde α^0).
2) The corresponding Cronbach-Mesbah curve plot created using the first 2 columns of the data.frame described above. Note that also the names of the removed items are reported in the graph.
### Author(s)
Michela Cameletti and Valeria Caviezel
### References
Curt, F., Mesbah, M., Lellouch, J. and Dellatolas, G. (1997) Handedness scale how many and which items? Laterality, 2, 137–154.
Hamon, A. and Mesbah, M. (2002) Questionnaire reliability under the Rasch model. Statistical Methods for Quality of Life Studies: Design, Measurement and Analysis. Mesbah, M., Cole, B.F. and Lee, M.L.T. (Eds.), Kluwer Academic Publishing, Boston, 155–168.
Mesbah, M. (2010) Statistical quality of life. Method and Applications of Statistics in the Life and Health Sciences. Balakrishnan, N. (Editor), Wiley, 839–864.
Nordmann, J., Mesbah, M., Berdeaux, G. (2005) Scoring of Visual Field Measured through Humphrey Perimetry: Principal Component Varimax Rotation Followed by Validated Cluster Analysis. Investigative Ophthalmology & Visual Science 46, 3169–3176.
See Also alpha.cronbach and cain
### Examples
data(cain)
out = alpha.curve(cain)
out
[Package CMC version 1.0 Index]
|
|
How to Convert a Part-to-Part Ratio to a Fraction. The place of 4 in the decimal 4 5.123 is 40 Let us consider the following examples. See more ideas about math classroom, 3rd grade math, fraction wall. Ejection fraction (EF) refers to how well your left ventricle (or right ventricle) pumps blood with each heart beat. You can always share this solution. This has been a guide to Fraction Number in Excel. Fraction Charts Worksheet. We can show fractions in two ways, one as 4âs, i.e., ¼, 2/4, ¾, and another one as 8âs, i.e., 2/8, 4/8, 6/8. I recommend you print them on colored cardstock paper and laminate for durability. Find the greatest common divisor (gcd) of the numerator and the denominator. FRACTION/DECIMAL/METRIC CONVERSION CHART 4th 8th 16th 32nd 64th Inch MM 1/64 .016 .397 1/32 .031 .794 3/64 .047 1.191 1/16 .063 1.588 How to convert decimal to fraction inches? 5th Grade. The following chart shows how minutes are converted to a fraction ⦠See more ideas about teaching math, math lessons, homeschool math. Use promo code DEC50 at checkout to claim this limited-time offer.. Start a 7-day free trial. Mathematics Chart. 0.24 14 0.49 29 0.74 44 0.99 59 0.25 15 0.50 30 0.75 45 1.00 60 Conversion Chart: Fraction of an Hour to Minutes. If you have heart failure and a lower-than-nor⦠4 3/8" Calculators, Tables, Charts for Converting Metric to Imperial and reverse. Your EF is expressed as a percentage. We can create a fraction of up to 3 digits. You can easily convert from fraction to decimal, as well as, from fractions of inches to millimeters. To write 24 as a fraction you have to write 24 as numerator and put 1 as the denominator. To find equivalent fractions, you just need to multiply the numerator and denominator of that reduced fraction (1 6) by the same integer number, ie, multiply by 2, 3, 4, 5, 6... 2 12 is equivalent to 4 24 because 1 x 2 = 2 and 6 x 2 = 12 3 18 is equivalent to 4 24 because 1 x 3 = 3 and 6 x 3 = 18 and cm. The fraction chart below can be saved as a picture and then printed out. This handy chart not only shows you equivalent fractions for over 50 fractions up to 16ths, but also shows you the decimal and percent conversions in a color-coded, handy chart. Example #1. Learn about fractions with fraction bars at MathPlayground.com! For example, letâs convert 3:2 to a fraction. 1. Advertisement. We can see an actual decimal number in the Formula bar. 3/25 = 0.12; Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome: Apply and extend previous understandings of operations with fractions to add, subtract, ⦠Convert 0.32 to fraction⦠I used this to show children equivalence beyond 1/10. Other activities that can be used to teach fractions are the clock activity which uses the clock face to show the fraction of minutes passed in an hour. If you like the video, please give it a thumbs up and leave a comment! How to convert fraction to percent. ©2020 Reade International Corp., PO Drawer 15039 Riverside, RI 02915 USA Fractions to Decimals e.g. Rewrite the decimal number as a fraction with 1 in the denominator$1.625 = \frac{1.625}{1}$Multiply to remove 3 decimal places. 4th Grade. Reduce the fraction by dividing the numerator and the denominator with the gcd. This calculator shows the steps and work to convert a fraction to a decimal number. Principally, we have to find the ratio of two numbers, the numerator and the denominator. For example, if an employee worked one hour and 20 minutes, you would type 1.333 in the Duration (Hours) field. Standard Wire Gauge to fraction and in decimal Parts of an inch, mm. Feel free to change the colours to suit. For example, in order to get a ⦠Convert a fraction to a decimal. May 29, 2020 - Explore tahira's board "fraction wall" on Pinterest. 3:2 = 3 2. Ejection fraction (EF) is a measurement doctors use to calculate the percentage of blood flowing out of your left and right ventricles with each heart contraction. Oct 8, 2020 - Explore Moi Khamvongsod's board "Fraction Chart" on Pinterest. Fun Games for Kids Fraction Bars Explore fraction concepts with fraction bars. Fractions to Decimals to Inches to MM Conversion Chart from READE. If you multiply 1/4 with 2, the result will be ½. Write the decimal fraction as a fraction of the digits to the right of the decimal period (numerator) and a power of 10 (denominator). Most times, EF refers to the amount of blood being pumped out of the left ventricle each time it contracts. 3rd Grade. Fraction to Decimal Conversion Chart Please convert all your dimensions to decimal notation, using the table below. Contents: Our free printable fraction strips are designed to make it easy to teach children fractions and fraction equalities. The following video lesson shares and easy 3-step method for converting a decimal to a fraction without a decimal to fraction chart! Weight conversion table.4536 kilograms 16 ounces 7000 grains 453.6 grams 28.35 grams 437.5 grains 2.2046 pounds 1000 grams 15.432 grains 1000 mg..0648 grams Avoirdupois 1 pound 1 pound 1 pound 1 pound 1 ounce 1 ounce 1 kilogram 1 ⦠Mathematics charts on this page are free to download in many formats including pdf, ppt and word. Start a 7-day free trial today and get 50% off unlimited access. Order and dates of presidents, world capitals, order and dates of statehood, roman numerals, world flags, multiplication, chemical elements, ⦠No Fractions! 1st Grade. Free Printable Fraction Charts This set of printable fraction ⦠This calculator will find all the factors of a number (not just the prime factors).It works on numbers up ⦠6th Grade. Additional calculators available at Digi-Key. Handy for table top reminder or classroom wall. Factors are usually positive or negative whole numbers (no fractions), so ½ × 24 = 12 is not listed.. All Factors Calculator. 2nd Grade. When you enter the amount of hours that an employee has worked in a time sheet, you must enter the minutes as a fraction of an hour. For example - 4.382 inches. This will allow you to fill in the fields. 1 23 is 1/10 The place of 5 in the decimal 4 5.123 is 5. Launch the activity and select the fractions mode, this mode also show equivalent fractions for ⦠It fits on one page and belongs in ⦠Here, you multiply top and bottom by 10 3 = 1000$\frac{1.625}{1}\times \frac{1000}{1000}= \frac{1625}{1000}$Find the Greatest Common Factor (GCF) of 1625 and 1000, if it exists, and reduce the fraction ⦠An EF that is below normal can be a sign of heart failure. The only difference is that the denominator should be to the ⦠ We have many more printables, including study charts and tables, flash cards, and printable exercises. Interactive fraction wall for use in the classroom. How to write the place value of the digit 45.123? These printables are available in color and black and white. On this page, you will find a collectvie of mathematics charts including fraction chart, measurement chart, rational number chart, place value chart and more. Simple calculator to arrange three or more fractions in order, either from least to greatest or from greatest to least by comparing two fractions at a time. Transforming a distance in its decimal form to its fraction inches is almost the same as converting any decimal to a regular fraction.Almost. For eighth's, divide the remainder, 0.382 by 0.125 and the answer is 3.056 so the fraction is a bit over 3 eighth's, therefore the answer ends up as approx. Equivalent Fractions Table / Chart. The place of 3 in the decimal 45.12 3 is 3/1000.. Code to add this calci to your website Just copy and paste the below code to your webpage where you want to display this calculator. 24 = 24/1 = 240/10 And finally we have: 24 as a fraction equals 240/10. Fraction wall showing up to 1/20. This Equivalent Fractions Table/Chart contains common practical fractions. The left ventricle is the heart's main pumping chamber. The fraction can optionally be reduced after converting if needed. Recommended Articles. Click the link above to select a plan and continue to checkout. For example, the proportion of peaches to oranges in a basket of ⦠More Math Games to Play MATH PLAYGROUND 1st Grade Games 2nd Grade Games 3rd Grade Games A part-to-part ratio is an expression of the relationship between two subsets of a set. Convert a ratio to a decimal. The place of 1 in the decimal 45. 3 Pack - Multiplication Tables Poster + Division + Fractions, Decimals & Percentages - Math Chart Set (Laminated, 18" x 24") 4.7 out of 5 stars 9 $3.95$ 3 . Downloadable Converter Calculator Fraction to decimal conversion 30 cm to inches conversion calculator printable decimal chart pflag measurement conversion chart inches time conversion chart minutes to Decimal To Fraction Chart Mashup Math9 Best Fraction To Decimal Chart Printable PrintableeMeasurement Conversion Chart Inches To DecimalsDecimal To Fraction Chart Mashup MathPrintable Decimal Chart ⦠The place of 2 in the decimal 45.1 2 3 is 2/100. Convert proper and improper fractions to decimals. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number. Title: Conversion chart.xls ⦠Double click the fractions to rotate through 90 degrees. Convert decimal to fraction or fraction to decimal with the use of Digi-Key's conversion calculator. 95 Shares and easy 3-step method for converting Metric to Imperial and reverse decimal! Finally we have to write 24 as a fraction of up to 3 digits, -! Dec50 at checkout to claim this limited-time offer.. Start a 7-day free trial as the denominator are available color. Of two numbers, the numerator and the denominator ⦠fraction wall many including... See an actual decimal number in the decimal 45.12 3 is 2/100 of the left ventricle the. - Explore tahira 's board fraction wall left ventricle each time it contracts hour and 20 minutes you! To millimeters find the ratio of two numbers, the numerator and put as... And put 1 as the denominator May 29, 2020 - Explore tahira 's board fraction ''. Difference is that the denominator of 3 in the Formula bar and tables flash. If you multiply 1/4 with 2, the result will be ½ ) of left! Fraction to a fraction of 2 in the Duration ( Hours ) field 3-step method for converting to... Black and white whole number most times, EF refers to the ⦠fraction wall, and printable.. For example, if an employee worked one hour and 20 minutes, you would 1.333... 24 = 24/1 = 240/10 and finally we have: 24 as a fraction you have to write as. Lessons, homeschool math this has been a guide to fraction fraction chart up to 24 in the decimal 4 5.123 5... It a thumbs up and leave a comment to the amount of blood being pumped out of the and... To convert fraction to a fraction to percent you would type 1.333 in fields! As well as, from fractions of inches to MM Conversion chart from READE paper and laminate for durability many... For durability print them on colored cardstock paper and laminate for durability needed... Two subsets of a set Part-to-Part ratio to a fraction of up to 1/20, including study charts tables. Decimal with the use of Digi-Key 's Conversion calculator fraction chart up to 24 3 is 3/1000 lesson and. 7-Day free trial normal can be a sign of heart failure 's Conversion calculator, as well,! You would type 1.333 in the Duration ( Hours ) field normal be... As, from fractions of inches to MM Conversion chart from READE decimal 45.1 3... Charts for converting Metric to Imperial and reverse fraction number in Excel get. This to show children equivalence beyond 1/10 method for converting a decimal to a fraction without a decimal a! Laminate for durability showing up to 3 digits normal can be a sign of failure! - Explore tahira 's board fraction wall showing up to 3 digits 95 May 29, 2020 Explore... Decimal number in Excel lessons, homeschool math can optionally be reduced after converting if needed of 5 in decimal. The ⦠fraction wall '' on Pinterest grade math, fraction wall showing to... And denominator by 10 as long as you get in numerator the whole number a. Please give it a thumbs up and leave a comment the steps and work to a... Out of the left ventricle is the heart 's main pumping chamber write place! Use promo code DEC50 at checkout to claim this limited-time offer.. a! Following examples 1.333 in the Formula bar relationship between two subsets of a set 1/4 with 2 the! Decimal 4 5.123 is 40 Let us consider the following chart shows minutes. Consider the following video lesson shares and easy 3-step method for converting Metric to and! Be to the amount of blood being pumped out of the left ventricle is heart! The following examples charts for converting Metric to Imperial and reverse, charts for converting decimal! Mathematics charts on this page are free to download in many formats including,... Use of Digi-Key 's Conversion calculator dividing the numerator and denominator by 10 as long as get... Are converted to a fraction ⦠how to convert a fraction you have to the... Continue to checkout laminate for durability convert from fraction to percent ¿ we have more... 3 is 2/100 on this page are free to download in many formats including pdf, ppt word. To fill in the fields and laminate for durability Hours ) field Conversion calculator common... To millimeters are converted to a fraction to decimal with the gcd have 24. Fraction you have to find the greatest common divisor ( gcd ) of the relationship between two of. Grade math, fraction wall difference is that the denominator with the use of Digi-Key Conversion... Fractions of inches to MM Conversion chart from READE if needed see an fraction chart up to 24 decimal number Excel. Us consider the following examples ideas about math classroom, 3rd grade math fraction! These printables are available in color and black and white minutes are to... Claim this limited-time offer.. Start a 7-day free trial to find the greatest divisor. Normal can be a sign of heart failure following chart shows how minutes are converted to a fraction ⦠to... Inches to millimeters out of the left ventricle is the heart 's main pumping chamber, ppt and word 3... To fraction chart up to 24 fraction inches 3 digits between two subsets of a set we have many more printables, including charts. For converting a decimal number in Excel has been a guide to fraction number in Excel 1.333 in decimal. This page are free to download in many formats including pdf, ppt and word Decimals to inches to Conversion. Ventricle each time it contracts lesson shares and easy 3-step method for Metric... Convert fraction to percent beyond 1/10 of the digit 45.123.. Start a 7-day trial. Pdf, ppt and word have: 24 as a fraction you have to 24. Result will be ½ Calculators, tables, flash cards, and printable.... Part-To-Part ratio to a fraction Start a 7-day free trial fun Games for Kids fraction Bars Explore concepts! Kids fraction Bars are available in color and black and white be ½ in its decimal form its. - Explore tahira 's board fraction wall showing up to 1/20 from fractions inches! Multiply 1/4 with 2, the result will be ½ 24 as a fraction to a.. Fraction wall the gcd, letâs convert 3:2 to a fraction convert a Part-to-Part ratio a! I recommend you print them on colored cardstock paper and laminate for durability, homeschool.... Download in many formats including pdf, ppt and word, 2020 - Explore tahira 's board wall... '' on Pinterest flash cards, and printable exercises are free to download in many formats pdf... As converting any decimal to a decimal to a fraction you have to find the common... Fraction chart 45.12 3 is 3/1000 convert from fraction to a decimal number to MM Conversion chart from.. Math classroom, 3rd grade math, math lessons, homeschool math digit 45.123 and leave a!... The ratio of two numbers, the numerator and the denominator should fraction chart up to 24 to the ⦠wall! Numerator and the denominator should be to the ⦠fraction wall 29, 2020 - Explore tahira 's board fraction... 24 as numerator and denominator by 10 as long as you get in numerator the number... Including pdf, ppt and word Conversion chart from READE decimal 4 is. Ppt and word, from fractions of inches to millimeters i recommend you print them colored. Optionally be reduced after converting if needed gcd ) of the left ventricle is the heart main! You multiply 1/4 with 2, the numerator and denominator by 10 as long as get... Download in many formats including pdf, ppt and word heart 's main pumping chamber denominator with the.. ( Hours ) field, EF refers to the fraction chart up to 24 fraction wall showing up to 1/20 fraction. From fraction to decimal, as well as, from fractions of to., and printable exercises greatest common divisor ( gcd ) of the digit 45.123 employee one!, you would type 1.333 in the decimal 4 5.123 is 5 a! Thumbs up and leave a comment the steps and work to convert a Part-to-Part to! Paper fraction chart up to 24 laminate for durability how minutes are converted to a fraction ⦠how to convert a Part-to-Part ratio a... Have many more printables, including study charts and tables, flash cards, and printable exercises and white or. Time it contracts Let us consider the following chart shows how minutes are converted to a fraction.Almost... 24/1 = 240/10 and finally we have: 24 as numerator and put 1 as the denominator ).... Below normal can be a sign of heart failure a thumbs up and leave a!. Page are free to download in many formats including pdf, ppt and word is almost same. A distance in its decimal form to its fraction inches is almost the same as converting any decimal to chart... 4 in the decimal 45.12 3 is 2/100 2020 - Explore tahira 's ... You to fill in the decimal 45.12 3 is 2/100 offer.. Start a 7-day free trial the result be! To the ⦠fraction wall '' on Pinterest is below normal can be a sign of heart failure Explore... » ¿ we have: 24 as a fraction without a decimal number in decimal... Math, math lessons, homeschool math the Formula bar 4 3/8 '' Calculators, tables charts! Is an expression of the digit 45.123 result will be ½ promo code at. Is below normal can be a sign of heart failure ⦠fraction wall showing to. To 1/20 shows how minutes are converted to a fraction without a decimal number ( Hours field.
|
|
# Tag Info
4
MSE has several advantages over MAE, but also some disadvantages. Just list some of them, include but not limited to: Decomposition of MSE into Variance and Bias square is one of the most famous advantages. This property helps us to understand the logic behind error, especially MSE, while MAE has no such mathematical meaning. MAE with absolute value ...
4
There is a package called "darch" http://cran.um.ac.ir/web/packages/darch/index.html Quote from CRAN: darch: Package for deep architectures and Restricted-Bolzmann-Machines The darch package is build on the basis of the code from G. E. Hinton and R. R. Salakhutdinov (available under Matlab Code for deep belief nets : last visit: 01.08.2013). ...
3
Artificial neural network: computational power (Wikipedia): The multi-layer perceptron (MLP) is a universal function approximator, as proven by the Cybenko theorem. However, the proof is not constructive regarding the number of neurons required or the settings of the weights. Work by Hava Siegelmann and Eduardo D. Sontag has provided a proof ...
2
The testing set´s size is ranging from 10% to 30% of the training set, and validation set's size is ~10% of the training set. To prevent risk of overfitting, the size of the training set must be at least five times the number of weights. For a three-layers network it has be suggests that the hidden layer (neurons) should have approximately ...
2
Actually a three layer neural network can model arbitrary function with the linear and logistic functions, which was proved by Kolmogorov in 1957 (Kolmogorov, Andrei Nikolaevich. "On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition." Dokl. Akad. Nauk SSSR. Vol. 114. No. 5. ...
2
To get you started, the Elements of Statistical Learning have a nice discussion about regularization, and also sound discussions of different models To judge whether a particular regularization is a good idea, you need to take into account you data as well. E.g. for the LASSO, does it make sense for your data to assume that you have noise-only variates ...
1
It is possible that the additional units are over-fitting the data. Formal analysis of neural networks is limited to broad statements because they're exceedingly difficult to manipulate analytically. An experiment to test this for a particular dataset, is to perform nested k-fold cross-validation. Select a $n$ observations of the data to perform nested ...
1
This is the implemented function (extracted from the C-sources; filennet.c, lines 156-165): static double sigmoid(double sum) { if (sum < -15.0) return (0.0); else if (sum > 15.0) return (1.0); else return (1.0 / (1.0 + exp(-sum))); }
1
Not much to say about computational difficulties, since I haven't used a 3D map with real data. I don't think it will impose a great overhead. You just have to add one more dimension in the distance and neighborhood functions. Theoretically a 3D map will produce better clustering results because it will have a more flexible grid to adapt to the dataset but ...
1
From the linked paper (Paper #1) Each chromosome is defined as a floating-point vector, whose length corresponds to the number of variable in a certain problem. Each element in a vector is called as a gene and each chromosome consists of $N(N-1)$ genes, which are floating point numbers in the range $[-1, 1]$. When computing the FCM classifier's ...
1
Please refer to paper SVM Incremental Learning, Adaptation, and Optimization, which proposed an online SVM for binary classification. The code of above paper can be found here. In the code, two ways of online training are introduced: 1) train the SVM incrementally on one example at a time by calling svmtrain() and 2) perform batch training, incrementing all ...
1
Based on your update pseudo code it looks like you're using a sigmoid output. In this case given an input $x$ your output should be $$\sigma(x) = \frac{1}{1 + e^{-(w^T x + b)}}.$$ It is worth noting that if you assume a log-loss function (which is what you should use for classification) your setup is just binary logistic regression. In this case your ...
1
"I don't understand one thing. How to calculate output for vector input x?" If by single layer perceptron you mean the input layer plus the output layer: Then for each input to the output node, take the values applied to the inputs and multiply them by their cosponsoring weight values. Then sum these weighted inputs. This sum of weighted inputs is then ...
1
Regretfully, I am not familiar with WEKA. Still, here is some ideas that might help to you to look for that you need. There is no bound on the number of steps required for a network to converge. I would stress two points, Neural networks are not guaranteed to converge to a global optima, but to a local optima. They solve non-convex problems, which suffer ...
Only top voted, non community-wiki answers of a minimum length are eligible
|
|
# Advances in Analysis, PDE’s and Related Applications
All abstracts
Size: 116 kb
Organizers:
• Tepper L Gill (Howard University)
• Marcia Federson (University of San Carlos)
• Erik Talvila (University of Fraser Valley)
• Erik Talvila
University of the Fraser Valley, Canada
The heat equation with the continuous primitive integral
PDF abstract
Size: 90 kb
A Schwartz distribution has a continuous primitive integral if it is the distributional derivative of a function that is continuous on the extended real line. This generalises the Lebesgue and Henstock--Kurzweil integrals. The Alexiewicz norm of f is $\|f\|=\sup|\int_If|$ where the supremum is over all intervals $I\subset\mathbb{R}$. The space of distributions integrable in this sense is then a Banach space isometrically isomorphic to the continuous functions on the extended real line with the uniform norm. Many properties familiar from Lebesgue integration continue to hold for these distributions. The one-dimensional heat equation is considered with initial data that is integrable in the sense of the continuous primitive integral. Let $\Theta_t(x)=\exp(-x^2/(4t))/\sqrt{4\pi t}$ be the heat kernel. With initial data $f$ that is the distributional derivative of a continuous function, it is shown that $u_t(x):=u(x,t):=f\ast\Theta_t(x)$ is a classical solution of the heat equation $u_{11}=u_2$. The estimate $\|{f\ast\Theta_t}\|_\infty\leq\|{f}\|/\sqrt{\pi t}$ holds. The initial data is taken on in the Alexiewicz norm, $\|{u_t-f}\|\to 0$ as $t\to 0^+$. The solution of the heat equation is unique under the assumptions that $\|{u_t}\|$ is bounded and $u_t\to f$ in the Alexiewicz norm for some integrable $f$.
• Sonia Mazzucchi
Universita degli Studi Trento (Italy)
Projective systems of functionals and generalized Feynman-Kac formulae
PDF abstract
Size: 73 kb
The construction of a functional integral representation for the solution of the Schroedinger equation, in other words the mathematical definition of "Feynman path integrals", requires an integration theory on infinite dimensional spaces which extends the Lebesgue one. In this talk I shall introduce a generalized approach to infinite dimensional integration which includes, on one hand, both probabilistic and oscillatory integrals and provides, on the other hand, the mathematical basis for the construction of generalized Feynman-Kac formulae. In particular it can be applied to the representation of the solution to partial differential equations which do not satisfy a maximum principle, such as, for instance, the Sch\"odinger equation or $N$-order heat-type equations of the form \begin{eqnarray*}\frac{\partial }{\partial t}u(t,x)&=&a\frac{\partial ^N}{\partial x^N}u(t,x), \\ u(0,x)&=&f(x) \end{eqnarray*} where $t\in {\mathbb R}^+, x\in {\mathbb R}, a\in {\mathbb C}$ and $N\in{\mathbb N}$.
• Irene Fonseca
Carnegie Mellon University, USA
Variational Models for Image Processing
PDF abstract
Size: 37 kb
The mathematical treatment of image processing is strongly hinged on variational methods, partial differential equations, and machine learning. The bilevel scheme combines the principles of machine learning to adapt the model to a given data, while variational methods provide model-based approaches which are mathematically rigorous, yield stable solutions and error estimates. The combination of both leads to the study of weighted Ambrosio-Tortorelli and Mumford-Shah variational models for image processing.
• Francisco Javier Mendoza Torres
The Convolution Theorem over a subset of bounded variation functions
PDF abstract
Size: 63 kb
In this talk we prove the Convolution Theorem for the Fourier integral transform over a subset of bounded variation functions which is dense in $L^{2}(\mathbb{R})$. Moreover, we study some features of those bounded linear transformations $T$ defined on that intersection with values in the space of bounded continuous functions on $\mathbb{R}$, for which the convolution identity $T(f\ast g)=Tf\cdot Tg$ holds.
• Jaqueline Godoy Mesquita
Generalized ODEs and measure differential equations: results and applications
PDF abstract
Size: 39 kb
In this talk, we present results concerning prolongation of solutions, boundedness of solutions as well as stability results for generalized ODEs. Also, using the correspondence between the solutions of generalized ODEs and the solutions of measure differential equations, we extend our results for these last equations, obtaining more general results than the ones found in the literature. Finally, by the correspondence between measure differential equations and dynamic equations on time scales, we also prove our the results for these last ones.
• George Chen
Global Existence for a Singular Gierer-Meinhardt and Enzyme Kinetics System
PDF abstract
Size: 39 kb
In this talk we discuss the existence results for a singular system subject to zero Dirichlet boundary conditions, which originally arose in studies of pattern-formation in biology and chemical reactions in Chemistry. The mathematical difficulties are that the system becomes singular near the boundary and it lacks a variational structure. We use a functional method to obtain both upper and lower bounds for the perturbed system and then use Sobolev embedding theorem to prove the existence of a pair of positive solutions under suitable conditions. This method is first used in a singular parabolic system and is completely different than the traditional methods of sub and super solutions.
• Mariana Smit Vega Garcia
University of Washington, USA
The singular free boundary in the Signorini problem
PDF abstract
Size: 39 kb
In this talk I will overview the Signorini problem for a divergence form elliptic operator with Lipschitz coefficients, and I will describe a few methods used to tackle two fundamental questions: what is the optimal regularity of the solution, and what can be said about the singular free boundary in the case of zero thin obstacle. The proofs are based on Weiss and Monneau type monotonicity formulas. This is joint work with Nicola Garofalo and Arshak Petrosyan.
• Luis Angel Gutierrez Mendez
Space of successions classics contained in the space of Henstock-Kurzweil integrable functions
PDF abstract
Size: 59 kb
In this talk, we will exhibit a technique that shows that certain spaces of successions classic and not classic are contained, as copies, in the space of the Henstock-Kurzweil integrable functions. In particular, we will prove that the spaces $c_{0}$ and $l_{p}$ are contained in the space of the Henstock-Kurzweil integrable functions.
• Kathryn Hare
Local dimensions of self-similar measures with overlap
PDF abstract
Size: 37 kb
The local dimension of a measure is a way to quantify its local behaviour. For example, the local dimension of Lebesgue measure is one everywhere, reflecting the fact that it is uniform in its concentration. For self-similar measures that satisfy a suitable separation condition, it is well known that the set of attainable local dimensions is a closed interval, but for measures which fail to satisfy this condition the situation is more complicated and unclear. In this talk we will discuss a general theory for a class of measures with overlap, which includes interesting examples such as Bernoulli convolutions and convolutions of Cantor measures, and we will see that different phenomena can arise.
• Juan Hector Arredondo Ruiz
On the Factorization theorem in the space of Henstock-Kurzweil integrable functions
PDF abstract
Size: 70 kb
We apply the factorization theorem of Rudin and Cohen to the space of Henstock-Kurzweil integrable functions $HK(R)$. This implies a factorization for the isometric spaces $A_C$ and $B_C$ . We also study in this context the Banach algebra $HK(R)\cap BV(R)$, which is also a dense subspace of $L^2(R).$ This space is in some sene analogous to $L^1(R) \cap L^2(R)$. However, while $L^1 (R) \cap L^2 (R)$ factorizes as $L^1(R) \cap L^2 (R) \ast L^1 (R)$, via the convolution operation $\ast$, it will be shown that $HK(R) \cap BV (R)\ast L^1 (R)$ is a Banach subalgebra of $HK(R) \cap BV (R)$. Joint work with Maria G. Morales
• Alejandro Vélez-Santiago
University of Puerto Rico
A quasi-linear Neumann problem of Ambrosetti-Prodi type in non-smooth domains
PDF abstract
Size: 39 kb
We investigate the solvability of the Ambrosetti-Prodi problem for the p-Laplace operator with Neumann boundary conditions. Using a priori estimates, regularity theory, a sub-supersolution method, and the Leray-Shauder degree theory, we obtain a necessary condition for the non-existence of solutions (in the weak sense), the existence of at least one solution, and the existence of at least two distinct solutions. Moreover,we establish global Hüeolder continuity for weak solutions of the Neumann problem of Ambrosetti{Prodi type on a large class of non-smooth domains.
• Marcia Cristina A. B. Federson
This talk will feature the construction of a Lebesgue measure and integral on any Banach space $\mathcal B$ with a Schauder basis. This theory has the advantage that the integral is computable from below as a limit of Lebesgue integrals on Euclidean space as the dimension $n\to\infty$, so that we may evaluate infinite dimensional quantities by means of finite dimensional approximation. Applications will be discussed.
|
|
Problem with biblatex and footnotes
I'm currently writing a research paper and want to manage my bibliography with biblatex. Everything is working fine except a minor annoyance:
Whenever I use the \footfullcite[pagenumber]{key} command there is no space between the full citation and the page number in the postnote.
I uploaded a minimal example here
Is there any way to solve this?
EDIT BY LOCKSTEP: Here's a boiled-down example that still shows the issue:
\documentclass{article}
\usepackage[style=authortitle]{biblatex}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@BOOK{test,
title = {The Infamous Test},
publisher = {Testington Test},
year = {2007},
author = {John Doe},
}
\end{filecontents}
\begin{document}
\null\vfill% just for the example
Postnote spacing/punctuation doesn't work for \verb|\footfullcite|,\footfullcite[1-10]{test}
although everything is correct for \verb|\footcite|.\footcite[1-10]{test}
\printbibliography
\end{document}
-
Welcome to TeX.sx!. Rather than a link to a ZIP file, it's preferred that the minimal example is spelled out in the question. – egreg Nov 4 '12 at 15:23
Okay, thanks for the info! – Timm Nov 4 '12 at 15:26
Can you tell more about your setting? What version of biblatex are you using? – egreg Nov 4 '12 at 15:48
I'm using MiKTeX 2.9 and the bundled biber backend in the newest version (Version: 4689, Date: 11/2/2012). – Timm Nov 4 '12 at 16:02
It's related to \finentry. At some point after 1.7 \blx@initunit was uncommented in the definition of \blx@finentry@usedrv. Not sure why. Using \protected\def\blx@finentry@usedrv{\unspace} should fix the issue. – Audrey Nov 4 '12 at 16:20
The missing postnote delimiter is due to a bug in the \finentry definition for \usedriver. For now add the following to your preamble:
\makeatletter
|
|
# Recent questions and answers in Nitrogen
### Which one of the following amines does not undergo acylation?
To see more, click for all the questions in this category.
|
|
# Journal of High Energy Physics
## List of Papers (Total 11,631)
#### Black holes and fourfolds
We establish a relation between the structure governing four- and five- dimensional black holes and multicenter solutions on the one hand and Calabi-Yau flux compactifications of M-theory and type IIB string theory on the other hand, for both supersymmetric and non-supersymmetric solutions. We find that the known BPS and almost-BPS multicenter black hole solutions can be...
#### Higher-spin fermionic gauge fields and their electromagnetic coupling
We study the electromagnetic coupling of massless higher-spin fermions in flat space. Under the assumptions of locality and Poincaré invariance, we employ the BRST-BV cohomological methods to construct consistent parity-preserving off-shell cubic 1 − s − s vertices. Consistency and non-triviality of the deformations not only rule out minimal coupling, but also restrict the...
#### Higgs mass and vacuum stability in the Standard Model at NNLO
We present the first complete next-to-next-to-leading order analysis of the Standard Model Higgs potential. We computed the two-loop QCD and Yukawa corrections to the relation between the Higgs quartic coupling (λ) and the Higgs mass (M h ), reducing the theoretical uncertainty in the determination of the critical value of M h for vacuum stability to 1 GeV. While λ at the Planck...
#### On flux quantization in F-theory II: unitary and symplectic gauge groups
We study the quantization of the M-theory G-flux on elliptically fibered Calabi-Yau fourfolds with singularities giving rise to unitary and symplectic gauge groups. We seek and find its relation to the Freed-Witten quantization of worldvolume fluxes on 7-branes in type IIB orientifold compactifications on Calabi-Yau threefolds. By explicitly constructing the appropriate four...
#### Anatomy of maximal stop mixing in the MSSM
A Standard Model-like Higgs near 125 GeV in the MSSM requires multi-TeV stop masses, or a near-maximal contribution to its mass from stop mixing. We investigate the maximal mixing scenario, and in particular its prospects for being realized it in potentially realistic GUT models. We work out constraints on the possible GUT-scale soft terms, which we compare with what can be...
#### Supersymmetric constraints from B s → μ + μ − and B → K * μ + μ − observables
We study the implications of the recent LHCb limit and results on B s → μ + μ − and B → K * μ + μ − observables in the constrained SUSY scenarios. After discussing the Standard Model predictions and carefully estimating the theoretical errors, we show the constraining power of these observables in CMSSM and NUHM. The latest limit on BR(B s → μ + μ −), being very close to the SM...
#### Future prospects for the determination of the Wilson coefficient $$C_{{^{{7\gamma }}}}^{\prime }$$
We discuss the possibilities of assessing a non-zero $$C_{{^{{7\gamma }}}}^{\prime }$$ from the direct and the indirect measurements of the photon polarization in the exclusive b → sγ(*) decays. We focus on three methods and explore the following three decay modes: B → K * (→ K S π 0)γ, B → K 1(→ Kππ)γ, and B → K * (→ Kπ)ℓ + ℓ −. By studying different New Physics scenarios we...
#### Stringy stability of charged dilaton black holes with flat event horizon
Electrically charged black holes with flat event horizon in anti-de Sitter space have received much attention due to various applications in Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, from modeling the behavior of quark-gluon plasma to superconductor. Crucial to the physics on the dual field theory is the fact that when embedded in string theory, black holes...
#### Mellin amplitudes for dual conformal integrals
Motivated by recent work on the utility of Mellin space for representing conformal correlators in AdS/CFT, we study its suitability for representing dual conformal integrals of the type which appear in perturbative scattering amplitudes in super-Yang-Mills theory. We discuss Feynman-like rules for writing Mellin amplitudes for a large class of integrals in any dimension, and find...
#### Implications of a modified Higgs to diphoton decay width
Motivated by recent results from Higgs searches at the Large Hadron Collider, we consider possibilities to enhance the diphoton decay width of the Higgs boson over the Standard Model expectation, without modifying either its production rate or the partial widths in the WW and ZZ channels. Studying effects of new charged scalars, fermions and vector bosons, we find that...
#### Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs
We investigate the Monte Carlo approach to propagation of experimental uncertainties within the context of the established “MSTW 2008” global analysis of parton distribution functions (PDFs) of the proton at next-to-leading order in the strong coupling. We show that the Monte Carlo approach using replicas of the original data gives PDF uncertainties in good agreement with the...
#### Supersymmetric vacua in N = 2 supergravity
We use the embedding tensor formalism to analyse maximally symmetric backgrounds of N = 2 gauged supergravities which have the full N = 2 supersymmetry. We state the condition for N = 2 vacua and discuss some of their general properties. We show that if the gauged isometries leave the SU(2) R-symmetry invariant, then the N = 2 vacuum must be Minkowski. This implies that there are...
#### Sigma terms and strangeness content of the nucleon with N f = 2 + 1 + 1 twisted mass fermions
We study the nucleon matrix elements of the quark scalar-density operator using maximally twisted mass fermions with dynamical light (u,d), strange and charm degrees of freedom. We demonstrate that in this setup the nucleon matrix elements of the light and strange quark densities can be obtained with good statistical accuracy, while for the charm quark counterpart only a bound...
#### Non-supersymmetric conifold
We find a new family of non-supersymmetric numerical solutions of IIB supergravity which are dual to the $$\mathcal{N} = 1$$ cascading “conifold” theory perturbed by certain combinations of relevant single trace and marginal double trace operators with non infinitesimal couplings. The SUSY is broken but the resulting ground states, and their gravity duals, remain stable, at...
#### Massive hermitian gravity
Einstein-Strauss Hermitian gravity was recently formulated as a gauge theory where the tangent group is taken to be the pseudo-unitary group instead of the orthogonal group. A Higgs mechanism for massive gravity was also formulated. We generalize this construction to obtain massive Hermitian gravity with the use of a complex Higgs multiplet. We show that both the graviton and...
#### Search for leptonic decays of W′ bosons in pp collisions at $$\sqrt {s} = {7}$$ TeV
A search for a new heavy gauge boson W′ decaying to an electron or muon, plus a low mass neutrino, is presented. This study uses data corresponding to an integrated luminosity of 5.0 fb−1, collected using the CMS detector in pp collisions at a centre-of-mass energy of 7 TeV at the LHC. Events containing a single electron or muon and missing transverse momentum are analyzed. No...
#### Discrete flavour groups, θ 13 and lepton flavour violation
Discrete flavour groups have been studied in connection with special patterns of neutrino mixing suggested by the data, such as Tri-Bimaximal mixing (groups A 4, S 4…) or Bi-Maximal mixing (group S 4…) etc. We review the predictions for sin θ 13 in a number of these models and confront them with the experimental measurements. We compare the performances of the different classes...
#### Alleviating the non-ultralocality of coset σ-models through a generalized Faddeev-Reshetikhin procedure
The Faddeev-Reshetikhin procedure corresponds to a removal of the non-ultralocality of the classical SU(2) principal chiral model. It is realized by defining another field theory, which has the same Lax pair and equations of motion but a different Poisson structure and Hamiltonian. Following earlier work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible to...
#### Hiding a heavy Higgs boson at the 7 TeV LHC
A heavy Standard Model Higgs boson is not only disfavored by electroweak precision observables but is also excluded by direct searches at the 7 TeV LHC for a wide range of masses. Here, we examine scenarios where a heavy Higgs boson can be made consistent with both the indirect constraints and the direct null searches by adding only one new particle beyond the Standard Model...
#### Reach the bottom line of the sbottom search
We propose a new search strategy for directly-produced sbottoms at the LHC with a small mass splitting between the sbottom and its decayed stable neutralino. Our search strategy is based on boosting sbottoms through an energetic initial state radiation jet. In the final state, we require a large missing transverse energy and one or two b-jets besides the initial state radiation...
#### Building SO(10) models from F-theory
We revisit local F-theory SO(10) and SU(5) GUTs and analyze their properties within the framework of the maximal underlying E 8 symmetry in the elliptic fibration. We consider the symmetry enhancements along the intersections of seven-branes with the GUT surface and study in detail the embedding of the abelian factors undergoing monodromies in the covering gauge groups. We...
#### Cross section ratios between different CM energies at the LHC: opportunities for precision measurements and BSM sensitivity
The staged increase of the LHC beam energy provides a new class of interesting observables, namely ratios and double ratios of cross sections of various hard processes. The large degree of correlation of theoretical systematics in the cross section calculations at different energies leads to highly precise predictions for such ratios. We present in this letter few examples of...
#### Inverted sfermion mass hierarchy and the Higgs boson mass in the MSSM
Abstract It is shown that MSSM with first two generations of squarks and sleptons much heavier than the third one naturally predicts the maximal stop mixing as a consequence of the RG evolution, with vanishing (or small) trilinear coupling at the high scale. The Higgs boson is generically heavy, in the vicinity of 125 GeV. In this inverted hierarchy scenario, motivated by the...
#### Wavefunctions and the point of E 8 in F-theory
AbstractIn F-theory GUTs interactions between fields are typically localised at points of enhanced symmetry in the internal dimensions implying that the coefficient of the associated operator can be studied using a local wavefunctions overlap calculation. Some F-theory SU(5) GUT theories may exhibit a maximum symmetry enhancement at a point to E 8, and in this case all the...
|
|
# GL_TEXTURE_RECTANGLE_NV or TEXTURE_2D
did anyone tryed GL_TEXTURE_RECTANGLE_NV with texture shader? or TEXTURE_2D with texture shader.
there’s only texture shaders demos with cubemaps.
can anybody tell me, where can i find a nice demo (with src of course) with this kind of target textures?
i am trying to make one test with this, but it’s not functional. i used nvidia’s dot_product_reflect demo as a base
I’ve tried them. You can use both of them. For rectangle textures you should notice that they don’t support mipmaps, their coordinates are [0,width)x[0,height), …
I think there are a few examples in nVidia’s SDK. One I remember that use both texture modes with nv_texture_shader is the texture_shader_offset_2d example (found at DEMOS\OpenGL\src exshd_offset_2d in the NVSDK).
(You can donwload the SDK at developer.nvidia.com)
Hope this helps.
Do you have that test, that u tried? If so, could you send me it?
This is a part of my code, but I don’t know, where I have mistake
void Init()
{
nvparse(
"!!RC1.0
"
"out.rgb = tex3;
"
);
nvparse_print_errors(stderr);
signed_normalmap.new_list(GL_COMPILE);
nvparse(
"!!TS1.0
"
"texture_2d();
"
"dot_product_2d_1of2(tex0);
"
"dot_product_2d_2of2(tex0);
"
"texture_2d();
"
);
nvparse_print_errors(stderr);
signed_normalmap.end_list();
}
void render()
{
glEnable(GL_REGISTER_COMBINERS_NV);
glActiveTextureARB( GL_TEXTURE0_ARB );
normals_byte.bind();
glActiveTextureARB( GL_TEXTURE3_ARB );
glBindTexture(GL_TEXTURE_2D, decal.GetId());
glEnable(GL_TEXTURE_2D);
signed_normalmap.call_list();
// cut–begin
glMultiTexCoord2fARB(GL_TEXTURE0_ARB, 0,0);
glMultiTexCoord2fARB(GL_TEXTURE1_ARB, 0,0);
glMultiTexCoord2fARB(GL_TEXTURE2_ARB, 0,0);
glMultiTexCoord2fARB(GL_TEXTURE3_ARB, 0,0);
glVertex2f(-1,-1);
glMultiTexCoord2fARB(GL_TEXTURE0_ARB, 0,1);
glMultiTexCoord2fARB(GL_TEXTURE1_ARB, 0,1);
glMultiTexCoord2fARB(GL_TEXTURE2_ARB, 0,1);
glMultiTexCoord2fARB(GL_TEXTURE3_ARB, 0,1);
glVertex2f(-1, 1);
glMultiTexCoord2fARB(GL_TEXTURE0_ARB, 1,1);
glMultiTexCoord2fARB(GL_TEXTURE1_ARB, 1,1);
glMultiTexCoord2fARB(GL_TEXTURE2_ARB, 1,1);
glMultiTexCoord2fARB(GL_TEXTURE3_ARB, 1,1);
glVertex2f( 1, 1);
glMultiTexCoord2fARB(GL_TEXTURE0_ARB, 1,0);
glMultiTexCoord2fARB(GL_TEXTURE1_ARB, 1,0);
glMultiTexCoord2fARB(GL_TEXTURE2_ARB, 1,0);
glMultiTexCoord2fARB(GL_TEXTURE3_ARB, 1,0);
glVertex2f( 1,-1);
// cut–end
glEnd();
glutSwapBuffers();
}
Originally posted by outTony:
Do you have that test, that u tried? If so, could you send me it?
I can’t send you anything. Sorry. But as I told you, you can find some examples in NVIDIA’s SDK.
[QUOTE]
nvparse(
"!!TS1.0
"
"texture_2d();
"
"dot_product_2d_1of2(tex0);
"
"dot_product_2d_2of2(tex0);
"
"texture_2d();
"
);
[\QUOTE]
Is your texture 0 signed bytes (or hilo), if not you should use:
nvparse(
"!!TS1.0
"
"texture_2d();
"
"dot_product_2d_1of2(expand(tex0));
"
"dot_product_2d_2of2(expand(tex0));
"
"texture_2d();
"
);
Anyway, I have checked and you are trying to do something similar to the dotproduct_2d you can find in NIVIDIA SDK (DEMOS\OpenGL\src\dot_product_2D). The code is not using nvparse for the texture shaders but you can convert it very easy.
Hope this helps.
Originally posted by outTony:
[b]Do you have that test, that u tried? If so, could you send me it?
This is a part of my code, but I don’t know, where I have mistake
void Init()
{
nvparse(
"!!RC1.0
"
"out.rgb = tex3;
"
);
nvparse_print_errors(stderr);
signed_normalmap.new_list(GL_COMPILE);
nvparse(
"!!TS1.0
"
"texture_2d();
"
"dot_product_2d_1of2(tex0);
"
"dot_product_2d_2of2(tex0);
"
"texture_2d();
"
);
nvparse_print_errors(stderr);
signed_normalmap.end_list();
}
void render()
{
glEnable(GL_REGISTER_COMBINERS_NV);
glActiveTextureARB( GL_TEXTURE0_ARB );
normals_byte.bind();
glActiveTextureARB( GL_TEXTURE3_ARB );
glBindTexture(GL_TEXTURE_2D, decal.GetId());
glEnable(GL_TEXTURE_2D);
signed_normalmap.call_list();
// cut–begin
glMultiTexCoord2fARB(GL_TEXTURE0_ARB, 0,0);
glMultiTexCoord2fARB(GL_TEXTURE1_ARB, 0,0);
glMultiTexCoord2fARB(GL_TEXTURE2_ARB, 0,0);
glMultiTexCoord2fARB(GL_TEXTURE3_ARB, 0,0);
glVertex2f(-1,-1);
glMultiTexCoord2fARB(GL_TEXTURE0_ARB, 0,1);
glMultiTexCoord2fARB(GL_TEXTURE1_ARB, 0,1);
glMultiTexCoord2fARB(GL_TEXTURE2_ARB, 0,1);
glMultiTexCoord2fARB(GL_TEXTURE3_ARB, 0,1);
glVertex2f(-1, 1);
glMultiTexCoord2fARB(GL_TEXTURE0_ARB, 1,1);
glMultiTexCoord2fARB(GL_TEXTURE1_ARB, 1,1);
glMultiTexCoord2fARB(GL_TEXTURE2_ARB, 1,1);
glMultiTexCoord2fARB(GL_TEXTURE3_ARB, 1,1);
glVertex2f( 1, 1);
glMultiTexCoord2fARB(GL_TEXTURE0_ARB, 1,0);
glMultiTexCoord2fARB(GL_TEXTURE1_ARB, 1,0);
glMultiTexCoord2fARB(GL_TEXTURE2_ARB, 1,0);
glMultiTexCoord2fARB(GL_TEXTURE3_ARB, 1,0);
glVertex2f( 1,-1);
// cut–end
glEnd();
glutSwapBuffers();
}[/b]
I have read your code now. And I have to ask you. Do you understand what dot_product_2d texture shader does?
It uses texcoord1 (s1,t1,r1) to do a dot product with the value of the texture (usually a normal map) from texture0 and texcoord2 (s2,t2,r2) to do a dot product with the same value to obtain s and t respectively to use it with the texture you have in unit 2.
You usually put light vector in texcoord1 and half-light vector in texcoord2 (both in tangent space). If you do the math and put a texture lookup in unit 2 you will have a diffuse and specular bumpaming per pixel.
Hope this helps.
propably you are right, i dont completly understand it.
light vector helps, but the surface is very rough. propably some vector have to be scaled down.
i am reading now textureshaders.pdf, there’s described everyhing but i have to decrypt it 1st.
can anybody tell my. two things?
1, how to scale vector
2, where i have to bind 2d texture to displace it?
|
|
Didier Verna's scientific blog: Lisp, Emacs, LaTeX and random stuff.
## LaTeX
Monday, January 28 2013
## FiXme 4.2 is out
I'm pleased to announce that, after more than two years, I've managed to put up a very small release of FiXme (my collaborative annotations tool for LaTeX2e) in which I didn't even author the two included changes...
Keep the faith. FiXme is still alive !
New in this veresion (4.2):
** Improve Danish translation
** Fix buglet in redefinition of \@wrindex
reported by Norman Gray.
Get it at the usual place.
Wednesday, March 21 2012
## Star TeX, the Next Generation
I'm happy to announce that my contribution to TUG 2012, the next TeX Users Group International conference, has been accepted. Please find the title and abstract below.
Star TeX, the Next Generation
In 2010, I asked Donald Knuth why he chose to design and implement TeX as a macro-expansion system (as opposed to more traditional procedure calls). His answer was that:
1. he wanted something relatively simple for his secretary who was not a computer scientist,
2. the very limited computing resources at that time practically mandated the use of something much lighter than a true programming language.
The first part of the answer left me with a slight feeling of skepticism. It remains to be seen that TeX is simple to use, and when or where it is, its underlying implementation has hardly anything to do with it.
The second part of the answer, on the other hand, was both very convincing and arguably now obsolete as well. Time has passed and the situation today is very different from what it was 50 years ago. The available computing power has grown exponentially, and so has our overall skills in language design and implementation.
Several ideas on how to modernize TeX already exist. Some have been actually implemented. In this talk, I will present mine. Interestingly enough, it seems to me that modernizing TeX can start with grounding it in an old yet very modern programming language: Common Lisp. I will present the key features that make this language particularly well suited to the task, emphasizing on points such as extensibility, scriptability and multi-paradigm programming. The presentation will include reflections about the software engineering aspects (internals), as well as about the surface layer of TeX itself. Most notably, I will explore the possibilities of providing a more consistent syntax to the TeX API, while maintaining backward compatibility with the existing code base.
Tuesday, July 19 2011
## LaTeX Coding Standards
EDIT: the paper is now freely available for non TUG members.
I'm happy to announce that my contribution to TUG 2011, the next TeX Users Group International conference, has been accepted. Please find the title and abstract below.
Towards LaTeX Coding Standards
Because LaTeX (and ultimately TeX) is only a macro-expansion system, the language does not impose any kind of good software engineering practice, program structure or coding style whatsoever. As a consequence, writing beautiful code (for some definition of "beautiful") requires a lot of self-discipline from the programmer.
Maybe because in the LaTeX world, collaboration is not so widespread (most packages are single-authored), the idea of some LaTeX Coding Standards is not so pressing as with other programming languages. Some people may, and probably have developed their own programming habits, but when it comes to the LaTeX world as a whole, the situation is close to anarchy.
Over the years, the permanent flow of personal development experiences contributed to shape my own taste in terms of coding style. The issues involved are numerous and their spectrum is very large: they range from simple code layout (formatting, indentation, naming schemes etc.), mid-level concerns such as modularity and encapsulation, to very high-level concerns like package interaction/conflict management and even some rules for proper social behavior.
In this talk, I will report on all these experiences and describe what I think are good (or at least better) programming practices. I believe that such practices do help in terms of code readability, maintainability and extensibility, all key factors in software evolution. They help me, perhaps they will help you too.
Thursday, December 16 2010
## DoX 2.2 is released
Hello, I'm happy to announce the release of DoX v2.2. DoX is a set of extensions to the Doc package, for LaTeX2e class and style authors.
New in this release: the ability to create new control-sequence based documentation items (for instance LaTeX lengths).
Tuesday, December 14 2010
## CurVe 1.16 is out
Hello,
I'm happy to announce the release of CurVe 1.16. CurVe is a CV class for LaTeX2e.
New in this release:
- An examples directory
- New \text macro to insert plain text in the middle of rubrics,
- Support for openbib option which was implicit before
- Fix incompatibilities with the splitbib package
- Handle the bibentry/hyperref incompatibility directly
- Implement old font commands letting packages using them (e.g. fancyhdr) work correctly
Friday, December 3 2010
## FiNK 2.2 is out
Hello,
I'm happy to announce the release of FiNK 2.2. FiNK is the LaTeX2e File Name Keeper. New in this release: FiNK is now compatible with the memoir class.
Grab it here
Wednesday, December 1 2010
## Nice feedback on my TUG 2010 paper
Here's a nice comment from a reader of the TUGBoat on my TUG 2010 paper entitled "Classes, Styles, Conflicts: the Biological Realm of LaTeX":
I really enjoy Didier Verna's paper (pp. 162-172). His analogies between LaTeX and microbiology is truly exciting! Being neither a TeXnician nor a (micro) biologist, the paper gives me more insight about LaTeX while at the same time giving me a glimpse to a world beyond my narrow field of knowledge. Please do extend my compliments to the author.
Tuesday, October 5 2010
## Classes, Styles, Conflicts: the Biological Realm of LaTeX
I'm pleased to announce that my article entitled "Classes, Styles, Conflicts: the Biological Realm of LaTeX" has been published in the TUGboat journal, Volume 32 N.2.
There is also a live video recording of the presentation. See http://www.lrde.epita.fr/~didier/resear ... rna.10.tug
Tuesday, March 9 2010
## Paper accepted at TUG 2010
Hello,
I'm happy to announce that I will be presenting a paper at TUG 2010, in San Francisco, for the 2^5th birthday of TeX. The abstract is given below:
Classes, Styles, Conflicts: the Biological Realm of LaTeX
Every LaTeX user faces the "compatibility nightmare" one day or another. With so much intercession capabilities at hand (LaTeX code being able to redefine itself at will), a time comes inevitably when the compilation of a document fails, due to a class/style conflict. In an ideal world, class/style conflicts should only be a concern for package maintainers, not end-users of LaTeX. Unfortunately, the world is real, not ideal, and end-user document compilation does break.
As both a class/style maintainer and a document author, I tried several times to come up with some general principles or a systematic approach to handling class/style cross-compatibility in a smooth and gentle manner, but I ultimately failed. Instead, one Monday morning, I woke up with this vision of the LaTeX biotope, an emergent phenomenon whose global behavior cannot be comprehended, because it is in fact the result of a myriad of "macro"-interactions between small entities, themselves in perpetual evolution.
In this presentation, I would like to draw bridges between LaTeX and biology, by viewing documents, classes and styles as living beings constantly mutating their geneTeX code in order to survive \renewcommand attacks...
Monday, September 21 2009
## FiXme 4.0 is out !
I'm happy to announce FiXme version 4.0
#### WARNING: this is a major release containing many new features and heavy
#### internals refactoring. FiXme 4.0 comes with unprecedented flexibiity,
#### unrivalled extensibility and unchallenged backward-INcompatibility.
What's new in version 4.0
=========================
* Support for collaborative annotations
suggested by Michael Kubovy
** Support for "targeted" notes and environments
(highlighting a portion of text), suggested by Mark Edgington.
** Support for "floating" notes
(not specific to any portion of text), suggested by Rasmus Villemoes.
** Support for alternate layout autoswitch in TeX's inner mode
suggested by Will Robertson.
** Support for automatic language tracking in multilingual documents
** Support for themes
** Extended support for user-provided layouts
** Support for key=value argument syntax in the whole user interface
** New command \fxsetup
** Homogenize log and console messages
** Heavy internals refactoring
Description
===========
FiXme is a collaborative annotation tool for LaTeX documents. Annotating a
document refers here to inserting meta-notes, that is, notes that do not
belong to the document itself, but rather to its development or reviewing
process. Such notes may involve things of different importance levels, ranging
from simple "fix the spelling" flags to critical "this paragraph is a lie"
mentions. Annotations like this should be visible during the development or
reviewing phase, but should normally disapear in the final version of the
document.
FiXme is designed to ease and automate the process of managing collaborative
annotations, by offering a set of predefined note levels and layouts, the
possibility to register multiple note authors, to reference annotations by
listing and indexing etc. FiXme is extensible, giving you the possibility to
create new layouts or even complete "themes", and also comes with support for
AUC-TeX.
FiXme homepage: http://www.lrde.epita.fr/~didier/softwa ... .php#fixme
## DoX v2.0 (2009/09/21) is out
I'm happy to announce the release of DoX v2.0 (2009/09/21).
New in this version:
* Optional argument to \doxitem idxtype option to change the item's index type
* Optional argument to \Describe<Item> and the <Item> environment
noprint option to avoid marginal printing
noindex option to avoid item indexing
* Extend \DescribeMacro, \DescribeEnv and their corresponding environments with the same features
The doc package provides LaTeX developers with means to describe the usage and the definition of new commands and environments. However, there is no simple way to extend this functionality to other items (options or counters for instance). DoX is designed to circumvent this limitation, and provides some improvements over the existing functionality as well.
Monday, September 14 2009
## DoX version 1.0 (2009/09/11) is now available
I'm happy to annouce the first public version of the DoX package for LaTeX2e.
The doc package provides LaTeX developers with means to describe the usage and the definition of new macros and environments. However, there is no simple way to extend this functionality to other items (options or counters for instance). The dox package is designed to circumvent this limitation.
Wednesday, July 22 2009
## FiXme 3.4 is out
I'm happy to announce the next edition of FiXme: version 3.4
New in this release:
** \fixme, \fxerror, \fxwarning and \fxnote are now robust
** Fix incompatibility with KOMA-Script classes when the lox file is inexistent
FiXme provides you with a way of inserting fixme notes in documents. Such notes can appear in the margin of the document, as index entries, in the log file and as warnings on stdout. It is also possible to summarize them in a list, and in the index. When you switch from draft to final mode, any remaining fixme note will be logged, but removed from the document's body. Additionally, critical notes will abort compilation with an informative message. FiXme also comes with support for AUC-TeX.
Wednesday, June 4 2008
## Beamer blocks and the Listings package
For many of my lectures, I use the Listings package for typesetting code excerpts, and include them in Beamer blocks. Providing nice shortcuts for doing that is not trivial if you want to preserve control over Listings options, and add a new one for the block's title. Here is a way to nicely wrap a call to \lstinputlisting inside a Beamer block.
First, let's use the xkeyval package to create a "title" option:
\define@cmdkey[dvl]{lst}[@dvl@lst@]{title}{}
Next, a low-level listing input command. This macro takes 4 arguments: an overlay specification, a title for the block, a list of options passed to Listings, and a file name for input:
%% \dvlinputlisting{overlay}{title}{lstoption=,...}{file}\newcommand\dvlinputlisting[4]{% \begin{block}#1{#2} %% #### WARNING: I need this hack because keyval-style options %% mess up the parsing. \expandafter\lstinputlisting\expandafter[#3]{#4} \end{block}}
And now, you can define all sorts of specialized versions for different languages. For example, here is one for Common Lisp code. The block title is "Lisp" by default, and a "lisp" extension is automatically added to the file name:
%% Language-specific shortcuts:%% The title option is used for the beamer block's title.%% All other options are passed to listings.%% \XXXinputlisting<overlay>[title=,lstoption=,...]{file}\newcommand<>\clinputlisting[2][]{% \def\@dvl@lst@title{Lisp}% \setkeys*[dvl]{lst}{#1}% \edef\@dvl@lst@options{language=lisp,\XKV@rm}% \dvlinputlisting{#3}{\@dvl@lst@title}{\@dvl@lst@options}{#2.lisp}}
Which you could call like this:
\clinputlisting<2->[title={Example 1}, gobble=2]{ex1}
As you can see, "title" is an option for the Beamer block, and all the others are dispatched to Listings. Cool.
Now, things are getting more complicated when you want nice shortcuts for inline environments, because nesting Beamer blocks with listings doesn't work. Fortunately, I figured out a trick based on the Verbatim package to simulate that. The idea is to store the contents of the listing environment in a temporary file, and use \lstinputlisting as before to include it. Clever right ?
:-)
Here is a generic environment for doing that. In the opening, we read the environment's contents and store it in the file \jobname.dvl. In the ending, we call our previous macro \dvlinputlisting on that file (actually, on a dynamically created argument list called \@dvl@args:
\usepackage{verbatim}\newwrite\lstvrb@out\def\@dvllisting{% \begingroup \@bsphack \immediate\openout\lstvrb@out\jobname.dvl \let\do\@makeother\dospecials\catcode\^^M\active \def\verbatim@processline{% \immediate\write\lstvrb@out{\the\verbatim@line}}% \verbatim@start}\def\@enddvllisting{% \immediate\closeout\lstvrb@out \@esphack \endgroup \expandafter\dvlinputlisting\@dvl@args}
And now, we can define all sorts of specialized versions for every language we're insterested in. Again, here is one for Common Lisp.
\newenvironment<>{cllisting}[1][]{% \def\@dvl@lst@title{Lisp}% \setkeys*[dvl]{lst}{#1}% \edef\@dvl@lst@options{language=lisp,\XKV@rm}% \xdef\@dvl@args{{#2}{\@dvl@lst@title}{\@dvl@lst@options}{% \jobname.dvl}} \@dvllisting}{% \@enddvllisting}
Which you can use like this:
\begin{cllinsting}<2->[title={Example 1},gobble=2] (defun foo (x) (* 2 x))\end{cllisting}
Don't forget that frames containing code excerpts like this are fragile!
Wednesday, February 27 2008
## FiNK 2.1.1 is released
I'm happy to announce the release of FiNK 2.1.1. This is a bugfix/documentation only release.
FiNK is a LaTeX2e package that keeps track of the files included (\input or \include) in your documents.
What's new in this version:
** Fix trailing whitespace in \fink@restore
Monday, February 25 2008
## CurVe 1.15 is out
I'm happy to announce the next edition of CurVe, a LaTeX2e class for writing curricula vitae.
What's new in this version:
** Support for itemize environments, suggested by Mirko Hessel-von Molo.
** Added some documentation about vertical spacing problems in |bbl| files, suggested by Seweryn Habdank-Wojewódzki.
Wednesday, November 28 2007
## FiXme version 3.3 is out
I'm happy to announce the next edition of FiXme: version 3.3
New in this release:
* Document incompatibility between marginal layout and the ACM SIG classes
* Honor twoside option in marginal layout
* Support KOMA-Script classes version 2006/07/30 v2.95b
* Documentation improvements
* Fix incompatibility with AMS-Art
* Fix bug in \fixme@footnotetrue
FiXme provides you with a way of inserting fixme notes in documents. Such notes can appear in the margin of the document, as index entries, in the log file and as warnings on stdout. It is also possible to summarize them in a list, and in the index. When you switch from draft to final mode, any remaining fixme note will be logged, but removed from the document's body. Additionally, critical notes will abort compilation with an informative message. FiXme also comes with support for AUC-TeX.
Tuesday, November 27 2007
## CurVe 1.14 is released
I'm happy to announce the next edition of CurVe: version 1.14.
CurVe is a Curriculum Vitae class for LaTeX2e. This version adds support for Polish, and an option to reverse-count bibliographic entries.
Enjoy !
Wednesday, November 14 2007
## FiNK 2.1 is released
I'm happy to announce the next edition of FiNK, the LaTeX2e File Name Keeper, version 2.1.
This package looks over your shoulder and keeps track of files \input'ed
(the LaTeX way) or \include'ed in your document. You then have a
currently being processed through several macros. FiNK also comes with
support for AUC-TeX.
This version fixes a bug preventing proper expansion in math mode.
Sunday, January 22 2006
## Generating PostScript and PDF from TeX
Some time ago, I was thinking about the generation of PostScript and/or PDF from TeX documents (I will speak indifferently of TeX and LaTeX). Knowing that several options are available, I was wondering which solution people preferred. This question triggered a thread on comp.text.tex from which I relate some interesting excerpts here. In order to clarify the debate, I have tweaked or modified several of the quotations. This is a personal manipulation which does not involve the original authors. For that reason, I don't associate them directly to the text below. Warning: the first person comments below are not all mine!
A last note: some arguments about the quality of the available visualization tools appeared in the thread. I have excluded them from the debate, since the central question was the quality of the rendering, not the ergonomy of the tools that handle them.
Participants (besides myself): LEE Sau Dan, George N. White III, David Kastrup, Mike Oliver, H.S. (??). Thanks to them for their comments.
## Options
### Direct approach:
TeX -> (tex) -> DVI -> (dvips) -> PostScriptTeX -> (pdftex) -> PDF
### Indirect approaches:
TeX -> (tex) -> DVI -> (dvips) -> PostScript -> (ps2pdf) -> PDFor:TeX -> (pdftex) -> PDF -> (pdf2ps) -> PostScript
And note that it is also possible to generate PDF from the DVI file...
## Direct or indirect approach ?
pdftex does not necessarily generate the same layout as tex. pdftex allows more flexibility in adjusting the character spacing, etc, and hence may break lines differently than Knuth's tex. It doesn't occur that often, though.
pdftex can produce visually more even margins (by allowing some glyphs to protrude), which in turn allows you to use slightly narrower gutters in multi-column layouts. Not only does this save trees, it also gives effectively longer lines and so reduces the number of bad breaks, rivers, etc. This is especially helpful if you are trying to use a CM-based font in a layout originally intended for Times-Roman.
One has to remember that if you want to use the direct approach, you won't be able to use target-specific additions in your source file, or will need different versions of parts of it (perhaps in conditionals) according to the target language. For instance, it is impossible to use pstricks with pdftex because pstricks is PostScript-specific (but see pdftricks...).
If your required packages vary according to the target language (e.g. you want hyperref for PDF output, but not for PostScript), you will most certainly have problems compiling your document in a single directory tree. That's because the aux files will vary according to your target language. So either you make clean before changing your target, or you compile (outside of the source tree) in different subtrees. This can be somewhat cumbersome, although a simple use of Makefiles and of the TEXINPUTS environment variable makes this process quite easy.
This only real disadvantage that remains is that you have to
compile your document entirely twice (once for
each target language), so it takes more time than with one of
the indirect approaches.
So bear in mind that a direct approach might give slightly different documents.
## Cons the PDF to PS conversion
PostScript Level 3 supports PDF with minimal translation. Older printers with Level 1 interpreters often choke on PS files created from PDF, and there are sometimes problems with Level 2 printers. In some circles PDF has a bad reputation based on bugs in early software and problems rendering PDF using old rasterizers. When a PDF file is translated to PS, the driver generally just loads PS code to define the PDF primitives. With current rasterizers this PS code is fairly simple, but with older rasterizers the code is considerably more complex and almost sure to give problems under stress.
The following arguments come from people programming PostScript directly, which is not supported with pdftex:
EPS -> PDF conversion means a loss of the PostScript elegance. Compact, repetitive code gets expanded, and hence file size gets inflated.
This is about using Postscript source translated to PDF, and the converting the PDF document to PostScript.
Compact Postscript code (such as fractals) will be expanded in this final Postscript file, thanks to PDF's Turing-incompleteness. This means an inflated final file size.
But if you need PDF output, you can't cope with its Turing-incompleteness, right?
However, some people note that:
The lack of support of literal Postscript code and EPS figures (yes, I know epstopdf) is irritating. I'm switching most of my drawings, etc. to METAPOST for its elegance, and it's good news to learn that pdftex can include METAPOST figures directly (as long as I don't insert literal Postscript with the 'special' command in METAPOST).
## Pro TeX -> DVI -> PS / PDF
EPS or EEPIC are not supported by pdftex. METAPOST is supported though.
However, unless you have a tightly controlled source of EPS figures, the conversion from EPS to PDF is a tricky step, and can require tweaks (and even bug fixes to the conversion tool) to deal with the idiosyncracies in individual files. This is much easier to get right and to debug if you convert each EPS to PDF separately than if you have problems with a document level conversion.
So this might eventually turn into an argument in favor of the direct approach.
## Pro TeX -> PDF -> PS (throwing DVI away)
But note that you can produce DVI with pdftex: use the command \pdfoutput=0
TeX has information that gets discarded in the DVI file but which can be used by pdftex. Information available to TeX macros can be put into \specials for dvips, but pdftex can also get information from TeX's internals.
Some people object:
You still haven't specified which particular \specials are causing problems. I have been using the hyperref package for some time. With this package, I can insert document infos such as author, title, etc (displayed in Acrobat Reader when you pop up the Document Info window (Ctrl-D in some versions)). The dvips driver of hyperref will insert appropriate pdfmark operators so that ps2pdf can generate it in the final PDF file. When you use pdftex instead (thus using the pdftex driver of hyperref), the macros are defined in such a way that the same info is generated on the output PDF file directly. In either case, the document info are there in the final PDF. The same is true for hyperlinks, crossreference likes, PDF form entry fields, etc. Also thumbnails and bookmarks.
PDF -> PS conversions are needed by many more people that use TeX, while conversions involving DVI files are only useful to a limited audience. There are more and better tools for PDF -> PS than for DVI -> anything. As a case in point, the most common tool for DVI -> PS is dvips, which is based on a raster graphics model and so can have problems (even when using scalable outline fonts) if the PS file is scaled.
dvips lays out the page using a raster grid determined by the resolution you specify. Sure, -Ppdf sets a high resolution, but if you need to scale a PS file created with dvips this causes problems. Y&Y's (commercial) dvips one does produce scalable PS.
About the quality of the tools, some people object:
Tools for DVI -> PS conversion are very good, stable and versatile. (e.g. the embedded T1 fonts contain only the glpyhs actually used in the document.)
This is an emotional and ironic argument that might be considered as not so relevant:
If all the programs with 'dvi' in their names stopped working, a few mathematicians would be annoyed but would soon learn to use PDF. If all the programs that work with 'pdf' files stopped working, CNN would cover the disaster 7/24. If we all stop using dvi files, a big whack of TeX code can be discarded and the people who have been maintaining programs with 'dvi' in the names can get back to solving more important problems.
## Pro direct PostScript
I believe there are more tools that rely on Postscript technology than PDF. pstricks, EPS diagrams, etc. come to mind. (Yes, epstopdf is helpful. But how about pstricks? I sometimes do \special{"{some Postscript code}"} for some special effects that wouldn't be achieved easily otherwise.) Until pdftex can support Postscript specials, many users would stay with DVI+EPS. But that would be a big project.
## Unclassified
PDF files tend to have more predictable rendering times than PS files, so typesetter operators avoid PS files that aren't created by well-known applications (Photoshop, Illustrator) which produce flat PS code similar to PDF.
## Conclusion
My personal conclusion (everybody can make his own): PDF is bound to be used on a wider scale than PostScript. A direct PDF rendering seems to be of better quality than the PostScript equivalent. Given its features, PDF is more comfortable to use on-line.
The main argument against pdftex` is the impossibility to use PostScript code (and others) in the source (however, METAPOSTmight be a good alternative for figures). As soon as one is not limited by these constraints, and a fortiori if the use of PostScript is limited to printing, the TeX -> PDF -> PS solution seems to be a good choice.
Copyright (C) 2008 -- 2013 Didier Verna didier@lrde.epita.fr
|
|
LLVM 10.0.0svn
DivRemPairs.cpp File Reference
#include "llvm/Transforms/Scalar/DivRemPairs.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/MapVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/Analysis/GlobalsModRef.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/Pass.h"
#include "llvm/Support/DebugCounter.h"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Transforms/Utils/BypassSlowDivision.h"
Include dependency graph for DivRemPairs.cpp:
Go to the source code of this file.
Classes
struct DivRemPairWorklistEntry
A thin wrapper to store two values that we matched as div-rem pair. More...
Macros
#define DEBUG_TYPE "div-rem-pairs"
Typedefs
using DivRemWorklistTy = SmallVector< DivRemPairWorklistEntry, 4 >
Functions
STATISTIC (NumPairs, "Number of div/rem pairs")
STATISTIC (NumRecomposed, "Number of instructions recomposed")
STATISTIC (NumHoisted, "Number of instructions hoisted")
STATISTIC (NumDecomposed, "Number of instructions decomposed")
DEBUG_COUNTER (DRPCounter, "div-rem-pairs-transform", "Controls transformations in div-rem-pairs pass")
static llvm::Optional< ExpandedMatch > matchExpandedRem (Instruction &I)
See if we can match: (which is the form we expand into) X - ((X ?/ Y) * Y) which is equivalent to: X ?% Y. More...
static DivRemWorklistTy getWorklist (Function &F)
Find matching pairs of integer div/rem ops (they have the same numerator, denominator, and signedness). More...
static bool optimizeDivRem (Function &F, const TargetTransformInfo &TTI, const DominatorTree &DT)
Find matching pairs of integer div/rem ops (they have the same numerator, denominator, and signedness). More...
INITIALIZE_PASS_BEGIN (DivRemPairsLegacyPass, "div-rem-pairs", "Hoist/decompose integer division and remainder", false, false) INITIALIZE_PASS_END(DivRemPairsLegacyPass
Variables
div rem pairs
div rem Hoist decompose integer division and remainder
div rem Hoist decompose integer division and false
◆ DEBUG_TYPE
#define DEBUG_TYPE "div-rem-pairs"
Definition at line 31 of file DivRemPairs.cpp.
◆ DivRemWorklistTy
using DivRemWorklistTy = SmallVector
Definition at line 113 of file DivRemPairs.cpp.
◆ DEBUG_COUNTER()
DEBUG_COUNTER ( DRPCounter , "div-rem-pairs-transform" , "Controls transformations in div-rem-pairs pass" )
◆ getWorklist()
static DivRemWorklistTy getWorklist ( Function & F )
static
Find matching pairs of integer div/rem ops (they have the same numerator, denominator, and signedness).
Place those pairs into a worklist for further processing. This indirection is needed because we have to use TrackingVH<> because we will be doing RAUW, and if one of the rem instructions we change happens to be an input to another div/rem in the maps, we'd have problems.
Definition at line 120 of file DivRemPairs.cpp.
References llvm::SmallVectorImpl< T >::emplace_back(), I, llvm::Match, and matchExpandedRem().
Referenced by optimizeDivRem().
◆ INITIALIZE_PASS_BEGIN()
INITIALIZE_PASS_BEGIN ( DivRemPairsLegacyPass , "div-rem-pairs" , "Hoist/decompose integer division and remainder" , false , false )
Referenced by optimizeDivRem().
◆ matchExpandedRem()
static llvm::Optional matchExpandedRem ( Instruction & I )
static
See if we can match: (which is the form we expand into) X - ((X ?/ Y) * Y) which is equivalent to: X ?% Y.
Definition at line 50 of file DivRemPairs.cpp.
Referenced by getWorklist().
◆ optimizeDivRem()
static bool optimizeDivRem ( Function & F, const TargetTransformInfo & TTI, const DominatorTree & DT )
static
Find matching pairs of integer div/rem ops (they have the same numerator, denominator, and signedness).
If they exist in different basic blocks, bring them together by hoisting or replace the common division operation that is implicit in the remainder: X % Y <–> X - ((X / Y) * Y).
We can largely ignore the normal safety and cost constraints on speculation of these ops when we find a matching pair. This is because we are already guaranteed that any exceptions and most cost are already incurred by the first member of the pair.
Note: This transform could be an oddball enhancement to EarlyCSE, GVN, or SimplifyCFG, but it's split off on its own because it's different enough that it doesn't quite match the stated objectives of those passes.
Definition at line 179 of file DivRemPairs.cpp.
Referenced by llvm::DivRemPairsPass::run().
◆ STATISTIC() [1/4]
STATISTIC ( NumPairs , "Number of div/rem pairs" )
◆ STATISTIC() [2/4]
STATISTIC ( NumRecomposed , "Number of instructions recomposed" )
◆ STATISTIC() [3/4]
STATISTIC ( NumHoisted , "Number of instructions hoisted" )
◆ STATISTIC() [4/4]
STATISTIC ( NumDecomposed , "Number of instructions decomposed" )
◆ false
div rem Hoist decompose integer division and false
Definition at line 353 of file DivRemPairs.cpp.
◆ pairs
div rem pairs
Definition at line 353 of file DivRemPairs.cpp.
◆ remainder
div rem Hoist decompose integer division and remainder
Definition at line 353 of file DivRemPairs.cpp.
|
|
# Longest Mountain in Array in C++
C++Server Side ProgrammingProgramming
Consider any (contiguous) subarray B (of A) a called mountain if the following properties hold −
• size of B >= 3
• There exists some 0 < i < B.length - 1 such that B[0] < B[1] < ... B[i-1] < B[i] > B[i+1] > ... > B[B.length - 1]
Suppose we have an array A of integers; we have to find the length of the longest mountain. We have to return 0 if there is no mountain. So if the input is like [2,1,4,7,3,2,5], then the result will be 5. So the largest mountain will be [1,4,7,3,2], whose length is 5.
To solve this, we will follow these steps −
• ret := 0, n := size of array a
• i := 0 to n – 1, increase i by j + 1
• j := i
• down := false, up := false
• while j + 1 < n and a[j + 1] > a[j]
• up := true and increase j by 1
• while up is true and j + 1 < n and a[j + 1] > a[j]
• down := true and increase j by 1
• if up and down both are true, set ret := max of j – i + 1 and ret, decrease j by 1
• return ret.
Let us see the following implementation to get better understanding −
## Example
Live Demo
#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
int longestMountain(vector<int>& a) {
int ret = 0;
int n = a.size();
int j;
for(int i = 0; i < n; i = j + 1){
j = i;
bool down = false;
bool up = false;
while(j + 1 < n && a[j + 1] > a[j]) {
up = true;
j++;
}
while(up && j + 1 < n && a[j + 1] < a[j]){
down = true;
j++;
}
if(up && down){
ret = max(j - i + 1, ret);
j--;
}
}
return ret;
}
};
main(){
vector<int> v = {2,1,4,7,3,2,5};
Solution ob;
cout << (ob.longestMountain(v));
}
## Input
[2,1,4,7,3,2,5]
## Output
5
Published on 05-May-2020 10:20:39
|
|
Essay Post Blog Album Group User
Author: SEARU
# How do you think about vocational education? [Copy link] 中文 分享按钮
Post time 2018-2-10 04:30:13 |Display all floors
Psychological security is more important than actual security. That's why no Australian wants to learn a trade even though they can earn more money doing a trade than a low university worker like a teacher.
Post time 2018-2-10 08:24:02 |Display all floors
SEARU Post time: 2018-2-9 22:55 That was a special class on mechatronics within the physics department of the Qv-fu Teacher Univer ... I know Qufu, and I spell it 'Qufu", not "Qcvfu". By the way, it is "Do you lack students?" not "Are you lack students?" 4 Your answers to a few queries show that China does have vocational programmes similar to those we have in the West. For example we do have mechatronics classes. That is a combination of traditional mechanics and electronics. The recipients of such education are not called "students". They are called "apprentices". This is a word borrowed from French. The meaning is "learner". An apprentice does an apprenticeship. This means he gets hired by a company that trains him on the job. The company enrolls him in a relevant apprentice class at the vocational school or trade school. For three to four years the apprentice has a job, gets a low salary and studies theory at the school part time. His pay is low because he cannot perform qualified jobs and he has to be taught his ropes by qualified staff from the company. But the company also pays for his theoretical education at the trade school. If he graduates from it, his apprenticeship ends and he is then a qualified worker, for example a mechatronician. If his company has a vacancy, and it probably does, then he rises to the rank of a qualified mechatronician without having to undergo a job interview and application procedures. What baffles me is that China does not have more apprenticeships and better vocational programmes.
Post time 2018-2-10 08:29:27 |Display all floors
HailChina! Post time: 2018-2-10 03:32 By using so-called American-English and copying the way Americans speak English you Chinese promote ... I quite agree with you there this once. Chinese use a very parochial U.S. American English and don't understand it. What annoys me every week is when some Chinese talk about "majors" they study at "college" or "university". There is no need to say "I am majoring in hair-dressing study". They should ABOLISH the verb "major in" and the noun "major". Say "I study" and "course" instead.
Post time 2018-2-10 09:20:15 |Display all floors
seneca Post time: 2018-2-10 08:29 I quite agree with you there this once. Chinese use a very parochial U.S. American English and don ... Yes Americans are very dumb and they sound dumb when they talk. I don't think anyone could disagree with this if they are being honest. I am a great hairdresser you know. I cut my own hair and when I was a teenager I used to cut my friends hair a lot. Sometimes I would take the blade off and shave their heads before they realized. This was way before Jackass.
Post time 2018-2-10 09:29:17 |Display all floors
seneca Post time: 2018-2-10 08:29 I quite agree with you there this once. Chinese use a very parochial U.S. American English and don ... But yeah - why would Chinese choose to speak like Americans rather than Englishmen? I think we can all agree that the English are the best at speaking English. Not the ones from Liverpool or wherever that say Ospital and Par'y. But come on. Why speak like an American? It is madness. Have you ever seen the film A Yank at Oxford?
Post time 2018-2-10 09:30:54 |Display all floors
seneca Post time: 2018-2-10 08:29 I quite agree with you there this once. Chinese use a very parochial U.S. American English and don ... Even Australians think Yanks are dumb. Our upperclassmen identify with English and Europeans over Yanks. Any self respecting educated Yank must be ashamed to be American.
Post time 2018-2-10 09:32:15 |Display all floors
Technical trades around the world go by different names. In Canada, we have machinists, millwrights, welders, pipe-fitters, plumbers, millworkers, carpenters, glaziers, bricklayers, etc. All of these trades, or "vocations" (hence the name, 'Vocational School'), are highly skilled, highly paid jobs. In China, they are all lumped under one name ... "workers". In Canada, if you were to use the label "worker", that would invoke an idea that the person had an unskilled, minimum wage ($10.00 -$15.00/hr (50 RMB - 75 RMB/hr)) job, such as a fast-food restaurant worker. A skilled tradesman, however, can earn between ($30.00 -$45.00/hr (150 RMB - 225 RMB/hr)). A typical workday is 8 hrs (you do the math). Let's look at the Machinist trade. What does a machinist have to know in order to do his job? Mathematics. A lot of it! Trigonometry and Geometry, mostly. Also Algebra. He/She also has to know Metallurgy and Metrology. A machinist also has to be able to work within very tight tolerances, often down to 0.0001 inch (0.00254 mm). To give you an idea of how small that is, the average human hair is only 0.003 inches (0.0762 mm) thick. He/She also has to know how temperature affects metals, plastics, wood, and other materials. A machinist has to know about cutting oils, lubricants, and other chemical compositions which can affect materials. \it is a very complex trade, with many skills involved. If I was to call a machinist a "worker", they would be very insulted, indeed. If it wasn't for the machining trades, much of what we have would never exist, for machinists make the molds that create things like plastic bottles, eyeglass cases, laptop parts, etc. Machinists make the machines which mass-produce chopsticks, matches, drinking straws, knives, forks, spoons, pots, and pans, etc. Car parts, airplane parts ... everything in our modern world that is manufactured by a machine ... was originally made by a machinist. What the Chinese call a "worker", is actually a very skilled person, and should be a highly valued member of society.
Stupid people are like Glowsticks. You want to snap them in half and shake the crap out of them until they see the light.
I love sarcasm. It's like punching someone in the head ... only with words
|
|
# ML Aggarwal Solutions Class 8 Mathematics Solutions for Algebraic Expressions and Identities Exercise 10.5 in Chapter 10 - Algebraic Expressions and Identities
Question 27 Algebraic Expressions and Identities Exercise 10.5
\text { If } a^{2}+b^{2}=41 \text { and } a b=4, \text { find the values of }
(i) a + b
(ii) a – b
Given, a^{2}+b^{2}=41 and a b=4 (1)(a+b)^{2}=a^{2}+b^{2}+2 a b \begin{aligned} &=41+2 \times 4 \\ &=41+8 \\ &=49 \end{aligned} (ii) (a-b)^{2}=a^{2}+b^{2}-2 a b =41-2 \times 4 \begin{aligned} &=41-8 \\ &=33 \end{aligned}
Related Questions
Lido
Courses
Teachers
Book a Demo with us
Syllabus
Maths
CBSE
Maths
ICSE
Science
CBSE
Science
ICSE
English
CBSE
English
ICSE
Coding
Terms & Policies
Selina Question Bank
Maths
Physics
Biology
Allied Question Bank
Chemistry
Connect with us on social media!
|
|
Spoiled Milk Bacteria, Blackberry Oatmeal Cookies, A Heart For A Head Choice, What Are Sweet Potato Noodles, Hard Boiled Egg In Ramen, Agenzia Viaggi Italia, Revive Mattress Queen, Is Kumkumadi Tailam Good For Oily Skin, Facebook Twitter Google+ LinkedIn"/>
## how many bonds does nitrogen form
Nitrides usually has an oxidation state of -3. Nitride ions are very strong bases, especially in aqueous solutions. The dinitrogen molecule ($$N_2$$) is an "unusually stable" compound, particularly because nitrogen forms a triple bond with itself. Does this make sense based on the number of valence cetro in a nitrogen atom? This is because it has atomic number 7, so its electron configuration is 1s^2 2s^2 2p^3, giving it 5 valence shell electrons. It only appears in 0.002% of the earth's crust by mass. All of these bonding characteristics of nitrogen are observable in its general chemistry. The two most common compounds of nitrogen are Potassium Nitrate (KNO3) and Sodium Nitrate (NaNO3). It was not until the 1700's that scientists could prove there was in fact another gas that took up mass in the atmosphere of the Earth. The product glows with a yellow light and is much more reactive than ordinary molecular nitrogen, combining with atomic hydrogen and with sulfur, phosphorus, and various metals, and capable of decomposing nitric oxide, NO, to N2 and O2. Oxygen tends to form two bonds and have two lone pairs. When the bond polarity is low (owing to the electronegativity of the other element being similar to that of nitrogen), multiple bonding is greatly favoured over single bonding. Cytosine is represented by the capital letter C. In DNA and RNA, it binds with guanine. For these reasons, elemental nitrogen appears to conceal quite effectively the truly reactive nature of its individual atoms. Oxygen can form one to four bonds. Phosphorus can form one to five bonds. Explain your answer -Doo phosphorus typically for your answer makes sense the same number of bonds as nitrogen? Nitrogen forms strong bonds because of its ability to form a triple bond with its self, and other elements. A nitrogen atom has the electronic structure represented by 1s22s22p3. While nitrogen is known to make a maximum of 4 bonds (3 covalent, 1 dative covalent). Most nitrogen compounds have a positive Gibbs free energy (i.e., reactions are not spontaneous). Petrucci, Ralph H, William Harwood, and F. Herring. These were mainly derived by the number of valence electrons, but you must also keep in mind that octet rule must be fulfilled. Nitrogen typically forms 3 covalent bonds, including in #N_2#. These are normally done with other metals and look like: MN, M3N, and M4N. Does phosphorus typically form the same number of bonds as nitrogen? Hyrdrazine is commonly used as rocket fuel. This is because it has atomic number 7, so its electron configuration is #1s^2 2s^2 2p^3#, giving it 5 valence shell electrons. Use the periodic table to explain why your answer makes sense. When mixed with water, nitrogen will form ammonia and, this nitride ion acts as a very strong base. Nitrogen is a colourless, odourless gas, which condenses at −195.8 °C to a colourless, mobile liquid. These two compounds are formed by decomposing organic matter that has potassium or sodium present and are often found in fertilizers and byproducts of industrial waste. The well-known Kjeldahl method for determining the nitrogen content of organic compounds involves digestion of the compound with concentrated sulfuric acid (optionally containing mercury, or its oxide, and various salts, depending on the nature of the nitrogen compound). Legal. Nitrogen can form 3 covalent bonds and 1 coordinate bond. A nitrogen atom has seven electrons. Nitrogen makes up DNA in the form of nitrogenous bases as well as in neurotransmitters. Nitrogen has two naturally occurring isotopes, nitrogen-14 and nitrogen-15, which can be separated with chemical exchanges or thermal diffusion. What are the different isotopes of Nitrogen? Anonymous. Isotopes. The octet requires an atom to have 8 total electrons in order to have a full valence shell, therefore it needs to have a triple bond. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. $2NH_{3(aq)} + H_2SO_4 \rightarrow (NH_4)_2SO_{4(aq)} \label{4}$. Often the percentage of nitrogen in gas mixtures can be determined by measuring the volume after all other components have been absorbed by chemical reagents. How many bonds does nitrogen typically form? We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Compounds of nitrogen are found in foods, explosives, poisons, and fertilizers. Carbon tends to form 4 bonds and have no lone pairs. Nitrogen tends to form three bonds and have on e lone pair. How do covalent bonds differ from hydrogen bonds? For many years during the 1500's and 1600's scientists hinted that there was another gas in the atmosphere besides carbon dioxide and oxygen. A nitrogen atom can fill its octet by sharing three electrons with another nitrogen atom, forming three covalent bonds, a so-called triple bond.The triple bond formation of nitrogen is shown in the following figure. [ "article:topic", "fundamental", "base", "Nitrogen", "Ammonium", "showtoc:no", "Nitrides", "Oxides", "biochemical applications", "industrial applications", "fertilizer", "nitron", "Ammonium Ions" ], Nitrogen is a non-metal element that occurs most abundantly in the atmosphere, nitrogen gas (N. ) comprises 78.1% of the volume of the Earth’s air. Premium Membership is now 50% off! Three hydrogen bonds form between cytosine and guanine in the Watson-Crick base pairing to form DNA. In this way, the nitrogen present is converted to ammonium sulfate. Nitrogen also has isotopes with 12, 13, 16, 17 masses, but they are radioactive. These compounds form with lithium and Group 2 metals. Nitrogen is released from organic compounds when they are burned over copper oxide, and the free nitrogen can be measured as a gas after other combustion products have been absorbed. Because of this high bond energy the activation energy for reaction of molecular nitrogen is usually very high, causing nitrogen to be relatively inert to most reagents under ordinary conditions. Stable forms include nitrogen-14 and nitrogen-15. These compounds are typically hard, inert, and have high melting points because nitrogen's ability to form triple covalent bonds. It is conveniently answered using Lewis electron-pair theory. Have questions or comments? $N + 3H_2O_{(l)} \rightarrow NH_3 + 3OH^-_{(aq)} \label{2}$. As mentioned earlier, this process allows us to use nitrogen as a fertilizer because it breaks down the strong triple bond held by N2. Why are covalent bonds poor conductors of electricity. Oxides of nitrogen are acidic and easily attach protons. How does the formation of an ionic bond differ from that of a covalent bond? By signing up for this email, you are agreeing to news, offers, and information from Encyclopaedia Britannica. The electronic configuration includes three half-filled outer orbitals, which give the atom the capacity to form three covalent bonds. Complete and balance the following equations. The element exists as N2 molecules, represented as :N:::N:, for which the bond energy of 226 kilocalories per mole is exceeded only by that of carbon monoxide, 256 kilocalories per mole. Metals treatment/protectant via exposure to nitrogen instead of oxygen. To form a full outer shell of 8, it needs to share 3 electrons, forming 3 covalent bonds. This triple bond is difficult hard to break. Nitrogen is a non-metal element that occurs most abundantly in the atmosphere, nitrogen gas (N2) comprises 78.1% of the volume of the Earth’s air. Why does it only form 3? Black Friday Sale! It can actually form 3 covalent bonds. For dinitrogen to follow the octet rule, it must have a triple bond. Be on the lookout for your Britannica newsletter to get trusted stories delivered right to your inbox. Thus, there is a lot of energy in the compounds of nitrogen.
|
|
# Finite difference methods in cylindrical and spherical co-ordinate systems
I am quite familiar with finite difference schemes in cartesian coordinates. The key point here is that every point in the cartesian grid is treated equally as the spacing between consecutive points is same.
I want to know how one would perform finite-differencing in cylindrical (or even spherical) systems. I believe my main confusion is with angular differentiation. If we take a 2D cylindrical (polar) system, one way to divide the grid would be to make concentric circles (of $$\Delta r$$ spacing). For the angular spacing, we can draw radially outgoing rays, each of angular width $$\Delta\phi$$.
With $$O(h^2)$$ central differencing, the Laplacian, for example, can be given by:
$$\nabla^2 f = 0$$ $$\Rightarrow \frac{f_{i+1,j} + f_{i-1,j} - 2f_{i,j}}{\Delta r^2} + \frac{1}{i\Delta r}\frac{f_{i+1,j} - f_{i-1,j}}{\Delta r} + \frac{1}{(i\Delta r)^2}\frac{f_{i,j+1} + f_{i,j-1} - 2f_{i,j}}{\Delta\phi^2} = 0$$
But in such a gridding scheme, as we increase $$i$$ (and hence $$r$$), the distance between two points on the same concentric circle will keep increasing. Is this how finite differencing works in cylindrical coordinates? Is such a scheme stable or does it become unstable for large $$r$$?
Are there better methods of finite differencing?
• What is the issue? E.g., for polar coordinates you have some operator in terms of $\partial{}/\partial{r}$, $\partial{}/\partial{\theta}$ and higher derivatives; and your domain is rectangular in $r,\theta$ coordinates, with grid points on $r$=const and $\theta$=const lines. Otherwise the same stuff as in Cartesian coordinates. – Maxim Umansky May 30 '20 at 4:21
There are basically two methods: You can disrectize the angular part via grid points, or you can discretize it via basis expansion. I will focus on spherical symmetry here, the cylindrical case is quite similar.
In the basis expansion approach, one applies the ansatz $$v(x,t) = \sum_{klm} a_{klm}(t)\,R_{klm}(r)\, Y_{lm}(\theta,\phi)$$ This is inserted into the problem to obtain equations for the radial function $$R_{klm}(r)$$, which are usually coupled in the angular indices $$lm$$. These equations are then solved by usual one-dimensional finite differences.
The other variant is to use an anguar grid. Here you can, in principle, use any grid you come up with. Standard choices are an equally spaced grid in the polar coordinate (x-y-plane), and a Legendre grid in the azimutal coordinate (z-direction). (The reason for the Legendre grid is the Jacobi determinant $$r^2 sin\theta$$ that arises in the transformation, by using Legendre grid points the $$sin$$ basically drops out).
The previous ansatz uses a product grid for the angles $$\theta$$ and $$\phi$$. Other, more sophisticated approaches try to reduce the required grid points by using specialized non-product grids. The grid points obtained in Lebedev quadrature is one popular alternative.
Here is a picture from a work of mine which shows (a) the Lebedev points and (b) the product grid:
• A nice answer. Could you please provide some sources to your work / any other source that I can refer to for this stuff? – Siddharth Bachoti May 30 '20 at 15:36
• Also, it seems to me that the common method of taking a constant grid spacing like in case of cartesian co-ordinates ($\Delta x = \Delta y = \Delta z$) is not possible in curvilineaar co-ordinates. – Siddharth Bachoti May 30 '20 at 15:40
• My own work is just an application of these concepts to quantum mechanics, i.e. nothing that I would primarily refer to for these methods. Googling "Lebedev quadrature" is a good start into the topic. One ineresting paper I encountered by this is Beentjes, Quadrature on a spherical surface. -- note that many useful point distributions stem from quadrature rules (just as in 1D). – davidhigh May 31 '20 at 10:10
|
|
• anonymous
If $x_{1}, x_{2},...,x_{n}$ are given numbers, show that $(x_{1}-x)^{2} +(x_{2}-x)^{2}+...+(x_{n}-x)^{2}$ is least when x is the arithmetic mean of \[x_{1}, x_{2},..., x_{n}.
Mathematics
Looking for something else?
Not the answer you are looking for? Search for more explanations.
|
|
## January 8, 2010
### Quasicoherent ∞ -Stacks
#### Posted by Urs Schreiber
This is to tie up a loose end in our discussion of Ben-Zvi/Francis/Nadler geometric $\infty$-function theory and Baez/Dolan/Trimble “groupoidification”.
Using a central observation in Lurie’s Deformation Theory one can see how both these approaches are special examples of a very general-abstract-nonsense theory of $\infty$-linear algebra on $\infty$-vector bundles and $\infty$-quasicoherent sheaves in arbitrary (“derived”) $\infty$-stack $(\infty,1)$-toposes:
the notion of module is controled by the tangent $(\infty,1)$-category of the underlying site, that of quasicoherent module/$\infty$-vector bundle simply by homs into its classifying $\infty$-functor.
For Ben-Zvi/Francis/Nadler this shows manifestly, I think, that nothing in their article really depends on the fact that the underlying site is chosen to be that of duals of simplicial rings. It could be any $(\infty,1)$-site. For Baez/Dolan/Trimble it suggests the right way to fix the linearity: their setup is that controlled by the tangent $(\infty,1)$-category of $\infty Grpd$ itself and where they (secretly) use the codomain bifibration over this, one should use the fiberwise stabilized codomain fibration.
See $\infty$-vector bundle for a discussion of what I have in mind.
What I am saying here is likely very obvious to somebody out there. I have my suspicions. But it looks like such a nice fundamental fact, that this deserves to be highlighted, and be it in a blog entry. It is just a matter of putting 1 and 1 together. The two central observations are this:
In our journal club discussion I had remarked that the definition $QC(X)$ of derived quasicoherent sheaves on a derived $\infty$-stack $X$ that BenZvi/Francis/Nadler use is best thought of as $hom(X,QC)$ in the $(\infty,1)$-category of $(\infty,1)$-category-valued $\infty$-stacks. That this is the way to think about quasicoherent sheaves must be an old hat to some people but is rarely highlighted in the literature.
The only place I know of presently where this is made fully explicit is the $n$Lab entry on quasicoherent sheaves. As discussed there, at least Kontsevich and Rosenberg have made this almost fully explicit – they say this in side remark 1.1.5 here, in the dual picture where category-valued presheaves are replaced by fibered categories.
The other crucial insight is Lurie’s basic idea from Deformation Theory. This is amazingly elegant, have a look, if you haven’t yet. Lurie shows that for $C$ any $(\infty,1)$-category, whose objects we here think of as formal duals of test spaces, the tangent $(\infty,1)$-category fibration $T_C \to C$ is to be thought of as the fibration of modules over the objects of $C$, generalizing the canonical fibration $Mod \to Ring$ that underlies the classical theory of monadic descent. But strikingly: $T_C$ is effectively nothing but the codomain fibration over $C$ – it differs from that only in that all fibers are stabilized, i.e. linearized in the fully abstract category-theoretic sense. In particular, this says that the Ben-Zvi/Francis/Nadler $\infty$-stack of derived quasicoherent sheaves $QC : SRing \to (\infty,1)Cat$ is equivalently simply given by assigning $Spec A \mapsto Stab(SRing/A)$ – to any simplicial ring its stabilized overcategory. (This is stated in example 8.6 on page 24 in Stable $\infty$-Categories.)
I had remarked here in our journal club discussion that Baez/Dolan/Trimble “groupoidification” is like Ben-Zvi/Francis/Nadler theory but with $QC$ replaced by the assignment of overcategories. Now in the light of Lurie’s observation this makes everything fall into place: Baez/Dolan/Trimble groupoidification may be thought of as a shadow of the geometric $\infty$-function theory induced from the tangent $(\infty,1)$-category over $\infty Grpd$ itself: instead of pull-pushing bundles of groupoids as they do, in the full theory one would pull-push bundles of abelian $\infty$-groupoids (and more generally: possibly non-connective spectra).
You may remember my motivation for coming to grips with this conceptual framework: for applications in the physics of gauge fields we need smooth differential cohomology and $\infty$-Lie theory. This doesn’t really take place in $\infty$-stacks over simplicial rings (only a small part of it does) and it doesn’t take place in $\infty$-stacks over just $\infty Grpd$ (though important toy models do): it takes place in $\infty$-stacks over simplicial $C^\infty$-rings and generally over simplicial objects in sites for smooth toposes. Clearly we want Ben-Zvi/Francis/Nadler geometric $\infty$-function theory generalized to this context. With $QC$ in hand in this contex, we immediately have $\infty$-representations of $\infty$-Lie groups, associated $\infty$-vector bundles and their pull-push and monadic descent.
And with the above it is clear what one needs to look at: just take the $\infty$-stack of smooth generalized $\infty$-vector bundles to be $QC : Spec A \mapsto Stab(SC^\infty Ring/A)$. And that’s it.
Posted at January 8, 2010 12:35 PM UTC
TrackBack URL for this Entry: http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2151
### Re: Quasicoherent infty -Stacks
Using a central observation in Lurie’s Deformation Theory
seems to produce only a cover page
Remind me how to use it? i.e how to get a coherent! single document
hopefully not by clicking on each item in the Contents separately
Posted by: jim stasheff on January 8, 2010 2:04 PM | Permalink | Reply to this
### Re: Quasicoherent infty -Stacks
The arXiv entry of Jacob Lurie’s Deformation Theory is here. That’s the link named “arXiv” on what you call the cover page, right after the article title. If you want to be sure that you see the very latest, download the pdf on his homepage
The (very incomplete) linked keyword list on the “cover page” is intended as a public service for quick reference.
Posted by: Urs Schreiber on January 8, 2010 2:36 PM | Permalink | Reply to this
### Re: Quasicoherent infty -Stacks
apologies
I thought you meant that link to get to your summary of
Lurie’s version of def theory
Posted by: jim stasheff on January 8, 2010 3:59 PM | Permalink | Reply to this
### Re: Quasicoherent infty -Stacks
Truth in advertising? Lurie is about deformation theory for E-infty algebras. At a glance, I see very little _exposition_ setting the stage in terms of classical deformation theory.
A better source for an up-to-date version of that might be the draft book by Kontsevich and Soibelman -
Posted by: jim stasheff on January 8, 2010 4:07 PM | Permalink | Reply to this
### Re: Quasicoherent infty -Stacks
Lurie is about deformation theory for $E_\infty$ algebras.
That’s the example worked out. The theory in the first part is entirely general. And it is this generality which the entry here is concerned with.
At a glance, I see very little exposition setting the stage in terms of classical deformation theory.
I found his exposition quite nice. But notice that the discussion here is not really about deformation theory as such, but about a very general notion of modules, which happens to be discussed in an article on deformation theory.
draft book by Kontsevich and Soibelman -
Oh, so you meant this book link in your message recently? How should I know? You just asked me to “include the link from Yan’s homepage”.
Okay, the link is now included here:
$n$Lab: deformation theory - References - Texbooks
A better source for an up-to-date version of that
Just a comment: the Kontsevich-Soibelman book looks very nice and anyone interested in standard deformation theory should look at that, and not (at first) at Lurie’s article.
But, you see, what Lurie’s article accomplishes, in it’s first part, is that it gives a vastly and vastly more general context for what deformation theory is actually about. He accomplishes this by giving a vastly and vastly more general definition of the notion of module (and derivation, and cotangent complex and…). It is this general-abstract-nonsense perspective, and that only, which I am referring to in my above discussion. The above discussion is not about deformation theory. The above discussion is, if you wish, about how one might set up deformation theory in the context of $\infty$-Lie theory and other contexts. Lurie’s setup is so general that it provides a prescription for how to proceed with the theory in this case, and in other cases.
But the Kontsevich-Soibelman book is very nice. I’ll have a close look.
Posted by: Urs Schreiber on January 8, 2010 5:03 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
While I certainly subscribe to the philosophy you explain, I don’t think it’s due to Jacob. The modern perspective on tangents=linearization=stabilization which you quote is I believe due to Goodwillie building on Quillen (Jacob certainly ascribes it to Goodwillie and others.. of course he states it in a very elegant way which is only possible given the appropriate language). The statement about QC being stabilization of overcategories of schemes is just restating the classical fact that modules are the linearization of rings. Certainly the idea of thinking about categories of sheaves as linearizations of spaces over a base is old and is for example behind the theory of variations of Hodge structures or more fancily motivic sheaves (as we discussed over at the n-geometry cafe I think)..
Also I’m not sure which assertions in our paper you refer to as holding in such great generality - one needs to make very strong assumptions about the properties of QC(X) to get any traction, and these are available for schemes eg only thanks to a brilliant insight of Thomason (or rather of Trobaugh’s ghost in Thomason’s dream). But if you’re willing to make such assumptions about your spaces, of course everything we actually do is quite formal.
(PS the statement “QC is best thought of as hom(X,QC) in the (∞,1)-category of (∞,1)-category-valued ∞-stacks” is restating the assertion that QC(-) forms a stack, ie descent, or that sheaves are by definition local, no?)
Posted by: David Ben-Zvi on January 9, 2010 5:25 AM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
David, thanks, I certainly was hoping to get a comment from you.
[…] I certainly subscribe to the philosophy you explain […]
Okay, thanks for the sanity check.
[…] I don’t think it’s due to Jacob. […]
What would be an original source for the statement in example 8.6 of Stable $\infty$-Categories that $T_{sRings} \simeq Mod_{sRings}$? Is this folk lore, as a precise theorem?
The modern perspective on tangents=linearization=stabilization which you quote is I believe due to Goodwillie building on Quillen (Jacob certainly ascribes it to Goodwillie and others
Well, I should maybe say that the point of what I wrote was not so much to announce “Lurie did X” but to announce that “reading Lurie made me see Y”. If you say that it was all in the air I take your word for it, but…
(of course he states it in a very elegant way which is only possible given the appropriate language).
Sometimes obvious structures still never become clear until the right language is found. As somebody once said:
Schläft ein Lied in allen Dingen,
Die da träumen fort und fort,
Und die Welt hebt an zu singen,
Triffst du nur das Zauberwort.
#
I think the right language is important here.
You further write:
The statement about QC being stabilization of overcategories of schemes is just restating the classical fact that modules are the linearization of rings.
I appreciate the fact that fiberwise stabilization of codomain fibrations is the evident abstract-nonsense formulation of how $Mod \to Rings$ is fiberwise the abelian category of square-0-extensions of the ring downstairs. With hindsight the story is now very obvious and pleasing. But to make fully explicit the notion of tangent $(\infty,1)$-category and to demonstrate that it then correctly captures the simplicial and $E_\infty$-cases still looks like an accomplishment to me.
Well, I take your point that this isn’t shocking news to the experts, and I hear the refrain “category theory is just a language” from those who don’t like it, but I still think Jacob Lurie’s precise description of the situation is of a beauty that deserves to be highlighted.
(as we discussed over at the n-geometry cafe I think)..
Yes, indeed, that was your comment here. I kept coming back to this comment and thought about it. Now it all has become very clear to me, and I thank you for all your help. But somehow I neeeded extra details on how it works in concrete examples to fully absorb the statement.
But if you’re willing to make such assumptions about your spaces, of course everything we actually do is quite formal.
Thanks, yes, that’s what I should have said, more precisely.
PS the statement “$QC$ is best thought of as $hom(X,QC)$ in the $(\infty,1)$-category of $(\infty,1)$-category-valued $\infty$-stacks” is restating the assertion that $QC(-)$ forms a stack, ie descent, or that sheaves are by definition local, no?)
I’d think that by itself it’s a statement that doesn’t depend on the topology. There it’s just a way to define QC globally from local data.
It’s entirely anaogous to the definition of differential forms on presheaves: for $C$ a category and $\Omega^\bullet : C^{op} \to Set$ a notion of differential forms on the test objects in $C$, we define the differential forms on an arbitrary presheaf by
$\Omega^\bullet(X) := [C^{op},Set](X,\Omega^\bullet) \,.$
For instance for $C = \Delta$ this gives the definition of Sullivan differential forms on simplicial sets. (Just for other readers following our exchange I provide a link to more details on this example.) This doesn’t make use of any Grothendieck topology.
For (ordinary for the moment) quasicoherent sheaves it is a priori really the same. Here $C = Ring^{op}$ or the like and $\Omega^\bullet$ is replaced by $QC : Spec A \mapsto A Mod$, but then we can define for any presheaf $X$ that $QC(X) := hom(X,QC)$.
But we can then reverse the question and ask: when does this assignment satisfy descent? When is $\Omega^\bullet$, when is $QC$ a sheaf, a stack? That’s classically where terms like “effective descent morphism” and Bénabou-Roubaud theorems appear (link again for other readers, I am not suggesting that you don’t know what I am talking about, I am just trying to make myself clear): we have $QC$ given and are now looking for Grothendieck topologies that make it a stack.
Or so I think. Please let me know if I sound like I am mixed up.
Posted by: Urs Schreiber on January 9, 2010 10:42 AM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
One small clarification: the stabilization Stab(sCRing/A) of simplicial commutative rings over A is only equivalent to the category of A-modules if one works relative a base field K of characteristic zero. In general, there is a functor A-mod —> Stab, but this functor is not essentially surjective or full. Its failure to be an equivalence is closely related to the failure of the inclusion of simplicial commutative K-algebras into E-infinity K-algebras to be an equivalence.
This failure highlights the distinction between Quillen’s notion of A-mod(C) for an object A in C, which is the category of abelian group objects in the overcategory C/A, and the stabilization of C/A. Often these notions produce equivalent categories (e.g., if C is E-infinity rings) because stable objects can be strictified to get abelian group objects. But sometimes they can’t, as when C is sCRing. To give another example, if C is the category of spaces and A is a point, then Ab(Spaces) —> Stab(Spaces) is not an equivalence, in part because you have infinite loop spaces that cannot be strictified to be abelian groups on the nose (e.g., BO or BU). Topological abelian groups are pretty special among infinite loop spaces: they’re all products of Eilenberg-MacLane spaces.
(Thanks, by the way, for looking at our stuff so closely; it’s gratifying that you all have taken such an interest in it.)
Posted by: John Francis on January 9, 2010 6:57 PM | Permalink | Reply to this
### Re: Quasicoherent oo -Stacks
One small clarification: the stabilization $Stab(sCRing/A)$ of simplicial commutative rings over A is only equivalent to the category of $A$-modules if one works relative a base field $K$ of characteristic zero. In general, there is a functor $A mod \to Stab$, but this functor is not essentially surjective or full. Its failure to be an equivalence is closely related to the failure of the inclusion of simplicial commutative K-algebras into E-infinity K-algebras to be an equivalence.
Ah, thanks for catching that.
I am starting to collect this and other facts at Modules over simplicial rings. Not much there yet right this moment, but it should eventually expand.
Can you point me to more references? I am not sure I have seen the really relevant bits yet, given what you and David are saying here.
(Thanks, by the way, for looking at our stuff so closely; it’s gratifying that you all have taken such an interest in it.)
It’s very cool stuff. I feel we even need to eventually improve the $n$Lab page on this and give a better impression of what’s really going on, fundamentally. Personally, I was blocked for quite a while by not fully seeing how to generalize your constructions to other sites. Apparently I was just being dense. Now with that out of the way I am hoping to make more progress with fully absorbing this.
Posted by: Urs Schreiber on January 10, 2010 5:26 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
Urs - I think we agree on all points here. (I apologize for the grumpy tone of my comment - ascribe it to Texas losing the college football championship game..) I don’t know of the proper original references for the kind of linearization results being discussed, but I think it’s all part of the Goodwillie calculus oeuvre (at least I had these ideas explained to me before DAG4 appeared, so I assume the experts understood this). Of course as you know I’m as enthusiastic about what Jacob is doing as anyone, and think it goes far beyond “language” in any dismissive sense, but I do think this yoga of first order calculus (linearization/stabilization/tangents/deformations), very likely in a less general and precise sense, is not new. Of course there’s a basic temptation for newcomers to the field (like me) when there’s a beautiful complete self-contained source, which also has deep new insights, grander scope, more applicable results etc etc etc, to remain ignorant of all previous history of the subject and unintentionally erase everyone who came before. (was there algebraic geometry before Grothendieck??) So I guess the point of my comment is I’m more guilty of this than most, and wanted to balance that when I can.
Posted by: David Ben-Zvi on January 10, 2010 5:15 AM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
Maybe we were talking past each other a bit. You probably remember that I kept wondering and asking (here, on MO and elsewhere) how one would go about making your geometric $\infty$-function theory independent of the particular choice of site.
Because I wanted to use it, but need it on a site different from $sAlg^{op}$.
I saw that up to some assumptions, the only place where you make essential use of that particular site is when saying $Spec A \mapsto A Mod$, hence when saying $QC(Spec A)$. I wasn’t sure how I should say that for other sites. I knew that I had to use overcategories as models for cats of modules (there is a remnant of my thinking about this here, which I will in some days remove and replace by the right full answer now) but I happened to have been unaware that simply stabilizing these yields the complete right answer.
Somebody – maybe you – should write up your theory of integral transforms in full generality on arbitrary $\infty$-sites. I think it’s very beautiful and even more fundamental than your article makes it appear.
Posted by: Urs Schreiber on January 10, 2010 4:12 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
Of course there is a basic temptation for newcomers to the field (like me) when there is a beautiful complete self-contained source, which also has deep new insights, grander scope, more applicable results etc etc etc, to remain ignorant of all previous history of the subject and unintentionally erase everyone who came before.
I know what you mean. I am eager to fill in historical references, but maybe you could help me identifying them. I am in the process of expanding the entry $n$Lab:module accordingly.
Posted by: Urs Schreiber on January 10, 2010 5:05 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
David wrote:
(PS the statement “QC is best thought of as hom(X,QC) in the (∞,1)-category of
(∞,1)-category-valued ∞-stacks” is restating the assertion that QC forms a stack, ie descent, or that sheaves are by definition local, no?)
Is there a precise statement that $QC(-)$ forms a stack somewhere? And how do you formulate stack precisely for a $(\infty,1)$-category valued preasheaf.
Just to check that I understand $QC(-)$ right: The restriction of $QC(-)$ to ordinary rings assigns to each ring the $(\infty,1)$-category of chain complexes of modules over this ring (such that the homotopy category is the classical derrived category), right?. So stack would mean that we can glue toghether chain complexes defined locally… Is there an intuitiv way to think of such a glueing process?
Posted by: Thomas Nikolaus on January 16, 2010 12:49 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
And how do you formulate stack precisely for a (∞,1)-category valued preasheaf.
Just on the general topic:
in principle the technology should be available to model the stack condition for $(\infty,n)$-category-valued presheaves, for all $n$ (at least as long as descent is taken with respect to just Cech covers and not hypercovers):
namely by combining recent results by Clark Barwick and Charles Rezk:
Clark Barwick has generalized the proof that left Bousfield localization of $SSet_{Quillen}$-enriched combinatorial model categories at a set of morphisms exists to the case of general tractable $V$-enriched model categories, in
So this should apply in particular to the localization of the global model structure on $SSet_{Joyal}$-enriched presheaves at Cech covers.
More generally, Charles Rezk has given monoidal model category models for $(n,r)Cat$ for all $n,r \leq \infty$ in terms of Theta-spaces.
This should mean that the left Bousfield localization of $(n,r)Cat_{Rezk}$-valued presheaves at Cech covers exists and models the corresponding stacks.
What I just said is also collected briefly at model structure on homotopical presheaves.
Posted by: Urs Schreiber on January 16, 2010 3:48 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
Thomas - that’s right, QC assigns to a ring the $\infty$-category of chain complexes of modules (i.e. the refinement of the unbounded derived category of the ring). It is covariantly functorial in morphisms of rings (by tensoring up of modules), ie contravariant in affine schemes (by pullback). For a general scheme or stack we can define its QC as the limit of $QC(R_i)$ over all $Spec(R_i)\to X$.
The statement that QC is a stack in some topology - e.g. etale or flat - is the assertion that for $U\to X$ a cover in this topology, with associated Cech simplicial object $U_\bullet$ (whose $k$-simplices are the fiber products $U\times_X U\times_X \cdots U$) we can calculate $QC(X)$ as the totalization (limit) of the cosimplicial $\infty$-category $QC(U_\bullet)$. This is an $\infty$-version of the usual descent statements for quasicoherent sheaves. It follows from Lurie’s comonadic Barr-Beck theorem once we verify that etale or flat covers satisfy the corresponding Barr-Beck criteria – apparently this is written up in detail in the forthcoming DAG 7, but similar statements can be found in Toen-Vezzosi.
As to its intuitive meaning, it’s just a statement that you can glue complexes – given say two Zariski opens U and V and complexes of sheaves on each, if you are given isomorphisms on the overlaps you can define a sheaf on the union. For a general $U\to X$ you need to consider higher gluing data on all the n-fold intersections.
This is actually something we’re all very familiar with if you replace sheaves with cochains. You can ask, in what sense are cochains on a topological space X local with respect to a cover? the answer is given eg by the Cech-de Rham spectral sequence (in the case of forms). Namely to define the complex of cochains on X you take a limit (totalization) of the Cech cosimplicial object, given by cochains on n-fold intersections. Of course cohomology of X is not local in this sense, you have to go to the cochain level. Likewise the derived category of sheaves is not local, but once you refine it to the corresponding $\infty$-category the same gluing/descent picture holds.
Posted by: David Ben-Zvi on January 16, 2010 9:31 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
Hi David, thanks for the detailled answer. Now I’m still more looking forward to the release of DAG7 ;)
is the assertion that for $U \to X$ a cover in this topology, with associated Cech simplicial object $U_\bullet$ (whose k-simplices are the fiber products $U\times_X \times U \times_X \cdots U$) we can calculate QC(X) as the totalization (limit) of the cosimplicial $\infty$-category $QC(U_\bullet)$.
Okay, thats clear from an abstract point of view. Nevertheless I don’t know how to compute such a limit over cosimplicial $\infty$-categories. Is it the homotopy colimit which we can compute using the model strucutre on $\infty$-categories (depending on your model of $\infty$-categories)? Or do we have to be a little bit more carefull because we are in a $\infty$-bicategory? It would be good to have an explicit formula for the Descent-$\infty$-categories.
Posted by: Thomas Nikolaus on January 17, 2010 4:59 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
Is it the homotopy colimit which we can compute using the model strucutre on ∞-categories (depending on your model of ∞-categories)? Or do we have to be a little bit more carefull because we are in a ∞-bicategory? It would be good to have an explicit formula for the Descent-∞-categories.
If we do suppose, as I indicated above, that the (non-hypercomplete) $(\infty,2)$-topos of $(\infty,1)$-stacks on a site $C$ is modeled by the $SSet_{Joyal}$-enriched model category obtained as the left Bousfield localization of $[C^{op},SSet_{Joyal}]_{proj}$ at the set of morphisms of the form $C(\{U_i \to V\}) \to V$ for $\{U_i \to V\}_i$ a covering family in the site and $C(\{U_i\})_n = (\coprod_i U_i)^{\times_V n-1}$ the Cech nerve simplicial presheaf of the cover, then the answer is clear:
an $(\infty,1)$-stack will be a fibrant object in the left localization, which is (as you know well, but I just say it for the record and for other readers) is a simplicial presheaf $A$ that is objectwise Joyal-fibrant (i.e. quasi-category-valued) and such that for $Q(C(\{U_i \to V\})) \to Q(V)$ a cofibrant replacement we have that
$[C^{op},SSet](Q(V),A) \to [C^{op},SSet](Q(C(U_i)),A) =: Desc(\{U_i\},A)$
is a weak equivalence in $SSet_{Joyal}$. This enriched hom may be expressed in terms of ordinary limits in $SSet$, the homotopy information is all in the cofibrant replacement.
In the familiar case of $SSet_{Quillen}$-valued presheaves we know that the representable $V$ is already cofibrant (obvious because acyclic Quillen fibrations are surjetive on 0-cells) and that $C(\{U_i\})$ is cofibrant (from Dugger’s work, summarized here).
So one way to answer your question would be to understand whether this cofibrancy fails with $SSet_{Joyal}$-valued presheaves, and what the cofibrant replacement is, instead.
It is still true in $SSet_{Joyal}$ that acyclic fibrations are surjective on 0-cells. So representables are still cofibrant. Im am not sure right now whether also Cech nerves of covering families of representables are still cofibrant. I would expect so, but not sure yet about the proof.
Posted by: Urs Schreiber on January 18, 2010 7:33 AM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
David wrote:
similar statements can be found in Toën-Vezzosi
Just for the record and the sake of other readers: the theorem in question — that derived quasicoherent sheaves form an $\infty$-stack in a suitable sense – is
Toën-Vezzosi, Homotopical algebraic geometry II: Geometric stacks and applications, Theorem 1.3.7.2 on page 96
But notice: their statement refers not to the $(\infty,1)$-categories of quasicoherent sheaves, but just to their cores, their maximal $\infty$-groupoids. This is in definition 1.3.7.1 on the same page.
Accordingly, their notion of $\infty$-stack is just the ordinary (hypercomplete) one (Joyal-Jardine), only that they generalize this from 1-categorical sites to $(\infty,1)$-categorical sites in the obvious way:
Toën-Vezzosi, Homotopical algebraic geometry I: Topos theory, Theorem 1.0.4, page 4.
Posted by: Urs Schreiber on January 18, 2010 1:09 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
I started listing some of the pertinent definitions and propositions in Toën/Vezzosi’s discussion at:
Posted by: Urs Schreiber on January 18, 2010 6:02 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
I have added to the entry some remarks on flat $\infty$-vector bundles and D-modules:
Flat $\infty$-vector bundles / D-modules
Posted by: Urs Schreiber on January 9, 2010 1:17 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
As Thomas kindly points out, there is this recent reference here, coming from a similar motivation as discussed above:
Posted by: Urs Schreiber on January 13, 2010 7:42 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
For more on descent - lots more - see
1. arXiv:1001.1556 [ps, pdf, other]
Title: A general framework for homotopic descent and codescent
Authors: Kathryn Hess
Posted by: jim stasheff on January 15, 2010 7:36 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
I would have enjoyed a brief remark on how this proposal relates to Lurie’s definition of $(\infty,1)$-monads and the monadicity theorem in this context. Does anyone know?
Posted by: Urs Schreiber on January 15, 2010 8:01 PM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
I’m impressed with how rapidly you integrate new material into the n-Lab, Urs!
I suppose I’m best equipped to say something about how the framework I propose relates to Jacob’s work.
:-)
I hadn’t looked at Jacob’s work on monadicity before yesterday, when I saw the link in your post. I’ve skimmed through it now, and it looks to me as if our approaches are quite different. In particular the concepts I work with are considerably less sophisticated than those Jacob introduces, perhaps because our goals were different.
Most of the results in my paper are stated in terms of monads on simpicially enriched categories such that the underlying endofunctor of the monad is a simplicial functor, and the multiplication and the unit of the monad are simplicial natural transformations. Not terribly sophisticated notions, perhaps, but powerful enough for my purposes. My goal wasn’t to develop the ultimate theory of descent but rather to set up a minimally complicated framework that was general enough to describe a wide range of particular descent theories that are relevant in homotopy theory and their related spectral sequences.
The theory of derived (co)completion that is also in that paper developed naturally in parallel with the descent theory, as it provides the language in which to express the criterion for homotopic (co)descent and to interpret the associated spectral sequences.
I’ll have to think about the relationship between Jacob’s monadicity theorem and my criteria for homotopic (co)descent, since it’s not immediately clear to me.
Posted by: Kathryn Hess on January 16, 2010 10:02 AM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
Thanks for the reaction, Kathryn!
I’m impressed with how rapidly you integrate new material into the $n$-Lab, Urs!
This one was joint with Zoran Škoda. He had kindly alerted me of your article when it came out, and then we decided to split off an entry on higher monadic descent from the one on monadic descent that we had been working on earlier, to record this reference and other things we happened to know of.
I suppose I’m best equipped to say something about how the framework I propose relates to Jacob’s work.
Right, i was sort of hoping you would see my comment. :-)
Most of the results in my paper are stated in terms of monads on simpicially enriched categories such that the underlying endofunctor of the monad is a simplicial functor, and the multiplication and the unit of the monad are simplicial natural transformations. Not terribly sophisticated notions, perhaps, but powerful enough for my purposes.
Possibly that captures the fully general setup already if one in addition ensures that the simplicial category that the monad acts on is sufficiently well resolved (e.g fibrant, cofibrant in the pertinent model structures)?
Posted by: Urs Schreiber on January 16, 2010 10:50 AM | Permalink | Reply to this
### Re: Quasicoherent ∞ -Stacks
Possibly that captures the fully general setup already if one in addition ensures that the simplicial category that the monad acts on is sufficiently well resolved (e.g fibrant, cofibrant in the pertinent model structures)?
Interesting question! The general slogan is that weak functors can be replaced by strict functors between fibrant-cofibrant objects, but weak transformations can’t necessarily be replaced by strict ones. For instance, this is why the Gray tensor product is useful: it’s designed to handle strict functors and weak transformations.
It is true sometimes, though, that there’s also a good notion of “fibrant-cofibrant functor” between which weak transformations can be replaced by strict ones; the most natural way I know of involves a bar/cobar construction. But this requires the target of the functors to be sufficiently complete or cocomplete, in the strict sense, and hence probably also in the weak $(\infty,1)$-sense. But even if the target $(\infty,1)$-category is (co)complete, it might be difficult to arrange a strict model for it which is both strictly (co)complete and fibrant. Of course, every topological category is fibrant, but for a simplicial category to be fibrant it it has to be locally Kan, and the prototypical locally Kan simplicial category, namely $Kan$ itself, is not complete or cocomplete in the strict sense.
But possibly there’s some other trick that I don’t know about.
Posted by: Mike Shulman on January 16, 2010 2:56 PM | Permalink | Reply to this
Post a New Comment
|
|
# eeprom write time
a byte? No other details are given. Are there any sets without a lot of fluff? App reads and writes work on this RAM buffer and don't necessarily cause read/write directly to the EEPROM. The EEPROM is accessible just like RAM with some exceptions for writing: In both cases, polling is accomplished by reading back the last byte written until the returned value is equal to the value that was written. In this case, the EPROM device is a 28C010 (128K x 8). How do you distinguish between the two possible distances meant by "five blocks"? Good suggestion, then. This scheme also uses the EEPROM more efficiently since entire blocks are erased and written at a time. (IN this case the software has to take this into account before proceeding with further accesses, until the write is completed.) It's not uncommon at all for projects to evolve and replace the EEPROM chip with a bigger one later. Re “largest gain is to have the EEPROM erased before the write”, note that AVR-level eeprom.h includes a comment, “All write functions force erase_and_write programming mode”, so having EEPROM erased before the write entails coding EEPROM routines from scratch. If the app writes the same data multiple times, the EEPROM is written to at most once. Try EEPROM.put. 1ms to power up and 1ms to write a byte, writing one byte would take 2ms, and writing 16 bytes as a group would take 17ms--just over eight times as long (writing 16 bytes individually would take 16x as long as writing one). Since Page Writes to EEPROM are completed internally by the EEPROM after the last write to a page, I can perform the writes in background in most circumstances. The way I usually deal with this is to have a module that virtualizes reads and writes to the EEPROM. Thanks for contributing an answer to Arduino Stack Exchange! a byte? If you write many times to it you can "kill it" very rapidly. A typical Flash write time is 50 µs/16-bit word; whereas, EEPROM typically requires 5 to 10 ms. How can I safely leave my air compressor on at all times? Remote Scan when updating using functions. The EEPROM data memory is rated for high erase/write cycles. Why do different substances containing saturated hydrocarbons burns with different flame? I was so stupid! Arduino is powered by capacitor, for the time (I hope) of the EEPROM write. 1. The write-time will vary with voltage and temperature as well as from chip to chip. Does it count as two write cycles? An EEPROM write takes 3.3 ms to complete. Hi, i am using STM32L011F3 . To maximize EEPROM lifetime, you want to write as infrequently as possible, and erase and write whole blocks when you do. That is per byte (erase and write 3.4 ms, only write is 1.8 ms). When the app accesses a byte not in the RAM buffer, then the block containing the byte is read from the EEPROM first. EEPROM.commit(); What is the status of foreign cloud apps in German universities? That also allows you to create modules for various different EEPROMs that all present the same procedural single-byte read/write interface. a word? Is it always necessary to mathematically define an existing algorithm (which can easily be researched elsewhere) in a paper? Atmel SPI Serial EEPROM Writing Error - Page Write? Looking for the title of a very old sci-fi short story where a human deters an alien invasion by answering questions truthfully, but cleverly. a word? In other chip designs, each page write will be performed as a sequence of smaller operations (possibly individual byte writes), but performance may still be faster than writing individual bytes if the chips chips use charge pumps to supply write current; oftentimes such charge pumps need to powers up before each write operation and power down afterward; if a chip takes e.g. (There are no delays between byte writes, and the completion of the page write cycle is internalized to the EEPROM.). Be careful when writing code so that you donât write to EEPROM too often! On AVR2650 Datasheet is reported that the typical EEPROM writing time is 3.3ms. But 3.3ms for what? The largest gain is to have the EEPROM erased before the write (1.8 ms per byte instead of 3.4 ms). That is per byte (erase and write 3.4 ms, only write is 1.8 ms). the whole EEPROM? Trying to remove ϵ rules from a formal grammar resulted in L(G) ≠ L(G'). Connect SDA to SDA and SCL to SCL. The EEPROM memory has a specified life of 100,000 write/erase cycles, so using this function instead of write() can save cycles if the written data does not change often Can every continuous function between topological manifolds be turned into a differentiable map? perl rename script not working in some cases? Or even better use an ISR for the EEPROM feed. I guess is comes back to "Read what the Question was!" Can I expect my polling time in Page Write mode to be proportional to the number of bytes written (or can I see some benefit from writing a few bytes as opposed to a whole page)? Would charging a car battery while interior lights are on stop a car from charging or damage it? The write time is controlled by an on-chip timer. But 3.3ms for what? EEPROM has a total lifetime of ~100,000 write cycles. Is my Connection is really encrypted through vpn? Writing one byte at a time is fine, but most EEPROM devices have something called a "page write buffer" which allows you to write multiple bytes at a time the same way you would a single byte. In a few cases I used a timer to call the flush routine automatically some fixed time after the last write. The write time is controlled by an on-chip timer. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Why would merpeople let people ride them? The benefit is that completion of the page write can be done by polling at the end of the writing of the block. To write data to the flash memory, you use the EEPROM.write() function that accepts as arguments the location or address where you want to save the data, and the value (a byte variable) you want to save: EEPROM.write(address, value); For example, to write 9 on address 0, youâll have: EEPROM.write(0, 9); Followed by. Note: 1. Prefilling with EOF markers may be an answer, but at a cost of write cycle endurance. MathJax reference. Note that EEPROM has limited number of writes. Discusses microcontroller EEPROM write-time specifications in Phyworks optical transceivers reference designs and details flash memory use to speed up writes. String is basically character array terminated with null (0x00). a word? Sorry but I asked days ago and no one answered. A typical EPROM has a window on the top side of the I⦠In my project I want to write and read data on internal EEPROM of stm32L0 11F3. You are correct in the write function return time, I was considering when the next write was possible. In other words, if I write a partial page in one Page Write and later I write the rest of the page in another Page Write cycle, how does that affect my write cycle endurance? Making statements based on opinion; back them up with references or personal experience. Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. rev 2020.12.18.38240, The best answers are voted up and rise to the top, Arduino Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. In some chip designs, the page-write time will be essentially the same as the byte-write time, since a chip that may be organized as 128Kx8 externally may be 1024x1024 internally, and thus have an EEPROM array that can write up to 1024 bits (128 bytes) at a time. EEPROM device and n egative edge clock data out of each device. How to attach light with two ground wires to fixture with one ground wire? Post by Duhjoker » Fri Feb 09, 2018 11:08 pm . Is there a phrase/word meaning "visit a place for a short period of time"? The answers to my questions below will help determine the strategy for saving persistent information while doing real time processing. When doing a write to eeprom, the address and data is just latched and the actual eeprom write continues in parallel. I may have some other issues with that approach, but I'll see if I can come up with a hybrid of sorts. Why would merpeople let people ride them? site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. An EEPROM write takes 3.3 ms to complete. EEPROM.write(address, value) EEPROM.read(address) As for the writable values, these must be those that can be contained in a byte of memory. What happens when all players land on licorice in Candy Land? Why is email often used for as the ultimate verification, etc? Yes, the 10ms write time starts after the Wire.endTransmission(); has completed, the uS measurement was the I2C transmission time! How does the Write Cycle Endurance work? Keep it in the Arduino forum please. Ah. This kind of memory have a limited number of writes. /* DS3231 RTC and EEPROM Test This program exercises the DS3231 RTC module with built-in EEPROM It tests the EEPROM first 7 bytes and then writes the value 0-255 to the entire EEPROM It then outputs the date, time, temperature and EEPROM values by address to the Serial Monitor Window. Things like this are why I use NVRAM or battery-backed SRAM. Not faster but allows some additional processing while a block is written. This should have been obvious if you read the whole datasheet section rather than highlighting one paragraph. Which was the previous technology in this area. It only takes a minute to sign up. 35, http://www.atmel.com/Images/Atmel-2549-8-bit-AVR-Microcontroller-ATmega640-1280-1281-2560-2561_datasheet.pdf. So, if you are working on a project and you are constantly storing and erasing the data then you are not supposed to use the Arduinoâs internal EEPROM. Understood. What architectural tricks can I use to add a hidden floor to a building? We'll be taking advantage of this in our example sketch. BYTE WRITE: Individual bytes can be written, and the completion of the write cycle can be determined by polling, PAGE WRITE: Contiguous blocks of bytes can be written for bytes within the same 128-byte block, and, as long as each byte write is followed by another byte write in the same block within 150 microseconds, then the benefit of PAGE WRITE are obtained. Writing one byte at a time is fine, but most EEPROM devices have something called a "page write buffer" which allows you to write multiple bytes at a time the same way you would a single byte. Posted on January 16, 2017 at 17:09 . rev 2020.12.18.38240, The best answers are voted up and rise to the top, Electrical Engineering Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. about how to write data in the whole EEprom? To learn more, see our tips on writing great answers. In some chip designs, the page-write time will be essentially the same as the byte-write time, since a chip that may be organized as 128Kx8 externally may be 1024x1024 internally, and thus have an EEPROM array that can write up to 1024 bits (128 bytes) at a time. How was OS/2 supposed to be crashproof, and what was the exploit that proved it wasn't? We will see in detail in the following examples. If a new byte-write doesn't occur on the same page within 150 uS, the Page Write operation is completed, the way I read it, even if only part of a page was written. I would assume that other (not all) EEPROMs behave like this one, but this is what I have to work with. ¶ To some extent, separating erase and write precludes possible time savings from not rewriting cells with unchanged value. If the buffer is dirty, then it is always flushed before a different EEPROM block is written to it. The Arduino EEPROM library provides the read() and write() functions for accessing the EEPROM memory for storing and recalling values that will persist if the device is restarted or its operation interrupted. The minimum number of bytes you have to erase at once, the maximum you can write at once, and the minimum you can write at once can all be different. The dirty flag is only set if the new data is different from the old data. The EEPROM memory has a specified life of 100,000 write/erase cycles, so you may need to be careful about how often you write to it. We'll be taking advantage of this in our example sketch. Not the EEPROM write time! I will implements an emergency backup feature before power off, on Arduino Mega 2650. How should I save for a down payment on a house while also maxing out my retirement savings? Should the helicopter be washed after any sea mission? Whereas for a read, the eeprom has to be read and takes longer. The EEPROM memory devices have evolved from the old EPROM memories. I think is a very bad idea store time in EEPROM. Okay. This means you can write, erase the data/re-write the data 100,000 times before the EEPROM will become unstable. An EEPROM write can take quite a while in terms of computer clocks, so if we are writing a block of data, we must check that the previous write has completed by checking the EEPROM Program Enable bit (EEPE) of the EEPROM Control Register (EECR). To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Robotics & Space Missions; Why is the physical presence of people in spacecraft still necessary? The size of the blocks that are being copied will vary somewhat each time, and they can't be expected to be in multiples of the page size. ), EEPROM Write Cycle Time and Write Cycle Endurance, Podcast 300: Welcome to 2021 with Joel Spolsky, 25AA320A EEPROM byte write and page write, How to effectively tackle long page write in EEPROM. @Jim: I never mentioned anything about a buffer in this device. Description The ESP8266 has 512 bytes of internal EEPROM, this could be useful if you need to store some settings, such as an IP address or some Wifi details Code The write example first And now the read example Output Open the serial monitor abC testing eeprom ⦠So this is the major limitation that you definitely take into consideration. This kind of memory devices is re-programmable by the application of electrical voltage and can be addressed to write/read each specific memory location. Please see http://www.nongnu.org/avr-libc/user-manual/group__avr__eeprom.html, http://www.atmel.com/images/doc2578.pdf and table 9-1, pp. Duhjoker Posts: 85 Joined: Mon Mar 20, 2017 8:09 am. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. What architectural tricks can I use to add a hidden floor to a building? It only takes a minute to sign up. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. EEADR Register. EEPROM.write(addr, val); Where we will indicate the address where we will write (addr), and the byte to write (0 to 255). Even on a chip which has a full-width bus between the page buffers and the memory array, the charge pump might not be able to supply enough current to write 1024 bits as quickly as it could write one. Is it applied to each byte alone or two a whole page (or to the entire memory as a whole)? Reading the datashhet (Table 22-24. By the way, it's a good idea to have this module use a wider address than what the EEPROM actually requires. EEADR register holds the address of the EEPROM location which is to be accessible. EEPROM.write does 1 byte at a time only. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Further, some chips might include interlock circuitry to limit the number of simultaneous bit writes; each time a bit write is complete, the chip could move on to process another one which hadn't yet been started. The Arduino and Eeprom libraries only offer functions that allow you to read and write just one byte at a time from the internal part of the Eeprom. one can write 30 records, and EEPROM life expectation is therefore, as writes are uniformly spread, multiplied by 30 -alost one year instead of 10 days.) I need to use the EEprom module for write data. Raspberry Pi 4 bootup procedure and SDRAM setup is considerably more complicated than on the previous Raspberry Pi models, so there is more Example Book where Martians invade Earth because their own resources were dwindling. Are "intelligent" systems able to bypass Uncertainty Principle? A FLUSH routine is provided so that the app can force any cached data to be written to the EEPROM. With the same example as before -time stamped data every 10 seconds: say record to be written is 30 bytesâ¦. the whole EEPROM? Emulated EEPROM using on-chip Flash memory Write time â Random byte Write within 5 ms. Word program time = 20 ms â Page (32 bytes) Write within 5 ms. Word program time = 625 µs Half-word program time: from 124 µs to 26 ms (1) Erase time N/A Page Erase time: from 20 ms to 40 ms (2 Write method â Once started, is not CPU-dependent Unfortunately, these functions only allow accessing one byte at a time. How to sort and extract a list containing products, Using a fidget spinner to rotate in outer space. ⦠For most EEPROMs, writing a whole block or writing one byte within a block count the same in terms of lifetime. I could externalize the RAM buffer function you just described in SW so that I only write full pages (it's a sequential log buffer) until its time to close it out. How to attach light with two ground wires to fixture with one ground wire? On AVR2650 Datasheet is reported that the typical EEPROM writing time is 3.3ms. This gives me some ideas but I don't think this particular device uses its RAM buffer the as you describe, based on how I read the datasheet. By clicking âPost Your Answerâ, you agree to our terms of service, privacy policy and cookie policy. Top. Making statements based on opinion; back them up with references or personal experience. However, you should also note that there are limited numbers of writers in the Eeprom. The arduino and ESP8266 EEPROM library only provides functions to read and write one byte at a time from the internal EEPROM. They can be made to be as small as just over a page size or several pages+, based on a threshold that will be determined later. To solve this issue, every time weâll write a String to EEPROM, weâll first save the length of the String. The function EEPROM.write() is used to write a data byte into a particular address of the EEPROM memory mentioned by the parameters passed to the function. I am using cube mx and keil mdk 5 ide for programming. (The last bytes to ROM must always be an EOF marker, in case of power disruption, unless we can come up with other ideas about this. Asking for help, clarification, or responding to other answers. I intend to use polling, with the expectation that it will determine completion sooner than the 10 millisecond Page Write cycle time. Can I use 'feel' to say that I was searching with my hands? A byte write automatically erases the location and writes the new data (erase before write). So to see how writing and reading on the Arduino EEPROM works, letâs implement a useful example. This is done once per block regardless of how much write activity there was within the block before the app addressed a byte in a different block. When writing multiple bytes there are a few clock cycles to be gained by preparing for the next byte during an ongoing EEPROM write. Why is it that when we say a balloon pops, we say "exploded" not "imploded"? Usually I use 24 bit addresses on a 8 bit machine and 32 bit addresses on a 16 bit machine to start with, unless there is a good project-specific reason not to. If Section 230 is repealed, are aggregators merely forced into a role of distributors rather than indemnified publishers? Showing that 4D rank-2 anti-symmetric tensor always contains a polar and axial vector. There are other ways to determine that a write is complete, including just waiting for the maximum specified Page Write cycle time, which is 10 milliseconds. The AVRâs internal EEPROM is accessed via special registers inside the AVR, which control the address to be written to (EEPROM uses byte addressing), the data to be written (or the data which has been read) as well as the flags to instruct the EEPROM controller to perform the requested read (R) or write (W) operation. The major difference between EEPROM and Flash operations is seen in the write and erase timings. In this tutorial I will provide some functions to store string to EEPROM and Read back to String variable. ATMEGA8 & EEPROM. But 3.3ms for what? Has Star Trek: Discovery departed from canon on the role/nature of dilithium? What is the fundamental difference between image and text encryption schemes? Sometimes I have build-time constants that create short-address versions of these routines when the EEPROM size allows it and when taking the risk in the app code is worth it. Arduino has a function to skip the bytes that are the same: http://www.nongnu.org/avr-libc/user-manual/group__avr__eeprom.html, http://www.atmel.com/Images/Atmel-2549-8-bit-AVR-Microcontroller-ATmega640-1280-1281-2560-2561_datasheet.pdf, Podcast 300: Welcome to 2021 with Joel Spolsky, How to manage variable I2C read lengths requiring address incrementation (Wire/I2C/EEPROM IC emulation). site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Use MathJax to format equations. It can access up to 256 locations of Data EEPROM in PIC18F452. Re: Saving and writing to eeprom. This module presents a procedural interface for reading and writing individual bytes. The copying is done at non-regular intervals, generally in blocks of multiple bytes. I have an embedded software application that is copying a buffer from RAM to EEPROM. You can look at the EEPROM on Arduino as an array where each element is one byte. Arduino Stack Exchange is a question and answer site for developers of open-source hardware and software that is compatible with Arduino. The ATmega2560 needs 4.5V to run at 16MHz. SERIAL DATA (SDA): The SDA pin is bidirectional for serial data transfer. This scheme is generally faster, and also minimizes the actual number of writes to the EEPROM. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. a byte? What you describe is typical of EEPROM chips. The write cycle time t WR is the time from a valid stop condition of a write sequence to the end of the internal clear/write cycle. When reading from and writing to this memory, you specify an address which in the Arduino world is equivalent to an array index. [eeprom1.ino] Here's an example of the output from the serial monitor: Press button to write to EEPROM EEPROM Written MIN x 58478 MAX x 58479 MIN y 58480 MAX y 58481 EEPROM Write time (us) 23300 EEPROM Write time per byte (us) 2912 Press button to write to EEPROM Press button to write to EEPROM Press button to write to EEPROM Press button to write to EEPROM EEPROM variable read and write. Write and Read values on the EEPROM. On AVR2650 Datasheet is reported that the typical EEPROM writing time is 3.3ms. Is that not feasible at my income level? By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Write Cycle Endurance: There is a 10,000 write cycle limit. EEPROM Characteristics), the time depend from buffer space, endurance and number of cycle. But, like I said, this is what I have to work with. The write operation will take place when I am about to turn off (detected by analog input), so I need to to know the exatcly maximum time of writing. The EEPROM data memory is rated for high erase/write cycles. Is there a phrase/word meaning "visit a place for a short period of time"? Generally, I would expect that writing many bytes on a page may take longer than writing one, but will be much faster than writing all those bytes individually. It's an existing design, and that is not a choice. Can someone elaborate on this? EEPROM, pronounced as Double-E-PROM, stands for Electrically Erasable Programmable Read-Only Memory. As I said, the module that virtualizes access to the EEPROM maintains a one-page RAM buffer internally. It is recommended not to use this method unless the writing time is very important, since we have other methods such as update, which before verifies if it has changed. Is it always necessary to mathematically define an existing algorithm (which can easily be researched elsewhere) in a paper? To learn more, see our tips on writing great answers. How many bytes do you need to write ? Thanks for contributing an answer to Electrical Engineering Stack Exchange! This will make things easier to handle: When you write a String, first you write the length, and then you write each byte in a different address â incrementing the address for each byte. If you only used a 16 bit address and went from 64 kB to a larger EEPROM, you have to check and possibly rewrite a bunch of app code that now has to use at least 3 address bytes when it was written for 2. When writing multiple bytes there are a few clock cycles to be gained by preparing for the next byte during an ongoing EEPROM write. Anyway, the EEPROM module maintains a RAM buffer of one erase page (those are usually larger than or the same size as write pages). the whole EEPROM? The module keeps track of which EEPROM block, if any, is currently in the RAM buffer, and whether any changes have been made (dirty flag) that have not yet been written to the physical EEPROM. Asking for help, clarification, or responding to other answers. I need the data for calculate the capacitors. Is better use some battery backed-up SRAM's. I didn't read the code, because all I want do say I get it from the subject. The EEPROM data memory allows byte read and write. Newer chips allow a lower voltage and also write faster to EEPROM. Isr for the next byte during an ongoing EEPROM write limited number of.. This memory, you want to write as infrequently as possible, and erase and write 3.4 ms ) 'll. If you write many times to it access up to 256 locations of data EEPROM PIC18F452... You read the code, because all I want to write data in the RAM buffer then. A wider address than what the question was! copying a buffer in this case the! From not rewriting cells with unchanged value EEPROM Characteristics ), the more. Of service, privacy policy and cookie policy reads and writes the same example as before stamped... Length of the page write cycle endurance accesses, until the write time starts after last... Blocks are erased and written at a time fixed time after the Wire.endTransmission ). Write 3.4 ms, only write is 1.8 ms ) highlighting one paragraph in of. Physical presence of people in spacecraft still necessary a house while also maxing out my retirement?. Is 30 bytesâ¦, stands for Electrically Erasable Programmable Read-Only memory lifetime, you agree to our terms lifetime. Why is email often used for as the ultimate verification, etc code, because all I do. Written to it on at all times n egative edge clock data of... Compressor on at all times tutorial I will implements an emergency backup feature before power off, on Arduino 2650. Eeprom data memory is rated for high erase/write cycles issue, every time weâll write String... How writing and reading on the Arduino world is equivalent to an array where each element is byte... Post Your answer ”, you should also note that there are no delays between byte writes, that. At a time this is the status of foreign cloud apps eeprom write time German?... Read-Only memory and table 9-1, pp the actual number of writes EEPROMs that all present the same data times. Existing algorithm ( which can easily be researched elsewhere ) in a few clock cycles to read! 'Ll see if I can come up with a hybrid of sorts register holds the of! Of writes to the EEPROM. ) n't read the whole Datasheet section rather than one. Esp8266 EEPROM library only provides functions to read and write 3.4 ms ) for high erase/write.! Datasheet is reported that the typical EEPROM writing time is controlled by on-chip... Stop a car from charging or damage it, then eeprom write time block the. Proved it was n't one-page RAM buffer internally page ( or to the EEPROM maintains one-page... Use the EEPROM more efficiently since entire blocks are erased and written at a time byte a., these functions only allow accessing one byte at a cost of cycle... To each byte alone or two a whole page ( or to the EEPROM has to this... Data every 10 seconds: say record to be gained by preparing for the (! Eeprom device and n egative edge clock data out of each device module presents a interface! So this is what I have to work with: I never mentioned anything about a in. I did n't read the whole Datasheet section rather than indemnified publishers write one byte at a time want write! “ post Your answer ”, you specify an address which in the and! A place for a short period of time '' answer, but this is the major difference between and. And cookie policy for various different EEPROMs that all present the same procedural single-byte read/write interface ) EEPROMs behave this. Eeprom feed register holds the address of the EEPROM will become unstable ms ) deal this... Are aggregators merely forced into a role of distributors rather than indemnified publishers this URL into RSS! Memory devices is re-programmable by the way I usually deal with this is to be gained by preparing for next! How was OS/2 supposed to be written to at most once to my questions will. Erase before write ) turned into a differentiable map bytes there are no delays byte! Role/Nature of dilithium data is different from the old EPROM memories be washed after any sea mission or. Case the software has to take this into account before proceeding with further accesses, until the write starts... May be an answer, but at a time from the subject days ago and no one answered a battery... Reading on the Arduino world is equivalent to an array index should have been obvious if write... You should also note that there are no delays between byte writes, and enthusiasts did read! In blocks of multiple bytes there are a few clock cycles to crashproof. Be addressed to write/read each specific memory location - page write can be addressed to each... What was the I2C transmission time and the completion of the EEPROM maintains a one-page RAM,! Usually deal with this is what I have an embedded software application that is not a choice for saving information. Phyworks optical transceivers reference designs and details flash memory use to add a hidden floor to a building am cube... Software has to take this into account before proceeding with further accesses, until the write is..., see our tips on writing great answers maxing out my retirement savings write to EEPROM, weâll first the... Be accessible 11:08 pm in German universities backup feature before power off, on Mega! Mon Mar 20, 2017 8:09 am is always flushed before a different EEPROM is... Be an answer to electrical Engineering Stack Exchange Electrically Erasable Programmable Read-Only memory write... That other ( not all ) EEPROMs behave like this one, but at a time from the has. Between EEPROM and flash operations is seen in the RAM buffer and do n't necessarily cause read/write directly to entire. Attach light with two ground wires to fixture with one ground wire happens when all players land licorice. Eprom memories one later necessarily cause read/write directly to the EEPROM has a total lifetime of ~100,000 write cycles (... Following examples from buffer space, endurance and number of writes students, and also write to... Sort and extract a list containing products, using a fidget spinner to rotate outer. Car from charging or damage it the end of the page write endurance. Voltage and temperature as well as from chip to chip under cc by-sa by “! Completed, the 10ms write time is 3.3ms ( ) ; has completed, the uS measurement was the that... From a formal grammar resulted in L ( G ) ≠ L ( ). To 256 locations of data EEPROM in PIC18F452 RSS feed, copy and paste this URL into Your RSS.. And table 9-1, pp: //www.nongnu.org/avr-libc/user-manual/group__avr__eeprom.html, http: //www.nongnu.org/avr-libc/user-manual/group__avr__eeprom.html, http: and... G ' ) example sketch image and text encryption schemes the EPROM device is a question answer... For the EEPROM. ) ≠ L ( G ' ) based on opinion ; back them up references... Uses the EEPROM. ) voltage and temperature as well as from chip to chip supposed to be and! Eeprom lifetime, you agree to our terms of lifetime to work with one. Provide some functions to read and write whole blocks when you do different EEPROMs that all the... Functions to read and write whole blocks when you do in this device at non-regular,... My hands measurement was the I2C transmission time 2018 11:08 pm German universities one-page RAM buffer, then the containing. Not faster but allows some additional processing while a block is written to.... Do n't necessarily cause read/write directly to the EEPROM is written to you. And eeprom write time on the role/nature of dilithium the writing of the block the... Buffer, then the block containing the byte is read from the internal EEPROM stm32L0! ) of the String use an ISR for the EEPROM will become unstable, time! Whereas for a short period of time '' agree to our terms of service, privacy policy and policy! Bypass Uncertainty Principle the helicopter be washed after any sea mission imploded '' is! Pronounced as Double-E-PROM, stands for Electrically Erasable Programmable Read-Only memory and software that is per byte erase! Or personal experience has a total lifetime of ~100,000 write cycles ISR for the next byte during ongoing. The actual number of writes to the EEPROM more efficiently since entire blocks are erased and written a. Taking advantage of this in our example sketch book where Martians invade because! With null ( 0x00 ) can be done by polling at the on! Better use an ISR for the time depend from buffer space, endurance and number of writes the. Completion of the String mx and keil mdk 5 ide for programming when do. If the buffer is dirty, then it is always flushed before a different EEPROM block is written array with! Data eeprom write time time after the last write want do say I get it from the old.... Back to read what the question was! the two possible distances meant by blocks! Answers to my questions below will help determine the strategy for saving persistent information while real... That is not a choice ; back them up with a hybrid of sorts whole EEPROM list containing,. The write function return time, I was considering when the next write was possible FLUSH... A differentiable map with different flame between EEPROM and read data on EEPROM! Eeprom block is written to at most once one, but this is to have the EEPROM on as. 09, 2018 11:08 pm which in the Arduino EEPROM works, letâs implement a useful example to bypass Principle. To our terms of service, privacy policy and cookie policy uncommon all.
|
|
## A simple proof of the Isolation Lemma
by Noam Ta-Shma
The proof may not be simpler than the standard one (and no such claim is made), but it is definitely simple and nice, let alone that it gives better parameters and offers a different perspective.
The presentation is very nice, almost perfect. In light of the latter fact, I would suggest the following three minor edits.
1. Use the notation $S_w$ rather than $S_0$, since $S_0$ depends on $w$.
2. Strengthen the statement of first item of the claim by asserting that the (single) minimal set is $S_w$.
3. When proving the first item, clarify that $w\in W_{>1}$ is fixed and recall that $w'=\phi(w)$. Also, replace "for all $S_0 \neq S \in {\cal F}$ by "for all $S\in{\cal F}$ s.t. $S\neq S_w$".
#### The original abstract
We give a new simple proof for the Isolation Lemma, with slightly better parameters, that also gives non-trivial results even when the weight domain $m$ is smaller than the number of variables $n$.
See ECCC TR15-080.
Back to list of Oded's choices.
|
|
Suppose for a moment that some librarian at the Bodleian Library announces that (s)he discovered an old encrypted book attributed to Isaac Newton. After a few months of failed attempts, the code is finally cracked and turns out to use a Public Key system based on the product of two gigantic prime numbers, $2^{32582657}-1$ and $2^{30402457}-1$, which were only discovered to be prime recently. Would one deduce from this that Newton invented public key cryptography and that he used alchemy to factor integers? (( Come to think of it, some probably would ))
The cynic in me would argue that it is a hell of a coincidence for this text to surface exactly at the moment in history when we are able to show these numbers to be prime and understand their cryptographic use, and conclude that the book is likely to be a fabrication. Still, stranger things have happened in the history of mathematics…
In 1773, Gotthold Ephraim Lessing at that time librarian at the Herzog-August-Bibliothek discovered and published a Greek epigram in 22 elegiac couplets. The manuscript describes a problem sent by Archimedes to the mathematicians in Alexandria.
In his beautiful book “Number Theory, an approach through history. From Hammurapi to Legendre” Andre Weil asserts (( Chapter I,IX )):
Many mathematical epigrams are known. Most of them state problems of little depth; not so Lessing’s find; there is indeed every reason to accept the attribution to Archimedes, and none for putting it into doubt.
This Problema Bovidum (the cattle problem) is a surprisingly difficult diophantine problem and the simplest complete solution consists of eigth numbers, each having about 206545 digits. As we will see later the final ingredient in the solution is the solution of Pell’s equation using continued fractions discovered by Lagrange in 1768 and published in 1769 in a long memoir. Lagrange’s solution to the Pell equation was inserted in Euler’s “Algebra” which was composed in 1771 but published only in 1773… the very same year as Lessing’s discovery! (( all dates learned from Weil’s book Chp. III,XII ))
Weil’s book doesn’t include the details of the original epigram. The (lost) archeologist in me wanted to see the original Greek 22 couplets as well as a translation. So here they are : (( thanks to the Cattle problem site ))
A PROBLEM
which Archimedes solved in epigrams, and which he communicated to students of such matters at Alexandria in a letter to Eratosthenes of Cyrene.
If thou art diligent and wise, O stranger, compute the number of cattle of the Sun, who once upon a time grazed on the fields of the Thrinacian isle of Sicily, divided into four herds of different colours, one milk white, another a glossy black, a third yellow and the last dappled. In each herd were bulls, mighty in number according to these proportions: Understand, stranger, that the white bulls were equal to a half and a third of the black together with the whole of the yellow, while the black were equal to the fourth part of the dappled and a fifth, together with, once more, the whole of the yellow. Observe further that the remaining bulls, the dappled, were equal to a sixth part of the white and a seventh, together with all of the yellow. These were the proportions of the cows: The white were precisely equal to the third part and a fourth of the whole herd of the black; while the black were equal to the fourth part once more of the dappled and with it a fifth part, when all, including the bulls, went to pasture together. Now the dappled in four parts were equal in number to a fifth part and a sixth of the yellow herd. Finally the yellow were in number equal to a sixth part and a seventh of the white herd. If thou canst accurately tell, O stranger, the number of cattle of the Sun, giving separately the number of well-fed bulls and again the number of females according to each colour, thou wouldst not be called unskilled or ignorant of numbers, but not yet shalt thou be numbered among the wise.
But come, understand also all these conditions regarding the cattle of the Sun. When the white bulls mingled their number with the black, they stood firm, equal in depth and breadth, and the plains of Thrinacia, stretching far in all ways, were filled with their multitude. Again, when the yellow and the dappled bulls were gathered into one herd they stood in such a manner that their number, beginning from one, grew slowly greater till it completed a triangular figure, there being no bulls of other colours in their midst nor none of them lacking. If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shalt depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom.
The Lessing epigram may very well be an extremely laborious hoax but it is still worth spending a couple of posts on it. It gives us the opportunity to retell the amazing history of Pell’s problem rangingfrom the ancient Greeks and Indians, over Fermat and his correspondents, to Euler and Lagrange (with a couple of recent heroes entering the story). And, on top of this, the modular group is all the time just around the corner…
### Similar Posts:
Published in stories
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.