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http://mathhelpforum.com/advanced-algebra/180970-question-field-extension.html
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# Thread: a question on field extension
1. ## a question on field extension
Let E/F an algebraic field extension and let p=CharF>0 .
Let a be an elemnt in E.
prove that there exists i>=0 such as a^p^i is separable.
i thought to use to fact that if F is a field with Char p >0, and
f(x)=g(x^p) for some g over F, then f(x) (which its root is a) isn't separable..
but i'm not quite sure how to use it...
2. You're on the right track. If $f(x)$ is not separable, then write $f(x) = g(x^p)$. If $g(x)$ is separable then we are done. If not, we can repeat the process, writing $g(x)$ as some $h(x^{p_2})$. Eventually you have to get a separable polynomial, and the result follows immediately.
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2017-02-23 04:48:40
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https://worldbuilding.stackexchange.com/questions/122382/determination-of-reasonable-volcanic-island-height-from-area
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# Determination of reasonable volcanic island height from area?
My islands (in the world I'm building) were formed from a volcanic hotspot. I want to build realistic islands, so I was wondering how tall volcanic islands are generally in relation to their area. Intuitively, there should be a rule, given that erosion of volcanic island mountains generally is accompanied by the island slowly subsiding in the sea, reducing the surface area and the height. Similarly, due to them mostly being shield volcanoes, the island's building from volcanism should have a similar area of lava correspond to the stacked up height of lava. So, is there a formula on how tall islands are based on their area? (+/- 3 percentage points should be fine)
For an example, here is Kauai, an old island, and Hawaii, a new one:
• 1,598.1 m tall vs 1,456 square km (Kauai)
• 4,207.2 m tall vs 10,430 square km (Hawaii)
If this is impossible, could you do an estimate for a single island chain (Emperor Seamounts/Hawaii)?
• your best bet is to find a few island of the approximate area you want, many other factors like the height of the seafloor and volcanic composition have much large effects. – John Aug 21 '18 at 0:33
• @John does the height of the seafloor have an effect? I would think that the cross section would look kinda like a cone so that the surface area to the height would be possible to model. About volcanic composition, I am mainly looking at basaltic lava, a lot like the Hawaiian islands. – JavaScriptCoder Aug 21 '18 at 0:38
• The seafloor has a big effect because it alters how much things like coral and subsidence can effect it. Other factors like how productive the volcano is and how fast the seafloor is moving will also have much larger effects. – John Aug 21 '18 at 0:41
• I've edited to have it focus on the Hawaiian islands and Emperor Seamounts. Would that be more answerable? – JavaScriptCoder Aug 21 '18 at 0:41
• Not really, you can find out the average slope (5-10%) of a shield volcano but that won't tell you much since it a large variance and many islands are made of more than one volcano/dike. Also erosion can drastically alter the height. – John Aug 21 '18 at 0:47
# For Hawaii, $H\propto\sqrt{A}$.
I looked at the islands on the Hawaiian-Emperor Seamount Chain with surface volcanoes, and plotted their surface area vs. their maximum elevation, using data from Wikipedia. I checked that the topography of each island is indeed dominated by the central volcano or volcanoes, although this is a bit complicated on some of the larger islands, as there are multiple active cones.
I left out a number of islands, atolls, seamounts, and guyots. The islands I used in my dataset are the main volcanic islands; the few extinct islands are extremely small. Seamounts and guyots are underwater, and therefore aren't helpful. Atolls, of course, are old and too eroded to give us any helpful data.
I then plotted the points logarithmically and fit a power-law model to the data, using this code by Aziz Alto. Power-laws are great in general, and are often the physicist's method of choice, so I figured it would be a decent starting point.
I found that $H\propto A^{0.54}$, or, essentially, $H\propto \sqrt{A}$, where $H$ is the maximum height of the volcano and $A$ is the area of the island. In particular, the best-fit equation I found was $$H=34.67\left(\frac{A}{\text{km}^2}\right)^{0.54}\text{ meters}$$ The $R^2$ statistic is rather good; $R^2=0.796$.
I doubt this relation has a physical meaning; I'm interpreting it as merely a statistical fit that will help you in your calculations and worldbuilding. Although the fact that the exponent is close to $1/2$ is nice, and maybe indicative of some physical law, I'm inclined to doubt it Maybe there's underlying physics; maybe there isn't. But I suppose it's a good enough solution, for your intents and purposes.
Here's the data again, with the best-fit model plotted:
For this chain, a good approximation is $H\propto\sqrt{A}$. Since the islands are roughly circular and $A\propto r^2$, $H\propto r$, which is something of an interesting result. It does seem to agree with a model of shield volcanoes as having straight sides of constant slope - although that is still a simplistic picture.
### Other chains
I decided to test this model on other chains. In particular, you asked about the Canary Islands and the Azores. For the Canary Islands, I found a reasonably poor fit ($R^2=0.0375$) for a best-fit power-law model of $H\propto A^{0.13}$. The distribution of heights for the seven main islands appears to be somewhat random, which is unhelpful. A possible reason for the discrepancy could be that the Hawaiian-Emperor Seamount Chain is composed largely of shield volcanoes, and this trend may not apply to other types, like stratovolcanoes.
The Azores were interest, yielding $H\propto A^{0.28}$, with $R^2=0.368$. If we remove an outlier, Pico Island, we get $H\propto A^{0.20}$, with $R^2=0.541$. This is better than the Canary Islands, but still not as good as Hawaii. I do notice that all three of these exponents are lower than Hawaii's, which is interesting. I suspect it's partially because of the lack of a clear power-law trend, from what I've seen.
### Notes
The Big Island of Hawaii does lower the power-law model a bit, but not by a huge amount (the exponent becomes $0.60$). It also lowers the proportionality constant somewhat.
• Is there a reason you left out most of the islands? the hawain chain has close to a hundred islands. – John Aug 21 '18 at 1:06
• @John I've only gotten to look at some of the data so far - more on the way. – HDE 226868 Aug 21 '18 at 1:06
• Still getting my vote a statistical approximation of the existing islands is about hte best possible answer.Although an error range would be a nice addition. – John Aug 21 '18 at 1:10
• @John I can get you the errors at some point in the future. I've looked through the other islands in the chain, and determined that the others are either atolls or underwater, meaning that they're not useful for the models here - in other words, they aren't surface volcanoes that we can use. – HDE 226868 Aug 21 '18 at 1:15
• Nice answer! I'll accept in 24 hrs if no other better answers appear. – JavaScriptCoder Aug 21 '18 at 1:17
A shield volcano is characterized by gentle upper slopes (about 5 degrees) with somewhat steeper lower slopes (about 10 degrees). The shield volcanoes are almost entirely composed of relatively thin lava flows built up over a central vent.
So, use those 5 and 10 degree slope angles and you should be able to generate realistic heights for any volcano you want based on basal diameter.
• that will ive you the base of the volcano not the island. – John Aug 21 '18 at 0:49
• Not... sure I understand the distinction you're making... if we're talking about the Hawaiian islands or anything like them, there isn't any difference. The island is the volcano, and vice versa. – Morris The Cat Aug 21 '18 at 0:54
• No the island is what is left of the volcano/s, The hawaiian chains are great examples most of the islands are made of more than one volcano, and all are in different stages of the island building process. Some are very far into the aroll stage, in which they may have virtually no height while still having the same area. – John Aug 21 '18 at 1:01
• Ahh, got it. I see what you're saying now. – Morris The Cat Aug 21 '18 at 1:03
I direct you to look at these references: https://en.wikipedia.org/wiki/Mount_Vesuvius, your better bet might be to look at this, since it was an actual island instead of Vesuvious. https://en.wikipedia.org/wiki/Krakatoa. Then there's the beautifully new island off the coast of Japan which is still growing, but I've had my eye on it since it first appeared some years ago. https://en.wikipedia.org/wiki/Nishinoshima_(Ogasawara) This one is of great interest to me particularly as judging by the placement of a former under water caldera, this one has the potential to actually be a permanent island unlike some newly formed volcanic islands. That and merging with an already existing island also contributes to it's chances of survival instead of merely falling back into the ocean as so many do. I'm neither a mathmatist nor a volcanologist so I can't give specific info. I hope this helps.
• Hi @VaniJoy, welcome to WB.SE! We hope you enjoy your stay here, and if you haven't already, take a look at the tour and the help center for our current policies and guidelines. Thanks for the info about this, however I was looking for an equation and HDE was able to generate one. – JavaScriptCoder Aug 23 '18 at 1:02
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2019-11-14 06:42:40
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https://msp.org/pjm/2020/309-2/p02.xhtml
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#### Vol. 309, No. 2, 2020
Recent Issues Vol. 311: 1 Vol. 310: 1 2 Vol. 309: 1 2 Vol. 308: 1 2 Vol. 307: 1 2 Vol. 306: 1 2 Vol. 305: 1 2 Vol. 304: 1 2 Online Archive Volume: Issue:
The Journal Subscriptions Editorial Board Officers Contacts Submission Guidelines Submission Form Policies for Authors ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Special Issues Author Index To Appear Other MSP Journals
Value distribution properties for the Gauss maps of the immersed harmonic surfaces
### Xingdi Chen, Zhixue Liu and Min Ru
Vol. 309 (2020), No. 2, 267–287
##### Abstract
We study the value distribution theory for the immersed harmonic surfaces and $K$-QC harmonic surfaces. We first investigate the value distribution properties for the generalized Gauss map $\Phi$ of an immersed harmonic surface, similar to the result of Fujimoto and Ru in the minimal surfaces case. After building a relation between $\Phi$ and the classical Gauss map $\mathfrak{𝔫}$ for the $K$-QC harmonic surfaces, we derive that, for a complete harmonic and $K$-quasiconformal surface immersed in ${ℝ}^{3}$, if its unit normal $\mathfrak{𝔫}$ omits seven directions in ${S}^{2}$ and any three of which are not contained in a plane in ${ℝ}^{3}$, then the surface must be flat. In the last section, under an additional condition, we give an estimate of the Gauss curvature for the $K$-QC harmonic surfaces, generalizing the result of the minimal surfaces in the case that the unit normal $\mathfrak{𝔫}$ omits a neighborhood of some fixed direction.
##### Keywords
harmonic immersion, quasiconformal mapping, value distribution theory, Hopf differential, conformal metric, Gauss map
##### Mathematical Subject Classification
Primary: 53C42, 53C43
Secondary: 30C65, 32H25
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2021-06-17 04:30:36
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http://www.physicsforums.com/showthread.php?p=3472731
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## Computational complexity with an epsilon
What does that mean when there's an $\epsilon$ in the complexity, such as
$O(n^{2+\epsilon})$ for every $\epsilon >0$
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Quote by yavanna What does that mean when there's an $\epsilon$ in the complexity, such as $O(n^{2+\epsilon})$ for every $\epsilon >0$
Welcome to PF, yavanna!
I would tend to take it very literally.
It says the complexity is greater than $O(n^{2})$.
But it is less than for instance $O(n^{2.1})$.
Note that a complexity of $O(n^{3})$ as well as $O(n^{4})$ implies a complexity of $O(n^{3})$.
Similar discussions for: Computational complexity with an epsilon Thread Forum Replies Career Guidance 11 General Physics 0 General Math 1 Programming & Comp Sci 3 General Math 3
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2013-06-19 07:35:52
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http://archive.numdam.org/item/COCV_1997__2__13_0/
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Smooth homogeneous asymptotically stabilizing feedback controls
ESAIM: Control, Optimisation and Calculus of Variations, Tome 2 (1997) , pp. 13-32.
@article{COCV_1997__2__13_0,
author = {Hermes, Henry},
title = {Smooth homogeneous asymptotically stabilizing feedback controls},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {13--32},
publisher = {EDP-Sciences},
volume = {2},
year = {1997},
zbl = {0872.93072},
mrnumber = {1440077},
language = {en},
url = {http://archive.numdam.org/item/COCV_1997__2__13_0/}
}
Hermes, Henry. Smooth homogeneous asymptotically stabilizing feedback controls. ESAIM: Control, Optimisation and Calculus of Variations, Tome 2 (1997) , pp. 13-32. http://archive.numdam.org/item/COCV_1997__2__13_0/
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2021-12-02 16:20:42
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http://dlmf.nist.gov/12.1
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# §12.1 Special Notation
(For other notation see Notation for the Special Functions.)
$x,y$ real variables. complex variable. nonnegative integers. real or complex parameters. arbitrary small positive constant.
Unless otherwise noted, primes indicate derivatives with respect to the variable, and fractional powers take their principal values.
The main functions treated in this chapter are the parabolic cylinder functions (PCFs), also known as Weber parabolic cylinder functions: $\mathop{U\/}\nolimits\!\left(a,z\right)$, $\mathop{V\/}\nolimits\!\left(a,z\right)$, $\mathop{\overline{U}\/}\nolimits\!\left(a,z\right)$, and $\mathop{W\/}\nolimits\!\left(a,z\right)$. These notations are due to Miller (1952, 1955). An older notation, due to Whittaker (1902), for $\mathop{U\/}\nolimits\!\left(a,z\right)$ is $\mathop{D_{\nu}\/}\nolimits\!\left(z\right)$. The notations are related by $\mathop{U\/}\nolimits\!\left(a,z\right)=\mathop{D_{-a-\frac{1}{2}}\/}\nolimits% \!\left(z\right)$. Whittaker’s notation $\mathop{D_{\nu}\/}\nolimits\!\left(z\right)$ is useful when $\nu$ is a nonnegative integer (Hermite polynomial case).
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2014-04-24 22:12:03
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http://quant.stackexchange.com/questions/7408/is-it-worth-preserving-orderbook-structure-when-building-it-from-individual-orde?answertab=active
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# Is it worth preserving orderbook structure when building it from individual orders?
Say I'm building an order book and two bids come in at price $p$ and volumes $v_1$ and $v_2$. Which option is better
• To store the order as $\{p, v_1+v_2\}$ or
• To store the order as $\{p,v_1\}$ and $\{p,v_2\}$ and then manually aggregate orders when I need, say, a bestBid value
Is there any analytical insight that can be gained from the actual size of the orders? If there is, can you point me to some literature in this field? Thanks.
Please note: there is nothing in the feed to indicate who the order came from and what order has been filled - all I have are the prices and volumes.
-
It depends on which bids came in, if both prices were equal and they represent the best bid then obviously you should aggregate the volumes. Otherwise, you allocate the volumes to the volume at each price level in the book that your new prices matched with. – Matt Wolf Mar 2 '13 at 4:19
@Freddy my question concerns whether volumes should be aggregated per price or not – Dmitri Nesteruk Mar 2 '13 at 16:32
@DmitriNesteruk Again, list examples. Don't say, "there is nothing in the feed to indicate who the order came from", since that is true of all exchanges with brokerage MPIDs. Just don't say that; it's tautology. Instead list the specific examples of your feed. – chrisaycock Mar 3 '13 at 19:48
new order 1: buy IBM $202.91 100 shares new order 2: buy IBM$202.91 200 shares
new order 3: buy IBM $202.91 100 shares cancel 2 execute 1 The only way to know that 100 shares are remaining is if you had stored the orders separately. - Thanks, but this is not the way data actually comes in. Data comes in as 'someone canceled their order for 200 shares' and 'deal executed for 100 shares'. – Dmitri Nesteruk Mar 3 '13 at 8:01 @DmitriNesteruk What feed are you taking in? NYSE OpenBook is a level, rather than order, oriented feed. Perhaps you're using that? I don't know any other US equities feed that isn't order based. In which case you're situation might dictate a different design. Your implied above it was an order based feed by stating you had the ability to separate the orders into their aggregate sizes. – Louis Marascio Mar 3 '13 at 13:04 @LouisMarascio, admittedly I am not too knowledgeable about US feeds, but I am confused by your above statement. The link to the OUCH protocol does not point to that being a order-based feed which operates on IDs. Could you please help me to understand? Thanks. – Matt Wolf Mar 3 '13 at 13:36 @Freddy OUCH is used for order entry, not market data. The relevant NASDAQ market data protocol is TotalView ITCH. – Louis Marascio Mar 3 '13 at 13:56 @Freddy NASDAQ, BATS, and DirectEdge all list just the order ID for cancel, replace, and execute. The symbol and side are only listed for the initial new order. – chrisaycock Mar 3 '13 at 14:27 The "correct" way is the way best suited to your trading. Regardless as to your data structure of choice, you have to maintain a list of all orders active on your book. That's because subsequent messages reference Order ID and you have to look up the corresponding order to determine the price level being acted upon. Given that you have to maintain a reference of all orders and their properties, it makes sense to not aggregate until you need to (at the api level). - I have never implemented an order book, but I don't see immediate benefits from this aggregation. If you merge the volumes, then during the actual execution you'll have additionally to take into account that these orders came from different market participants. This seems to add additional complexity to your implementation. From the point of view of market liquidity measures it makes a difference if you have one large order of volume$v$or many small orders with total volume$v\$.
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2015-03-29 16:33:17
|
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|
https://www.semanticscholar.org/paper/Minimizing-Condition-Number-via-Convex-Programming-Lu-Pong/49265acb68a79194f91b272624bf5e3358c25d15
|
# Minimizing Condition Number via Convex Programming
@article{Lu2011MinimizingCN,
title={Minimizing Condition Number via Convex Programming},
author={Zhaosong Lu and Ting Kei Pong},
journal={SIAM J. Matrix Anal. Appl.},
year={2011},
volume={32},
pages={1193-1211}
}
• Published 1 November 2011
• Computer Science, Mathematics
• SIAM J. Matrix Anal. Appl.
In this paper we consider minimizing the spectral condition number of a positive semidefinite matrix over a nonempty closed convex set $\Omega$. We show that it can be solved as a convex programming problem, and moreover, the optimal value of the latter problem is achievable. As a consequence, when $\Omega$ is positive semidefinite representable, it can be cast into a semidefinite programming problem. We then propose a first-order method to solve the convex programming problem. The…
Controlling singular values with semidefinite programming
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• 2015
This paper considers the problem of optimal design of experiments, and a two-step inference strategy is proposed that entails the minimization of a convex integral functional under linear constraints.
Minimizing the Condition Number to Construct Design Points for Polynomial Regression Models
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• 2013
A new optimality criterion is studied, the K-optimality criterion, for constructing optimal experimental designs for polynomial regression models, which shows that there is always a symmetric $K-optimal design with exactly$p+1$support points including the boundary points$-1$and$1\$.
K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging
• Medicine, Mathematics
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• 2015
This paper proposes a new approach to solve the K-optimal GES design problem for fourth-order tensor-based diffusion profile imaging as a tractable semidefinite programming problem and shows that the proposed design leads to the minimum signal deviation.
Sparse shift-varying FIR preconditioners for fast volume denoising
Splitting-based CT reconstruction algorithms decompose the reconstruction problem into a iterated sequence of “easier” subproblems. One relatively memory-efficient algorithm decomposes the
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• Computer Science
2017 IEEE International Conference on Robotics and Automation (ICRA)
• 2017
This work presents a framework for online generation of robust motion plans for robotic systems with nonlinear dynamics subject to bounded disturbances, control constraints, and online state constraints such as obstacles and demonstrates the approach through simulations of a 6-state planar quadrotor navigating cluttered environments in the presence of a cross-wind.
Metric selection in fast dual forward-backward splitting
• Mathematics, Computer Science
Autom.
• 2015
This paper proposes several methods, with different computational complexity, to find a space on which the algorithm performs well, and evaluates the proposed metric selection procedures by comparing the performance to the case when the Euclidean space is used.
A Unified Framework for Manifold Landmarking
• Computer Science, Mathematics
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• 2018
This paper proposes a novel active manifold learning method that combines geometric manifold landmarking methods with algebraic ones and achieves this by using the Gershgorin circle theorem to construct an upper bound on the learning error that depends on the landmarks and the manifold's alignment matrix.
Active manifold learning via a unified framework for manifold landmarking.
• Mathematics
• 2017
The success of semi-supervised manifold learning is highly dependent on the quality of the labeled samples. Active manifold learning aims to select and label representative landmarks on a manifold
Robust Feedback Motion Planning via Contraction Theory
We present a framework for online generation of robust motion plans for robotic systems with nonlinear dynamics subject to bounded disturbances, control constraints, and online state constraints such
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The condition number is a Clarke regular strongly pseudoconvex function and it is proved that a global solution of the problem can be approximated by an exact or an inexact solution of a nonsmooth convex program.
Primal-dual first-order methods with O (1/e) iteration-complexity for cone programming.
• Mathematics
• 2011
In this paper we consider the general cone programming problem, and propose primal-dual convex (smooth and/or nonsmooth) minimization reformulations for it. We then discuss first-order methods
Primal-dual first-order methods with $${\mathcal {O}(1/\epsilon)}$$ iteration-complexity for cone programming
• Mathematics, Computer Science
Math. Program.
• 2011
This paper discusses first-order methods suitable for solving primal-dual convex and nonsmooth minimization reformulations of the cone programming problem, and proposes a variant of Nesterov’s optimal method which has outperformed the latter one in the authors' computational experiments.
A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
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A nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form that replaces the symmetric, positive semideFinite variable X with a rectangular variable R according to the factorization X=RRT.
Probing the Pareto Frontier for Basis Pursuit Solutions
• Computer Science, Mathematics
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• 2008
A root-finding algorithm for finding arbitrary points on a curve that traces the optimal trade-off between the least-squares fit and the one-norm of the solution is described, and it is proved that this curve is convex and continuously differentiable over all points of interest.
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Computational experiments with linear optimization problems involving semidefinite, quadratic, and linear cone constraints (SQLPs) are discussed and computational results on problems from the SDPLIB and DIMACS Challenge collections are reported.
On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators
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This paper shows, by means of an operator called asplitting operator, that the Douglas—Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm, which allows the unification and generalization of a variety of convex programming algorithms.
On the Closedness of the Linear Image of a Closed Convex Cone
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A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency.
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This paper describes how to work with SeDuMi, an add-on for MATLAB, which lets you solve optimization problems with linear, quadratic and semidefiniteness constraints by exploiting sparsity.
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2022-01-18 13:29:49
|
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https://anadat-r.davidzeleny.net/doku.php/en:data:morse
|
David Zelený
en:data:morse
# Rothkopf's experiment with Morse codes
## Source of data
Rothkopf (1957), data used here were distilled from library xgobi1)
## Description of the dataset
The aim of the study was to show, which Morse codes are the most easy to be confused. Each Morse code is a set of short (0.05 sec) and/or long (0.15 sec) beeps. Experiment was joined by 598 respondents, and Rothkopf played each of them different combinations of Morse codes, separated by short pause. Each respondent should quickly decide, whether the played codes were the same or different. The result is confusion matrix, in which each number represents number of cases when respondents consider the given combination of codes to be different. The higher the number, the easier are the codes recognisable.
The example of the matrix morse.dist is below:
A B C D E F G .- 0 167 169 159 180 164 163 -. . . 167 0 96 79 163 95 139 -.-. 169 96 0 141 166 115 137 -.. 159 79 141 0 172 136 100 . 180 163 166 172 0 183 182 ..-. 164 95 115 136 183 0 156 –. 163 139 137 100 182 156 0
I created also another dataset, which two attributes of each Morse code: the length (number of beeps), and the ration between the number of long and short beeps. The example of matrix morse.attr is as below:
length ratio.short.long 2 0.5 4 0.75 4 0.5 3 0.6666667 1 1 4 0.75 3 0.3333333
morse.dist <- read.delim ('https://raw.githubusercontent.com/zdealveindy/anadat-r/master/data/morsecodes-dist.txt', row.names = 1, head = T)
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2021-04-22 14:40:22
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=140&t=60954
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Electromotive force
Mulin_Li_2J
Posts: 105
Joined: Sat Aug 17, 2019 12:16 am
Electromotive force
Is electromotive force of a cell decreasing over time as the redox reaction approaches its equilibrium? Or electromotive is like the largest possible cell potential of a cell?
PranaviKolla2B
Posts: 114
Joined: Fri Aug 30, 2019 12:17 am
Re: Electromotive force
What is the electromotive force of a cell?
Eesha Sohail 1D
Posts: 100
Joined: Sat Aug 17, 2019 12:16 am
Re: Electromotive force
Electromotive force refers to the potential difference between the two electrodes in a cell. As the cell goes to equilibrium, the E goes to zero.
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2020-05-26 13:17:01
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http://math.stackexchange.com/questions/211880/reducing-invertible-matrix-in-an-equation-of-matrix?answertab=active
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reducing invertible matrix in an equation of matrix
Assume that $A^\mathrm{T}A$ is invertible and that $A$ is $3\times 3$, $B$ is $3\times 1$, $\alpha$ is $3\times 1$. How does the expression above reduce?
just to $A^\mathrm{T}B$ ?
-
The information you've given is contradictory: $A$ cannot be both invertible and non-square. – Hurkyl Oct 12 '12 at 22:41
A $\,3\times 1\,$ matrix (or vector, as you wish to look at it) – DonAntonio Oct 12 '12 at 22:42
@Hurkyl We can, however, assume that the $3\times 3$ matrix $A^TA$ is invertible (which is what we're inverting anyways). Unless I've forgotten some important theorem. – Arthur Oct 12 '12 at 22:47
If $A$ is rectangular, it doesn't reduce further. – Ganesh Oct 12 '12 at 22:50
hmm you guys are right, that makes no sense. If we assume that ATA is invertible, then what does this reduce to? – mugetsu Oct 12 '12 at 23:13
If $A$ is square and $A^tA$ is invertible then of course $A$ is invertible, and your expression simplifies to $A^{-1}B$.
-
could you explain the steps for me? thanks – mugetsu Oct 14 '12 at 3:25
You know that $(XY)^{-1}=Y^{-1}X^{-1}$? Apply that to $(A^tA)^{-1}$. – Gerry Myerson Oct 14 '12 at 4:18
The expression itself does not reduce (though there are more complicated methods that are efficient at solving it). I believe your equation may be based on the desire to solve $$A\vec{\alpha}=B$$ given $A$ and $B$, with $A$ underdetermined, meaning it has fewer columns than rows, which is consistent with your problem statement of $5$ rows and $3$ columns for $A$. This equation has no exact solution, thus the next best thing is sought.
As there is no exact solution, consider that a solution that is the "closest" of all possible. With the notion of "close" as the Euclidean distance, it becomes what is called a Least Squares equation. To give you the very abbreviated version of Least Squares, left multiply both sides of the equation to get $$A^TA\vec{\alpha}=A^TB$$ If you are not yet familiar with Least Squares, for now know that the reason for this is to have something invertible to work with ($A^TA$ will have an inverse) and to keep things in terms of the range of $A$. Thus, to solve it, again left multiply both sides of the equation to get $$(A^TA)^{-1}A^TA\vec{\alpha}=(A^TA)^{-1}A^TB$$ which reduces to $$\vec{\alpha}=(A^TA)^{-1}A^TB$$
This equation then has a solution, and it can be shown to be the closest solution of $\vec{\alpha}$ to the original equation $A\vec{\alpha}=B$
Back again to your original question if it is reduceable; the answer is no-- though there are ways of going about solving this without calculating every middle step as I have shown here, and that would take quite a bit more explaining than I have done thus far.
-
thanks for the help. I think i misinterpreted the problem and now I'm going with A as a 3x3 matrix – mugetsu Oct 13 '12 at 0:08
The only way for the equation to reduce is if $A$ actually is invertible, then it would reduce to $\alpha=A^{-1}B$ – adam W Oct 13 '12 at 0:29
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2015-01-31 00:03:32
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https://www.maplesoft.com/support/help/MapleSim/view.aspx?path=DocumentTools%2FAddPaletteEntry
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DocumentTools
Parameters
entry - string ; the name of the task to add to the custom Snippets palette palette_name - string ; the name of the Snippets palette that entry will be added to icon_name - (optional) string ; the name of the icon to associate with entry
Description
• The AddPaletteEntry command adds a task to a Snippets palette. If the palette does not already exist, it will be created using the default option values. See DocumentTools[AddPalette] for information on creating a Snippets palette.
• The task added to the palette must first be created and saved as a Task Template.
• If the optional icon=icon_name parameter is not provided, a default text icon is used. See DocumentTools[AddIcon] for information on how to create icons for this purpose.
• After the task is added to a palette, the associated task template can be inserted into a worksheet by clicking its icon in the palette.
• To remove an entry from a palette, use DocumentTools[RemovePaletteEntry].
Examples
> $\mathrm{with}\left(\mathrm{DocumentTools}\right):$
The palette entry in this first example will have a "text" icon with the name "Task_1". If the palette "My first palette" does not exist, it will be created and added to the top of the palette dock.
> $\mathrm{AddPaletteEntry}\left("Task_1",\mathrm{palette}="My first palette"\right)$
For the next example, we first create a palette and store an icon for the task, and then add the task with its icon to the palette.
> $\mathrm{AddPalette}\left("My second palette",\mathrm{position}="bottom"\right)$
> $\mathrm{AddIcon}\left("Task 2 icon",\mathrm{path}="/where/the/icon/file/is.png"\right)$
> $\mathrm{AddPaletteEntry}\left("Task_2",\mathrm{palette}="My second palette",\mathrm{icon}="Task 2 icon"\right)$
Compatibility
• The DocumentTools[AddPaletteEntry] command was introduced in Maple 16.
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2022-07-01 09:03:11
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https://www.isa-afp.org/entries/Simplicial_complexes_and_boolean_functions.html
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# Simplicial Complexes and Boolean functions
Title: Simplicial Complexes and Boolean functions Authors: Jesús Aransay, Alejandro del Campo (alejandro /dot/ del-campo /at/ alum /dot/ unirioja /dot/ es) and Julius Michaelis Submission date: 2021-11-29 Abstract: In this work we formalise the isomorphism between simplicial complexes of dimension $n$ and monotone Boolean functions in $n$ variables, mainly following the definitions and results as introduced by N. A. Scoville. We also take advantage of the AFP representation of ROBDD (Reduced Ordered Binary Decision Diagrams) to compute the ROBDD representation of a given simplicial complex (by means of the isomorphism to Boolean functions). Some examples of simplicial complexes and associated Boolean functions are also presented. BibTeX: @article{Simplicial_complexes_and_boolean_functions-AFP, author = {Jesús Aransay and Alejandro del Campo and Julius Michaelis}, title = {Simplicial Complexes and Boolean functions}, journal = {Archive of Formal Proofs}, month = nov, year = 2021, note = {\url{https://isa-afp.org/entries/Simplicial_complexes_and_boolean_functions.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Jordan_Normal_Form, ROBDD
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2022-01-23 15:52:21
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https://www.physicsforums.com/threads/showing-that-a-given-metric-is-riemannian.576951/
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# Homework Help: Showing that a given metric is Riemannian
1. Feb 12, 2012
### demonelite123
So I have the hyperboloid in $\mathbb{R}^3$ given by $x^2 + y^2 - z^2 = -1$. I define the scalar product of 2 tangent vectors (a1, b1, c1) and (a2, b2, c2) at a point as a1a2 + b1b2 - c1c2.
I want to show that this defines a Riemannian metric on the hyperboloid. I know that a Riemannian metric must be linear, symmetric, and positive definite. Linearity and symmetry I have checked easily but I am confused on the positive definite portion. The problem tells me to show that it is a Riemannian metric but it seems like it does not satisfy the positive definite requirement. The matrix associated with $a_1^2 + b_1^2 - c_1^2$ is just the 3x3 identity matrix with the (3, 3) entry being -1 instead of 1. Thus, the eigenvalues of this matrix are 1, 1, and -1 so it seems to me that this is actually indefinite since the eigenvalues are not all the same sign.
Am I correct in saying this or is there something I am missing? thanks!
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2018-05-21 13:18:15
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https://www.gradesaver.com/textbooks/math/other-math/thinking-mathematically-6th-edition/chapter-2-set-theory-2-1-basic-set-concepts-exercise-set-2-1-page-59/112
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# Chapter 2 - Set Theory - 2.1 Basic Set Concepts - Exercise Set 2.1: 112
{New Zealand}
#### Work Step by Step
{x|x is a country in which the percentage having used marijuana $\geq$ 22.2%} In the graph there is one country in which the percentage having used marijuana $\geq$ 22.2% is New Zealand New Zealand = 22.2% therefore the answer = {New Zealand}
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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2018-06-23 16:27:56
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http://golem.ph.utexas.edu/category/2007/03/poissonsigma_models_lie_algebr.html
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## March 16, 2007
### Poisson-Sigma Models, Lie Algebroids, Deformations and Higher Analogues in Vienna
#### Posted by Urs Schreiber
This summer the Erwin-Schrödinger Institute in Vienna hosts a program
Poisson Sigma Models, Lie Algebroids, Deformations and Higher Analogues
Organizers: H. Bursztyn, H. Grosse and T. Strobl
August 1 to September 30, 2007
There seems to be no web page with further details yet.
The list of topics in the title are related to the stuff I was blogging about almost two years ago on the String Coffee Table:
I will spend a period of two weeks in the time Aug 1 to Sept 30 in Vienna, still having to decide which two weeks exactly. If any other $n$-Café-reader will be there, too, we could maybe coordinate our visits. Just drop me an email, if so.
The ESI is a great place to stay. With blackboards even in the bathrooms. I was there once, last year, and blogged about it here:
Posted at March 16, 2007 6:22 PM UTC
TrackBack URL for this Entry: http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/1207
### Re: Poisson-Sigma Models, Lie Algebroids, Deformations and Higher Analogues in Vienna
I’ve been invited to speak at this get-together, so it would be nice to see you there. I haven’t worked out my schedule yet. I definitely can’t come before August 9th, and Bob Coecke has invited me to speak on categorical quantum logic from the 10th to the 12th, which seems awfully tempting. Then I’m free ‘til September 10th, when I’m visiting Sheffield for the British Topology Meeting — and thus Bruce Bartlett, and Eugenia Cheng!
So, there’s an interval August 12 - September 10 when I can do whatever I want, modulo the fact that I’m married. This means Lisa and I will mainly reside in Greenwich, England, where we’ll be housesitting for a friend. But, I’d like to visit the ESI for a portion of that interval.
(Of course “modulo” is the wrong word, since my motion is constrained to a subspace, not a quotient space. But, mathematicians think it’s cool to say “modulo”.)
Posted by: John Baez on March 16, 2007 8:19 PM | Permalink | Reply to this
### Re: Poisson-Sigma Models, Lie Algebroids, Deformations and Higher Analogues in Vienna
So, there’s an interval August 12 - September 10 when I can do whatever I want
Thanks for letting me know! I’ll keep this time window in mind. Would very much enjoy seeing you in a more relaxed time frame than last time.
Posted by: urs on March 19, 2007 1:45 PM | Permalink | Reply to this
### Re: Poisson-Sigma Models, Lie Algebroids, Deformations and Higher Analogues in Vienna
I have now made my hotel reservation. I’ll be in Vienna
August 13th to August 26th, 2007 .
I am staying in “Pension Ani” (if I understood the ESI secretary correctly, that is…)
Posted by: urs on May 11, 2007 12:13 PM | Permalink | Reply to this
### Re: Poisson-Sigma Models, Lie Algebroids, Deformations and Higher Analogues in Vienna
I’m attempting to get a room at ‘Pension Ani’ from Saturday August 18th to Sunday August 26th. I’ll try to let you know if this works — I’m writing this now just in case I forget to tell you later!
I look forward to being more relaxed than I was when I saw you at the Fields Institute! You can never have much fun when you’re the host of the party.
Posted by: John Baez on May 14, 2007 6:39 PM | Permalink | Reply to this
### Re: Poisson-Sigma Models, Lie Algebroids, Deformations and Higher Analogues in Vienna
Now there is a web-page for this event.
Posted by: urs on May 4, 2007 4:47 PM | Permalink | Reply to this
### Re: Poisson-Sigma Models, Lie Algebroids, Deformations and Higher Analogues in Vienna
Here is the list of seminar talks, all taking place in the ESI Schrödinger lecture hall.
U. S. (Hamburg)
String and Chern-Simons Lie 3-Algebras, 2007 08 14, 09:30
Calin-I. Lazaroiu (Trinity College)
Open topological string theories, 2007 08 14, 11:00
Open topological string theories II, 2007 08 16, 09:30
Alexei Kotov (University of Luxembourg)
Dirac geometry and Dirac sigma models, 2007 08 15, 11:00
Dirac geometry and Dirac sigma models II, 2007 08 16, 11:00
Jae-Suk Park (Korea Institute for Advanced Studies)
Classical and quantum aspects of BV quantization, 2007 08 15, 09:30
Classical and quantum aspects of BV quantization II, 2007 08 17, 09:30
Hans-Christian Herbig (Goethe-Universität Frankfurt)
Deformation quantization of singular symplectic quotients, 2007 08 15, 16:30
Daniel Grumiller (TU-Wien)
Poisson-sigma model for two-dimensional gravity with non-metricity, 2007 08 17, 11:00
Martin Bojowald (Penn State University)
Toward a loop quantization of Poisson Sigma Models 2007 08 17, 16:30
Posted by: Urs Schreiber on August 9, 2007 2:21 PM | Permalink | Reply to this
Read the post String and Chern-Simons Lie 3-Algebras
Weblog: The n-Category Café
Excerpt: A talk on Chern-Simons Lie n-algebras.
Tracked: August 10, 2007 6:19 PM
Read the post On BV Quantization. Part I.
Weblog: The n-Category Café
Excerpt: On BV-formalism applied to Chern-Simons theory and its apparent relation to 3-functorial extentended QFT.
Tracked: August 17, 2007 10:06 PM
Read the post More on Tangent Categories
Weblog: The n-Category Café
Excerpt: More comments on the nature of tangent categories and their relation to the notion of shifted tangent bundles to differential graded spaces.
Tracked: August 21, 2007 10:47 AM
Read the post That Shift in Dimension
Weblog: The n-Category Café
Excerpt: What makes the Kontsevich-Cattaneo-Felder theorem tick? How can it be that an n-dimensional quantum field theory is encoded in an (n+1)-dimensional one?
Tracked: August 25, 2007 2:33 AM
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2014-08-23 01:34:45
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http://www.lastfm.es/user/tdiamond8/library/music/Ned's+Atomic+Dustbin/_/All+I+Ask+Of+Myself+Is+That+I+Hold+Together?from=1305175909&to=1336798309&rangetype=year&setlang=es
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# Colección
Música » Ned's Atomic Dustbin »
## All I Ask Of Myself Is That I Hold Together
10 scrobblings | Ir a la página del tema
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All I Ask Of Myself Is That I Hold Together 3:06 18 Nov 2011, 14:58
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All I Ask Of Myself Is That I Hold Together 3:06 9 Ago 2011, 15:06
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All I Ask Of Myself Is That I Hold Together 3:06 28 Jun 2011, 15:49
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2014-09-18 10:16:11
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http://mail-archives.apache.org/mod_mbox/db-derby-dev/200703.mbox/%3C20070312195204.GF3557@trapper.coreless.net%3E
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# db-derby-dev mailing list archives
##### Site index · List index
Message view
Top
From Anders Morken <ander...@stud.ntnu.no>
Subject Re: Commit problems after upgrading svn
Date Mon, 12 Mar 2007 19:52:05 GMT
Laura Stewart:
> I opened a cygwin window, applied a patch, and ran svn status. It worked.
> Since there was a new file added by the patch, I performed svn add.
> Then when I tried to run svn status again, I got this message:
>
> \$ svn stat
> svn: This client is too old to work with working copy 'src\ref';
>
> Does it mean for me to upgrade cygwin client?
Yes, Subversion changed their working copy format between 1.3 and 1.4,
so if you've touched your working copy with a 1.4 client (such as the
TortoiseSVN you mention) you'll have to use 1.4+ to work with it.
> How do I do that?
Here's an announcement from the cygwin project regarding an updated
package being available for cygwin, so you should be home free if you
can run the cygwin installer/updater:
http://cygwin.com/ml/cygwin-announce/2006-12/msg00004.html
http://cygwin.com/packages/subversion/
On the front page they link to http://cygwin.com/setup.exe with the text
"Install or update now!", so I figure that one's what you want. I'm not
using cygwin myself, so no guarantees. But good luck. =)
--
Anders Morken
My opinions may have changed, but not the fact that I am right!
Mime
View raw message
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2017-04-30 01:48:34
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https://electronics.stackexchange.com/tags/noise/new
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# Tag Info
## New answers tagged noise
1 vote
### GNU radio FRS transceiver
Your antenna requires a ground plane to be effective. It's a magnetic mount (magmount) antenna, that is to be placed on a metallic plate having a minimum diameter of 300 mm (the larger the better). ...
• 11.1k
Accepted
### 500 mV p-p noise in two stage photodiode amplifier output
I would start by looking in this direction: - Your power supply noise is less than 3 decades above your power supply filter cut-off point i.e. 160 Hz --> 1.6 kHz --> 16 kHz --> 160 kHz. This ...
• 389k
1 vote
### How to mitigate noise from DC-DC converter used for reverse biasing diode?
Your scope might be picking up inductive pulses from the regulator, especially in its ground lead. Try moving your probe away from the regulator, even to the opposite side of the board. You can ...
• 40.9k
1 vote
### Why does touching LEDs' ground terminal light them dimly?
Case 1: The LEDs don't light up since the applied DC voltage, for three of them in series, is as low as or even lower than the forward voltage of one of them. Case 2: The LEDs light up dimly on ...
• 11.1k
1 vote
### Why does touching LEDs' ground terminal light them dimly?
First of all, 3 leds connected in series adds up to about 9.9 volts. Three volt power supply would work if leds are connected in parallel, if the supply carries enouph current. The leds lighting up ...
### Why am I getting such widely ranging values from this TMP36 in this circuit?
https://github.com/Joe0x7F/TMP36 The TMP36 is a terribly unstable device. Try a MCP9701A or a LMT87.
1 vote
### ESP32 restarting when relay is turned on
I think it is unlikely that you are actually getting those high voltage transients on the 3.3 V logic rail, or you would be seeing damage to those components. More likely the transients form the AC ...
• 956
1 vote
### ESP32 restarting when relay is turned on
You can check the reset reason of the ESP32 through esp_reset_reason() If it's "brownout detector" you know the spikes are the cause and you need better ...
• 205
### How to eliminate the noise of this circuit?
EMG is easiest done with active electrodes, with effective electrode wire lengths approximately zero. The signal amplitude is lower than EKG's - in fact, EKG is a cumbersome common-mode artifact in ...
### How to find noise sources from noise figure data?
I think that the frequency is not necessary here. It might indicate that we are dealing with noise above the 1/f flicker noise regime. Accordingly, the white noise (thermal noise), can be described ...
• 395
Accepted
### What is the dimension of Attenuation in the LC-EMI filter design formula?
The computed attenuation $Att_{LC}$ is probably in linear units. That is, the input signal is 1878 times the output signal, or a gain of 0.532m. I much prefer working in gain rather than attenuation,...
• 144k
Accepted
### DM and CM EMI emissions measurement in LTspice
Both of the terms for CM and DM noise need to be divided by two. In the picture below you can see how CM and DM currents are flowing and how they can be separated. Source: AnalogDialogue article
• 1,653
1 vote
### Reduce noise on 2m I2C bus using motorcycle power
As suggested by others, the right way to do it would be to choose a more robust protocol and shielded cables. However, if for any reason you have to use the I2C protocol and the shielding is not ...
• 326
Accepted
### How to have a wider spectrum of FFT at LTspice?
If you're doing an AC analysis in LT spice then you need to change the max sweep frequency in the .AC statement. If you're doing a .trans analysis and converting it with the fft later then you need to ...
• 64.4k
1 vote
Accepted
### How to calculate RMS noise from datasheet?
EE&O ... How to calculate RMS noise from datasheet? S/N ratio is just defined for 1 frequency $Fmclk=25 MHz$ and $Fout=Fmclk/4096$. But I would not consider it is a "normal" s/n ...
• 6,031
1 vote
Accepted
### Mixer noise calculation
A mixer doesn't necessarily generate noise. However, there are several ways in which in it can degrade the noise of a system. Via signal attenuation. If the mixer drops the signal level 6 or 7 dB, ...
• 144k
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2022-08-15 18:59:40
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https://www.avenue-sm.ru/how-to-solve-a-pythagorean-theorem-problem-16027.html
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# How To Solve A Pythagorean Theorem Problem
Remember though, that you could use any variables to represent these lengths.
Remember though, that you could use any variables to represent these lengths.
Tags: Problem Solving PicturesLogistics Business Plan SampleRural Poverty In America EssayRhetorical Essays On Food IncStatement Writing For CourtAir Pollution English Essay
This is common unless you are working on an applied problem.
There are many different kinds of real-life problems that can be solved using the Pythagorean theorem.
You can still use the Pythagorean theorem in these types of problems, but you will need to be careful about the order you use the values in the formula. The side opposite the right angle has a length of 12.
Therefore, we will write: $$8^2 y^2 = 12^2$$ This is the same as: $$64 y^2 = 144$$ Subtracting 64 from both sides: $$y^2 = 80$$ Therefore: $$\beginy &= \sqrt \\ &= \sqrt \\ &= \bbox[border: 1px solid black; padding: 2px]\end$$ In this last example, we left the answer in exact form instead of finding a decimal approximation.
After one hour, the hiker walking south has covered 2.8 miles and the hiker walking west has covered 3.1 miles.
At that moment, what is the shortest distance between the two hikers? Label any unknown value with a variable name, like x.
This is something that you will not need to do in every course, but it does come up.
A right triangle has a hypotenuse of length $$2x$$, a leg of length $$x$$, and a leg of length y.
But, the length of any side of a triangle can never be negative and therefore we only consider the positive square root.
In other situations, you will be trying to find the length of one of the legs of a right triangle.
## Comments How To Solve A Pythagorean Theorem Problem
• ###### Pythagorean Theorem Calculator
Pythagorean Theorem calculator, formula, work with steps, step by step calculation, real world and practice problems to learn how to find any unknown side length of a right triangle.…
• ###### Pythagoras Theorem - Math Is Fun
It is called "Pythagoras' Theorem" and can be written in one short equation a 2 + b 2 = c 2. Note c is the longest side of the triangle; a and b are the other two sides ; Definition. The longest side of the triangle is called the "hypotenuse", so the formal definition is…
• ###### Pythagorean theorem intro problems article
Pythagorean theorem intro problems. CCSS Math 8. G. B.7. Practice using the Pythagorean theorem to solve for missing side lengths on right triangles. Each question is slightly more challenging than the previous. Practice using the Pythagorean theorem to solve for missing side lengths on right triangles. Each question is slightly more.…
• ###### How to solve a pythagorean theorem problem
How to solve a pythagorean theorem problem. Asherman’s Syndrome All you need to know. Surrogacy can make your dream of child come true. Asherman’s Syndrome It’s possible to get pregnant after treatment. Ways to start an argumentative essay spatial problem solving with cuisenaire rods tangram-type problems.…
• ###### Word problems on Pythagorean Theorem
Learn how to solve different types of word problems on Pythagorean Theorem. Pythagoras Theorem can be used to solve the problems step-by-step when we know the length of two sides of a right angled triangle and we need to get the length of the third side.…
• ###### Pythagorean theorem word problems - Basic
Pythagorean theorem word problems. Pythagorean problem # 2 A 13 feet ladder is placed 5 feet away from a wall. The distance from the ground straight up to the top of the wall is 13 feet Will the ladder the top of the wall. If you can solve these problems with no help, you must be a genius! Recommended Scientific Notation Quiz Graphing.…
• ###### Use Pythagorean theorem to find right triangle
Find the length of the hypotenuse or a leg of a right triangle using the Pythagorean theorem. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.and *.are unblocked.…
• ###### Uses of Pythagoras's Theorem in Real Life
You may have heard about Pythagoras's theorem or the Pythagorean Theorem in your math class, but what you may fail to realize is that Pythagoras's theorem is used often in real life situations. Gain a better understanding of the concept with these real-world examples.…
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2021-08-01 06:31:27
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https://www.zbmath.org/?q=ra%3Atorres-falcon.yolanda+ai%3Aspadaro.santi
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# zbMATH — the first resource for mathematics
A short proof of a theorem of Juhász. (English) Zbl 1229.54004
If $$X$$ is a topological space, then $$t(X)$$, (respectively, $$\psi(X)$$, $$L(X))$$ denotes the tightness (respectively, pseudocharacter, Lindelöf number) of $$X$$. The cardinal function $$F(X)$$ is defined to be the supremum of the lengths of free sequences in $$X$$. A theorem originally proved by B. Shapirovskii [Sov. Math., Dokl. 13, 215–219 (1972); translation from Dokl. Akad. Nauk SSSR 202, 779–782 (1972; Zbl 0252.54002)] states that if $$X$$ is Hausdorff, then $$|X|\leq 2^{\psi(X)\cdot t(X)\cdot L(X)}$$. A generalization by I. Juhász appeared in his book [Cardinal Functions in Topology – ten years later. Mathematical Centre Tracts 123. Amsterdam: Mathematisch Centrum. IV (1980; Zbl 0479.54001)], to the effect that if $$\{X_\alpha:\alpha<\lambda\}$$ is a nested family of subsets of $$X$$ whose union is $$X$$ and $$t(X_\alpha)\cdot\psi(X_\alpha)\cdot L(X_\alpha)\leq\kappa$$, then $$|X|\leq 2^\kappa$$. The present paper gives a one page proof of this last theorem using elementary submodels and which also shows that $$|X|\leq 2^{\psi(X)\cdot F(X)\cdot L(X)}$$.
##### MSC:
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
Full Text:
##### References:
[1] Arhangelʼskii, A., The power of bicompacta with first axiom of countability, Soviet math. dokl., 10, 951-955, (1969) · Zbl 0191.20903 [2] Dow, A., An introduction to applications of elementary submodels to topology, Topology proc., 13, 1, 17-72, (1988) · Zbl 0696.03024 [3] Engelking, R., General topology, Sigma ser. pure math., vol. 6, (1989), Heldermann Verlag Berlin · Zbl 0684.54001 [4] Hajnal, A.; Juhász, I., Having a small weight is determined by the small subspaces, Proc. amer. math. soc., 79, 4, 657-658, (1980) · Zbl 0432.54003 [5] Hodel, R.; Vaughan, J., Reflection theorems for cardinal functions, Topology appl., 100, 1, 47-66, (2000), Special issue in honor of Howard H. Wicke · Zbl 0943.54003 [6] Juhász, I., Cardinal function in topology - ten years later, Math. centre tracts, vol. 123, (1980), Mathematisch Centrum Amsterdam · Zbl 0479.54001 [7] I. Juhász, Private communication. [8] Juhász, I.; Szentmiklóssy, Z., Increasing strengthenings of cardinal function inequalities, Fund. math., 126, 3, 209-216, (1986) · Zbl 0614.54004 [9] Shapirovskii, B., On discrete subspaces of topological spaces; weight, tightness and Suslin number, Soviet math. dokl., 13, 215-219, (1972) · Zbl 0252.54002 [10] S. Spadaro, Discrete sets, free sequences and cardinal properties of topological spaces, Doctoral dissertation, Auburn University, 2009. [11] Tkachenko, M.G., Chains and cardinals, Soviet math. dokl., 19, 2, 382-385, (1978) · Zbl 0404.54002 [12] Tkachenko, M.G., The behavior of cardinal invariants under the union operation for a chain of spaces, Moscow univ. math. bull., 33, 4, 39-46, (1978) · Zbl 0416.54003 [13] Tkachenko, M.G., Sum theorems for the tightness and π-character in the class of compact spaces, Comment. math. univ. carolin., 24, 1, 51-62, (1983) · Zbl 0523.54003 [14] Tkachenko, M.G.; Torres Falcón, Y., Unions of chains in dyadic compact spaces and topological groups, Proceedings of the first joint Japan-Mexico meeting in topology, Morelia, 1999, Topology appl., 121, 1-2, 25-32, (2002) · Zbl 1009.54007 [15] Torres Falcón, Y., Unions of chains of subgroups of a topological group, Appl. gen. topol., 2, 2, 227-235, (2001) · Zbl 1018.54004
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.
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2021-09-26 11:01:35
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https://tex.stackexchange.com/questions/200326/how-to-compile-a-tex-file-so-that-some-portion-can-be-optionally-not-compiled
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# How to compile a tex file so that some portion can be optionally not compiled?
In C, we can write something for some part of the code, and give gcc some option for whether we would like to compile that part of code. It saves us from modifying the C code.
In LaTex, is there a similar way for pdflatex?
Thanks.
• Many editors support commenting code by shortcuts. This could be handy. Or you move the line \end{document} to your desired last line. Or you search this side for conditionals, define some rule debugtrue, debugfalse and start your code-blocks with \ifdebug. – LaRiFaRi Sep 9 '14 at 14:29
• Thanks, do you know the examples for the last method? Alternatively, can we choose to or not to compile a portion of code by specifying only to pdflatex without touching the code again? – Tim Sep 9 '14 at 14:33
• see for example tex.stackexchange.com/questions/47576/… – David Carlisle Sep 9 '14 at 14:39
1. Move your \end{document} up to the place where you want to stop compiling
2. Comment out the block of code, you do not want to compile (the editors do have shortcuts for this)
3. Define conditionals in order to block parts for whatever you need:
% arara: pdflatex
\newif\ifdebug
\documentclass{article}
\debugtrue
%\debugfalse
\begin{document}
\ifdebug
Debug is set to true
\else
Debug is set to false
\fi
\end{document}
In order to check for the possible use of PDFLaTeX or others, you should have a look on the packages ifpdf, ifluatex, ifxetex which define such conditionals for you. The command would read \ifpdf ... \else ... \fi and respectively for the others.
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2019-09-22 12:16:50
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http://kyco.hagen-wiedemann.de/physics-classroom-waves-interference-concept-builder.html
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# Physics Classroom Waves Interference Concept Builder
Resonance and the Sounds of Music Decibel Concept Builder 3. Physics was known as natural philosophy until the late 18th century. Use the Escape key on a keyboard (or comparable method) to exit from full-screen mode. Get important questions of Wave for Board exams. There are 10 different situations to analyze and three Activities. Young was the English physicist who first did an. Color Vision. In equation form, intensity is. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. If you're thinking in terms of particles, it means a particle can be in two places at once. Start learning today with flashcards, games and learning tools — all for free. Refine this search by either clicking on the terms in boxes to the right or typing a. All image, videos, documents, and resources are used for educational purposes. Since waves are spread out in space and time, energy density is often a more useful concept than energy. Is a Teaching Guide For Physics Classroom: Waves and Wavelike. Download Hecht E. Student questions: Adding waves graphically (30 minutes) Discussion: Recapping wave ideas. As most commonly used, the term interference usually refers to the interaction of waves which are correlated or coherent with each other, either because they come from the same source. Students explore wave reflection, patterns from interfering waves, and the Doppler Effect. Physics in Motion is a new digital series for high school physics from Georgia Public Broadcasting. Others are qualitative, such as performing flame tests, examining the interference of light waves, comparing metals to nonmetals, exploring Boyle's Law, doing litmus tests, and electroplating. In this video I will show you how to develop the interference of waves equation traveling Skip navigation Sign in. This interactive tutorial is an excellent introduction to the wave nature of light. My notes are verbatim from the lecture. As the sound wave propagates, it creates a wave front that fills the surface area of an ever-expanding sphere. Circuit Builder Circuits. Sound Waves Welcome, this is a learning resource for AS and A Level wave and sound physics. the first activity - wave anatomy - provides the learner practice with identifying crests and troughs in a transverse wave pattern and compressions and rarefactions in a longitudinal wave pattern. 21 videos Play all PHYSICS 19 MECHANICAL WAVES Michel van. The following are key concepts/big ideas in physics: The universe is made of matter and energy. Our many rooms of physics demos, accumulated over the past century, display subtle physics concepts ranging from electromagnetism, to kinematics, to optics. With an animation button, they can start and stop the motion of the waves. Interference & the Principle of Superposition When two waves interact, the principle of superposition says that the resulting wave function is the sum of the two individual wave functions. Let me explain. In this text, we shall explore such periodic sound waves. Diffraction reveals the geometry of the diffracting object. Periodic Motion, Waves & Sound for Physics 101 | Brainscape. This item is part of The Physics Classroom, a web-based collection of tutorials for high school physics students. there are three activities included in this concept builder. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Meaning of cohérence. Download or View 11th Physics important questions for exam point of view. If you've been to a large gig or a festival in recent years, you've no doubt had the pleasure of hearing line arrays of loudspeakers in action. Analyze the motion of particles in a medium in the presence of transverse and longitudinal waves. Study Periodic Motion, Waves & Sound flashcards from 's class online, or in Brainscape's iPhone or Android app. Choose from 500 different sets of physics flashcards on Quizlet. 3(b) is our first example of a free-body diagram, which is a technique used to illustrate all the external forces acting on a body. Physics mathematical skills handbook H156 H157 H556 H557 - This mathematical skills handbook is designed to accompany the AS and A Level specifications in Physics A and Physics B (Advancing Physics) for teaching from September 2015. On the atomic scale, it is a disturbance of atoms that is far more ordered than their thermal motions. Title Wave demonstrations: water, sound, light (Inquiry Based) Description These are all the clicker questions from my wave activities in one file. The illustration above explores constructive and destructive wave interference between two waves moving in opposite directions. Interference refers to the superposing of two or more coherent waves to produce regions of maxima and minima in space, according to the principle of superposition. Estimate the order of magnitude of a physical quantity. 12 - Data-Based and Statistical Reasoning - 9 cards Physics Ch. There is a small hot spot in the top-left corner. The effect is that of the addition of the amplitudes of the individual waves at each point affected by more than one wave. Imenda University of Zululand, South Africa ABSTRACT Many researchers have reported the incidence and prevalence of alternative. This is consistent with the fact that light must interact with an object comparable in size to its wavelength in order to exhibit significant wave effects such as this single slit diffraction pattern. Sound Waves and Music. You can use a whiteboard or your own paper. Student questions: Adding waves graphically (30 minutes) Discussion: Recapping wave ideas. Classroom Management Strategies To Take Control Of Noisy Students Wave Interference 1 of 2 | Doc Physics - Duration: Thin Film Interference - The Art of Physics (with POV Ray. Students build on basic physical science principles by exploring in-depth the nature and characteristics of energy and its dynamic interaction with matter. Materials: •. We serve Denver and all suburbs. This interactive lab allows you to hear and experiment with the beat frequency created by the interference of two waves. there are three activities included in this concept builder. The energy however is passed along the water from one wave to the other. July 1, 2006 CODE OF FEDERAL REGULATIONS 33 Parts 125 to 199 Revised as of July 1, 2006 Navigation and Navigable Waters Containing a codification of documents of general applicability and future effect As of July 1, 2006 With Ancillaries. Holt Physics Section Reviews This workbook consists of review and reinforcement activities that focus on key skills or concepts from a section of the Holt Physicstext. , beats, standing waves, interference patterns). Light Waves and Color The behavior of light waves is introduced and discussed; polarization, color, diffraction and interference are introduced as supporting evidence of the wave nature of light. Interference is such a fundamental aspect of waves that observing interference is proof that something is a wave. 1 Section 3 Wave Interactions - reflection, refraction, diffraction, interference, standing wave Learn with flashcards, games, and more — for free. Waves have been of interest to philosophers and scientists alike for thousands of years. Like all electromagnetic waves, light can travel through a vacuum. Questions in the same group are rather similar to one another. The interference that occurs when two waves. Physics in Motion is a new digital series for high school physics from Georgia Public Broadcasting. When two or more sound waves from different sources are present at the same time, they interact with each other to produce a new wave. Constructive and destructive interference result from the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. There is a small hot spot in the top-left corner. Complete solutions are available for all practice problems. Find out more about the BSc (Hons) BSc (Hons) Physics course within the School of Physics, Astronomy and Mathematics at the University of Hertfordshire. (Here action and reaction refer to forces. The questions are all fill-in the-blank. Wherever light goes, the electric and magnetic fields are disturbed perpendicular to the direction of propagation. Certified, hand-picked Physics tutors in Aurora, CO. Velocity and force vectors are shown. Finally, we will explore what happens when two or more waves share the same space, in the phenomena known as superposition and interference. Know what students know, teach what students need. The turning back of a wave at a boundary of a new medium is called. In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena. Mr Sultana is an architect have questions ready. Diffraction. And we can count which order we're at, so this is a quick way to figure out if you had something with two holes in it you could figure out how close they're separated even if you don't have a ruler that small, it's a quick way. The Sound and Waves investigations open up fascinating questions for hands-on explorations that are guaranteed to grab your students' attention. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. The body is represented by a single isolated point (or free body), and only those forces acting on the body from the outside (external forces) are shown. com, 1-800-501-9571. The Physics Hypertextbook is a reaction to the three big problems with textbooks: lack of writer's voice, layouts that reduce readability, and outdated economics. You've got a barrier with two holes in it, but these holes are so small and so close together we characterize them as slits, and double because there's two of them. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. These important questions will play significant role in clearing concepts of Physics. Make waves with a dripping faucet, audio speaker, or laser! Add a second source to create an interference pattern. Physics World represents a key part of IOP Publishing's mission to communicate world-class research and innovation to the widest possible audience. Diffraction manifests itself in the apparent bending of waves around small obstacles and the spreading out of waves past small openings. This 12 question worksheet with teacher answer key provides a way for students to follow along with the Bill Nye Waves DVD. Items in the group's pool include diagrams of diffraction and two-point source interference patterns and photos of ripple tank experiments, interference patterns on still water, and much more. Overview: This section introduces the properties of waves and wave motion. Standing wave, combination of two waves moving in opposite directions, each having the same amplitude and frequency. Spatial and Temporal coherence. Light is a transverse, electromagnetic wave that can be seen by the typical human. Marek Slipksi of RIT originally created this document to aid physics students in high school. Circuit Builder Circuits. Download Hecht E. Schaum’s Outline of College Physics 12ed 2018 torrent or any other torrent from Other > E-books Direct download via magnet link. Article by:Ouma George,Awel Eshetu and Bassein Natalia. This worksheet is intended to accompany the Wave Properties PowerPoint (Wave Properties. The Concept Builder is coded to select at random a question from each group until a student is successful. Interference, diffraction, and the principle of superposition are important concepts for understanding several applications of waves. Force and Motion Concept Builder The Force and Motion Concept Builder is a tool that challenges the learner to make the connection between balanced and unbalanced forces and the type of motion an object experiences. Download or View 11th Physics important questions for exam point of view. In this video I will show you how to develop the interference of waves equation traveling Skip navigation Sign in. ), refraction, resonance, phased arrays, and the Doppler effect. Constructive and destructive interference of light waves is also the reason why thin films, such as soap bubbles, show colorful patterns. Coetzee Tshwane University of Technology, South Africa S. image distance, size, and real vs. The Interference with Synchronous Sources model displays the interference pattern on a screen due to between one and twenty point sources. This item is part of The Physics Classroom, a web-based collection of tutorials for high school physics students. Spatial and Temporal coherence. wave interference wave pulse superposition So let's talk about wave interference this is what happens when waves collide. Refraction. Periodic Motion, Waves & Sound for Physics 101 | Brainscape. A sound wave (like any wave) is often referred to as an energy-transport phenomenon. Alternative conceptions held by first year physics students at a South African university of technology concerning interference and diffraction of waves A. Transverse waves consist of high parts or peaks called crests and low parts called troughs. Questions in the same group are rather similar to one another. The Physics Classroom » Physics Interactives » Vectors and Projectiles » The Monkey and the Zookeeper » The Monkey and the Zookeeper Notes Notes: The Monkey and the Zookeeper Interactive is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The questions are divided into 10 different Question Groups. His father, Charles Schuster Zane, had been active in Republican Party circles beginning in the late 1850s and had replaced Abraham Lincoln in the law firm of Lincoln and Herndon in March 1861, when Lincoln left Illinois to take the oath of office as. The goal however is a deeper understanding of the physics of waves and sound than. The front is always _____ to the direction the wave is traveling. Physics in Motion is a new digital series for high school physics from Georgia Public Broadcasting. 2015-06-03 – Wave Interference Worksheet /Homework due 4/12/18. The concept of energy wasn't invented until after he died. Your guide to physics on the web. Light is a transverse electromagnetic wave that can be seen by a typical human. Our understanding of the physical world is not complete until we understand the properties and behaviors of waves. Transverse waves consist of high parts or peaks called crests and low parts called troughs. projectile_motion_test_review. Diffraction. docx: File Size: 14. The Physics Classroom » Concept Builders » Newton's Laws » Balanced vs. Covers the physics of oscillations and wave phenomena, including driven oscillations and resonance, mechanical waves, sound waves, electromagnetic waves, standing waves, Doppler effect, polarization, wave reflection and transmission, interference, diffraction, geometric optics and optical instruments, wave properties of particles, particles in. Quantum Tunneling and Wave Packets: Quantum Wave Interference: Radiating Charge: Radioactive Dating Game: Radio Waves & Electromagnetic Fields: The Ramp: Ramp: Forces and Motion: Reactions & Rates: Resistance in a Wire: Resonance: Reversible Reactions: Rutherford Scattering: Semiconductors: Signal Circuit: Simplified MRI: Sound: States of. Interference and sound waves. The interference that occurs when two waves. Reflection and Refraction of Light Waves [Huygens' Principle] - This applet is a tutorial which explains the reflection and the refraction of waves by the principle of Huygens. The Physics Classroom » Concept Builders » Waves and Sound Waves and Sound A Concept-Builder is an interactive questioning module that presents learners with carefully crafted questions that target various aspects of a concept. Interference and Beats. Electric Field Hockey. Slinkies make sound because they vibrate when they stretch out. would make you all fall in love. The Physics Classroom » Minds On Physics the App » MOP the App Part 5 Minds On Physics the App - Part 5 The app version of the Minds On Physics program is currently available as six different apps with each app covering a different set of topics. Learn physics with free interactive flashcards. Some basic ideas about waves can be demonstrated using mechanical waves along strings or springs, ripples on water, or special wave machines. AP Physics 1 AP Physics Review Contact Big Ideas, Notes and Remediation The Physics Classroom Concept Builder. This is consistent with the fact that light must interact with an object comparable in size to its wavelength in order to exhibit significant wave effects such as this single slit diffraction pattern. Interference of waves from two point sources good Place the two point sources on top of each other and look at the result. When two or more sound waves from different sources are present at the same time, they interact with each other to produce a new wave. Unit Title: The Wave Nature of Light. MY PHYSICS LESSONS Over 30 years I teach Physics in a secondary school, out of which 20 last years I teach Regents Physics course in NYC public high school. This interactive lab allows you to hear and experiment with the beat frequency created by the interference of two waves. tomorrows second period physics class will have a guesst speaker be prepared with questions. The final basic course covering the laws of thermodynamics, reflection and refraction of light, interference and diffraction, radiation, atomic physics, waves and corpuscles, and nuclear physics. Constructive and destructive interference result from the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Quizlet makes simple learning tools that let you study anything. With that said, the approach here will be to understand music and musical instruments first, and to study the physics of waves and sound as needed to push the understanding of the music concepts. 11 - Reasoning About the Design and Execution of - 17 cards Physics Ch. In this diagram, the black wave shows the resulting wave from the interference between the red and blue waves. It demonstrates waves in two dimensions, including such wave phenomena as interference, diffraction (single slit, double slit, etc. 3: Conductors and insulators. Physical Sciences K-8: Wave Energy Units. Learn faster with spaced repetition. The effect is that of the addition of the amplitudes of the individual waves at each point affected by more than one wave. Waves are all around us in many forms and are important to just about every branch of physics. But why are line arrays the current 'best practice' in large-scale PA, how did they evolve, and will they ever filter down to more modest gig venues?. Interference is the name physicists use for this kind of combination of waves. However, the quiz at the end is very basic in these regards The Physics Classroom: What is a wave? - This page can provide. Suppose that your professor sets up two sound speakers in the front of your classroom and uses an electronic oscillator to produce sound waves of a single frequency. Documents Link to actual document will need to log in. An index of Wave animations from the Physics Classroom ; Beat Frequencies in Sound - A beat frequency or beat wave is a sound of fluctuating volume caused when you add two sound waves of slightly different frequencies. Interference and sound waves. A Physics Toolbox Physics LE Generator PhET Lab DC Circuit Builder Physics Websites Gizmos Physics Classroom Khan Academy Hyper Physics MIT Open Courseware Formal Lab Reports Formal Lab Report Rubric Formal Lab report Rubric PDF Free Fall Lab Sample Graph Textbook PDF Math/Algebra Tutorials Scientific Notation Tutorial Significant Figure Tutorial. A second resource from the Physics classroom webpage. Lasers (java) Atomic Models (java) Neon Lights (java) Charges and Fields. Put up a barrier to explore single-slit diffraction and double-slit interference. We will then expand our exploration of oscillatory motion and waves to include concepts such as simple harmonic motion, uniform circular motion, and damped harmonic motion. Unbalanced Forces » Teacher Notes Notes: The Balanced vs. Again, best used as background reading for students and to help teachers new to the subject to prepare lessons, there are some useful diagrams in the text which help to explain interference. For example, students could be asked to create: one fast and one slow traveling wave, a standing wave with two antinodes, or two pulse waves headed toward destructive interference. Circuit Symbols and Diagrams. The questions are divided into 10 different Question Groups. Prepares a plan for an experiment. Interference of waves from two point sources good Place the two point sources on top of each other and look at the result. The phenomenon of interference occurs not only with light waves, but also with all frequencies of electromagnetic waves and ail other types of waves, such as sound and water waves. Waves have been of interest to philosophers and scientists alike for thousands of years. Interference, diffraction, and the principle of superposition are important concepts for understanding several applications of waves. Our many rooms of physics demos, accumulated over the past century, display subtle physics concepts ranging from electromagnetism, to kinematics, to optics. Ripples in water. To get the most out of physics, you'll need a solid understanding of algebra and a. An index of Wave animations from the Physics Classroom ; Beat Frequencies in Sound - A beat frequency or beat wave is a sound of fluctuating volume caused when you add two sound waves of slightly different frequencies. The Interactives are intended to be used by the individual student or learner who is attempting to further understand the concept or by a teacher-led classroom as part of a lesson or homework assignment. • Optics Simulation with COMSOL Multiphysics® • Simulating Graphene-Based Photonic and Optoelectronic Devices • Live Demo – Graphene Frequency and Time Domain Modeling. In this video David explains what constructive and destructive interference means as well as how path length differences and pi shifts affect the interference. Answer to: A helium-neon laser( \lambda = 633 \ nm) illuminates a single slit and is observed on a screen 1. Sound waves above 20 kHz are known as ultrasound and are not perceptible by humans. I'm having trouble figuring out what was done on a certain step. Approach these problems methodically. Although we've done concept maps in this class before, I briefly explain that concept maps can be used as a tool to assess prior knowledge and show a blank model on the front board. This is the second half of a two-semester calculus-based introductory physics sequence for engineering students. Electromagnetic radiation, in classical physics, the flow of energy at the universal speed of light through free space or through a material medium in the form of the electric and magnetic fields that make up electromagnetic waves such as radio waves, visible light, and gamma rays. Throughout the course, the student is shown how chemistry reveals the amazing design that exists all around us. Questions in the same group are rather similar to one another. The diagram above gives a side view of transverse water wave. Description Mix colors of light with adjustable brightness. A displacement against distance graph , or wave profile , shows the displacement of points along the medium at one instant of time. Title Wave demonstrations: water, sound, light (Inquiry Based) Description These are all the clicker questions from my wave activities in one file. Buoyancy Playground. A comprehensive listing of McGraw Hill's Schaum's Outline Series. Overview: This section introduces the properties of waves and wave motion. Spatial coherence is a concept of wave disturbance describing the correlation between periodic transmitted energy (wave signals) from one point to another,it can also be said that it is a mutual interdependence or connection of variable wave quantities of two different points in a given instant of time,the. Created by David SantoPietro. 1 Section 3 Wave Interactions - reflection, refraction, diffraction, interference, standing wave Learn with flashcards, games, and more — for free. Physics in Motion is a new digital series for high school physics from Georgia Public Broadcasting. Light is a transverse, electromagnetic wave that can be seen by the typical human. Use the sliders to change the light intensities. Accelerate your understanding of how matter and energy work. , the application of fields in motors and generators and the concept of electric current using Ohm?s Law. Now it's really kind of a strange term to use for what actually happens because when waves actually are both affecting a medium at the same time they don't really interfere with each other although that's what we call it. I'm having trouble figuring out what was done on a certain step. With that said, the approach here will be to understand music and musical instruments first, and to study the physics of waves and sound as needed to push the understanding of the music concepts. Interference and Beats. 3rd For every action there is an equal and opposite reaction. They use an interactive applet to manipulate the phase, wavelength, amplitude, and phase velocity of two waveforms and observe the resulting sum. A wave front is the portion of the medium’s surface in which all particles are _____. This simulation is from The Physics Classroom's Physics Interactives collection. The Waves, Sound and Light chapter of this SAT Physics Help and Review course is the simplest way to master the properties of waves. With WileyPLUS, students will develop a conceptual understanding of physics: Conceptual Examples, Concepts & Calculations, Focus on Concepts homework material, Check Your Understanding questions, Concept Simulations ( an online feature) and more. Created by Raman Pfaff. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. This situation is known as a superposition of states. For example, students could be asked to create: one fast and one slow traveling wave, a standing wave with two antinodes, or two pulse waves headed toward destructive interference. A second resource from the Physics classroom webpage. Update to V11 to future-proof your sessions, ensure. This course is an applied physics study of the basic laws and principles of electrostatics, direct current, magnetism, induction, alternating current, electromagnetic waves, geometrical optics, interference and diffraction. Waves on a String. These videos are also used for "flipped classroom. Graph Skillschallenge students to make the connection between physics principles, equations, and their visual representation in a graph. The Interactives are intended to be used by the individual student or learner who is attempting to further understand the concept or by a teacher-led classroom as part of a lesson or homework assignment. Use dotted lines to draw the wave fronts created by these adjacent waves. The wavelength increases from top to bottom, and the distance between the sources increases from left to right. Approach these problems methodically. They construct an explanation of how a standing wave forms using wave vocabulary words such as constructive interference, destructive interference, incident, and reflected waves. So they understand the concepts of waves. A sound wave (like any wave) is often referred to as an energy-transport phenomenon. Concept that it is a repeated oscillation about a point in language appropriate to your students. The wave nature of light was first illustrated through experiments on diffraction and interference. One example of a transverse wave is a water wave where the water moves up and down as the wave passes through the ocean. Created by Raman Pfaff. A set of three classroom demonstrations to be used with PhET simulations Wave on a String, Sound, and Wave Interference. Download Hecht E. The goal however is a deeper understanding of the physics of waves and sound than. Electric Field Hockey. Quantum Tunneling and Wave Packets: Quantum Wave Interference: Radiating Charge: Radioactive Dating Game: Radio Waves & Electromagnetic Fields: The Ramp: Ramp: Forces and Motion: Reactions & Rates: Resistance in a Wire: Resonance: Reversible Reactions: Rutherford Scattering: Semiconductors: Signal Circuit: Simplified MRI: Sound: States of. com are an excellent way to get practice with the wave properties and concepts that are foundational in this unit. Our many rooms of physics demos, accumulated over the past century, display subtle physics concepts ranging from electromagnetism, to kinematics, to optics. There is a small hot spot in the top-left corner. Unbalanced Forces Concept Builder is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. A simple touch on the screen can send a single 2D pulse wave in all. Diffraction. Introduction to Waves. Periodic Motion, Waves & Sound for Physics 101 | Brainscape. The phenomenon of interference occurs not only with light waves, but also with all frequencies of electromagnetic waves and ail other types of waves, such as sound and water waves. AP Physics 1: Waves 9: Interference Physics B / AP Physics 1 and 2 lesson videos are designed for students who have never had physics before. Light and Color Lesson Plans. Marek Slipksi of RIT originally created this document to aid physics students in high school. It will also help students who are having difficulties studying for an exam or doing homework by visualizing various different cases. Read topic 5 waves, answer first section of multiple choice questions. Physics, 11th Edition By John D. Concept 1 - Simple Harmonic Motion Concept 2 - Resonance Equations Concept 3 - Wave Motion Concept 4 - Resonance Concept 5 - Sound Concept 6 - Doppler Effect. They use an interactive applet to manipulate the phase, wavelength, amplitude, and phase velocity of two waveforms and observe the resulting sum. The online campaigning activities of the UK’s new prime minister, Boris Johnson, have already caught the eye of the country’s data protection watchdog. This program focuses on conceptual understanding, problem solving, as well as real-world applications and relevance. Repost as my first post got swamped 😔 I just want to know what A Level physics entails. Know what students know, teach what students need. Serving students, teachers and classrooms. Refine this search by either clicking on the terms in boxes to the right or typing a. The distance between two successive crests or two successive troughs is the wavelength for a transverse wave. Spatial and Temporal coherence. Apply the concepts of accuracy, precision, uncertainty, and significant figures to measurements and calculations. Diffraction manifests itself in the apparent bending of waves around small obstacles and the spreading out of waves past small openings. Write down the equation/concept and then step through the logic/math to arrive at your answer. Force and Motion Concept Builder The Force and Motion Concept Builder is a tool that challenges the learner to make the connection between balanced and unbalanced forces and the type of motion an object experiences. Electric Field Hockey. The questions are divided into 10 different Question Groups. Created by Raman Pfaff. Currently, it includes kinematics, mechanics, special relativity, waves, sound, electricity and magnetism. Dinosaur Play Set With Bike,volley ball log Nivia Water Resistant Outer good grip optimal performance,Wilson WTB0533 EX3 BasketBall Official FIBA 3 x 3 Game Ball Size6 Outdoor 887768403089. The wave nature of light was first illustrated through experiments on diffraction and interference. Lasers (java) Atomic Models (java) Neon Lights (java) Charges and Fields. The Physics Classroom » Concept Builders » Waves and Sound » Wave Properties » Questions Rocking the Boat - Questions The Rocking the Boat Concept Builder is comprised of 27 questions. Wiggle the end of the string and make waves, or adjust the frequency and amplitude of an oscillator. In 1807, an English physicist named Thomas Young asserted that light has the properties of a wave in an experiment called Young's Interference Experiment. Current items in the group's pool include the following two videos which coordinate with Lesson 1 of the Sound Waves and Music chapter of The Physics Classroom Tutorial. animations and video film clips. The Physics Classroom » Concept Builders » Vectors and Projectiles » Trajectory - Angle Launched Projectiles Trajectory - Angle Launched Projectiles Trajectory - Angle Launched Projectiles is a Concept Builder that takes a numerical approach to the trajectory of a projectile. A classroom lesson presentation pack consisting of 67 slides related to waves including characteristics and classifications of longitudinal and transverse waves, understanding the relationship between wavelength, frequency, period and velocity of waves, understanding the occurrence of resonance and damping of waves, understanding the wave phenomenon and factors affecting reflection, refraction and diffraction of various types of waves (water waves, sound waves and light waves), understanding. This adding together of waves is known as constructive interference because the waves combine to construct a new, bigger wave. Classroom Management Strategies To Take Control Of Noisy Students Wave Interference 1 of 2 | Doc Physics - Duration: Thin Film Interference - The Art of Physics (with POV Ray. For example, the study detailed in Sidebar 1 shows some of the difficulties students have in making sense of the concept of a photon. Write down the equation/concept and then step through the logic/math to arrive at your answer. The Concept Builder is coded to select at random a question from each group until a student is successful with that group of questions. They use an interactive applet to manipulate the phase, wavelength, amplitude, and phase velocity of two waveforms and observe the resulting sum. 2015-06-03 – Wave Interference Worksheet /Homework due 4/12/18. Analyze wave behavior during reflection, and image characteristics created from it (i. The Physics Classroom. CH 25: Vibrations & Waves. It's a bit like lots of waves overlapping each other. Power is the rate at which energy is transferred by the wave. And still other Interactives provide game-like environments that require the user to use a physics concept to meet a challenge. The illustration above explores constructive and destructive wave interference between two waves moving in opposite directions. Thin-film interference. It is a complex topic but among the most intriguing in physics. UDL Toolkit. Explore the wonderful world of waves! Even observe a string vibrate in slow motion. Interference is such a fundamental aspect of waves that observing interference is proof that something is a wave. 80 \ m behind the slit. In human physiology and psychology, sound is the reception of such waves and their perception by the brain. Apply the concepts of accuracy, precision, uncertainty, and significant figures to measurements and calculations. The Physclips project provides multimedia education in introductory physics at different levels. Items in the group's pool include diagrams of diffraction and two-point source interference patterns and photos of ripple tank experiments, interference patterns on still water, and much more. Using the Concept Builder The Wave Interference Concept Builder is shown in the iFrame below. Our understanding of the physical world is not complete until we understand the properties and behaviors of waves. Start learning today with flashcards, games and learning tools — all for free. The Physics Classroom » Concept Builders » Waves and Sound Waves and Sound A Concept-Builder is an interactive questioning module that presents learners with carefully crafted questions that target various aspects of a concept. In many instances, sound is a periodic wave, and the atoms undergo simple harmonic motion. Diffraction manifests itself in the apparent bending of waves around small obstacles and the spreading out of waves past small openings. I'm having trouble figuring out what was done on a certain step. - [Voiceover] Young's Double Slit experiment looked a little something like this. The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump’s favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. “Obama bad; Trump good” is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump’s character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don’t assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts “will go down the tubes.” That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It’s only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That’s baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you’ll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I’m not smart enough to know how much of this was Bush’s “fault.” But he had been in office for six years when the trouble started. So, if it’s ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama’s second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama’s seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump’s campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump’s second year, 2018, the GDP grew 2.9 percent, equaling Obama’s best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it’s natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it’s 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here’s a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that’s the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of $1.4 trillion at the beginning of the Obama administration, to$585 billion in 2016 (Obama’s last year in office), will be back up to $960 billion this fiscal year, and back over$1 trillion in 2020. (Here’s the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported:
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2019-11-18 02:18:30
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https://www.zenodo.org/record/3559462/export/xd
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Project deliverable Open Access
# Identification of the surface state influence in representing the Arctic warming by coordinated atmosphere-only simulations (D3.1)
Gao, Yongqi; Davy, Richard; Suo, Lingling; Gastineau, Guillaume; Kwon, Young-Oh; Semenov, Vladimir; Liu , Yang
### Dublin Core Export
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<dc:creator>Gao, Yongqi</dc:creator>
<dc:creator>Davy, Richard</dc:creator>
<dc:creator>Suo, Lingling</dc:creator>
<dc:creator>Gastineau, Guillaume</dc:creator>
<dc:creator>Kwon, Young-Oh</dc:creator>
<dc:creator>Liu , Yang</dc:creator>
<dc:date>2019-09-30</dc:date>
<dc:description>Summary:
Arctic amplification metrics: The surface air temperature (SAT) anomalies, trends and variability have been used to quantify the Arctic amplification (AA). The use of different metrics, as well as the choice of dataset can affect conclusions about the magnitude and temporal variability of AA. We reviewed the established metrics of AA to see how well they agree upon the temporal signature of AA and assess the consistency in these metrics across commonly-used datasets which cover both the early and late 20th century warming in the Arctic. We find the NOAA 20th Century Reanalysis most closely matches the observations when using metrics based upon the trends, variability and the amplification of SAT anomalies in the Arctic, and the ERA 20th Century Reanalysis is closest to the observations in the SAT anomalies and variability of SAT anomalies. The largest differences between the century-long reanalysis products and observations are during the early warming period. In the modern warming period, the high density of observations strongly constrains all the reanalysis products, whether they include satellite observations or only surface observations. Thus, all the reanalysis and observation products produce very similar magnitudes and temporal variability in the degree of AA during the recent warming period (Davy et al., 2018).
Sea ice free Arctic contributes to the projected warming minimum in North Atlantic: Projected global warming is not spatially uniform and one of the minima in warming occurs in the North Atlantic (NA). Several models from the Coupled Model Intercomparison Project Phase 5 even projected a slight NA cooling in 2081–2100 relative to 1986–2005. Here we show that, by coupled model simulations, an autumn (September to November) sea-ice free Arctic contributes to the NA warming minimum by weakening the Atlantic meridional overturning circulation (Suo et al., 2017).
Design and finalize the set-up for the atmosphere-only model coordinated experiments: Four multi-model atmospheric coordinated experiments have been designed and finalized in order to reveal the climate impacts in the Northern Hemisphere of the warming Arctic. The atmospheric experiments will use daily SST and sea-ice concentration from 1979 to 2014 from the CMIP6 HighResMIP protocol. The first experiment uses daily varying SST and sea ice concentration. A second experiment will use varying SST while keeping climatological sea ice concentration. The difference between the two simulations will allow investigating the impacts of the warming Arctic. This protocol is built from HighResMIP and will allow investigating the influence of using high horizontal resolution. Two supplementary experiments will use daily varying SST and sea ice after removal of the multidecadal Pacific or Atlantic variability. These two experiments have never been performed before and will also allow distinguishing the specific impacts of the oceanic multi-decadal variability.
Completed the coordinated experiments by the nine of ten atmosphere-only models: All the four coordinated experiments have been completed and model outputs were made available to all Blue-Action partners.
Warm Pacific can intensify the Arctic warming: Multi-model simulations from Blue-Action showed that the transition from warm Pacific to cold Pacific (Pacific Decadal Oscillation from positive phase to negative phase) during 1979-2013 damped the Arctic warming. The Arctic warming likely will be intensified in the forthcoming decades given the PDO switched to positive phase since 2014.</dc:description>
<dc:description>The Blue-Action project has received funding from the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement No 727852.</dc:description>
<dc:identifier>https://zenodo.org/record/3559462</dc:identifier>
<dc:identifier>10.5281/zenodo.3559462</dc:identifier>
<dc:identifier>oai:zenodo.org:3559462</dc:identifier>
<dc:relation>info:eu-repo/grantAgreement/EC/H2020/727852/</dc:relation>
<dc:relation>doi:10.5281/zenodo.3559461</dc:relation>
<dc:relation>url:https://zenodo.org/communities/blue-actionh2020</dc:relation>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:title>Identification of the surface state influence in representing the Arctic warming by coordinated atmosphere-only simulations (D3.1)</dc:title>
<dc:type>info:eu-repo/semantics/report</dc:type>
<dc:type>publication-deliverable</dc:type>
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57
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2020-11-29 02:32:04
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http://krisjanisgaidis.com/blog/2014/06/11/expandable-text-cell/
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Learn how to implement an expandable text cell which automatically cuts off the text at a specified number of lines; just like in the reviews section of the App Store!
## Code
I’ve posted the full code for this blog post on GitHub:
https://github.com/kgaidis/blog-expandable-text-cell
## Project Classes
#### ExpandableLabelTableViewCell
A simple UITableViewCell that gives us an outlet to an ExpandableLabel, which is just a subclass of UILabel.
#### ExpandableLabelCellModel
An NSObject that contains information on how each cell will be presented. First we have NSString *string, which contains the text that will go inside the label. Then we have BOOL expanded, which is used to track whether the cell has been expanded already. This is a very important class because it controls how many lines of text the cell will display via kMaxNumberOfLines.
#### ViewController
The view controller is pretty standard. We populate the cell models with random-sized strings, implement UITableViewDelegate / UITableViewDataSource, and just display the cells. Most of the logic is handled by ExpandableLabelCellModel and ExpandableLabel.
#### ExpandableLabel
The most important part of the project and why you came to see this blog post! This special UILabel subclass handles all of the truncation. We will talk about how ExpandableLabel is implemented step-by-step below, but I’ll summarize the most important parts here. First we must decide whether we need to truncate the text in the cell, if we decide to truncate, we append “…More” to the truncated text. Truncation is decided by the labels numberOfLines property. If the value is 0, it means that we do not want to truncate the text. If the value >0, we must calculate whether the text of the UILabel fits the numberOfLines. If the text fits, we want to leave it alone and display it in its full form, otherwise, we truncate it.
## ExpandableLabel Functionality
#### Let’s truncate!
The -(void)truncate function first checks whether we should truncate the text in the label. If it decides not to truncate, we don’t do anything! Otherwise, the function decides how many characters fit the label via numberOfCharactersThatFitLabel function. Once we know that number, we just do simple truncating math, append “…More”, add some NSAttributedString attributes and set the label text!
#### When to truncate?
The project calls truncate in layoutSubviews. Whether this is the right place to call the function can be arguable, but there is one very important thing to keep in mind: the calculations are done based off the UILabel bounds, so make sure they are correct before calling the truncate function!
#### Should we be truncating?
As stated above, truncation is decided by the labels numberOfLines property. If the value is 0, it means that we do not want to truncate the text. If the value >0, we must calculate whether the text of the UILabel fits the numberOfLines. First we calculate the actualHeightOfText: the height of the UILabel if we were to display every line of text. Then we calculate the desiredHeightOfText: the height of the UILabel with respect to the value of numberOfLines. If desiredHeightOfText < actualHeightOfText we want to truncate!
#### How many characters fit a rectangle?
The most important function in the whole project! Apple’s Core Text library provides CTFramesetterSuggestFrameSizeWithConstraints function. We can pass a CFRange called the fitRange (“On return, contains the range of the string that actually fit in the constrained size.”) to the function. By passing in the desired rectangle of the UILabel and by taking the length from the fitRange, we get the number of characters that fit our desired label!
## Conclusion
And that’s it! Keep in mind that this functionality can be applied to many different UX cases. For example, Facebook’s “… Continue Reading” button, which pushes to a new view controller upon the press of the button.
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2020-08-08 13:57:33
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https://mathoverflow.net/questions/151873/large-abelian-characteristic-subgroups-in-abelian-by-countable-groups
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# Large abelian characteristic subgroups in abelian-by-countable groups
Does there exist a group with a normal countable-index abelian subgroup but without characteristic countable-index abelian subgroups?
It is well known that any finite-index subgroup contains a normal (in the whole group) finite-index subgroup. A lesser-known proposition states that
($*$) any group having an abelian finite-index subgroup has a characteristic abelian finite-index subgroup.
(There are also a bunch of related not-so-easy facts [Self-advertisement]).
K. Podoski and B. Szegedy gave the best-known numerical version of ($*$) (Theorem 5.1) and remarked that one cannot replace finite with countable in ($*$); however, their example has no characteristic abelian countable-index subgroups just because it has no normal abelian countable-index subgroups.
Here is an example (the group $H_K^\mathbf{Q}$ defined below, which is actually a split extension abelian-by-countable).
Let $(Q,\le)$ be a total ordering. Let $K$ be a countable (possibly finite) field. Let $V^Q_K=K^{(Q)}$ be the free $K$-module with basis $(e_q)_{q\in Q}$. Let $G^Q_K$ be the group of $K$-module automorphisms $g$ of $V_K$ such that $g(e_q)-e_q\in\mathrm{Vect}_Q(\{e_r:r<q\})$ for every $q$ (it can be thought as a upper unipotent group of $Q\times Q$-matrices over $K$).
Define a cut as a subset $I$ of $Q$ such that both $I$ and its complement $I^c$ are nonempty, and such that $i<j$ for all $i\in I$ and $j\in I^c$. For every cut $I$ with complement $J=I^c$ and $g\in G^Q_K$, let $p_I(g):V^I_K\to V^I_K$ be its restriction to the stable subspace $V^I_K$, and let $r_I(g):V^J_K\to V^J_K$ be the induced automorphism modulo the stable subspace $V^I_K$. (Visually, $I$ defines a $2\times 2$ block decomposition, $p_I(g)$ is the northwest block and $r_I(g)$ is the southeast block of $g$.)
Obviously, $p_I$ and $r_I$ are homomorphisms, and if $P_I$ and $R_I$ are their kernels, then $N_I=P_I\cap R_I$ is is a normal abelian subgroup in $G^Q_K$.
Now we specify to $Q=\mathbf{Q}$, the rationals with the usual ordering. Still, $N_I$ is not of countable index in $G^\mathbf{Q}_K$. So we define $H^Q_K$ as the normal subgroup of $G^Q_K$ of elements $g$ such that for every cut $I$, both matrices $p_I(g)$ and $r_I(g)$ are finitely supported (i.e. finitely many non-diagonal elements are nonzero). Then $N_I\cap H^\mathbf{Q}_K$ is normal abelian of countable index in $H_K^\mathbf{Q}$.
It remains to see that $H_K^\mathbf{Q}$ has no abelian characteristic subgroup of countable index. This is rather easy: the first observation (an easy play with commutators(*)) is that every nontrivial normal subgroup $N$ of $H_K^\mathbf{Q}$ contains an elementary matrix $e_{ij}(s)$ for some $i<j$ and $s\neq 0$. All such matrices are conjugate under the full automorphism group of $H_K^\mathbf{Q}$ (to vary $s$, use diagonal matrices, and to vary $(i,j)$, use that the group of order-preserving permutations of $\mathbf{Q}$ is 2-transitive). Hence if $N$ is characteristic, it contains all elementary matrices, and thus the (non-abelian) subgroup they generate.
Hence the only abelian characteristic subgroup of $H_K^\mathbf{Q}$ is the trivial subgroup $\{1\}$: we have to check that it does not have countable index, i.e. $H_K^\mathbf{Q}$ is uncountable: indeed for every subset $L$ of $\mathbf{N}\smallsetminus\{0\}$, consider the matrix $k_L$ with same entries as the identity except $(k_L)_{-i,i}=1$ for all $i\in L$. Then $L\mapsto k_L$ is injective, $k_L$ belongs to $H_K^\mathbf{Q}$ for every $L$, hence $H_K^\mathbf{Q}$ has continuum cardinal.
Edits:
(1) (*) Starting from a non-identity element $g$ in $G_K^\mathbf{Q}$, its commutator with a suitable elementary matrix yields a non-identity element $h$ such that $h-1$ has finite rank; in particular if $g\in H_K^\mathbf{Q}$ then so does $h$, and it follows that $h$ is finitely supported. Then $h$ lies in the nilpotent subgroup $G_K^I$ for some finite subset $I$ of $\mathbf{Q}$. So the normal subgroup of $H_K^\mathbf{Q}$ generated by $g$ contains a central element of $G_K^I$, showing that any nontrivial normal subgroup of $H_K^\mathbf{Q}$ contains a non-identity elementary matrix.
(2) Actually, a similar argument shows that the only normal abelian subgroup of $H_K^\mathbf{Z}$ stable under the shift automorphism $\alpha$ (conjugation by the automorphism $(e_n\mapsto e_{n+1})_{n\in\mathbf{Z}}$) is the trivial subgroup $\{1\}$. Note that $H_K^\mathbf{Z}$ is residually nilpotent, while $H_K^\mathbf{Q}$ is a perfect group.
(3) Incidentally, with the notation of (2), the semidirect product $\langle\alpha\rangle\ltimes H_K^\mathbf{Z}$ has a countable index abelian subgroup but no normal one. I don't know whether the Podoski-Szegedy example is similar (I don't have access to their article right now).
• Thank you, Yves!! Surely, you mean $g(e_q)\in e_q+Vect(\dots)$ in the first paragraph. Also, $G_K$ in the second paragraph is the same as $G_K^Q$. Furthermore, I guess that the "easy play with commutators" is something like the following. The commutator of any matrix and an elementary matrix is finitely supported, i.e. this commutator lies in a finite-dimensional unitriangular subgroup $UT_n(K)$ which is nilpotent and, hence, any its non-trivial normal subgroup non-trivially intersects the centre, which consists of elementary matrices. – Anton Klyachko Dec 14 '13 at 22:36
• @AntonKlyachko I edited the typos. For the commutators I had a similar argument in mind (although yours is more elegantly written than what I had in mind). Note that "the commutator of any matrix and an elementary matrix is finitely supported" holds in $H$ but not in $G$. – YCor Dec 14 '13 at 22:44
• Excuse me, Yves. I do not understand your comment. The finitely supported matrices form a normal subgroup of $G$, right? If they do, then the commutator must be finitely supported. – Anton Klyachko Dec 15 '13 at 0:06
• @Anton: I don't see what you mean: if you consider the matrix $g$ with same entries as identity except $g_{1j}=1$ for all $j>1$, then $[e_{01},g]_{0j}=1$ for all $j>1$. (Note that $G$ is the set of upper unipotent matrices for which all columns are finitely supported, though lines can be infinitely supported.) – YCor Dec 15 '13 at 0:41
• Oh, yes. I mixed up finitely supported matrices and matrices $f$ with finite $\hbox{rank}(f-1)$ (i.e operators $f$ such that $\hbox{ker}(f-1)$ is of finite codimension). The latter form a normal subgroup but the former do not. Inside $H$, these two subgroups coincides, right? (I mean, their intersections with $H$ coincides.) – Anton Klyachko Dec 15 '13 at 2:03
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2019-10-15 10:08:57
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http://www.math.ufl.edu/~fgarvan/ramanujan/vol14/issue2/0484-2004/ABSTRACT.html
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THE RAMANUJAN JOURNAL, Vol. 14, No. 2 (2007), 277-304.
# Grande valuers du nombre de factorisations d'un entier en produit ordonné de facteurs premiers
MOHAND-OUAMAR HERNANE
Institut de Mathématiques, Université Houari Boumédienne, BP 32, El Alia, 16111 Bab Ezzouar, Alger, Algeria
Email: hernane_m@caramail.com
JEAN-LOUIS NICOLAS
Institut Camille Jordan, Mathématiques, Université Claude Bernard (Lyon 1), 69622 Villeurbanne cedex, France
Email: jlnicola@in2p3.fr
Homepage: http://math.univ-lyon1.fr/~nicolas/
Received January 6, 2004; Accepted February 14, 2005
Abstract. Among various functions used to count the factorizations of an integer $n$, we consider here the number of ways of writing $n$ as an ordered product of primes, which, if $n = q_1^{\alpha_1} q_2^{\alpha_2} \cdots q_k^{\alpha_k}$, is equal to the multinomial coefficient $h(n) = \frac{(\alpha_1+\alpha_2+\cdots+\alpha_k)!} {\alpha_1! \alpha_2! \cdots \alpha_k!}$. The function $P(s) = \sum_{\mbox{$p$prime}} p^{-s}$, sometimes called the prime zeta function , plays an important role in the study of the function $h$. We denote by $\lambda = 1.399433\dots$ the real number defined by $P(\lambda ) = 1$. The mean value of the function $h$ satisfies $\frac{1}{x} \sum_{n\le x} h(n) \sim -\frac{1}{\lambda P' (\lambda )} x^{\lambda -1}$. In this paper, we study how large $h(n)$ can be. We prove that there exists a constant $C_1 > 0$ such that, for all $n \ge3$, $\log h(n) \le \lambda \log n - C_1 \frac{(log n)^{1/\lambda}} {\log\log n}$ holds. We also prove that there exists a constant $C_2$ such that, for all $n \ge3$, there exists $m \le n$ satisfying $\log h(m) \ge \lambda \log n - C_2 \frac{(log n)^{1/\lambda}} {\log\log n}$. Let us call $h$-champion an integer $N$ such that $M < N$ implies $h(M) < h(N)$. S. Ramanujan has called highly composite a $\tau$-champion number, where $\tau(n) = \sum_{d\mid n}1$ is the number of divisors of $n$. We give several results about the number of prime factors of an $h$-champion number $N$, about the exponents in the standard factorization into primes of such an $N$ and about the number $Q(X)$ of $h$-champion numbers $N \le X$. At the end of the paper, several open problems are listed.
Keywords: Factorization, highly composite numbers, prime zeta function, optimization
2000 Mathematics Classification: Primary 11A25; 11N37
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2013-05-22 17:27:14
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https://brilliant.org/discussions/thread/cubic-number-pattern/?sort=new
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# Cubic Number Pattern
Hey guys, I just want to share this simple things. I have found pattern of cubic number, and now I want to share it to you.
$$0^{3} = 0$$
$1^{3} = 1$
$2^{3} = 8 = 3 + 5$
$3^{3} = 27 = 7 + 9 + 11$
$4^{3} = 64 = 13 + 15 + 17 + 19$
$5^{3} = 125 = 21 + 23 + 25 +27 + 29$
$6^{3} = 216 = 31 + 33 + 35 + 37 + 39 + 41$
$7^{3} = 343 = 43 + 45 + 47 + 49 +51 + 53 + 55$
$8^{3} = 512 = 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71$
$9^{3} = 729 = 73 + 75 + 77 + 79 + 81 + 83 + 85 + 87+ 89$
and so on and on and on !
Do you get the pattern ? Okay, any comments will be appreciated. Thank you...
Note by Jonathan Christianto
5 years, 10 months ago
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$\sum_{i=1}^{n} \left(n(n-1)-1+2i\right) = n\times n(n-1)-n+n(n+1) = n^3$
- 5 years, 10 months ago
$\displaystyle \sum _{ k=0 }^{ n-1 }{ \left( { n }^{ 2 }-n+1+2k \right) ={ n }^{ 3 } }$
The cube creeps into this thing because of that first term ${ n }^{ 2 }$
As an example, this is true also, but the sum are quartics.
$\displaystyle \sum _{ k=0 }^{ n-1 }{ \left( { n }^{ 3 }-n+1+2k \right) ={ n }^{ 4 } }$
In fact, for any $a$, this is true
$\displaystyle \sum _{ k=0 }^{ n-1 }{ \left( { n }^{ a }-n+1+2k \right) ={ n }^{ a+1 } }$
- 5 years, 10 months ago
Thanks for formula for ANY power.
- 5 years, 6 months ago
Correct me if I am wrong. So, for $n^{2}$ it will be
$\sum_{k=0}^{n-1} (n+1+2k) = n^{2}$
- 5 years, 10 months ago
Actually, leave out $n$, since ${n}^{1}-n=0$, and we have the classic sum of odd numbers $1+2k$ to make squares.
- 5 years, 10 months ago
The cube of an integer $n$ can be written as sum of $n$ consecutive odd numbers, first odd number being $(n-1)^2-n$.
- 5 years, 10 months ago
Let me give you a pattern:
$1^{3} = 1^{2} = 1$
$1^{3}+2^{3} = (1+2)^{2} = 9$
$1^{3}+2^{3}+3^{3} = (1+2+3)^{2} = 36$
$1^{3}+2^{3}+3^{3}+4^{3} = (1+2+3+4)^{2} = 100$
In general,
$\boxed{1^{3}+2^{3}+\cdots+n^{3} = (1+2+\cdots+n)^{2}}$
Can you figure out why this is? ;)
- 5 years, 10 months ago
Sum of cubes = n(n+1)(n)(n+1)/4= [n(n+1)/2]^2= [Sum of the numbers]^2
- 5 years, 10 months ago
In boxed part, $1^3+2^3$
- 5 years, 10 months ago
I have edited it! $\ddot\smile$
- 5 years, 10 months ago
- 5 years, 10 months ago
It should be $1^3=1^2=1$ in first row to make it (look like) a pattern. $\ddot\smile$
- 5 years, 10 months ago
Indeed it should, thanks for spotting that!
- 5 years, 10 months ago
General term
$(n^2 - n + 1) + (n^2 - n + 3) + ..... + (n^2 + n -1) = n^3$
- 5 years, 10 months ago
Can you give the example please ??
- 5 years, 10 months ago
what are you not able to understand , can you tell?
- 5 years, 10 months ago
@U Z You have given me the general term. Can you give the example ?? For example, the result of $3^{3}$ using the general term. Can you catch it ??
- 5 years, 10 months ago
$3^3=(3^2-3+1)+(3^2-3+3)+(3^2-3+5)\\=7+9+11\\=27$
- 5 years, 10 months ago
I got it now, thanks...
- 5 years, 10 months ago
By the way, a good pattern and the thing I observed is There is a difference of 2 between consecutive numbers
- 5 years, 10 months ago
Odd number means difference of 2.
- 5 years, 6 months ago
Can you explain it to me ?? For additional information for me, hehehe...
- 5 years, 10 months ago
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2020-12-01 00:09:21
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https://www.gamedev.net/forums/topic/306914-matrix-question/
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# OpenGL Matrix question
This topic is 5022 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Hi, I am trying to sort my model by material. However currently I render the code using the following -
for(int z = 0; z < _3ds_->numNodes; z++)
{
NodeInfo *node = &_3ds_->pNodes[z];
glMultMatrixf((float *)&node->matrix);
glTranslatef(node->pivot[0], node->pivot[1], node->pivot[2]);
for(int i = 0; i < _3ds_->numGroups; i++)
{
Groups *g = &_3ds_->pGroups;
int size = g->numFaces;
glMultMatrixf((float *)&g->matrix);
for(int j = 0 ; j < size; j++)
{
glMaterialfv(GL_FRONT, GL_AMBIENT, (float *)&g->faceList[j].material.ambient);
glMaterialfv(GL_FRONT, GL_DIFFUSE, (float *)&g->faceList[j].material.diffuse);
glMaterialfv(GL_FRONT, GL_SPECULAR, (float *)&g->faceList[j].material.specular);
glMaterialfv(GL_FRONT, GL_SHININESS, (float *)&g->faceList[j].material.shininess);
unsigned int texId = tex.GetTextureID(g->faceList[j].material.textureName);
glEnable(GL_TEXTURE_2D);
glBindTexture(GL_TEXTURE_2D, g->faceList[j].material.texId);
glBegin(GL_TRIANGLES);
glNormal3fv((float *)&g->faceList[j].normal);
for(int k = 0; k < 3; k++)
{
glTexCoord2fv( (float *)&_3ds_->texel[g->faceList[j].face[k]]);
glNormal3fv((float *)&g->normals[3 * j + k]);
glVertex3fv((float *)&_3ds_->verts[g->faceList[j].face[k]]);
}
glEnd();
}
}
}
However if I sort using the material the matrix transformation for each vertex will also change and I will need to keep a set of transformation matrix per vertex. Is there a way to send opengl information about matrix transformation per vertex when doing VBO's or do I need to multiply each vertex by the matrix before storing it to send a batch of vertices sorted on material basis for rendering. Thanks
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I'd suggest you split your model up into sub-meshes BEFORE executing your main loop. This pre-processing will significantly improve your performance. That way, you just need to specify a transform for each batch of vertices rather than per-vertex.
Basically just throw the triangles with the same material into the same sub-mesh. Then your code will look something like follows:
[sourcefor (int z = 0; z < preprocessednodes->numNodes; z++){ PPNodeInfo *node = preprocessednodes->pNodes[z]; glPushMatrix(); glMultMatrixf((float *)&node->matrix); glTranslatef(node->pivot[0], node->pivot[1], node->pivot[2]); for (int i = 0; i < node->numSubMeshes; i++) { // setup the material for this sub-mesh glMaterialfv(GL_FRONT, GL_AMBIENT, (float *)&node->submesh.material.ambient); glMaterialfv(GL_FRONT, GL_DIFFUSE, (float *)&node->submesh.material.diffuse); glMaterialfv(GL_FRONT, GL_SPECULAR, (float *)&node->submesh.material.specular); glMaterialfv(GL_FRONT, GL_SHININESS, (float *)&node->submesh.material.shininess); // setup the texture etc... // now render your entire sub-mesh glBegin(GL_TRIANGLES); for (j = 0; j < size; j++) { glTexCoord2fv( (float *)&_3ds_->texel[g->faceList[j].face[0]]); glNormal3fv((float *)&g->normals[3 * j + 0]); glVertex3fv((float *)&_3ds_->verts[g->faceList[j].face[0]]); glTexCoord2fv( (float *)&_3ds_->texel[g->faceList[j].face[1]]); glNormal3fv((float *)&g->normals[3 * j + 1]); glVertex3fv((float *)&_3ds_->verts[g->faceList[j].face[1]]); glTexCoord2fv( (float *)&_3ds_->texel[g->faceList[j].face[2]]); glNormal3fv((float *)&g->normals[3 * j + 2]); glVertex3fv((float *)&_3ds_->verts[g->faceList[j].face[2]]); } glEnd(); glPopMatrix(); } }
There are TONS of optimizations you could do here as well.
1.) instead of outright rendering your sub-meshes as you render the mesh, you could add your sub-mesh to a linked list (based on material). Then traverse each linked list, setup the material once and render the submeshes in the linked list, setting up the material only once per sub-mesh. This will reduce material state change even between multiple 'parent' meshes.
2.) Tristrip your sub-meshes (for NVidia cards), or optimize your triangle indices such that they you get good triangle cache hits (mainly for ATI cards)
3.) Put your sub-meshes in a display list or in a vertex-array/VBO.
4.) You could put your translate into your matrix (since the matrix contains a translation component anyway!) ie.
glMultMatrixf((float *)&node->matrix);
glTranslatef(node->pivot[0], node->pivot[1], node->pivot[2]);
would just become:
glMultMatrixf((float *)&node->matrix);
I'm sure there's more, but that's just it off the top of my head...
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2018-12-13 23:13:56
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https://peguru.com/2019/08/wave-trap/
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# Wave Trap: Learn the Purpose, Cost, and Lead Time to Procure
### Purpose of wave trap
A wave trap, also known as line trap, is a band-stop or notch filter. It blocks the high-frequency carrier signal and allows 60hz power frequency. A wave trap, CCVT, line tuner, and carrier relays – work hand-in-hand implementing Power Line Carrier pilot protection.
The trap is mounted either horizontally or vertically. It is sized to handle the continuous load current and the mechanical stress generated by the high magnitude fault current for a short time period.
The GIF below shows how the carrier frequency is contained using the wave traps. The frequency that travels on the line is chosen from a range of 30kHz to 500kHz. So, while the trap is tuned to block this frequency, it allows the 60hz power frequency through.
One additional item factored into the trap design is how the inductance of the trap reacts with the capacitive elements in the substation. Because of capacitance in various equipment, shown in the image below, a series resonant circuit is formed with the inductance in wavetrap. This mini-circuit diminishes the inductive impedance leading to more carrier signal leaking through the trap.
One way to combat this issue begins by introducing a resistor into the wavetrap’s tuning hardware (one that contains the capacitor). Although adding this resistance (typically 400 ohms, matching t-line characteristic impedance) decreases the peak impedance offered to the carrier signal, it limits the resonance. This logic, however counter-intuitive, is a worthwhile trade-off.
### Cost of wave trap
• 69kV 1200Amp wave trap: ~$12,000 each • 138kV 2000Amp wave trap: ~$12,000 each
• 230kV 2000Amp wave trap: ~$25,000 each • 345kV 3000Amp wave trap: ~$30,000 each
Note: The cost of any support structure is not included.
### Lead time to procure wave trap
~20 weeks
Information on cost and lead time is for your general knowledge only. Contact vendor with your equipment specifications for actual figures.
##### Attempt the quiz
/7
Substation Major Equipment
It's only stupid-simple, let's begin.
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2021-09-19 08:11:31
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https://socratic.org/questions/why-are-f-block-elements-placed-separately
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# Why are f block elements placed separately?
If you're asking why the $f$-block elements have their own location separate from the main table...
The $f$-block elements are places apart from the main table primarily to conserve space. With these elements included, the table would have 32 columns! (You can find tables including them anywhere online.)
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2020-01-19 22:23:41
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http://www.algebra-by-example.com/dividing-decimals.html
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# Dividing Decimals
You'll learn methods for dividing decimals by a whole number, by another decimal, and by a fraction. It's really easy once you get the hang of it, and it will repay your investment in time and effort many folds as you progress in learning Algebra.
## Decimal Division By A Whole Number
Dividing a decimal by a whole number can be done reliably (that is, with minimum chance of making mistakes) using long division. Of course, once you've had enough practice, you can use shorter and more advance techniques to get the answers faster.
You'll see how to do long division in the examples below. And yeah, be sure to line up the decimal points vertically.
Example
Divide the following.
(a) 73.8 ÷ 12
(b) 143.55 ÷ 15
Solution
Notice that the decimal points are in line. No mis-alignments like shown below.
## Decimal Division By A Decimal
When dividing a decimal with a decimal, we can reuse the techniques we learned from dividing a decimal by a whole number. Simply change the divisor (at the right side of the ÷) into a whole number first by multiplying both divisor and dividend with the same number, then proceed with the long division.
Example
Divide the following.
(a) 24.032 ÷ 16
(b) 0.304 8 ÷ 0.48
Solution
(a) First, convert the denominator (1.6) into a whole number by multiplying both the numerator (24.032) and denominator by 10.
Therefore, 24.032 ÷ 1.6 = 15.02
Therefore, 0.304 8 ÷ 0.48 = 0.635
## Decimal Division By The Powers of 10
Dividing decimals by powers of 10 (e.g. 0.001, 0.01, 0.1, 10, 100, 1000, and so on) is a special case. You can use long division to solve it, but it's not the fastest and most efficient way to do it. Here's a method that can only be used in this case.
When dividing a decimal with a power of 10, shift the decimal to the left according to the number of zeros in the power of 10. For instance,
When dividing a decimal with 0.1, 0.01 or 0.001, shift the decimal point to the right according to the number of decimal places in 0.1, 0.01 or 0.001. For instance,
Example
Divide the following.
(a) 2.033 ÷ 1000
(b) 19.253 ÷ 0.001
Solution
(a) 2.033 ÷ 1000 = 0.00233
(b) 19.253 ÷ 0.001 = 19253
## Here's a Tip...
When multiplying or dividing a decimal by a power of 10 (10, 100, 1000, …) or a decimal like 0.1, 0.01 or 0.001, the decimal point can be shifted as follows:
## Decimal Division By A Fraction
It's not difficult to divide a decimal by a fraction. You'll first need to change “÷” into “×”, `then change the fraction into its reciprocal. It's a fancy way of saying that you need to flip the fraction upside down (numerator becomes the denominator, and vice versa). Solve it after that. See the example below.
Example
Divide the following.
Solution
## Dividing Decimals Word Problems
Example
A rope is 32.16 m long. It is cut into identical pieces, each measuring 8.04 m long. How many pieces were cut from the rope?
Solution
Return from Dividing Decimals to Arithmetic
Return Home to Algebra-by-Example.com
## Unclear about a concept? Or see something missing?
Do you have questions about what you've read in this section? Is something missing? Post your question or contribution here and I'll get to it as soon as I can.
If you're sending in a problem you need help with, please also describe what you've tried to get a response.
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2014-08-21 18:00:15
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http://www.chegg.com/homework-help/questions-and-answers/find-the-exact-length-of-the-curvey-lnex-1-ex-1-on-the-interval-ab-and-a-0i-know-that-the--q3029540
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Find the exact length of the curve: y = ln{(e^(x) +1)/(e^(x)-1)} a
find the exact length of the curve:
y = $$ln((e^x + 1)/(e^x -1))$$ on the interval [a,b] and a > 0
I know that the formula for arc length is $$\sqrt{1+[f'(x)]^2}$$ but this just gets complicated with this equation.
• y can be written as y= ln(ex+1)-ln(ex1)
y' =-2e^x / e^2x -1
since arc length is given by √(1+[f(x)]^2)
f(x) = y'
arc length =√(1+4/e^2x)
• Anonymous commented
Thank you, but the issue that i'm having is simplifying this, then finding the integral on [a,b]
• Anonymous commented
f '(x) not correct
• y = ln[(ex+1)/(ex-1)]
dy/dx =[ (ex-1)/(ex+1) ] [ex (ex-1) - (ex)(ex+1)]/(ex-1)2
= [ (ex-1)/(ex+1) ] [-2ex]/(ex-1)2
= -2ex /(e2x-1)
length of the curve = intgral of sq root of [ 1 + (dy/dx)2]
= integral of sq root of [ (e2x+1)2/(e2x-1)2]
= integral of [ (e2x+1)/(e2x-1)]
put e2x = u ==> 2e2x = du
= integral of (u+1)/(u-1) (du/2)
= (1/2) integral of [ (u+1)/(u-1)]du
= (1/2)integral of [ 1 + 2/(u-1) ] du
= (1/2) u + ln(u-1)
= e2x/2 + ln(e2x-1)
Get homework help
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2013-05-26 07:46:01
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https://chemistry.stackexchange.com/questions/31337/2-4-dinitrophenyl-hydrazine-test
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# 2,4-dinitrophenyl hydrazine test
I found this reaction over here:
which illustrates the carbonyl test but looks fuzzy.
Assuming that the R in the product is a typo for H, I couldn't conserve the number of Nitrogen atoms.
What is the correct reaction?
Is this correct?
Is there a possibility of a methyl substitution on the ring in a variant of this test?
As you have already imagined, there is no magical $\ce{NO2}$ to $\ce{CH3}$ conversion in this classical reaction ;-)
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2021-06-19 04:11:08
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http://my2iu.blogspot.ch/2011/08/
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## Saturday, August 13, 2011
### Getting Type 1 Postscript Fonts from pdflatex
For the past several years, I've been using pdflatex to generate PDFs from my LaTeX, and it usually works like a charm. All modern versions of pdflatex correctly use type 1 (vector) postscript fonts and not type 3 (bitmap) fonts.
Just today, I was generating a PDF for a camera-ready, but whenever I looked at the list of fonts in the document, I kept seeing type 3 fonts there. I couldn't figure out where those type 3 fonts were coming from. I initially thought they might be from some figures, but that ended up not being the case. After playing with my document for a while, I discovered that the problem was that I was using some non-English characters, which was causing problems for LaTeX. Apparently my default installation of LaTeX had type 1 fonts that only covered the standard English character set (plus some accents). When I used characters like French guillemets quotation marks, LaTeX would need to use type 3 fonts because those were the only versions of the fonts with those characters. Using \usepackage[T1]{fontenc} did nothing since my LaTeX installation simply didn't have the necessary fonts.
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2017-06-24 15:44:59
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http://mathoverflow.net/feeds/question/76254
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What is so "plactic" about the plactic monoid? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T02:46:33Z http://mathoverflow.net/feeds/question/76254 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/76254/what-is-so-plactic-about-the-plactic-monoid What is so "plactic" about the plactic monoid? Oliver 2011-09-24T01:49:01Z 2012-01-22T04:09:51Z <p>The <a href="http://en.wikipedia.org/wiki/Plactic_monoid" rel="nofollow"><em>plactic monoid</em></a> is the monoid consisting of all words from the alphabet $\mathbb{Z}^+$ modulo certain relations. It is important mainly because its elements enumerate semistandard Young tableaux. </p> <p>I believe the plactic monoid was introduced by Knuth, but without that name. Lascoux and Schützenberger named it "<em>le monoïde plaxique</em>" in a French paper (1981) of the same name. (DISCLAIMER: I have never seen that paper; perhaps my second question is answered in it.)</p> <p>Several questions: </p> <p>1) How did <em>plaxique</em> $\rightarrow$ <em>plactic</em>? (This isn't the most obvious Anglicization; note that the <a href="http://www.ams.org/mathscinet-getitem?mr=646486" rel="nofollow">MathSciNet entry</a> for the original Lascoux/Schützenberger paper translates the title as <em>"Plaxic'' monoids</em>.) Who introduced the latter form of the word and why?</p> <p>2) What is <em>plactic/plaxique</em> supposed to mean? As far as I know neither was a word in their respective languages before being applied to the word <em>monoid/monoïde</em>. I am entertaining an etymology from Greek $\pi \lambda \alpha \xi$ "flat surface," but I don't find it very compelling.</p> http://mathoverflow.net/questions/76254/what-is-so-plactic-about-the-plactic-monoid/76396#76396 Answer by mhum for What is so "plactic" about the plactic monoid? mhum 2011-09-26T07:50:41Z 2011-09-26T08:07:16Z <p>You can find the original Lascoux & Schützenberger paper <a href="http://igm.univ-mlv.fr/~berstel/Mps/Travaux/A/1981-1PlaxiqueNaples.pdf" rel="nofollow">here</a>. My French (especially mathematical French) is not great, so I haven't been able to determine how the term "<em>plaxique</em>" comes in. However, I can observe that L&S first introduce <em>la congruence plaxique</em> and define <em>le monoïde plaxique</em> as the quotient of the free monoid over the congruence. So, it seems to me that they were really thinking of the congruence as plactic/plaxic more than the monoid itself (perhaps a fine distinction?). They highlight the relevant properties of the congruence in Proposition 2.5, so maybe that provides a clue?</p> <p>EDITED TO ADD: A quick scan of the OED yields no results for either "plactic" or "plaxic", but there is one result for the Latin "<em>plaxus</em>" under the etymology for the obsolete word "plash" (To bend down and interweave (stems partly cut through, branches, and twigs) so as to form a hedge or fence.):</p> <blockquote> <p>an unattested post-classical Latin form *plaxus , alteration of classical Latin <em>plexus</em> , past participle of <em>plectere</em> to plait, interweave, twine (see plexus n.)</p> </blockquote> <p>So, perhaps "<em>plaxique</em>" is meant to invoke a sense of intertwining or weaving? I could see how that could apply to the congruence relation. </p> <p>Bonus fun fact: Plaxico Burress makes an appearance in the OED in a citation for the entry "return date":</p> <blockquote> <p>New York Giants star receiver and gun nut Plaxico Burress breezed in and out of Manhattan Criminal Court in 15 minutes yesterday, with little happening besides the setting of a June 15 return date.</p> </blockquote> http://mathoverflow.net/questions/76254/what-is-so-plactic-about-the-plactic-monoid/76425#76425 Answer by quim for What is so "plactic" about the plactic monoid? quim 2011-09-26T13:54:21Z 2011-09-26T13:54:21Z <p>This is wild speculation, stemming only from the italian abstract to <a href="http://igm.univ-mlv.fr/~berstel/Mps/Travaux/A/1981-1PlaxiqueNaples.pdf" rel="nofollow">Lascoux & Schützenberger</a>. There, "monoide a placche" is used alongside the parallel construction "varietà a bandiere" (flag varieties). At the end of the "préface," "la cohomologie des variétés drapeaux sur les corps finis" appears (again, drapeau=flag) as one of the connections worth mentioning. It may be plausible to think of a "plaque" as a "rigid flag", or a "discrete flag". Which then prompts the <a href="http://mathoverflow.net/questions/58339/origin-of-terms-flag-flag-manifold-flag-variety" rel="nofollow">question</a> about the origin of <em>that</em> name...</p> http://mathoverflow.net/questions/76254/what-is-so-plactic-about-the-plactic-monoid/86352#86352 Answer by Oliver for What is so "plactic" about the plactic monoid? Oliver 2012-01-22T04:09:51Z 2012-01-22T04:09:51Z <p>The English translation of <em>Symmetric Functions, Schubert Polynomials and Degeneracy Loci</em> by Laurent Manivel contains the following footnote on the phrase "<em>plactic ring</em>":</p> <blockquote> <p>From the Greek $\pi \lambda \alpha \xi$, flat place, stone plate, tablet. This terminology is due to Lascoux and Sch\"utzenberger.</p> </blockquote> <p>There is no evidence provided for this assertion, but the fact that the author is French makes me suspicious that he has insider information. There is no discussion of why this name was chosen or what it is meant to suggest.</p>
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2013-05-23 02:46:27
|
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http://mathhelpforum.com/algebra/47948-prove-print.html
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prove that
• Sep 6th 2008, 04:17 PM
perash
prove that
• Sep 6th 2008, 09:23 PM
Soroban
Hello, perash!
I got the first half . . .
Quote:
$\text{Let: }\:A \;=\;\sqrt[3]{3 + 12\sqrt[3]{11} - 6\sqrt[3]{121}}\;\text{ and }\;B \;=\;\sqrt[3]{16 - 27\sqrt[3]{11} + 9\sqrt[3]{121}}$
$\text{Show (without using a calculator) that:}$
. . $(a)\;\;A + B \:=\:1\qquad\qquad (b)\;\;A\cdot B \:< \:\frac{1}{4}$
I happened to notice that: . $\begin{array}{ccc}3 + 12\sqrt[3]{11} - 6\sqrt[3]{121} &=& \left(\sqrt[3]{11} - 2\right)^3 \\ \\[-3mm] 16 -27\sqrt[3]{11} + 9\sqrt[3]{121} &=& \left(3 - \sqrt[3]{11}\right)^3 \end{array}$
(a) Therefore: . $A + B \;=\;\sqrt[3]{\left(\sqrt[3]{11}-2\right)^3} + \sqrt[3]{\left(3-\sqrt[3]{11}\right)^3} \;=\;\left(\sqrt[3]{11} - 2\right) + \left(3 - \sqrt[3]{11}\right) \;=\;1$
• Sep 7th 2008, 06:06 PM
sportsfan93b
Quote:
Originally Posted by Soroban
Hello, perash!
I got the first half . . .
I happened to notice that: . $\begin{array}{ccc}3 + 12\sqrt[3]{11} - 6\sqrt[3]{121} &=& \left(\sqrt[3]{11} - 2\right)^3 \\ \\[-3mm] 16 -27\sqrt[3]{11} + 9\sqrt[3]{121} &=& \left(3 - \sqrt[3]{11}\right)^3 \end{array}$
(a) Therefore: . $A + B \;=\;\sqrt[3]{\left(\sqrt[3]{11}-2\right)^3} + \sqrt[3]{\left(3-\sqrt[3]{11}\right)^3} \;=\;\left(\sqrt[3]{11} - 2\right) + \left(3 - \sqrt[3]{11}\right) \;=\;1$
In your final solution wouldnt the cube route and the 3rd pwr cancel out?
• Sep 7th 2008, 06:14 PM
Jhevon
Quote:
Originally Posted by sportsfan93b
In your final solution wouldnt the cube root and the 3rd pwr cancel out?
what do you mean? they did cancel out...
• Sep 7th 2008, 06:14 PM
11rdc11
What do you mean? It did cancel out in part A or did I misunderstand your question?
Lol I was too slow.
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2017-12-17 05:02:03
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https://homework.cpm.org/cpm-homework/homework/category/CC/textbook/CCA2/chapter/Ch10/lesson/10.1.3/problem/10-50
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Home > CCA2 > Chapter Ch10 > Lesson 10.1.3 > Problem10-50
10-50.
Consider the sequence of multiples of 11 that are less than 100. Write them as a series and find the sum. Homework Help ✎
11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99
495
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2019-10-16 17:43:54
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https://www.baryonbib.org/bib/36db7d36-c50f-4d2d-95db-ef895fb69246
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PREPRINT
36DB7D36-C50F-4D2D-95DB-EF895FB69246
Neutrino-pair emission in a strong magnetic field
E. N. E. van Dalen, A. E. L. Dieperink, A. Sedrakian, R. G. E. Timmermans
arXiv:nucl-th/0005029
Submitted on 11 May 2000
Abstract
We study the neutrino emissivity of strongly magnetized neutron stars due to the charged and neutral current couplings of neutrinos to baryons in strong magnetic fields. The leading order neutral current process is the one-body neutrino-pair bremsstrahlung, which does not have an analogue in the zero field limit. The leading order charged current reaction is the known generalization of the direct Urca processes to strong magnetic fields. While for superstrong magnetic fields in excess of ${10}^{18}$ G the direct Urca process dominates the one-body bremsstrahlung, we find that for fields on the order ${10}^{16}-{10}^{17}$ G and temperatures a few times ${10}^{9}$ K the one-body bremsstrahlung is the dominant process. Numerical computation of the resulting emissivity, based on a simple parametrization of the equation of state of the $npe$-matter in a strong magnetic field, shows that the emissivity of this reaction is of the same order of magnitude as that of the modified Urca process in the zero field limit.
Preprint
Comment: 11 pages, 6 figures, to appear in A&A
Subjects: Nuclear Theory; Astrophysics
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2022-09-24 15:34:57
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http://pubman.mpdl.mpg.de/pubman/faces/viewItemOverviewPage.jsp?itemId=escidoc:2082580
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de.mpg.escidoc.pubman.appbase.FacesBean
Deutsch
Hilfe Wegweiser Impressum Kontakt Einloggen
# Datensatz
DATENSATZ AKTIONENEXPORT
Freigegeben
Zeitschriftenartikel
#### Measurement of the χb(3P) mass and of the relative rate of χb1(1P) and χb2(1P) production
##### MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons30313
Blouw, J.
Division Prof. Dr. Werner Hofmann, MPI for Nuclear Physics, Max Planck Society;
http://pubman.mpdl.mpg.de/cone/persons/resource/persons30339
Britsch, M.
Division Prof. Dr. Werner Hofmann, MPI for Nuclear Physics, Max Planck Society;
http://pubman.mpdl.mpg.de/cone/persons/resource/persons37734
Fontana, Marianna
Division Prof. Dr. Werner Hofmann, MPI for Nuclear Physics, Max Planck Society;
http://pubman.mpdl.mpg.de/cone/persons/resource/persons37740
Popov, Dmitry
Division Prof. Dr. Werner Hofmann, MPI for Nuclear Physics, Max Planck Society;
http://pubman.mpdl.mpg.de/cone/persons/resource/persons30992
Schmelling, M.
Division Prof. Dr. Werner Hofmann, MPI for Nuclear Physics, Max Planck Society;
http://pubman.mpdl.mpg.de/cone/persons/resource/persons37744
Volyanskyy, Dmytro
Division Prof. Dr. Werner Hofmann, MPI for Nuclear Physics, Max Planck Society;
http://pubman.mpdl.mpg.de/cone/persons/resource/persons31206
Zavertyaev, M.
Division Prof. Dr. Werner Hofmann, MPI for Nuclear Physics, Max Planck Society;
##### Volltexte (frei zugänglich)
1409.1408.pdf
(Preprint), 755KB
##### Ergänzendes Material (frei zugänglich)
Es sind keine frei zugänglichen Ergänzenden Materialien verfügbar
##### Zitation
LHCb Collaboration, Aaij, R., Adeva, B., Adinolfi, M., Affolder, A., Ajaltouni, Z., et al. (2014). Measurement of the χb(3P) mass and of the relative rate of χb1(1P) and χb2(1P) production. Journal of high energy physics: JHEP, 2014(10): 088. doi:10.1007/JHEP10(2014)088.
The production of $\chi_b$ mesons in proton-proton collisions is studied using a data sample collected by the LHCb detector, at centre-of-mass energies of $\sqrt{s}=7$ and $8$ TeV and corresponding to an integrated luminosity of 3.0 fb$^{-1}$. The $\chi_b$ mesons are identified through their decays to $\Upsilon(1S)\gamma$ and $\Upsilon(2S)\gamma$ using photons that converted to $e^+e^-$ pairs in the detector. The relative prompt production rate of $\chi_{b1}(1P)$ and $\chi_{b2}(1P)$ mesons is measured as a function of the $\Upsilon(1S)$ transverse momentum in the $\chi_b$ rapidity range $2.0<y<4.5$. A precise measurement of the $\chi_b(3P)$ mass is also performed. Assuming a mass splitting between the $\chi_{b1}(3P)$ and the $\chi_{b2}(3P)$ states of 10.5 MeV/$c^2$, the measured mass of the $\chi_{b1}(3P)$ meson is $m(\chi_{b1}(3P))= 10515.7^{+2.2}_{-3.9}(stat) ^{+1.5}_{-2.1}(syst) MeV/c^2.$
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2018-02-18 03:18:45
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https://www.physicsforums.com/threads/can-i-split-up-the-left-hand-side-of-an-ode.712270/
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# Can I split up the left hand side of an ODE?
1. Sep 24, 2013
### GreenAce92
Should I just assume that any problems that involve integrating factor will always result in a perfect integral pair? That's probably not the right terminology but for instance if I have a differential equation which has had an integrating factor multiplied to both sides, then the left hand side most likely becomes a 'perfect integral' as an arbitrary example, a left hand side is y' e^2t + 2y e^2t which if I integrate this as a whole, I would say well that is y e^2t.
Can I assume that this will always be the case in terms of an entry level differential equations class? What happens if the left hand side is not easy to differentiate ?
Last edited: Sep 24, 2013
2. Sep 24, 2013
### UltrafastPED
You will learn a number of techniques; each will apply to a certain class of linear ordinary differential equations.
You should not expect a particular technique to work on every ODE.
3. Sep 24, 2013
### HallsofIvy
Staff Emeritus
What do you mean by "perfect integral"? In all except "pathological cases", both sides will be continuous which will certainly be "integrable". But I suspect that you mean "An integral that I can do" and that, of course, depends upon you!
(I remember in my very first d.e. course, first chapter, I was able to reduce a d.e. in a homework problem to an integral but just wasn't able to do the integral. The solution to the very next problem in the text was in the back of the book so I looked- and found that the answer was given in terms of an integral!)
If the problem is a "book home work" problem the either it is one that has been "made up" to be comparatively easy or you are expected to leave it as an integral. If you are talking about "real life", engineering problems, then "almost all" differential equations can be solved only numerically.
Did you mean to say "differentiate" here? You want to integrate to find the solution. And the whole point of an "integrating factor" is to get the left hand side in the form "$d\phi$" which has the obvious integral "$\phi$".
4. Sep 26, 2013
### GreenAce92
Thank you for the responses, reading my own posts it would seem clear that I have not been doing my work thus I don't even know what words I am using.
I have been studying and the material has been making sense
Still I find that lately I haven't had a good learning experience, specifically to me, I think that learning has become "this is what you want to do, find this on the test..." it's not really on "intuition" or instinct
When I read a real life problem like a lake draining and filling, or salt dissolving, it seems to make sense but at the same time, these methods seem like I am just expected to apply them. I can't say that the proof wasn't shown to us, I think the books cover the proofs of why these methods are valid...
Anyway, thank you for your time.
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2017-08-22 16:04:37
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http://math.stackexchange.com/questions/158110/find-all-functions-with-fx-y-fx-y-2-fx-fy-and-lim-limits-x
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# Find all functions with $f(x + y) + f(x - y) = 2 f(x) f(y)$ and $\lim\limits_{x\to\infty}f(x)=0$.
Determine all functions $f \colon\mathbb{R}\to\mathbb{R}$ satisfying the following two conditions:
(a) $f(x +y) + f(x - y) = 2 f(x) f(y)$ for all $x, y\in\mathbb{R}$;
(b) $\lim\limits_{x\to\infty}f(x) = 0$.
I found this problem in IMO 1985 longlist. I have been able to figure out that there is one solution of the form $f(x) = 0$ for all $x$.
Any other function satisfying the above has to have $f(0) = 1$ and $f(x) = f(-x)$.
However I don't know how to proceed.
Any thoughts?
-
Why is it that $f(0)=1$ if $f\neq0$? – miniBill Jun 14 '12 at 9:26
@miniBill: If $f\neq 0$ choose $x$ with $f(x)\neq 0$. Then take $y=0$ and apply the cancellation law to equation (a). – Shane O Rourke Jun 14 '12 at 11:25
Understood, thanks :) – miniBill Jun 14 '12 at 15:00
For any $x_0,y\in\mathbb{R}$, let $x=y+x_0$, then we have
$f(2y+x_0)+f(x_0)=2f(y+x_0)f(y)$
Hence,
$f(x_0) = 2f(y+x_0)f(y)-f(2y+x_0),\quad \forall y\in\mathbb{R}$
Consequently,
$\displaystyle f(x_0) = \lim_{y\to\infty}\left[f(x_0)\right] = \lim_{y\to\infty}\left[2f(y+x_0)f(y)-f(2y+x_0)\right] = 0$.
-
This argument generalizes much more easily than mine. – Erick Wong Jun 14 '12 at 5:24
I don't understand why you can say that $f(x_0)=\lim_{y\to\infty}\left[...\right]$ – miniBill Jun 14 '12 at 9:15
@miniBill The second to last line is true for all $y$ (in $\mathbb R$), so you can take the limit of $y$ to infinity and get the same value, but we know that value is also $0$. – Mark Hurd Jun 14 '12 at 10:19
I'm still not convinced that $f(x) = g(x,y) \forall y$ implies $f(x) = \lim_{y\to\infty}g(x,y)$ – miniBill Jun 14 '12 at 10:44
@miniBill You just take the limit of both sides. You don't need anything for that - in the end both sides are equal. Then on the LHS the sequence is constant and on the RHS we may use the assumption. – Simon Markett Jun 14 '12 at 10:47
Using $x=y$, we have $f(2x) = 2f(x)^2 - 1$. Pick $X>0$ large enough so that $|f(x)| < 1/2$ for all $x \ge X$. Then $|f(2X)| > 1/2$, a contradiction.
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Your argument is a nice one! – user17762 Jun 14 '12 at 5:30
With $y=x$, the condition is $f(2x)+f(0)=2f(x)^2$, not what you wrote. Taking $x\to\infty$ in the correct condition, we find that $f(0)=0$. – Jonathan Sep 5 '12 at 23:21
@Jonathan Did you not notice that $f(0)=1$? – Erick Wong Sep 6 '12 at 1:10
That's not a condition of the problem. You can show that $f(0)=f(0)^2$ so either $f(0)=0$ or $f(0)=1$. The limit condition rules out the possibility of $f(0)=1$. – Jonathan Sep 6 '12 at 1:43
@Jonathan Now you're just being deliberately obtuse. You can just as easily show that $f(x) = f(x) f(0)$ so either $f$ is identically zero or $f(0)=1$. Notice the OP already deduced this. – Erick Wong Sep 6 '12 at 4:27
This is really a comment, not a solution, but I don't have that option. If one only considers the functional equation (a), then there are lots of interesting solutions, namely $\cos ax$ and $\cosh ax$. If one "cheats" and uses imaginary arguments, one can combine these in one formula. By the standard method of inserting a power series and comparing coefficients, one can show that these are the only analytic solutions. Presumably, minimal smoothness conditions on a solution would imply analyticity. However, there are pathological non-measurable solutions. Of course, these solutions are not relevant for the original question since they do not vanish at infinity.
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2015-01-28 09:36:32
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https://chat.stackexchange.com/transcript/3740/2018/10/15
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11:01 PM
The tag has been created - surely this tag name was discussed before. Or am I confusing this with the tag of the same name on MathOverflow?
0
I am trying to understand the definition of the double handlebody that is given here: https://warwick.ac.uk/fac/sci/maths/people/staff/karen_vogtmann/tcc2016/lecture_1_oct_15_2014_edited.pdf page 9 and 10. That is, it is $\#_{n} S^1 \times S^2$ or two handlebodies ($\#_{n} S^1\times D^2$) identif...
Since the list of new tags says (topology) x 2, I suppose that one question with that tag (perhaps the one where it was created) was deleted.
I have simply removed the tag from this instance: math.stackexchange.com/posts/2957001/revisions
This tag was mentioned, for instance, here: chat.stackexchange.com/transcript/3740/2017/10/12
4
Resolved (a first step, anyway). The topology⇒general-topology tag synonym has been removed. Problem: I feel that there are quite a number of questions tagged with both general-topology AND algebraic-topology where the former is not really fitting. My understanding being that General Topolo...
SEDE shows one deleted question with the (topology) tag: data.stackexchange.com/math/query/883845/… - of course, that is the status from the last update of the data in SEDE. The deleted question is: Show that $\int {a_n}\ \in l^1$ is the sum $\sum_{n=1}^\infty a_n$ using Lebesgue Theory.
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2021-06-20 23:33:42
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https://hal-espci.archives-ouvertes.fr/LPT
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## Présentation du LPT
Le LPT (UMR 5152, Laboratoire de Physique Théorique) est un laboratoire de recherche localisé sur le campus de l'Université Paul Sabatier de Toulouse. Il a été fondé en 1991 et a été créé administrativement en 2003. Les chercheurs du LPT étaient rattachés au Laboratoire de Physique Quantique au sein du Groupe de Physique Théorique. L'expertise du LPT couvre les domaines de la matière condensée et la matière molle ainsi que la physique statistique et la physique non-linéaire.
Le LPT est membre de l’IRSAMC (Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes).
=> Les publications du LPT avant 2003 : HAL-LPQ_GPT.
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### Derniers dépôts, tout type de documents
[tel-02009806] Effects of information quantity and quality on collective decisions in human groups (2/14/19)
In this thesis, we were interested in the impact of the quantity and quality of information ex- changed between individuals in a group on their collective performance in two very specific types of tasks. In a first series of experiments, subjects had to estimate quantities sequentially, and could revise their estimates after receiving the average estimate of other subjects as social information. We controlled this social information through virtual participants (which number we controlled) giving information (which value we controlled), unknowingly to the subjects. We showed that when subjects have little prior knowledge about a quantity to estimate, (the loga- rithms of) their estimates follow a Laplace distribution. Since the median is a good estimator of the center of a Laplace distribution, we defined collective performance as the proximity of the median (log) estimate to the true value. We found that after social influence, and when the information provided by the virtual agents is correct, the collective performance increases with the amount of information provided (fraction of virtual agents). We also analysed subjects' sensitivity to social influence, and found that it increases with the distance between personal estimate and social information. These analyses made it possible to define five behavioral traits: to keep one's opinion, to adopt that of others, to compromise, to amplify social information or to contradict it. Our results showed that the subjects who adopt the opinion of others are the ones who best improve their performance because they are able to benefit from the infor- mation provided by the virtual agents. We then used these analyses to construct and calibrate a model of collective estimation, which quantitatively reproduced the experimental results and predicted that a limited amount of incorrect information can counterbalance a cognitive bias that makes subjects underestimate quantities, and thus improve collective performance. Further experiments have validated this prediction. In a second series of experiments, groups of 22 pedestrians had to segregate into clusters of the same "color", without visual cue (the colors were unknown), after a short period of random walk. To help them accomplish their task, we used an information filtering system (analogous to a sensory device such as the retina), taking all the positions and colors of individuals in input, and returning an acoustic signal to the subjects (emitted by tags attached to their shoulders) when the majority of their k nearest neighbors was of a different color from theirs.
[hal-02000196] $SU(4)$ topological RVB spin liquid on the square lattice (2/13/19)
[hal-01998097] Competing Bose-glass physics with disorder-induced Bose-Einstein condensation in the doped S = 1 antiferromagnet Ni(Cl(1−x)Br(x))2−4SC(NH2)2 at high magnetic fields (2/7/19)
[hal-01997431] Thermoelectricity of cold ions in optical lattices (1/30/19)
[hal-01995980] Wikipedia network analysis of cancer interactions and world influence (2/14/19)
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2019-02-17 13:43:21
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https://www.physicsforums.com/threads/linear-differential-equation-in-strange-form.466478/
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# Linear Differential Equation in Strange Form
## Homework Statement
ydx - 4(x + y^6)dy = 0
## Homework Equations
Need to get into the form of dy$$/dx$$ + f(x)y = G(x)
(Standard Form)
## The Attempt at a Solution
ydx = 4(x + y^6)dy
y = 4(x + y^6) dy/dx
y$$/4(x + y^6)$$ = dy/dx
then I don't know how to get it in the Standard form
All help is appreciated, thanks!
HallsofIvy
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2021-05-15 09:10:31
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https://iris.unisalento.it/handle/11587/393454
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The ARGO–YBJ experiment is a full-coverage air shower detector located at the Yangbajing Cosmic Ray Observatory (Tibet, People’s Republic of China, 4300 m a.s.l.). The high altitude, combined with the full-coverage technique, allows the detection of extensive air showers in a wide energy range and offer the possibility of measuring the cosmic ray proton plus helium spectrum down to the TeV region, where direct balloon/space-borne measurements are available. The detector has been in stable data taking in its full configuration from November 2007 to February 2013. In this paper the measurement of the cosmic ray proton plus helium energy spectrum is presented in the region 3–300 TeV by analyzing the full collected data sample. The resulting spectral index is γ = −2.64 \pm 0.01, the error is dominated by systematic uncertainties. The accurate measurement of the spectrum of light elements with a ground based air shower detector demonstrates the possibility of extending these measurements at larger energies, where galactic cosmic ray sources should run out of power in accelerating light elements.
### Cosmic ray proton plus helium energy spectrum measured by the ARGO-YBJ experiment in the energy range 3–300 TeV
#### Abstract
The ARGO–YBJ experiment is a full-coverage air shower detector located at the Yangbajing Cosmic Ray Observatory (Tibet, People’s Republic of China, 4300 m a.s.l.). The high altitude, combined with the full-coverage technique, allows the detection of extensive air showers in a wide energy range and offer the possibility of measuring the cosmic ray proton plus helium spectrum down to the TeV region, where direct balloon/space-borne measurements are available. The detector has been in stable data taking in its full configuration from November 2007 to February 2013. In this paper the measurement of the cosmic ray proton plus helium energy spectrum is presented in the region 3–300 TeV by analyzing the full collected data sample. The resulting spectral index is γ = −2.64 \pm 0.01, the error is dominated by systematic uncertainties. The accurate measurement of the spectrum of light elements with a ground based air shower detector demonstrates the possibility of extending these measurements at larger energies, where galactic cosmic ray sources should run out of power in accelerating light elements.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/393454
##### Attenzione
Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo
• ND
• 45
• 37
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2022-09-28 15:14:29
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https://labs.tib.eu/arxiv/?author=STAR%20Collaboration:%20B.%20Abelev
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• ### Near-side azimuthal and pseudorapidity correlations using neutral strange baryons and mesons in d+Au, Cu+Cu and Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV(1603.05477)
Aug. 1, 2016 nucl-ex
We present measurements of the near-side of triggered di-hadron correlations using neutral strange baryons ($\Lambda$, $\bar{\Lambda}$) and mesons ($K^0_S$) at intermediate transverse momentum (3 $<$ $p_T$ $<$ 6 GeV/$c$) to look for possible flavor and baryon/meson dependence. This study is performed in $d$+Au, Cu+Cu and Au+Au collisions at $\sqrt{s_{{NN}}}$ = 200 GeV measured by the STAR experiment at RHIC. The near-side di-hadron correlation contains two structures, a peak which is narrow in azimuth and pseudorapidity consistent with correlations due to jet fragmentation, and a correlation in azimuth which is broad in pseudorapidity. The particle composition of the jet-like correlation is determined using identified associated particles. The dependence of the conditional yield of the jet-like correlation on the trigger particle momentum, associated particle momentum, and centrality for correlations with unidentified trigger particles are presented. The neutral strange particle composition in jet-like correlations with unidentified charged particle triggers is not well described by PYTHIA. However, the yield of unidentified particles in jet-like correlations with neutral strange particle triggers is described reasonably well by the same model.
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2020-06-02 04:51:35
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https://stats.stackexchange.com/questions/501199/is-pearsons-chi-squared-test-of-independence-conditional-on-marginal-distributi
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# Is Pearson's chi-squared test of independence conditional on marginal distributions?
The Wikipedia page on Pearson's chi-squared test states that a difference to Fisher's exact test is that the latter makes the "assumption of fixed marginal distributions". I assume that applies to the use of chi-squared as a test of independence, because that is what Fisher's exact test does.
However, the description of the chi-squared test for independence clearly shows that it is a goodness-of-fit test which compares the observed joint distribution $$O_{i,j}$$ to the one expected under independence from the marginal distributions, $$E_{i,j} = N p_{i\cdot} p_{\cdot j},$$ which in turn are estimated from the observed marginals, $$p_{i\cdot} = \frac{O_{i\cdot}}{N} = \frac1N \sum_j O_{ij},$$ and correspondingly for $$p_{\cdot j}$$. As far as I can see that means that the test is conditional on given $$N$$, $$p_{i\cdot}$$, and $$p_{\cdot j}$$.
Can someone clear this up? Maybe Wikipedia is simply wrong?
With the chi-square test, in contrast, only the total number of counts, $$N$$, is taken as pre-specified. Although you do observe particular row totals and column totals, those are not fixed by design. Unlike with pre-specified row and column totals, the statistical test must take into account the sampling variability that might have led to those observed row and column totals, given only the toal number of counts.
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2021-08-06 02:22:37
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https://dsp.stackexchange.com/questions/50167/how-do-i-plot-the-square-of-the-amplitude-response
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# How do I plot the square of the amplitude response?
I have calculated the transfer function of an FIR filter
$$y[n] = x[n] + α · x[n − R]$$ This is what I have $$H(z) = 1 + αz^{-R}$$
Now I should plot the square of the amplitude response. So I calculated the frequency response by inserting e^jωTs for z. I should choose α = 1/2 and R = 3. So I get
$$H(e^{jωTs}) = 1 + αe^{-RjωTs} = 1 + \frac{1}{2} e^{-3jωTs}$$
$$|H(e^{jωTs})|^{2} = (1 + αe^{-RjωTs})^{²} = 1 + \frac{1}{2} e^{-6jωTs}$$
I am also not sure here about the algebra of the square of the magnitude.
Now I should plot from 0 to ωs and I think I am missing Ts. I should probably just choose a value, right? How is the usual approach?
• You have (at least) one issue with your "squared amplitude" the first equality in the last line does not hold, one should multiply $H()$ by its conjugate Jun 27 '18 at 14:59
• I don’t know what Ts is but I don’t like it. Also, that isn’t how you square numbers. Once you change it to multiply by the complex conjugate, don’t forget to FOIL! Oct 23 '18 at 12:41
If the impulse response $$h[n]=\delta[n]+\alpha \delta[n-R]\hspace{1cm}=\{1,0,0,...\alpha\}$$ with the ellipsis being R presumably, the Fourier transform $$H(\omega)=e^{-j 0 \omega}+\alpha e^{-jR \omega}=1+\alpha e^{-jR \omega}\hspace{1 cm}\exists\hspace{1 cm}\mathbb{C}$$ where magnitude is defined as $$\sqrt{x^{2}+y^{2}}=|x+iy|$$
Since we want the square of the amplitude response $$=|H(\omega)|^2$$, we can square the real and imaginary parts of the transform$$\Re{\{H(\omega)\}}^{2}+\Im{\{H(\omega)\}}^{2}\hspace{.5cm}=\hspace{.5cm}(1+\alpha \cos(-R\omega))^{2}+\alpha \sin(-R\omega)^2\hspace{.5cm}\exists\mathbb{R}$$ Then plot from $$\omega=[0,\pi)$$
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2021-10-15 22:55:32
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https://www.electro-tech-online.com/threads/pic-as-a-keyboard.159557/
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# PIC as a Keyboard
#### Suraj143
##### Active Member
I want PIC to send data via UART to PC so the PC will see as a key press.Is there any simple program to see this? All I found on internet using arduino & they using a keyboard library.
Is there any PIC example? Sending one or two key data is ok for me to understand.
Thanks
#### Nigel Goodwin
##### Super Moderator
What do you mean 'see as a key press'? - all you do is send ASCII data via the serial port (or on a modern PC via a serial/USB converter). You need some kind of program running on the PC in order to access the incoming text data.
#### Suraj143
##### Active Member
What do you mean 'see as a key press'? - all you do is send ASCII data via the serial port (or on a modern PC via a serial/USB converter). You need some kind of program running on the PC in order to access the incoming text data.
I mean there is no any keyboard connect to the PC.From PIC I send keyboard commands from UART.
#### Nigel Goodwin
##### Super Moderator
It's not really anything to do with the PIC, or the Arduino, both just send plain ASCII data out the serial port - the keyboard library for the Arduino is simply for connecting a matrix keypad to the PIC.
If you want the PC to do something with the data it needs to be running a program to do so, usually that's just a comms program.
#### Suraj143
##### Active Member
I mean when you just send ASCII characters via serial it needs a terminal program to see.
But when you send keystroke commands it will act likes a button pressed on the keyboard.
#### Nigel Goodwin
##### Super Moderator
OK, not a standard Arduino library then - you could probably do it with a suitable USB capable PIC? - essentially you're trying to build a USB PC keyboard using a PIC.
A quick google finds at least one suitable starting point.
#### Suraj143
##### Active Member
Many thanks That will make my requirement.I'm making a MIDI octopad, software is FL studio.Want to give MIDI signals via serial port to "serial MIDI" bridge software.All the examples are done with arduinos.SO I have to write from the begining to PIC micro.
#### rjenkinsgb
##### Well-Known Member
I'm making a MIDI octopad, software is FL studio.Want to give MIDI signals via serial port to "serial MIDI" bridge software.
MIDI just uses absolutely conventional serial comms and easily be done with a PIC, nothing special is required.
See below for the relevant MIDI transmit routines from a product we designed for a customer many years ago. I've commented them to try and make the various parts clear.
The full unit used piezo disc transducers, read by the PIC ADC channels to give touch sensitivity, with a 20KHz interrupt routine reading the input values. We made the electronics to fit the customers device enclosure.
The UART output just needs to drive a buffer with a couple of 220 Ohm resistors connected to that and 5V to give a standard MIDI output.
Ideally it should be buffered - but a typical PIC had got adequate current drive capability if you do not mind a direct external connection.
Or you can use a PNP transistor and switch the positive side, so UART pin low is still "current on" at the output.
Hardware interface info here:
You will need to add the main program with initialisation and a loop that continually checks for new keypresses.
If you want "note off" as well, send note on for that note using the same keypress function, but with a velocity of zero.
C:
// Buffer allocation
int tx_chan;
int buf[64];
int bufin;
int bufout;
int bufcount;
// Device setup, using CCS C compiler:
#include <18f452.h>
//#device icd=true
// HS = Normal xtal, H4 = pll * 4...
#fuses H4, NOWDT
#use delay(clock = 40000000)
#use rs232(BAUD = 31250, XMIT = PIN_C6, RCV = PIN_C7)
// Initialisation
void clearall(void)
{
bufin = 0;
bufout = 0;
bufcount = 0;
tx_chan = 10; // Channel 10 is MIDI percussion
}
// Routine to add a character/byte to the buffer
void putbuf(int i)
{
buf[bufin++] = i;
bufcount++;
bufin &= 0x3f;
}
// MIDI keypress function:
// n is note number, v is velocity
void keydown(int n, int v)
{
if(bufcount < 61)
{
putbuf(0x90+tx_chan);
putbuf(n & 0x7f);
putbuf(v & 0x7f);
}
}
// Routine to send "all off" command
void all_off(void)
{
putbuf(0xb0 + tx_chan);
putbuf(0x7b);
putbuf(0);
}
// Buffer transmit routine - call continuously from the program main loop
void sendata(void)
{
if(bufin == bufout)
{
bufcount = 0;
return;
}
{
putchar(buf[bufout++]);
bufout &= 0x3f;
bufcount--;
}
}
// Function to chek if UART TX ruffer is empty & ready for a new character
{
#bit pir1_txif=0xf9e.4;
#asm
movlw 1
movwf _return_
btfss pir1_txif
clrf _return_
nop
#endasm
}
#### Suraj143
##### Active Member
Many thanks rjenkinsgb
Here is my structure. I read piezo analog readings & process it & make MIDI strings & send via PIC UART to "MIDI Serial" software.That part I can do.After that from FL studio I map MIDI notes to its octopad note map.
The case I may occur in future is everytime I need FL studio.Is there any method to play MIDI without a PC?I just thinking to store MIDI wave files to an SD card MP3 player & call them from a UART thing.
#### rjenkinsgb
##### Well-Known Member
MIDI existed before PCs!
It was created to allow instruments to be directly connected and control each other.
I do not understand the "MIDI - Serial bridge" ??
The MIDI out from the PIC device can directly connect to any other standard MIDI instrument, or to a MIDI<>USB interface for a PC.
Re. storing .WAV files and playing them - that's exactly what this gadget does, another product from the same time.
The required set of .WAV files were built in to an EPROM that fitted the big socket, in this case.
That's not got "touch sensitivity" though, the PIC used was nowhere near powerful enough for complex audio processing.
For MIDI music playback, you can link to any keyboard/synthesiser that has MIDI in, or to a stand-alone MIDI sound module such as a Roland Sound Canvas. I have an SC-88 in my setup.
It appear you want near enough the exact same device as the mini drum kit, but set to MIDI channel 1 (or whichever) rather than channel 10 for percussion.
What PIC device do you have? As long as it is suitable, I can build you a version and let you have the .hex file for it.
ps. Personally, I do not like FL. I would highly recommend Tracktion though, and there is a completely free version of that with no restrictions at all.
#### Suraj143
##### Active Member
I do not understand the "MIDI - Serial bridge" ??
The MIDI out from the PIC device can directly connect to any other standard MIDI instrument, or to a MIDI<>USB interface for a PC.
In my method you dont need any musical instruments.All you need is a PC/laptop.PIC serial output connected to the PC via a TTL-USB cable Thats it.
The FL studio only supports MIDI devices.We dont have such devices/ instruments.We have only PIC part. So here comes the "MIDI - Serial bridge" which will makes a MIDI port to FL studio.
Whats the eeprom you using to store wave files? This is where I got stucked.
#### rjenkinsgb
##### Well-Known Member
So here comes the "MIDI - Serial bridge" which will makes a MIDI port
Gotcha!
That allows a normal RS232 port to appear as a MIDI interface to programs. Neat!
The midi player device used a 27C1001, if I remember right. I wrote a PC program that that could be used to import .wav files and build a binary image for the eprom, with an index to the various sound samples so the PIC program could associate the MIDI note with the appropriate sample, once the EPROM version was created.
#### Nigel Goodwin
##### Super Moderator
Gotcha!
That allows a normal RS232 port to appear as a MIDI interface to programs. Neat!
I'm still a bit baffled? - MIDI is simply a serial port?, just of a specific speed. The Commodore Amiga could easily be used for Midi via it's serial port, and I did projects for a couple of simple interfaces which were published in a couple of magazines. For those old enough to remember Joystick (game) ports on PC's, that also usually included a Midi specific serial port.
#### rjenkinsgb
##### Well-Known Member
I'm still a bit baffled? - MIDI is simply a serial port?, just of a specific speed.
Hardware wise, yes, just a serial port with a simple current loop interface; but no present music software will see a normal COM port as a MIDI interface.
They all expect a software translation layer between a physical (or virtual) port and the logical MIDI devices.
That's what the "Hairless MIDI" driver does, it provides the logical MIDI port that can be recognised by music software, allowing a COM port to be used for MIDI.
#### Nigel Goodwin
##### Super Moderator
Hardware wise, yes, just a serial port with a simple current loop interface; but no present music software will see a normal COM port as a MIDI interface.
They all expect a software translation layer between a physical (or virtual) port and the logical MIDI devices.
That's what the "Hairless MIDI" driver does, it provides the logical MIDI port that can be recognised by music software, allowing a COM port to be used for MIDI.
OK, so just PC software.
#### rjenkinsgb
##### Well-Known Member
Yep. That's what initially confused me, as "Midi to serial" seemed nonsensical - but it was not a physical conversion.
#### Suraj143
##### Active Member
Is there is a way to store WAV files into a flash memory in binary format? I have never done that.....!!
#### Nigel Goodwin
##### Super Moderator
Is there is a way to store WAV files into a flash memory in binary format? I have never done that.....!!
Yes, it's just a simple data array.
Depending how much 'quality' you're looking for even an 8 bit audio file is pretty decent quality - the Commodore Amiga (second mention in this thread ) only had 8 bit audio, but it gave absolutely stunning 8 bit stereo sound. Even more impressive as way back then all a PC could do was make a 'beep'.
If you google for 'esp32 play wav file' there are plenty of examples.
Or, a simple PIC version:
#### Suraj143
##### Active Member
Thanks.That links help me a lot.
Finally I want to play wav files when I get UART commands.Let say I have 300+ wave files stored in SD card.PIC will send UART number ' 1- 300'.The player should instantly play that particular WAV file.
I think ESP32 is much a better choice for this.It's supports more files than that PIC project.
|
2020-08-10 11:32:49
|
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http://www.gabormelli.com/RKB/Marginal_Probability_Function
|
# Marginal Probability Function
A marginal probability function is a multivariate probability function that reports the marginal probability value for an event (without aposteriori knowledge of the events for the other random variables).
## References
### 2009
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Marginal_distribution
• In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. The term marginal variable is used to refer to those variables in the subset of variables being retained. These terms are dubbed "marginal" because they used to be found by summing values in a table along rows or columns, and writing the sum in the margins of the table. The distribution of the marginal variables (the marginal distribution) is obtained by "marginalising" over the distribution of the variables being discarded.
• The context here is that the theoretical studies being undertaken, or the data analysis being done, involves a wider set of random variables but that attention is being limited to a reduced number of those variables. In many applications an analysis may start with a given collection of random variables, then first extend the set by defining new ones (such as the sum of the original random variables) and finally reduce the number by placing interest in the marginal distribution of a subset (such as the sum). Several different analyses may be done, each treating a different subset of variables as the marginal variables.
• ...
• Given two random variables $X$ and $Y$ whose joint distribution is known, the marginal distribution of $X$ is simply the probability distribution of $X$ averaging over information about Y. This is typically calculated by summing or integrating the joint probability distribution over Y.
• For discrete random variables, the marginal probability mass function can be written as Pr(X = x).
|
2019-12-08 11:25:43
|
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|
http://eprint.iacr.org/2009/154
|
## Cryptology ePrint Archive: Report 2009/154
Algorithms to solve massively under-defined systems of multivariate quadratic equations
Yasufumi Hashimoto
Abstract: It is well known that the problem to solve a set of randomly chosen multivariate quadratic equations over a finite field is NP-hard. However, when the number of variables is much larger than the number of equations, it is not necessarily difficult to solve equations. In fact, when n>m(m+1) (n,m are the numbers of variables and equations respectively) and the field is of even characteristic, there is an algorithm to solve equations in polynomial time (see [Kipnis et al, Eurocrypt'99] and also [Courtois et al, PKC'02]). In the present paper, we give two algorithms to solve quadratic equations; one is for the case of n>(about)m^2-2m^{3/2}+2m and the other is for the case of n>m(m+1)/2+1. The first algorithm solves equations over any finite field in polynomial time. The second algorithm requires exponential time operations. However, the number of required variables is much smaller than that in the first one, and the complexity is much less than the exhaustive search.
Category / Keywords: multivariate quadratic equation
Date: received 1 Apr 2009, last revised 28 Jun 2010
Contact author: hasimoto at isit or jp
Available format(s): PDF | BibTeX Citation
Note: Presented at Industrial Track in ACNS2010
Short URL: ia.cr/2009/154
[ Cryptology ePrint archive ]
|
2016-07-23 09:46:04
|
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|
http://debasishg.blogspot.com/2009/09/side-effects-with-kestrel-in-scala.html
|
## Sunday, September 06, 2009
### Side-effects with Kestrel in Scala
Consider the following piece of logic that we frequently come across in codebases ..
1. val x = get an instance, either create it or find it
2. manipulate x with post-creation activities (side-effects)
3. use x
Step 2 is only for some side-effecting operations, maybe on the instance itself or for some other purposes like logging, registering, writing to database etc. While working on the serialization framework sjson, I have been writing pieces of code that follows exactly the above pattern to create Scala objects out of JSON structures. Now if you notice the above 3 steps, step 2 looks like being a part of the namespace which calls the function that sets up x. But logically step 2 needs to be completed before we can use x. Which means that step 2 is also a necessary piece of logic that needs to be completed before we hand over the constructed instance x to the calling context.
One option of course is to make Step 2 a part of the function in Step 1. But this is not always feasible, since Step 2 needs access to the context of the caller namespace.
Let's look at an idiom in Scala that expresses the above behavior more succinctly and leads us into implementing one of the most popularly used objects in combinatory logic.
Consider the following method in Scala that creates a new instance of a class with the arguments passed to it ..
def newInstance[T](args: Array[AnyRef])(implicit m: Manifest[T]): T = { val constructor = m.erasure.getDeclaredConstructors.first constructor.newInstance(args: _*).asInstanceOf[T]}
I can use it like ..
newInstance[Person](Array("ghosh", "debasish"))
for a class Person defined as ..
case class Person(lastName: String, firstName: String)
It's often the case that I would like to have some operations on the new instance after its creation which will be pure side-effects. It may or may not mutate the new instance, but will be done in the context of the new instance. I can very well do that like ..
val persons = new ListBuffer[Person]()val p = newInstance[Person](Array("ghosh", "debasish"))persons += p // register to the listpersons.foreach(mail("New member has joined: " + p)) // new member mail to all//.. other stuff
It works perfectly .. but we can make the code more expressive if we can somehow be explicit about the context of the block of code that needs to go with every new instance of Person being created. Maybe something like ..
newInstance[Person](Array("ghosh", "debasish")) { p => persons += p persons.foreach(mail("New member has joined: " + p)) //.. other stuff}
This clearly indicates that the side-effecting steps of adding to the global list of persons or sending out a mail to every member is also part of the creation process of the new person. The effect is the same as the earlier example, only that it delineates the context more clearly. Though at the end of it all, it returns only the instance that it creates.
Consider another example of a good old Java bean ..
class Address { private String street; private String houseNumber; private String city; private String zip; //.. //.. getters and setters}
Working with a reflection based library it's not uncommon to see code that instantiates the bean using the default constructor and then allow clients to set the instance up with custom values .. something like ..
var p = Person(..)val pAddress = newInstance[Address](null) {a => a.setStreet("Market Street") a.setHouseNumber("B/102") a.setCity("San Francisco") a.setZip("98032") p.address = a p.mail("Your address has been changed to: " + a) }
Once again the block is only for side-effects, which can contain lots of other custom codes that depends on the caller's context. Make it more concise, DSLish using the object import syntax of Scala ..
var p = Person(..)val pAddress = newInstance[Address](null) {a => import a._ setStreet("Market Street") setHouseNumber("B/102") setCity("San Francisco") setZip("98032") p.address = a p.mail("Your address has been changed to: " + a) }
Looks like a piece of idiom that can be effective as part of your programming repertoire. Here is the version of newInstance that allows you to make the above happen ..
def newInstance[T](args: Array[AnyRef])(op: T => Unit)(implicit m: Manifest[T]): T = { val constructor = m.erasure.getDeclaredConstructors.first val v = constructor.newInstance(args: _*).asInstanceOf[T] op(v) v}
Looking carefully at newInstance I realized that it is actually the Kestrel combinator that Raymond Smullyan explains so eloquently in his amazing book To Mock a Mockingbird. A bird K is called a Kestrel if for any birds x and y, (Kx)y = x. And that's exactly what's happening with newInstance. It does everything you pass onto the block, but ultimately returns the new instance that it creates. A nice way to plug in some side-effects. Reg has blogged about Kestrels in Ruby - the tap method in Ruby 1.9 and returning in Rails. These small code pieces may not be as ceremonious as the popularly used design patterns, but just as effective and provide deep insights into how our code needs to be structured for expressivity. Next time you discover any such snippet that you find useful for sharing, feel free to write a few lines of blog about it .. the community will love it ..
Anonymous said...
why would I use
val x = newInstance[javax.swing.JTextField](Array(int2Integer(20))) { tf=>
tf.setBackground(java.awt.Color.WHITE)
}
val y = new javax.swing.JTextField(20) {
setBackground(java.awt.Color.WHITE)
}
I still get the side-effect within the construction scope, which I think was the original intent.
Debasish said...
As I mentioned in the post, this idiom is most effective when you are writing reflection based libraries where you instantiate classes based on reflection. Methods like newInstance comes in handy in such cases. And the kestrel can be used to apply side-effects in the proper context. And this idiom is not specific to instantiation only. You can also write Kestrel combinators for any other generic operation for which you would like to have some side-effects before handing it over to the user.
Seth Tisue said...
"You can also write Kestrel combinators for any other generic operation", or you could just write it once and be done:
def kestrel[T](x: T)(f: T => Unit) = { f(x); x }
a handy debugging tool using this:
def printing[T](x: T) = kestrel(x)(println)
so then e.g.:
scala> printing(3 + 3) + printing(2 + 2)
6
4
res6: Int = 10
Debasish said...
Seth -
It may not be as simple as you have defined with kestrel taking a single argument besides the closure. Have a look at typical Rails code that uses Kestrel like the following:
bank = returning Bank.find(...) do |b|
log "bank #{b} found"
end.bank
Here find can take various arguments. Hence I mentioned that it can be as generic but depending on the application or the domain.
Seth Tisue said...
That example works just fine with my version. You can pass any expression as the first argument:
kestrel(Bank.find(...)) { b =>
...
}
Debasish said...
oops .. sure it does. I missed it .. actually your implementation works fine for all kestrels that passes the newly instantiated / found object into the side-effecting block. I was going through Reg's blog and discovered this interesting variation in Ruby ..
Contact = Struct.new(:first, :last, :email) do
def to_hash Hash [*members.zip(values).flatten]
end
end
Struct takes an initializer block, but it doesn't pass the new class to the block as a parameter, it evaluates the block in the context of the new class.
These are some of the non-generic variations that we can have in implementing Kestrel. But your solution looks good for the majority of use cases. Thanks.
Rusco said...
Very useful !!!
But coming from Java I am still struggling with "Any"s, like in this case:
case class Person(age: Int, name: String) {
println ("in person")
}
def newInstance[T](args: scala.Array[AnyRef])
(implicit m: scala.reflect.Manifest[T]): T = {
val constructor = m.erasure.getDeclaredConstructors.first
constructor.newInstance(args: _*).asInstanceOf[T]
}
//now:
newInstance[Person](
scala.Array(new java.lang.Integer(44), "Martin Odersky"))
//why not:
newInstance[Person](
scala.Array(44, "Martin Odersky"))
I expected automatic / implicit casting to RichInt, but this is not what the 2.7.6 compiler requires ?!
jherber said...
|
2017-11-24 20:29:21
|
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https://documen.tv/question/please-help-its-due-at-12-its-2-questions-will-mark-brainliest-1-rick-buys-a-remote-control-car-22377811-77/
|
## PLEASE HELP! ITS DUE AT 12! ITS 2 QUESTIONS! WILL MARK BRAINLIEST 1: Rick buys a remote control car to resell. He pays $28 in ap Question PLEASE HELP! ITS DUE AT 12! ITS 2 QUESTIONS! WILL MARK BRAINLIEST 1: Rick buys a remote control car to resell. He pays$28 in applies a mark up of 10%. what is his reselling price?
write an expression:
find the retail price:
2: A bicycle shop marks down each bicycle selling price by 30% for a holiday sell. what is the sale price of a bicycle that regularly cost $150? write an expression: find the sale price: <3 in progress 0 4 days 2021-07-20T10:36:34+00:00 1 Answers 2 views 0 ## Answers ( ) 1. Answer: 1) The first expression is found by using the formula retail price = original cost + markup. If p is the original price, then the expression is p + 0.1p. The second expression can be found by simplifying the first expression. This gives 1.1p b) Substituting p = 28 into the second expression gives 1.1(28) = 30.8 so the selling price is$30.80
Step-by-step explanation:
i don’t know number 2 hope that helps
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2021-07-24 04:53:12
|
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|
https://en.wikipedia.org/wiki/Moving_crack_(metalworking)
|
# Moving crack (metalworking)
A moving crack is a crack that propagates with some speed due to loading and unloading of a metal work material.[clarification needed] When loading and unloading is being done, a large fraction of irreversible energy associated with those actions is eventually dissipated as heat and other part is being stored in the work material due to change in material structure and constraints caused dislocation pile-ups, etc.[1] The fraction of heat dissipated in material (${\displaystyle \beta }$) depends on type of material of fracture model is being used there. By conducting some experiments, it is found that the fraction ${\displaystyle \beta }$ dissipated as heat may be as large as 0.85-0.95 for metals,[2][3] but this value doesn't depend on the magnitude and rate of deformation.[3][4] So according to work of Mason, ${\displaystyle \beta }$ can be as small as 0.5 for aluminium and steel at low value of strains only and for titanium at both and low value of strains.
## Heat generation and temperature increment
In general, the amount of loading and unloading energy which is converted into heat is for unit volume having high value. So this large value of heat generation per unit of volume results in substantial rise in temperature of the tip of the moving crack. This temperature rise can be of several hundred degrees Celsius as found in experiment done by Mason and Rosakis[5] and others. The process region near tip of moving crack is the zone for maximum temperature.[6]
## Temperature measurement
Mostly, for measurement of temperature at tip of moving crack mode-I of fracture is being preferred. But maximum temperatures are expected for other two modes-(I, II)of fracture due large deformations with shear banding, particularly with high confining pressure, where impact generated shear bands is due to the impact load itself.[6] According to a study by Zhou et al.[7] and Rosakis et al.(1997)[8] on impact produced shear bands of mode-II gives a result of temperature rises of over 1650 K for C-300 steel. These temperatures are being measured by special purpose high precision thermocouple.
## Mathematical formulation of temperature of moving crack tip
If one applies the cell model of material and given total energy supply as ${\displaystyle A}$ to a central cell (this can be found by the area of a cohesion-decohesion curve)[citation needed], with heat generated = ${\displaystyle \beta A}$, where ${\displaystyle \beta }$ = fraction of energy supplied converted into heat energy and considering adiabatic temperature rise i.e. no heat is going out by conduction, temperature rise becomes:
${\displaystyle T={\frac {\beta A}{\rho cd^{3}}}}$
where ${\displaystyle \rho }$ = density, ${\displaystyle c}$ = specific heat, ${\displaystyle d^{3}}$ = volume of the cell.[9] The above calculation of T conduction of heat from the body has been neglected and this assumption is not valid.
Revising this for conduction using the moving crack tip governing equation for heat conduction for the upper half of the crack (${\displaystyle y>0}$, where ${\displaystyle y=0}$ is the plane passing through crack) in ${\displaystyle x}$-direction is
${\displaystyle \Delta T-{\frac {1}{a^{2}}}{\frac {\partial T}{\partial t}}=-{\frac {1}{\lambda }}{\frac {\partial Qv}{\partial t}}}$[10]
where ${\displaystyle T}$ is temperature at time ${\displaystyle t}$, ${\displaystyle \lambda }$ is conductivity of material, ${\displaystyle a^{2}}$ is the diffusivity of material ${\displaystyle {\frac {\lambda }{\rho c}}}$, and ${\displaystyle Qv(x,y,z,t)}$ is the heat per unit volume. Solving this heat conduction equation using Laplace transform, one gets
${\displaystyle T={\frac {Qv}{\rho c}}\operatorname {erf} \left({\frac {h}{4a{\sqrt {t}}}}\right)}$
where, ${\displaystyle \operatorname {erf} (z)={\frac {2}{\sqrt {\pi }}}\int _{0}^{z}e^{-t^{2}}\,\mathrm {d} t.}$ is the error function.
Using the final equation of ${\displaystyle T}$, one can calculate the temperature at the tip of the moving crack.
## References
1. ^ Ewalds, H.L.; Wanhill, R.J.H. (1984). Fracture Mechanics. Edward Arnold. ISBN 0-7131-3515-8.
2. ^ Taylor, G. I.; H. Quinney (1934). "The Latent Energy Remaining in a Metal after Cold Working". Proceedings of the Royal Society A. 143: 307–326. doi:10.1098/rspa.1934.0004.
3. ^ a b Bever, M.B.; D.L. Holt; A.L. Titchener (1973). "The stored energy of cold work". Prog. Mat. Sci. 17 (1).
4. ^ Mason, J.J.; Rosakis, A.J.; Ravichandran, G. (1994). "On the strain and strain rate dependence of the fraction of plastic work converted into heat: an experimental study using high speed infrared detectors and the Kolsky bar". Mechanics of Materials. 17: 135–145. doi:10.1016/0167-6636(94)90054-x.
5. ^ Mason, J. J.; A. J. Rosakis (1993). "On the Dependence of the Dynamic Crack Tip Temperature Fields in Metals Upon Crack Tip Velocity and Material Parameters". SM Report. 92 (3).
6. ^ a b D’Amico, F.; G. Carbone; M.M. Foglia; U. Galietti (2013). "Moving cracks in viscoelastic materials: Temperature and energy-release-rate measurements". Engineering Fracture Mechanics. 98: 315–325. ISSN 0013-7944. doi:10.1016/j.engfracmech.2012.10.026.
7. ^ Zhou, S.J; P.S. Lomdahl; R. Thomson; B.L. Holian (1996). "Dynamic crack processes via molecular dynamics". Phys. Rev. Lett. 76: 2318–2321. PMID 10060667. doi:10.1103/physrevlett.76.2318.
8. ^ Rosakis et al.(1997)
9. ^ Yunus A. Cengel - Thermodynamics
10. ^ Heat transfer by J.P.Holman (conduction equation)
|
2017-10-18 02:25:36
|
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|
https://tex.stackexchange.com/questions/418283/citation-number-color
|
# citation number color
I am writing my thesis in latex. But I wanna change "some" citation numbers color in text. my citation number color setting is as follows:
\usepackage[unicode=true,pagebackref=true,
%\usepackage{todonotes}
\usepackage[firstpage]{draftwatermark}
\SetWatermarkText{\ \ \ pishnevis}
\SetWatermarkScale{1.2}
}
{
%\usepackage[disable]{todonotes} % final without TODOs
}
as you see, the above setting makes my citation number color to blue. but I want to change some citation colors to black.
for example only:
\cite{turnow2012flow}
changes to black not blue.
You can use the \hypersetup command to change the citation command. Enclosing it in a group {...} will make the change. Thus for example
\newcommand{\redcite}[1]{{\hypersetup{citecolor=red}\cite{#1}}}
provides a basic citation command that prints the citation in red instead of the current default.
\documentclass{article}
\newcommand{\redcite}[1]{{\hypersetup{citecolor=red}\cite{#1}}}
\begin{document}
\cite{article-minimal}
\redcite{article-minimal}
\cite{article-minimal}
\bibliographystyle{plain}
\bibliography{xampl}
\end{document}
|
2019-10-22 21:37:14
|
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|
http://crypto.stackexchange.com/questions?page=35&sort=votes
|
# All Questions
669 views
### is this RSA private key valid?
is this RSA private key valid? First, here's the RSA private key in question: ...
322 views
### A discrete-log-like problem, with matrices: given $A^k x$, find $k$
Let $p$ be a large prime; we will work in $GF(p)$. Let $A$ be a $n\times n$ matrix. Also, let $x$ be a $n$-vector and $k$ a positive integer. Suppose we are given $p$, $A$, $x$, and $y$. The goal ...
1k views
### Implementing AES encryption for firmware distribution system
I need to implement an AES encryption for firmware distribution system. I have a bootloader that can decrypt various AES variants (ECB,CBC,CTR). When I approached this I found few issues that aren't ...
224 views
### How to communicate authentication tag for GCM?
I have written some code to do AES in GCM. I currently manually append the tag property to the ciphertext, is this the proper way to communicate the authentication tag?
511 views
### How can I solve the discrete logarithm modulo 2q+1 if I can solve it in the subgroup of order q?
As part of my cryptography course I came across an exercise that neither me or my friends could figure out. The problem statement is as follows: Let $p$ be a large prime of the form $p = 2q + 1$ ...
293 views
### Does Identity-Based Encryption actually solve any problem?
Identity based encryption schemes [*] seem to have great potential in high-latency Delay-Tolerant and mobile, ad-hoc networks since they apparently seem to avoid the need for key negotiation and ...
155 views
### Proof of work scheme with one and only one correct answer
I need a problem that has one and only one solution, such that the solution is hard to find but easy to verify. I need to be able to generate the problem deterministically from a random seed. So ...
244 views
### Is this streamable combination of encryption and MAC secure?
I want to combine encryption and MAC. For encryption I use AES-256 with CBC and PKCS5Padding. For MAC I use HmacSHA512. I use the Encrypt-then-Mac approach (calculate MAC over the ciphertext and ...
273 views
### LFSR dynamic mutation
In normal LFSR, the state is a function of the initial seed, taps positions and time, nothing else. I've seen a modification of LFSR that works like this: ...
915 views
### Efficient and stateless anti-forgery method
One use of an anti-forgery token is to prevent Cross-Site Request Forgery (CSRF) attacks. The attacker doesn't need to sniff the wire in order to carry out a CSRF attack. This attack relays on the ...
150 views
### Does security under ROM imply exactly what?
I'm not sure I understand really the implications of proofs of security in the random oracle model. Does a proof of security in ROM translate to a reduction of security of the crypto-system to the ...
533 views
### Can one group the SHA-256 outputs depending on partial inputs?
Is it possible to predict a hash key based on half key? Let's have some example: I have 100000000 hash results, and they are generated by either ...
2k views
### How to attack a general polyalphabetic cipher?
I am able to decrypt vigenere cipher text using the index of coincidence and chi test. However out of interested how do you go about attacking ciphertext that was encrypted using a mix alphabet ...
510 views
### How can one break a monoalphbetic substitution chipher at pseudorandom text?
Does anybody know how to break monoalphbetic substitution cipher, if it is applied to some pseudorandom text (for example to some surrogate key filed in a database)? Let us assume that we have only ...
231 views
### How common are SEED certificates outside of Korea? When is support required?
I'm looking at the SEED algorithm and would like to know if this is still in common usage. Can anyone tell me when I would need to implement this standard, either as a client or a server?
77 views
### Hashing a Diffie-Hellman result
In many implementations, the result of the Diffie-Hellman algorithm is hashed. I read that: Hashing the shared secret point prevents an attacker from gaining more information about the EC private ...
116 views
### EdDSA Signature Algorithm - hash of secret key
Why does EdDSA use the (SHA512) hash of the secret key as the exponent for the public key rather than using the secret key value directly? This seems inefficient and I can't see how it adds any extra ...
77 views
116 views
### Generic group model: use of polynomials in the proof of the master theorem
I've been looking at the paper of Boneh, Boyen, Goh Hierarchical Identity Based Encryption with Constant Size Ciphertext which contains a general theorem (Theorem A.2) about the advantage of an ...
74 views
### Statistical tests for pseudorandom permutations
I'm implementing a format-preserving encryption scheme similar to those described in the literature. I want to sanity test my PRP using some statistical tests like TestU01. However, I'm not sure how ...
216 views
### Using Lattice-based cryptography for TLS\SSL
Given the general benefits of Lattice-based cryptography, such as: Post quantum Security Security from worst case scenario Efficiency What could the outlook of shifting from RSA \ ECC-based ...
104 views
### OTT service using FPE
Would it be possible to create an Over-The-Top communication utility that will encrypt voice using format preserving encryption (voice clear-text to audio encrypted stream) and send that over an ...
195 views
### Implementing CD serial key system
I am trying to create a system where to unlock the application one needs to enter a serial code. I have read many articles on the theme but there are two problems bugging me. One is, If I have a ...
484 views
### Is there a generic attack on encrypted CRC32 when used as a MAC?
I am examining a protocol that uses CRC32 as a MAC (see note 1) the weaknesses of this method but I would nevertheless like to see if it is just weak or actually relatively easily to break. The ...
69 views
### Are HMACs based on hashes with larger bit-lengths also more secure?
When doing encrypt-then-mac, I can choose to use a hmac as the MAC. For example, I could use a hash like SHA-256 or SHA-512 (by using it as a keyed hash) to create that HMAC. Does it increase ...
127 views
### McEliece and cryptanalysis
What is the computational time to break McEliece on a quantum computer? I've seen that polynomial time algorithms exist, but for special conditions. What about the general case?
307 views
### Can a homomorphic encryption scheme be made CCA2 Secure?
Is it possible to modify a homomorphic encryption scheme so that it can be CCA2 secure? From the definition of a homomorphic scheme, it seems that it is malleable, which would result in lack of CCA2 ...
152 views
### How do I decide what mode to use?
I'll be using AES from OpenSSL. I understand why I don't want to use ECB from reading pages like this Wikipedia article, which has a great example of what happens when you attempt to encrypt with ...
125 views
### Use of less than secure random numbers for 'a' during an SRP proof of password
With Secure Remote Password protocol SRP6a random numbers are used for s, a and b. Where ...
139 views
### Hide message length in symmetric key cryptography
Is there any way to hide message length from adversary in symmetric key cryptography? Suppose we want to hide message length from active and efficient adversaries.
167 views
### Hash collision resistance of $\mathcal H^\prime(m) = \mathcal H(\mathcal H(m)|m)$
So far as I can find, every method better at producing hash collisions in cryptographic hashes than generic collision search involves finding some metric for the distance between two messages' hashes ...
214 views
### Is there an algorithm to check if an elliptic curve is secure?
As I understand it elliptic curves are of the form $y^2 = x^3 + ax + b$ Where $a$ and $b$ are the curve parameters. However not all parameters will give a curve suitable for crypto purposes. Is there ...
75 views
### What is the Geometric Generalised T' Method?
This page by Nicolas T. Courtois mentions Geometric Generalised T' Method. It is described as an advanced geometric algorithm, never published, for finding extra linearly independent equations at ...
791 views
### Is PKCS #1 v1.5 RSA encryption padding secure under these conditions?
The PKCS #1 v1.5 padding scheme for RSA has been proven to have some weakness when used with TLS for example. My question is: is it still secure under the following conditions? Alice sends a ...
170 views
### Private set intersection, using a semi-trusted server
Alice has a set $S$ of words. Bob has a set $T$ of words. They want to compute the intersection $S \cap T$ of their words, with the help of a semi-trusted third party Trent. Trent runs a central ...
917 views
### Questions about OAEP for RSA
I have two questions about OAEP for RSA. How are the number of bits to pad with 0 chosen? For example, if I'm sending a 255 byte message with RSA-2048 I have 8 unused bits (1 byte). Should I split ...
153 views
### Reason for difference in assumptions for practical private-key and public-key crypto
Theoretical cryptography tells us that everything in the world of private-key cryptography (CCA-secure symmetric encryption, message authentication codes, etc.) can be built from one-way functions and ...
137 views
### Encrypting a TCP connection between two unknown nodes
I'm writing an application for controlling computers from a client. I'd very much like it if the connection is secure and only authenticated clients are allowed access. The workflow will be ...
1k views
### Good entropy source for generating openssl keys
I need to generate a CA (4096-bit RSA) and server keys for openvpn and I want them to be "top quality". Here is my plan: gather entropy from multiple sources (saving individual files): FreeBSD ...
281 views
### Brute Force on 3DES with Reduced Keyspace and Unknown IV
I'm trying to brute force a 3DES problem given a reduced keyspace (ie I know the first half of the key) but with an unknown IV. The code decrypts to plaintext. My first thought was that I could set ...
165 views
### Cryptanalysis of AES on SSD with TRIM enabled
Attack scenario: SSD physically retrieved from a computer that is turned off. The entire disk is encrypted with AES 256-bit (GNU/Linux, LUKS). The SSD has had TRIM enabled for several years and the ...
187 views
### Keyed digest function with odds of collision below the birthday bound?
I wonder if it is possible to devise a function $F(K,S,R_S)\mapsto D$ where: $K$ is some key (I have freedom on $K$, it could even be generated by a trusted party); $S$ is in $\{0,1\}^s$, say ...
175 views
### Can I use the ChaCha core as a 256-bit to 256-bit one-way function?
I'm looking to implement Lamport signatures as a little fun project, and I need a fast one way function that maps $\{0,1\}^{256} \rightarrow \{0,1\}^{256}$. I was wondering whether I could safely use ...
652 views
### RSA least significant bit oracle attack
I have been reading up on RSA attacks and came across one that could be called a least-significant-bit (LSB) oracle attack. For the sake of clarity lets define RSA primes $(p, q)$, private key $d$ ...
|
2015-08-31 02:34:33
|
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|
https://mathemerize.com/tag/different-equations-of-straight-lines/
|
## Equation of Straight Lines in all Forms
Here, you will learn equation of straight lines in all forms i.e. slope form, intercept form, normal form and parametric form etc. Let’s begin – A relation between x and y which is satisfied by co-ordinates of every point lying on a line is called equation of the straight lines. Here, remember that every one …
|
2022-09-28 20:19:28
|
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|
https://blog.csdn.net/zwj1452267376/article/details/47173431
|
# Doing Homework again
Time Limit: 1000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 8730 Accepted Submission(s): 5157
Problem Description
Ignatius has just come back school from the 30th ACM/ICPC. Now he has a lot of homework to do. Every teacher gives him a deadline of handing in the homework. If Ignatius hands in the homework after the deadline, the teacher will reduce his score of the final test. And now we assume that doing everyone homework always takes one day. So Ignatius wants you to help him to arrange the order of doing homework to minimize the reduced score.
Input
The input contains several test cases. The first line of the input is a single integer T that is the number of test cases. T test cases follow.
Each test case start with a positive integer N(1<=N<=1000) which indicate the number of homework.. Then 2 lines follow. The first line contains N integers that indicate the deadlines of the subjects, and the next line contains N integers that indicate the reduced scores.
Output
For each test case, you should output the smallest total reduced score, one line per test case.
Sample Input
3
3
3 3 3
10 5 1
3
1 3 1
6 2 3
7
1 4 6 4 2 4 3
3 2 1 7 6 5 4
Sample Output
0
3
5
#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
struct stu
{
int d;
int s;
}a[1010];
int cmp(stu a,stu b)
{
return a.s>b.s;
}
int main()
{
int t,n,i,j,mark[1010],count,sign;
scanf("%d",&t);
while(t--)
{
memset(mark,0,sizeof(mark));
scanf("%d",&n);
for(i=0;i<n;i++)
scanf("%d",&a[i].d);
for(i=0;i<n;i++)
scanf("%d",&a[i].s);
sort(a,a+n,cmp);
count=0;
for(i=0;i<n;i++)
{
sign=0;
for(j=a[i].d;j>0;j--)
{
if(mark[j]==0)
{
mark[j]=1;//标记完成的学科，和用掉的整天
sign=1;
break;
}
}
if(!sign)
count+=a[i].s;
}
printf("%d\n",count);
}
return 0;
}
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2020-10-24 12:56:50
|
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|
https://xianblog.wordpress.com/tag/monte-carlo-statistical-methods/
|
## fiducial simulation
Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on April 19, 2018 by xi'an
While reading Confidence, Likelihood, Probability), by Tore Schweder and Nils Hjort, in the train from Oxford to Warwick, I came upon this unexpected property shown by Lindqvist and Taraldsen (Biometrika, 2005) that to simulate a sample y conditional on the realisation of a sufficient statistic, T(y)=t⁰, it is sufficient (!!!) to simulate the components of y as y=G(u,θ), with u a random variable with fixed distribution, e.g., a U(0,1), and to solve in θ the fixed point equation T(y)=t⁰. Assuming there exists a single solution. Brilliant (like an aurora borealis)! To borrow a simple example from the authors, take an exponential sample to be simulated given the sum statistics. As it is well-known, the conditional distribution is then a (rescaled) Beta and the proposed algorithm ends up being a standard Beta generator. For the method to work in general, T(y) must factorise through a function of the u’s, a so-called pivotal condition which brings us back to my post title. If this condition does not hold, the authors once again brilliantly introduce a pseudo-prior distribution on the parameter θ to make it independent from the u’s conditional on T(y)=t⁰. And discuss the choice of the Jeffreys prior as optimal in this setting even when this prior is improper. While the setting is necessarily one of exponential families and of sufficient conditioning statistics, I find it amazing that this property is not more well-known [at least by me!]. And wonder if there is an equivalent outside exponential families, for instance for simulating a t sample conditional on the average of this sample.
## accelerating MCMC
Posted in Books, Statistics, University life with tags , , , , , , , , , , , , on April 11, 2018 by xi'an
As forecasted a rather long while ago (!), I wrote a short and incomplete survey on some approaches to accelerating MCMC. With the massive help of Victor Elvira (Lille), Nick Tawn (Warwick) and Changye Wu (Dauphine). Survey which current version just got arXived and which has now been accepted by WIREs Computational Statistics. The typology (and even the range of methods) adopted here is certainly mostly arbitrary, with suggestions for different divisions made by a very involved and helpful reviewer. While we achieved a quick conclusion to the review process, suggestions and comments are most welcome! Even if we cannot include every possible suggestion, just like those already made on X validated. (WIREs stands for Wiley Interdisciplinary Reviews and its dozen topics cover several fields, from computational stats to biology, to medicine, to engineering.)
## MCMC with multiple tries
Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , on April 5, 2018 by xi'an
Earlier this year, Luca Martino wrote and arXived a review on multiple try MCMC. As its name suggests, the starting point of this algorithm is to propose N potential moves simultaneously instead of one, possibly according to N different proposal (conditional) densities, and to select one by a normalised importance sampling weight. The move is accepted by a Metropolis-Hastings step based on the ratio of the normalisation constants [at the current and at the one-before-current stages]. Besides the cost of computing the summation and generating the different variates, this method also faces the drawback of requiring N-1 supplementary simulations that are only used for achieving detailed balance and computing a backward summation of importance weights. (A first section of the review is dedicated to independent Metropolis-Hastings proposals, q(θ), which make life simpler, but are less realistic in my opinion since some prior knowledge or experimentation is necessary to build a relevant distribution q(θ).) An alternative covered in the survey is ensemble Monte Carlo (Neal, 2011), which produces a whole sample at each iteration, with target the product of the initial targets. This reminded me of our pinball sampler, which aimed at producing a spread-out sample while keeping the marginal correct. Although the motivation sounds closer to a particle sampler. Especially with this associated notion of an empirical approximation of the target. The next part of the review is about delayed rejection, which is a natural alternative approach to speeding up MCMC by considering several possibilities, if sequentially. Started in Antonietta Mira‘s 1999 PhD thesis. The difficulty with this approach is that the acceptance probability gets increasingly complex as the number of delays grows, which may annihilate its appeal relative to simultaneous multiple tries.
## X entropy for optimisation
Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on March 29, 2018 by xi'an
At Gregynog, with mounds of snow still visible in the surrounding hills, not to be confused with the many sheep dotting the fields(!), Owen Jones gave a three hour lecture on simulation for optimisation, which is a less travelled path when compared with simulation for integration. His second lecture covered cross entropy for optimisation purposes. (I had forgotten that Reuven Rubinstein and Dirk Kroese had put forward this aspect of their technique in the very title of their book. As “A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning”.) The X entropy approaches pushes for simulations restricted to top values of the target function, iterating to find the best parameter in the parametric family used for the simulation. (Best to be understood in the Kullback sense.) Now, this is a wee bit like simulated annealing, where lots of artificial entities have to be calibrated in the algorithm, due to the original problem being unrelated to an specific stochastic framework. X entropy facilitates concentration on the highest values of the target, but requires a family of probability distributions that puts weight on the top region. This may be a damning issue in large dimensions. Owen illustrated the approach in the case of the travelling salesman problem, where the parameterised distribution is a Markov chain on the state space of city sequences. Further, if the optimal value of the target is unknown, avoiding getting stuck in a local optimum may be tricky. (Owen presented a proof of convergence for a temperature going to zero slowly enough that is equivalent to a sure exploration of the entire state space, in a discrete setting, which does not provide a reassurance in this respect, as the corresponding algorithm cannot be implemented.) This method falls into the range of methods that are doubly stochastic in that they rely on Monte Carlo approximations at each iteration of the exploration algorithm.
During a later talk, I tried to recycle one of my earlier R codes on simulated annealing for sudokus, but could not find a useful family of proposal distributions to reach the (unique) solution. Using a mere product of distributions on each of the free positions in the sudoku grid only led me to a penalty of 13 errors…
1 2 8 5 9 7 4 9 3
7 3 5 1 2 4 6 2 8
4 6 9 6 3 8 5 7 1
2 7 5 3 1 6 9 4 8
8 1 4 7 8 9 7 6 2
6 9 3 8 4 2 1 3 5
3 8 6 4 7 5 2 1 9
1 4 2 9 6 3 8 5 7
9 5 7 2 1 8 3 4 6
It is hard to consider a distribution on the space of permutations, 𝔖⁸¹.
## Bayes Comp 2018 [call for guest posts]
Posted in Mountains, pictures, Statistics, Travel, University life with tags , , , , , , , on March 26, 2018 by xi'an
As the next MCMski conference, now called Bayes Comp, is starting in Barcelona, Spain, March 26-29, I welcome all guest posts covering the conference, since I am not going to be there! Enjoy!
## an interesting identity
Posted in Books, pictures, Statistics, University life with tags , , , , , , , , on March 1, 2018 by xi'an
Another interesting X validated question, another remembrance of past discussions on that issue. Discussions that took place in the Institut d’Astrophysique de Paris, nearby this painting of Laplace, when working on our cosmostats project. Namely the potential appeal of recycling multidimensional simulations by permuting the individual components in nearly independent settings. As shown by the variance decomposition in my answer, when opposing N iid pairs (X,Y) to the N combinations of √N simulations of X and √N simulations of Y, the comparison
$\text{var} \hat{\mathfrak{h}}^2_N=\text{var} (\hat{\mathfrak{h}}^1_N)+\frac{mn(n-1)}{N^2}\,\text{var}^Y\left\{ \mathbb{E}^{X}\left\{\mathfrak{h}(X,Y)\right\}\right\}$
$+\frac{m(m-1)n}{N^2}\,\text{var}^X\left[\mathbb{E}^Y\left\{\mathfrak{h}(X,Y)\right\}\right]$
unsurprisingly gives the upper hand to the iid sequence. A sort of converse to Rao-Blackwellisation…. Unless the production of N simulations gets much more costly when compared with the N function evaluations. No wonder we never see this proposal in Monte Carlo textbooks!
## amazing appendix
Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , , , on February 13, 2018 by xi'an
In the first appendix of the 1995 Statistical Science paper of Besag, Green, Higdon and Mengersen, on MCMC, “Bayesian Computation and Stochastic Systems”, stands a fairly neat result I was not aware of (and which Arnaud Doucet, with his unrivalled knowledge of the literature!, pointed out to me in Oxford, avoiding me the tedium to try to prove it afresco!). I remember well reading a version of the paper in Fort Collins, Colorado, in 1993 (I think!) but nothing about this result.
It goes as follows: when running a Metropolis-within-Gibbs sampler for component x¹ of a collection of variates x¹,x²,…, thus aiming at simulating from the full conditional of x¹ given x⁻¹ by making a proposal q(x|x¹,x⁻¹), it is perfectly acceptable to use a proposal that depends on a parameter α (no surprise so far!) and to generate this parameter α anew at each iteration (still unsurprising as α can be taken as an auxiliary variable) and to have the distribution of this parameter α depending on the other variates x²,…, i.e., x⁻¹. This is the surprising part, as adding α as an auxiliary variable was messing up the update of x⁻¹. But the proof as found in the 1995 paper [page 35] does not require to consider α as such as it establishes global balance directly. (Or maybe still detailed balance when writing the whole Gibbs sampler as a cycle of Metropolis steps.) Terrific! And a whiff mysterious..!
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2018-04-20 21:56:23
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https://www.physicsforums.com/threads/debt-limit-vote.381680/
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# News Debt limit Vote
#### DivingMullah
Debt limit Vote....
The House of Representatives will vote on increasing the nation’s debt limit. Presumably, this will spur conservatives and deficit peacocks to claim that the President Obama has gone on some kind of spending binge and has run up tons and tons of new debt. Despite these claims, the truth is that only a tiny fraction of our current debt burden is due to actions taken by President Obama.
On the day President Obama was inaugurated, publicly held debt was $6.3 trillion. Today it is$7.8 trillion. But, of course, pinning that entire $1.5 trillion increase on President Obama would be incredibly dishonest since Obama was handed a massive budget shortfall. After all, the Congressional Budget Office was projecting a deficit of$1.2 trillion for fiscal year 2009 even before Obama was sworn in. To blame the current administration for all the new debt accrued last year is to deliberately ignore that inconvenient fact.
But it is also true that President Obama did take actions that increased the deficit and therefore incurred additional debt. President Obama signed a 2009 omnibus appropriations act that increased non-defense discretionary spending by about $30 billion (with more than a third of that increase going to veterans’ health programs and international affairs), and a defense budget that increased spending by about$36 billion.
He also signed a reauthorization of the Children’s Health Insurance Program which increased spending by $1 billion. And of course, he supported and signed the American Recovery and Reinvestment act which resulted in$112 billion in additional spending, and $88 billion in tax cuts. All together, President Obama’s actions led to$267 billion worth of new debt in fiscal year 2009.
On October 1, 2009, fiscal year 2010 started, and since then we’ve amassed another $300 billion in debt. While it is probably unfair to ascribe even all of this debt to President Obama (given the economic conditions and the lingering budgetary damage from the Bush administration), for simplicity’s sake, let’s go ahead and do so anyway. All together then, President Obama is responsible for less than$600 billion of our current tally of publicly held debt. That’s less than 8 percent of the total.
It’s worth noting that a much larger percentage of our current debt was run up under President Bush. During his eight years in office, publicly held debt went from $3.3 trillion at the start of fiscal year 2002 (his first full fiscal year in office) to$6.3 trillion on the day he left office. That $3 trillion was the largest increase in publicly held debt under a single President in the history of the United States, and accounts for nearly 40 percent of our current total. That’s why it’s the very definition of peacockery for Republican Senators to vote against raising the debt limit (as 39 of them did last week) claiming to be all for fiscal discipline, when it was a Republican president who got us here. Diving Mullah Related General Discussion News on Phys.org #### Brian_C Re: Debt limit Vote.... Democrats were in control of Congress for four of Bush's eight years. Last time I checked, they're the ones who approve the budget. #### russ_watters Mentor Re: Debt limit Vote.... All together then, President Obama is responsible for less than$600 billion of our current tally of publicly held debt. That’s less than 8 percent of the total.
Do you find it at all disturbing that he's done that in just a year and a month? And what do you think about his debt projections moving forward?
#### Gokul43201
Staff Emeritus
Gold Member
Re: Debt limit Vote....
Democrats were in control of Congress for four of Bush's eight years.
Sure, if 2=4
#### DivingMullah
Re: Debt limit Vote....
Democrats were in control of Congress for four of Bush's eight years. Last time I checked, they're the ones who approve the budget.
First of all congress swing back to Dems in 2006 not in 2004, secondly two out of three branches of government was still being controlled by Republicans....
Please point to the expenditures that were passed by Democrats and not vetoed by President Bush. Democrats did not have the 67 majority to be veto proof.
The single most important factor is the legacy of President George W. Bush’s legislative agenda. Overall, changes in federal law during the Bush administration are responsible for 40 percent of the short-term fiscal problem. For example, we estimate that the tax cuts passed during the Bush presidency are reducing government revenue collections by $231 billion in 2009. Also, because of the additions to the federal debt due to Bush administration policies, the government will be paying$218 billion more in interest payments in 2009.
Had President Bush not cut taxes while simultaneously prosecuting two foreign wars and adopting other programs without paying for them, the current deficit would be only 4.7 percent of gross domestic product this year, instead of the eye-catching 11.2 percent—despite the weak economy and the costly efforts taken to restore it. In 2010, the deficit would be 3.2 percent instead of 9.6 percent.
Three times each year, the Congressional budget office releases revised estimates of its budget projections going forward 10 years. In each of these revisions, the CBO describes how its current estimate has changed from its previous estimate, and why. By studying these estimates, we can attribute the change in the federal bottom line to various factors: specific legislative policies, changing economic conditions, and technical modifications.
Specifically, in January of 2001, just as President George W. Bush was taking office, the Congressional Budget Office projected that in fiscal year 2009, the federal budget would enjoy a $710 billion surplus. Today the Congressional Budget Office says that the budget will have a$1.6 trillion deficit, a swing of $2.3 trillion. This had nothing to do with the Congress but rather irresponsible spending by the previous adminstration. Sorry but numbers do not support your argument. Diving Mullah #### WhoWee Re: Debt limit Vote.... The House of Representatives will vote on increasing the nation’s debt limit. Presumably, this will spur conservatives and deficit peacocks to claim that the President Obama has gone on some kind of spending binge and has run up tons and tons of new debt. Despite these claims, the truth is that only a tiny fraction of our current debt burden is due to actions taken by President Obama. On the day President Obama was inaugurated, publicly held debt was$6.3 trillion. Today it is $7.8 trillion. But, of course, pinning that entire$1.5 trillion increase on President Obama would be incredibly dishonest since Obama was handed a massive budget shortfall. After all, the Congressional Budget Office was projecting a deficit of $1.2 trillion for fiscal year 2009 even before Obama was sworn in. To blame the current administration for all the new debt accrued last year is to deliberately ignore that inconvenient fact. But it is also true that President Obama did take actions that increased the deficit and therefore incurred additional debt. President Obama signed a 2009 omnibus appropriations act that increased non-defense discretionary spending by about$30 billion (with more than a third of that increase going to veterans’ health programs and international affairs), and a defense budget that increased spending by about $36 billion. He also signed a reauthorization of the Children’s Health Insurance Program which increased spending by$1 billion. And of course, he supported and signed the American Recovery and Reinvestment act which resulted in $112 billion in additional spending, and$88 billion in tax cuts. All together, President Obama’s actions led to $267 billion worth of new debt in fiscal year 2009. On October 1, 2009, fiscal year 2010 started, and since then we’ve amassed another$300 billion in debt. While it is probably unfair to ascribe even all of this debt to President Obama (given the economic conditions and the lingering budgetary damage from the Bush administration), for simplicity’s sake, let’s go ahead and do so anyway. All together then, President Obama is responsible for less than $600 billion of our current tally of publicly held debt. That’s less than 8 percent of the total. It’s worth noting that a much larger percentage of our current debt was run up under President Bush. During his eight years in office, publicly held debt went from$3.3 trillion at the start of fiscal year 2002 (his first full fiscal year in office) to $6.3 trillion on the day he left office. That$3 trillion was the largest increase in publicly held debt under a single President in the history of the United States, and accounts for nearly 40 percent of our current total.
That’s why it’s the very definition of peacockery for Republican Senators to vote against raising the debt limit (as 39 of them did last week) claiming to be all for fiscal discipline, when it was a Republican president who got us here.
Diving Mullah
Diving Mullah, let me be the first to welcome you to the PF. Please take note of the Rules and make sure you support all of your posts.
#### DrClapeyron
Debt limit Vote = Spending more
Peanuts. The USofA does not suddenly change because it has a new president. Same old song and dance.
#### Brian_C
Re: Debt limit Vote....
Sure, if 2=4
Jim Jeffords left the Republican Party in May 2001, giving Democrats control of the Senate until January of 2003. You act like the Republicans had total control until 2006, which isn't true.
#### zomgwtf
Re: Debt limit Vote....
Do you find it at all disturbing that he's done that in just a year and a month?
Why does this matter at all???
#### Gokul43201
Staff Emeritus
Gold Member
Re: Debt limit Vote....
You act like the Republicans had total control until 2006, which isn't true.
"Act like"? What does that even mean?
I never stated that Republicans had total control until 2006. I only disputed your assertion that the Dems had control over Congress for 4 years. They didn't; they had control for 2 years.
#### Gokul43201
Staff Emeritus
Gold Member
Re: Debt limit Vote....
DM, there are a whole lot of numbers in the OP. You should make it a practice to provide citations for them (starting now), so we know you are not pulling them out of the air, and also so we can independently verify them if we so wish.
Last edited by a moderator:
#### mheslep
Gold Member
Re: Debt limit Vote....
Columnist Jonah Goldberg's response to the charge that Republicans are hypocrites for suddenly caring about deficits (paraphrasing the OP)
Goldberg said:
Well, maybe. But then so are liberals for suddenly not caring about deficits. (That part always gets left out.)
In addition to increasing the debt to \$7.8 trillion over the fiscal year 2009, the CBO shows the Presidents's fiscal plan will continue to increase the debt in absolute terms to http://www.cbo.gov/ftpdocs/110xx/doc...r_Senate.shtml" [Broken]
Last edited by a moderator:
Gold Member
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2019-11-19 20:58:05
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https://quantumcomputing.stackexchange.com/questions/9257/can-a-classical-limit-of-qubit-emerge-on-a-classical-computer
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# Can a classical limit of qubit emerge on a classical computer? [closed]
Hello,
I am uncertain; however, today at a toy museum, I might have captured a qubit on a classical computing structure, “ a broken 90-marble abacus,” as shown in the attached photos above.
I did not use it correctly, but if we set the first photo to be the state “0”, then the next one is “1”. You may say the third photo shows 0.5, but you can also say that it is a bit closer to 0 or 1. Thus, while we observe this purple marble positioned between 0 and 1, we cannot tell if it moves to 0 or 1 until we measure its displacement. Therefore, I wonder if it can be said that the classical limit of qubit emerged on classical computer in this third photo? Its probability of being 0 or 1 is fifty-fifty.
The picture below gives a further explanation with a chart of marble A's location. In abacus computing, the states of A are limited to four states, namely, resting at 0 or 1, or moving toward 0 or 1. A cannot rest between 0 and 1. Abacus computing is observed by taking two photographs during its sequence giving two locations of A. When taking the first shot, we can know A's location and not sure if it is moving or resting. Then we take a second shot and know how it moves. After all, we can tell or predict its outcome 0 or 1. Thus, when we observe the initial location of A, this is the state of the classical limit of qubit, which has fifty-fifty probability of becoming 0 or 1, until secondary observation.
This concept can be extended to tossing coin or tumbling dice. If the observer is unable to predict those outcomes by observing those motions, the observer can tell only classical probabilities.
Thank you,
Ryoji
• Your example can serve only as a model for explanation what a qubit is. But abacus is macroscopic entity, hence it cannot show a quantum behavior and it is not a quantum system. Dec 19 '19 at 19:45
• Dear Martine, all objects in the real world, small and large, are quantum systems in the sense of being subject to quantum mechanics at all times. Classical physics is always at most an approximation that may be more or less good for some purposes. The abacus doesn't effectively preserve quantum coherence and becomes complicated but that doesn't change the fact that the fundamental laws that govern it are still the laws of quantum mechanics. Dec 21 '19 at 9:23
A computer that may be visualized in this simple way, like abacus with moving marbles, where the locations of the marbles are continuous, including 0.5, is called an "analog computer" and it is a different, and much simpler, thing than a quantum computer.
What may be changed continuously in a quantum computers aren't the observable locations (or voltages) themselves but the probability amplitudes for each configuration. When it comes to allowed values of each qubit, each of them may still be just 0 or 1 and nothing in between. However, the quantum computer allows each qubit to be indeterminate, having some probability to be 0 and some probability to be 1.
In fact, each of the $$2^N$$ configuration of $$N$$ qubits may be given some probability that is independent from others. And quantum mechanics makes it more juicy. It's not just probabilities $$p_i$$, $$i=1 \dots 2^N$$, that specify the state of the quantum computer at the moment. Instead, it's complex numbers, the probability amplitudes, $$c_i$$ related to $$p_i$$ by $$p_i=|c_i|^2$$, that are needed to describe the state of the quantum computer at a given moment.
An operation performed by the quantum computer is some particular linear transformation (given by a matrix, $$2^N \times 2^N$$) of these $$2^N$$ complex numbers. This calculation involving $$2^N \times 2^N$$ continuous numbers could be simulated by a complicated classical computer with lots of memory and representation for the continuous numbers.
However, this operation that looks complicated in the simulation is achieved by the quantum computer's step that is basically comparably difficult to an operation of a classical computer with $$N$$ single bits that just maps some bits to a simple function of the neighbors.
The quantum computer doesn't allow "any" operation with the matrices to be done and it doesn't allow the complex numbers to be measured. Instead, just the bits themselves, with results either 0 or 1, may be measured by the quantum computer. So the class of quantum computers or quantum simulations is "more special" than the class of operations done on a classical computer with $$2^N$$ complex numbers. But despite this restriction, the quantum computer is capable of doing some things much more quickly than the classical computers.
A usable quantum compouter was first built by Google and, at least according to some precise definitions of the term, has achieved "quantum supremacy" which means quickly doing a calculation that could only be done very slowly at the world's fastest classical computers.
• Just note on the first quantum computer. I think that IBM Q was the first one. Additionally, "quantum supremacy" is fancy term used widely nowadays. I would be careful with general statements like "which means quickly doing a calculation that could only be done very slowly at the world's fastest classical computers" because speed-up depends on particular task (e.g. exponential speed-up for integer factoring - Shor while only quadratic for database searching - Grover). Dec 19 '19 at 19:20
• in the classical computing, the purple marble is allowed only 4 states. resting at 0 or 1, and moving from 0 to 1 and opposite direction (not allowed resting at 0.5). so when we take the picture like third one, we can obtain information of the marble's location and we are still not sure which direction it moves. then we take the second shot, we see it moved slightly to 0 or 1. Dec 19 '19 at 19:51
• Luboš Motl and Martin Vesely, thank you for your comments. I added further explanation with picture. I think qubit can be visualized in the classical limit on the classical computer. Dec 20 '19 at 12:05
• Dear Martine, the speedup surely depends on the task and people are careful about quantum supremacy - except for SJWs who find the term racist and not careful enough LOL. Quantum supremacy takes place when any kind of task is solved much more quickly by the quantum computer than the classical one. It is obvious that the speedup will be almost non-existent for some particular tasks. Preskill and the people who defined the quantum supremacy did so carefuly and if you are not careful, it's your fault, not theirs. Dec 21 '19 at 9:25
• Hi, I think the first gear up to any classical commands would come with existing voltage bit generated semiconductors by replacing logic gates to what I suggested at the latter part of my paper ryoji.info/cqc.pdf . Google also used semiconductors but with quantum spins as bit at nearly 0k environment. I guess the most stable quantum bit is plasmon generated on graphens or like these. Dec 22 '19 at 2:17
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2021-09-25 09:22:14
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https://zenodo.org/record/3528256/export/csl
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Preprint Open Access
# Towards a Cloud-Based Controller for Data-Driven Service Orchestration in Smart Manufacturing
Tountopoulos, Vasilios; Kavakli, Evangelia; Sakellariou, Rizos
### Citation Style Language JSON Export
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"publisher": "Zenodo",
"DOI": "10.5281/zenodo.3528256",
"language": "eng",
"title": "Towards a Cloud-Based Controller for Data-Driven Service Orchestration in Smart Manufacturing",
"issued": {
"date-parts": [
[
2018,
10,
2
]
]
},
"abstract": "<p>The orchestration of smart manufacturing service operations and processes arises as a challenging step in the realization of the Industry 4.0 vision. This paper presents the work in progress towards the specifications of a controlling environment for data-driven orchestration of software services in future smart manufacturing scenarios. The paper discusses the role and significance of multi-aspect data in the management of manufacturing operations and proposes a reference architecture for controlling the orchestration of the respective data services, following the work that has been conducted in the context of the EU-funded project DISRUPT.</p>",
"author": [
{
"family": "Tountopoulos, Vasilios"
},
{
"family": "Kavakli, Evangelia"
},
{
"family": "Sakellariou, Rizos"
}
],
"note": "Preprint of a research paper accepted at the 6th International Conference on Enterprise Systems, Limassol, Cyprus / 01-02 October, 2018",
"type": "article",
"id": "3528256"
}
45
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2021-09-16 10:58:32
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https://www.gradesaver.com/textbooks/science/chemistry/chemistry-and-chemical-reactivity-9th-edition/chapter-9-bonding-and-molecular-structure-orbital-hybridization-and-molecular-orbitals-9-2-valence-bond-theory-review-check-for-section-9-2-page-354/1
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## Chemistry and Chemical Reactivity (9th Edition)
Sulfur is making three $\sigma$ bonds and one $\pi$, having a trigonal planar geometry.
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2020-10-27 00:46:07
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https://www.springerprofessional.de/vortical-flow-development-in-round-ducts-across-scales-for-engin/16521476
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## Weitere Artikel dieser Ausgabe durch Wischen aufrufen
01.04.2019 | Research Article | Ausgabe 4/2019
# Vortical flow development in round ducts across scales for engine inlet applications
Zeitschrift:
Experiments in Fluids > Ausgabe 4/2019
Autoren:
Tamara Guimarães, K. Todd Lowe, Walter F. O’Brien
Wichtige Hinweise
## Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
## Abstract
Turbofan engine performance depends highly on the characteristics and conditions of the inlet flow. Swirl distortions, caused by non-uniformities in flows arising from boundary layer or ground/fuselage vortex ingestion, are of concern and need to be fully understood to guarantee the efficiency and safety of propulsion systems. To investigate a fundamental single-vortex distortion development in a duct at different Reynolds numbers, a StreamVane distortion generating device was designed and experimentally analyzed in a small-scale low-speed wind tunnel ($$Re_{\text{D}} \approx 500 \times 10^3$$) and in a full-scale engine testing rig ($$Re_{\text{D}} \approx 3 \times 10^6$$). Stereoscopic particle image velocimetry was used to measure the three-component velocity fields at discrete measurement planes downstream of the distortion device. Results show that the main features of the secondary flow are generated very similarly in both scales, and that its axial development is also overall very similar and mostly driven by two-dimensional (2D) vortex dynamics. Induced velocities arising from the proximity of the vortex to the duct wall cause the vortex center to convect circumferentially around the duct, in the same sense as the vortex rotation, as it travels downstream. The unsteady flow in the different measurement planes of the wind-tunnel experiment shows the development of local instabilities related to the turbulent development of the vortex. This work shows that the development of this vane-generated, vortex-dominated flow is largely Reynolds number independent for the covered range, so that details of similar duct-bounded flows can be analyzed in depth in small-scale experiments, decreasing development efforts and cost.
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2019-04-20 10:23:43
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https://mathstodon.xyz/@ColinTheMathmo?max_id=101384722017014154
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The internet used to be a city: it had its weird bohemian districts, its flea markets, its high-rises and back alleys. Now it's just a shopping mall, and I miss my old city so much
Some passes of the visible from the UK overnight - I'll tweet/toot warnings closer to the time
Genuinely terrible to see footage of protesters outside the HoC screaming and shouting the kind of appalling language previously confined to the front pages of our newspapers.
Never put off until tomorrow what you can do the day after tomorrow. -- Mark Twain
In about half an hour, UK pass, starting at 07:23:44, duration 177 secs, visible, Magnitude -1.4
In about half an hour, UK pass, starting at 05:50:07, duration 141 secs, bright, Magnitude -2.5
Some passes of the visible from the UK overnight - I'll tweet/toot warnings closer to the time
Trying to write my blog post about computing the answer to the other rope around the world problem, but find myself shaving a yak.
My phone said it wasn't raining, but I looked outside and it was. One of the few times windows proved better than Android.
In about half an hour, UK pass, starting at 06:39:56, duration 247 secs, bright, Magnitude -2.5
In about half an hour, UK pass, starting at 05:07:15, duration 57 secs, visible, Magnitude -0.9
Some passes of the visible from the UK overnight - I'll tweet/toot warnings closer to the time
How do you end up with a small fortune at a casino? Start with a large fortune.
In about half an hour, UK pass, starting at 07:30:16, duration 309 secs, visible, Magnitude -1.9
In about half an hour, UK pass, starting at 05:57:04, duration 176 secs, very bright, Magnitude -3.3
@fjfish Hiya - do you have a moment to read something quickly and give me your first impressions?
Some passes of the visible from the UK overnight - I'll tweet/toot warnings closer to the time
Rather pleased, last night I found a way to do the calculations for the *other* rope around the world problem in my head. Lovely.
I'm not lost, I know exactly where I am. I'm just temporarily uncertain of where everything else is.
In about half an hour, UK pass, starting at 06:46:42, duration 289 secs, very bright, Magnitude -3.1
A Mastodon instance for maths people. The kind of people who make $\pi z^2 \times a$ jokes.
Use $ and $ for inline LaTeX, and $ and $ for display mode.
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2019-01-24 05:36:42
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https://chemistry.stackexchange.com/questions/107100/molecular-orbital-explanation-of-why-the-protonation-of-the-oxygen-atom-makes-a
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# Molecular orbital explanation of why the protonation of the oxygen atom makes a carbonyl group more electrophilic
I was working on nucleophilic addition reactions to the carbonyl group (namely, hemiacetal formation) when I came across the following explanation for the use of acid catalyst and how it increases reaction rate:
In acid (dilute HCl, say), the mechanism is different in detail. The first step is now protonation of the carbonyl group’s lone pair: the positive charge makes it much more electrophilic so the addition reaction is faster.
The reaction at hand is the following:
Ignoring the presence of the positive formal charge on the oxygen, I am trying to understand on a molecular orbital theory level why this makes sense. I'm suspecting that this somehow lowers carbon's LUMO ($${π}^{*}$$ orbital), which would enhance the electrophilicity of carbon.
Would someone be able to give an explanation to the enhanced electrophilicity of the carbonyl group based on molecular orbital theory?
References
Clayden, J., Greeves, N., Warren, S. Organic chemistry, 2nd ed.; Oxford University Press: New York, 2012.
• I think title should reflect you wanna talk about MOs. – Mithoron Dec 27 '18 at 17:18
I think this is exactly what is responsible, even from the MO viewpoint. From the MO perspective, the electrophilicity of the carbonyl group can be viewed as how energetically-accessible is the $$\ce {C=O \pi ^*}$$ MO to the nucleophile's HOMO. The protonation of the oxygen atom effectively decreases the energies of all MOs of the carbonyl, including the $$\ce {C=O \pi ^*}$$ MO. Why? The proton is positively-charged. By attaching to the oxygen atom, there is a net decrease in the potential energy of the molecule due to there being more electron-nuclei attractive forces in the resultant entity. Hence, protonation makes the $$\pi ^*$$ LUMO more accessible to the attacking nucleophile, increasing electrophilicity.
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2019-10-22 06:57:27
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http://archived.moe/a/thread/12252817
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216KiB, 480x360, sepihgphsgpsdhghc0.png
No.12252817
/r/ has failed me, so I'll try and ask here.
What's the name of this anime?
Pic related.
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2016-10-23 16:17:37
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https://mathematica.stackexchange.com/questions/103289/how-to-automatically-have-contourlabels-in-middle-of-contour-lines-if-specific-l?noredirect=1
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How to automatically have ContourLabels in middle of Contour lines if specific levels are not specified?
I looked at all the questions/answers relating to placement of ContourLabels but could not find an answer to this. Some of the answers before are based on user giving before-hand, the Contours levels to use, using the option Contours -> {v1, v2, ....}.
But if one just want to use Contours->number, then it gets hard to figure how to solve this.
The labels that show up are not in the nice locations and hard to read. I'd like them to be in the middle of the contour lines. This is how Matlab actually does it by default.
Here is a MWE, and I also show the Matlab result.
Clear[x,y]
f = (11 - x - y)^2 + (1 + x + 10 y - x y)^2;
ContourPlot[f, {x, 0, 20}, {y, 0, 15},
Contours -> 10, ContourShading -> None,
ContourLabels -> Function[{x, y, z},
Text[z, {x, y}]], AspectRatio -> Automatic, PlotRangePadding -> 2]
I am trying to get closer output to Matlab's
clear; close all;
x = 0:0.05:20;
y = 0:0.05:15;
[x,y] = meshgrid(x,y);
z = (11-x-y).^2 + (1+x+10*y-x.*y).^2;
[C,h] =contour(x,y,z,10);
clabel(C,h)
I also noticed that Matlab seems to have additional heuristics in placing labels. It does not label all the lines if the space is tight. Notice the top levels are not labeled in Matlab. Also the text is not written over the lines, but there is space in the line where the text goes. This makes it easier to read.
But my main question I have is how to put the labels in the middle of the level lines, where it is more pleasing to see than on the edges.
If someone knows of a package to use for this, I will try it. I looked at few here http://packagedata.net/ but did not see anything yet. Looked at sciDraw package also. I think Contour label placement in Mathematica should be improved more.
Version 10.3.1. windows.
Related questions
Custom contour labels in ContourPlot
How do I add contour labels to contour plot?
FYI, I found the book Mathematica graphics which has an function called LabelContourLines[], which from the example shown, seems to do what I want. Page 348 in the book:
Here is how Mathematica 10.3.1. gives, for the same example in the book. Notice the difference :
ContourPlot[x y, {x, -2, 2}, {y, -2, 2}, ContourShading -> False,
Contours -> 10, ContourLabels -> All]
I do not have this book around myself, but will try to see if the author has the software on the net to use or I can look for it at the university library.
It looks like the above function is what I am looking for. But the book is old (1994), and do not know if book software will even work on current Mathematica even if I find it.
This is a good question which I had tried to work on several years ago, and I just revisited it to see if the code could be useful.
I had initially only worked on rotating the contour labels to be tangential with the contours, but in the code it turned out to be quite easy to add a line that also attempts to center the labels along the contour. My simple approach is to estimate the center of the contour by just choosing the midpoint in the Line specification defining that particular contour.
The code comes with comments, but it's quite lengthy:
Clear[rotateContourLabels];
rotateContourLabels::usage =
"The function rotateContourLabels accepts the output of ContourPlot \
or ListContourPlot, assuming they were made with the option \
ContourLabel-> All. The plot is passed via the required first \
argument. The function rotates the labels of all contours to be \
approximately parallel to the iso-lines. The optional LabelFunction \
can specify a custom label style in the form of a function f[#1, #2, \
#3], where {#1, #2} is the 2D location vector of the label, and #3 \
the value of the plotted function at that location. For examples see \
the documentation on ContourLabels. The default label style is given \
by the function Text[#3,{#1,#2}]&. A second option, Alignment, \
influences the placement of the labels along the contour. The default \
Alignment -> Automatic leaves the original placement intact, any \
other value will shift the labels to an estimated center position \
along the contour.";
Options[rotateContourLabels] = {LabelingFunction -> (Text[#3, {#1, \
#2}] &), Alignment -> Automatic};
rotateContourLabels[plot_, OptionsPattern[]] :=
Module[{gc = plot[[1]] , valueList, pointList, rotatePoint,
labelCoordinatesIndexed, directionVector},
(******* Created by Jens U. Nöckel, August 17, 2009,
Catch[
labelCoordinatesIndexed =
Quiet@Check[gc[[-1, -1, All, 2]], Throw[plot]];
valueList = Quiet@Check[gc[[-1, -1, All, 1]], Throw[plot]];
If[Last[Dimensions[labelCoordinatesIndexed]]==2,
pointList = labelCoordinatesIndexed,
pointList = Quiet@Check[gc[[1, labelCoordinatesIndexed]],
Throw[{"The plot must have the option ContourLabels->All !!!",
plot}]]];
(** gc is the GraphicComplex, gc[[1]] a list of 2D points.
The list of contour labels is contained in plot[[1,-1,-1]] =
gc[[-1,-1]] and we want to replace this list. **)
(* Local function definition: *)
rotatePoint[labelPoint_] :=
Module[{pt, extractSecant , allContourLines, contourPoints2D,
contourPointsIndexed , closestContourIndexed,
closestPointIndexed},
pt = labelPoint;
allContourLines =
Map[First,(**
The First extracts the list of line points from the Line \
expressions collected in the next line: **)
Cases[Flatten@
MapAll[If[SameQ[Head[#], Line], #, Apply[List, #]] &,
gc[[-1]]], _Line]];
(** Line can be nested inside other non-
list expressions such as Tooltip,
so the above flattens all levels of the expression except for \
before it proceeds to collect the Lines using Cases. **)
{contourPoints2D, contourPointsIndexed} =
(** Given a point pt,
find out for each contour what is its closest point to pt.
Return this information both as 2D points and as a list of \
indices counted within each contour. **)
Transpose[
Map[
First@Nearest[
# -> Transpose[{#, Range[Length[#]]}],
pt
] (** End First@Nearest **)&,
Map[gc[[1, #]] &, allContourLines]
](* End Map *)
] (* End Transpose *);
{closestContourIndexed, closestPointIndexed} =
(** Given a point pt, find closest contour.
Give its index in the list of contours,
and the index of the closest point within this contour. **)
First[Nearest[
contourPoints2D ->
Transpose[{Range[Length[contourPoints2D]],
contourPointsIndexed}],
pt
]];(* End First@Nearest *)
If[OptionValue[Alignment] =!= Automatic,
(* Alignment refers to the placement of labels on contours.
If not Automatic,
try to approximately center the labels according to contour \
length, measured by points in their line: *)
closestPointIndexed =
Floor[Length[allContourLines[[closestContourIndexed]]]/2];
pt = Part[gc[[1]],
allContourLines[[closestContourIndexed,
closestPointIndexed]]]];
extractSecant = (** Given the closest point to pt,
record it and its next neighbor on the same contour line.
The two points are returned as real 2D points,
determined from their indices. **)
{
allContourLines[[closestContourIndexed, closestPointIndexed]] (*
The first point *),
Quiet@
Check[allContourLines[[closestContourIndexed,
closestPointIndexed + 1]],
allContourLines[[closestContourIndexed,
closestPointIndexed - 1]]] (*
The second sequential point -
here I want to avoid falling outside the range of the contour \
point list. *)
};
(* The rotation aims to make this vector parallel to the \
contour. We approximate the contour direction by taking two points on \
the contour and forming their difference: *)
directionVector = Apply[Subtract,
(** The two required points are found from the list gc[[1]] : **)
Part[gc[[1]],
(*
The Part of gc[[1]] we're looking for is a set of two points \
that define the secant closest to the contour label: *)
extractSecant]
];
(** Here starts the body of rotatePoint: **)
Composition[
(* The composition sandwiches a rotation around the origin \
between a translation to the origin and its inverse: *)
TranslationTransform[pt],
Quiet@Check[RotationTransform[{
{1, 0}, (*
The reference direction for the rotation is the horizontal: \
*)
(Sign[directionVector[[1]]] directionVector)
(*
To avoid rotations outside [-Pi,Pi] the above \
statement places the direction vector into the first or fourth \
}] (* End RotationTransform *)
, Identity (*
No rotation happens if for some reason we can't get a valid \
direction vector *)],
TranslationTransform[-labelPoint]
] (* End Composition *)
] ;(** End function rotatePoint **)
(**** Main function body: *****)
ReplacePart[plot, {1, -1, -1} ->
(** the replacement is a geometric transformation of the \
original list gc[[-1,-1]]: **)
Append[Transpose[pointList], valueList]],
(**
What follows is the list of transformations for each contour \
label: **)
Map[rotatePoint, pointList]}]]
]]
This defines a function rotateContourLabels which takes an existing plot and post-processes it. As always with post-processing, I have to make some assumptions about how the input was prepared:
In the ContourPlot or ListContourPlot that serves as the input, you must set either the option ContourLabels -> True or ContourLabels -> All.
With this assumption, you can then use the function as follows:
a = ContourPlot[Im[(x + I y)^(1/2)], {x, -1, 1}, {y, -1, 1},
Contours -> 20, ContourLabels -> True]
This is the original output in Mathematica 10.2.
Now the usage example:
rotateContourLabels[a, Alignment -> Center,
LabelingFunction -> (Text[#3, {#1, #2},
Background -> Directive[Opacity[.5], White]] &)]
I think this result is an improvement (given that it's fully automatic), although of course the centering is not perfect.
Edit
For completeness, here is the OP's minimum working example:
Clear[x, y]
f = (11 - x - y)^2 + (1 + x + 10 y - x y)^2;
b = ContourPlot[f, {x, 0, 20}, {y, 0, 15}, Contours -> 7,
ContourShading -> None, ContourLabels -> True,
AspectRatio -> Automatic, PlotRangePadding -> 2];
rotateContourLabels[b, Alignment -> Center,
LabelingFunction -> Function[{x, y, z}, Text[z, {x, y}]]]
Note that I added the label function as an option to rotateContourLabels instead of the original plot (which I called b). I also decreased the number of contours to 7 so the labels are more readable. The placement of the labels is obviously much better than the original. The background I chose in the first example would probably also make this plot look a little better.
Finally, here is my automatic version of the book example in the question:
c = ContourPlot[x y, {x, -2, 2}, {y, -2, 2}, ContourShading -> False,
Contours -> 10, ContourLabels -> All];
rotateContourLabels[c, Alignment -> Center,
LabelingFunction -> (Text[#3, {#1, #2}, Background -> White] &)]
One could probably also add an option to place the labels at the ends of the contours instead of the center, but I haven't done that yet (because it usually looks ugly, even though Mathematica seems to like doing that by default...).
• i tried to run this last example but i get the following message "The plot must have the option ContourLabels->All !!!". I am using Mathematica 11.1.1 May 16, 2017 at 12:33
• @Valerio Thanks for pointing this out. It appears to be a change in the way label coordinates are stored internally. My code makes assumptions about this internal storage. I think it's fixed now, and should also still work with older Mathematica versions.
– Jens
May 16, 2017 at 16:27
• @Nasser: Have you improved Jens's rotateContourLabels function? It seems that it does not label properly when the space is tight. Also, sometimes the directions of the text are inappropriate! :( I have some sample pics but cannot show them in a comment. Jul 25, 2017 at 21:23
• @H.R. maybe you can post code to reproduce the plots? I can't guarantee that I can fix it, but I'd like to know what you're seeing. I did a small fix recently to keep up with changes in version 11... maybe go back to the earlier version in the revision history and see if that works better (i.e. perhaps I broke something in my May edit of the answer).
– Jens
Jul 25, 2017 at 21:45
• @H.R. Thanks, I see what's going on. But it looks like for those scrunched-up contours you may be better off with this more manual approach.
– Jens
Jul 25, 2017 at 23:00
The software is located at http://library.wolfram.com/infocenter/Books/3753/ as a .tar and a .zip file.
Update
How about a shameless lifting of one of the references you mention and adding a Rotate function?
ContourPlot[x y, {x, -2, 2}, {y, -2, 2}, ContourShading -> False,
Contours -> 10,
ContourLabels -> (Rotate[Text[" " <> ToString[#3] <> " ", {#1, #2},
Background -> White], -ArcTan[#2/#1]] &)]
For other curves one would need to determine the tangent to the curve at point {#1, #2}.
• Thanks for the link. I downloaded and installed it. But as expected, it does not work with 10.3.1. This is an old package from version 3.0 ! I get lots of errors: !Mathematica graphics but what I will do next, is locate this specific function in the package, and try to make it work for 10.3.1. I've always had problems running old packages in new Mathematica versions. Something always changes. The LabelContour function is very complicated 450 lines long ! Jan 4, 2016 at 0:43
• @Nasser. Bummer!
– JimB
Jan 4, 2016 at 1:23
• Ok, I tried for the last 40 minutes, but too many problems to resolve. This package was done using old graphics and uses too many old options and such, and it will need much longer time to fix. But I think it will be worth it. I am really surprised that WRI did not integrate some of the functions in this package in Mathematica. This package has been around for only 20 years! I guess WRI is busy with cloud computing now and has no time to work on such basic things like contour labels location :) Jan 4, 2016 at 1:37
• @H.R. sorry, do not think I ever did. Jun 14, 2017 at 21:01
• In general, determining the tangent to a curve is not really applicable in closed form and a numerical algorithm should be employed. Jul 25, 2017 at 20:49
I was unable to run the function written by Jens in Mathematica 12.0 cause of multiple errors caused by an altered (?) ContourPlot's realisation. So I have rewrote rotateContourLabels function to adopt it to a newer Mathatica version. For my own purposes I use the following realisation:
Clear[rotateContourLabels];
rotateContourLabels::usage =
"The function rotateContourLabels accepts the output of ContourPlot \
or ListContourPlot, assuming they were made with the option \
ContourLabel-> All. The plot is passed via the required first \
argument. The function rotates the labels of all contours to be \
approximately parallel to the iso-lines. The optional LabelFunction \
can specify a custom label style in the form of a function f[#1, #2, \
#3], where {#1, #2} is the 2D location vector of the label, and #3 \
the value of the plotted function at that location. For examples see \
the documentation on ContourLabels. The default label style is given \
by the function Text[#3,{#1,#2}]&. A second option, Alignment, \
influences the placement of the labels along the contour. The default \
Alignment -> Automatic leaves the original placement intact, any \
other value will shift the labels to an estimated center position \
along the contour.";
Options[rotateContourLabels] = {
LabelingFunction -> (Text[#3, {#1, #2}]&),
Alignment -> Automatic
};
rotateContourLabels[plot_, OptionsPattern[]] := With[{
gcIdx = Sequence[1,1], (* index of a GraphicsComplex inside a Graphics *)
ppIdx = Sequence[1 ], (* index of a list of 2d-points in the GC *)
ccIdx = Sequence[2,2], (* index of a list of contour lines in the GC *)
llIdx = Sequence[2,3], (* index of a list of labels in the GC *)
case = Identity
}, Block[{gc = plot[[gcIdx]],
pointList, contourList, labelList, contourIdxs, contourPoss, labelValues, labelIdxs,
labelPoints, getClosestLine, getClosestPoints, makeTransforms, origins, transforms,
plotRange, plotRatio, plotScale, computeLabel, rangeRatio
}, Catch[
(*-- extract basic data containters --*)
pointList = Quiet@Check[gc[[ppIdx]], plot]; (* {{x,y} ...} *)
contourList = Quiet@Check[gc[[ccIdx]], plot]; (* {{<style ...>, Line[List[..]]} ...} *)
labelList = Quiet@Check[gc[[llIdx]], plot]; (* {Inset[val, idx] ...} *)
plotRange = First /@ Differences /@ (PlotRange /. Options[plot]);
rangeRatio = plotRange[[2]] / plotRange[[1]];
plotRatio = AspectRatio /. Options[plot];
(*-- normalize extracted data --*)
contourIdxs = Cases[contourList, Line[idxs_] :> idxs, \[Infinity]]; (* {{point_idx ...} ...} *)
contourPoss = Map[pointList[[#]]&, contourIdxs, {2}];
labelValues = labelList[[;;, 1]];
labelIdxs = labelList[[;;, 2]];
labelPoints = pointList[[labelIdxs]];
If [Length@contourPoss == 0,
Return@plot
];
(*----> helper functions --*)
(** Lablel rotation angle **)
getLabelAngle = Function[{baseVector, targetVector}, With[{
(* Map targetVector to [-\[Pi], \[Pi]] angle *)
base = baseVector Sign[baseVector [[1]]],
dest = targetVector Sign[targetVector[[1]]]
}, With[{
\[Alpha] = VectorAngle[base, dest] Sign[(dest-base)[[2]]]
},
(** \[Alpha] \[LongDash] unscaled angle = arctan[y_0 / x_0]
* \[Beta] \[LongDash] scaled angle = arctan[y_1 / x_1] = arctan[y_1 / x_0]
* y_1 = ar_target x_1 = ar_target x_0
* y_0 = ar_range x_0
** => \[Beta] = arctan[ar_target/ar_range tan[\[Alpha]]] **)
ArcTan[plotRatio/rangeRatio Tan[\[Alpha]]]
]]];
(** find positions of the closest contour and the line's closest point **)
getClosestLine = Function[{idxOrPos}, Block[{},
Switch[Length @ idxOrPos
, case @ 0, Block[{idx = idxOrPos, checks, positions},
getClosestLine[pointList[[idx]]]
]
, case @ 2, Block[{pos = idxOrPos,
closestPoint, closestPoints, closestLinePos, closestPointPos
},
closestPoints = Map[First@Nearest[#1, pos]&, contourPoss];
closestPoint = First@Nearest[closestPoints, pos];
closestLinePos = Position[closestPoints, closestPoint][[1,1]];
closestPointPos = Position[contourPoss[[closestLinePos]], closestPoint][[1,1]];
{closestLinePos, closestPointPos}
]
, _, Throw[{"unsupported index ot position type ", idxOrPos}]
]
]];
(** the function finds points linked to a specified point **)
getClosestPoints = Function[{linePos, pointPos}, Block[{idxs,
lineLen = Length@contourIdxs[[linePos]]
},
idxs = With[{alignment = OptionValue[Alignment]}, Switch[alignment
, Automatic, {-1, 0, 1} + pointPos
, Center , {-1, 0, 1} + \[LeftFloor]lineLen/2\[RightFloor]
, _, Throw[{"Unsupported Alignment type ", OptionValue[Alignment]}]
]];
idxs = idxs /. a_?(# < 1 || # > lineLen&) -> None;
idxs
]];
(** the function calclates a geometry transformation and a new label origin **)
makeTransforms = Function[{pos}, Block[{
idxOr2DPos, linePos, pointPos, basePointPoss, originPoint,
basePointIdxs, secantVector, pointCoords, basePoints, transform
},
(* >> get closest points to a target label anchor *)
{linePos, pointPos} = getClosestLine[labelIdxs[[pos]]];
basePointPoss = getClosestPoints[linePos, pointPos];
basePointIdxs = If[# =!= None, contourIdxs[[linePos, #]], None]& /@ basePointPoss;
basePoints = If[# =!= None, pointList[[#]]]& /@ basePointIdxs;
originPoint = basePoints[[2]];
basePoints = DeleteCases[basePoints, None];
Assert[Length@basePoints >= 2];
(* >> compute an right-direction-vector *)
secantVector = basePoints[[-1]] - basePoints[[1]];
(* >> composite a rotation operator *)
With[{
angle = getLabelAngle[{1, 0}, secantVector],
origin = originPoint
},
transform = Rotate[#, angle]&;
];
{originPoint, transform}
]];
computeLabel = Function[{x, y, labelValue, transform}, Block[{label},
label = Replace[OptionValue[LabelingFunction][x, y, labelValue]
, {
Text[v_, p_List, o_List, r___] :> Text[v, r],
Text[v_, p_List, r___] :> Text[v, r],
Text[v_, r___] :> Text[v, r]
}
];
Text[transform @ label, {x, y}]
]];
(*----< helper functions --*)
(*-- main: transform original plot's labels --*)
{origins, transforms} = Map[makeTransforms, Range[Length@labelPoints]]\[Transpose];
, Join[origins\[Transpose], {labelValues, transforms}]
]]
]]]
As a result it's possible to get the same result on the presented examples like
c = ContourPlot[x y, {x, -2, 2}, {y, -2, 2}
, Contours -> 10
, ContourLabels -> All
, Background -> White
];
rotateContourLabels[c
, Alignment -> Center
, LabelingFunction -> (Text[#3, {#1, #2}, Background -> White] &)
]
and
a = ContourPlot[Im[(x + I y)^(1/2)], {x, -1, 1}, {y, -1, 1}
, Contours -> 20
, ContourLabels -> True
, Background->White
];
rotateContourLabels[a
, Alignment -> Center
, LabelingFunction -> (Text[#3, {#1, #2}
, Background -> Directive[Opacity[.5], White]
] &)
]
Edited:
Also, Mathemarica tries to adjust plot's aspect ratio to a specified value (Option: AspectRatio). The adjustment shears all plot contents, including all rotated lables (Text[..] filds are not sheared). To prevent labels from transformations I've started to wrap labels into a Text[, {position}] command, where can be Rotate[Text["lebel"], angle]. The artifact was clearly visible in plots where max[x_y_range] / min[x_y_range] >> 1
With[{
equation = Subscript[\[Sigma], sb] (Subscript[\[Epsilon], w] Subscript[T, w]^4 - Subscript[\[Epsilon], 0] Subscript[T, 0]^4) + h (Subscript[T, w] - Subscript[T, 0]) /. {
Subscript[\[Sigma], sb] -> 5.670373 10^-8,
Subscript[T, 0] -> 273,
Subscript[\[Epsilon], 0] -> 0.95,
Subscript[\[Epsilon], w] -> 0.35
},
vars = Sequence[{h, 2, 10}, {Subscript[T, w], 273, 273 + 100}]
},
d = ContourPlot[equation, vars
, ContourLabels -> All
, Contours -> 10
, Background -> White
];
d = rotateContourLabels[d
, Alignment -> Center
, LabelingFunction -> (Text[" " <> ToString@#3 <> " ", {#1, #2}
, Background -> Directive[Opacity[.8], White]
]&)
]
]
JimB's answer is great, I wish I'd found it years ago. That said, sometimes I have data where the contours are very irregular, and I don't want a break in the contour line. Below is a simple version of the solution I use. This also gives control on label placement, one of the original concerns.
Considering the graphic used above;
cPlot = ContourPlot[x y, {x, -2, 2},{y, -2, 2}, ContourShading->False, Contours->10]
Then utilizing the Graphics option in Arrowheads
Arrowheads[{spec1, spec2, ...}]
Where each spec is {size, position, graphic}
Then use Replace (/.) to swap Line heads for Arrow, and prepend the contents of Tooltip with the desired Arrowheads, taking the Tooltip text to be the value used inside.
cPlot /. {Line@x___ :> Arrow@x} /. {Tooltip[{y___}, z_] :> Tooltip[{Arrowheads[{{Automatic, 0.5, Graphics@Text[ToString[z] <> "\n"]}}], y}, z]}
The 0.5 inside of Arrowheads places the label in the middle of each Line. Additional labels can be added by doing something like the following;
Arrowheads[{{s1, pos1, graphic1}, {s2, pos2, graphic2}, ...}]
|
2022-05-26 01:57:17
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23276259005069733, "perplexity": 5632.497598674811}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662595559.80/warc/CC-MAIN-20220526004200-20220526034200-00569.warc.gz"}
|
https://pos.sissa.it/336/042/
|
Volume 336 - XIII Quark Confinement and the Hadron Spectrum (Confinement2018) - A: Vacuum structure and confinement
Conformal Perturbation description of Deconfinement.
M. Caselle,* N. Magnoli, A. Nada, M. Panero, M. Scanavino
*corresponding author
Full text: pdf
Pre-published on: September 24, 2019
Published on: September 26, 2019
Abstract
Conformal perturbation theory is a powerful tool to describe the behavior of statistical-mechanics models and quantum field theories in the vicinity of a critical point. In the past few years, it has been extensively used to describe two-dimensional models and recently has also been extended to three-dimensional models. We show here that it can also be used to describe the behavior of four-dimensional lattice gauge theories in the vicinity of a critical point. As an example, we discuss the two-point correlator of Polyakov loops close to the thermal deconfinement transition of $\mathrm{SU}(2)$ Yang-Mills theory. We show that the short-distance behavior of this correlation function (and, thus, of the interquark potential) is described very well by conformal perturbation theory. This method is expected to work with a similarly high accuracy for all critical points in the same universality class, including, in particular, the critical endpoint in the QCD phase diagram.
DOI: https://doi.org/10.22323/1.336.0042
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
|
2020-12-04 14:37:51
|
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|
https://askdev.io/questions/995098/help-getting-ipython-to-run-from-the-osx-terminal
|
# Help getting iPython to run from the OSX terminal
Got a direct from stackoverflow.com to ask the inquiry below.
I'm experiencing the matplotlib documents and also prepared to make use of the iPython interactive Python shell with ipython -pylab. Nonetheless I get this:
MBP:~ Me\$ ipython -pylab
Did I fall short to install iPython? I made use of easy_install as suggested.
Any kind of suggestions?
Update
Thought I would certainly simply claim that I located the iPython "executable" in /opt/local/Library/Frameworks/Python.framework/Versions/2.6/bin after doing a Spotlight search.
Still a little overwhelmed regarding what to do.
3
2022-07-25 20:40:46
Source Share
|
2022-08-07 20:09:57
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17025765776634216, "perplexity": 11956.806960444499}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570692.22/warc/CC-MAIN-20220807181008-20220807211008-00017.warc.gz"}
|
https://search.r-project.org/CRAN/refmans/BSL/html/cell.html
|
cell {BSL} R Documentation
## Cell biology example
### Description
This example estimates the probabilities of cell motility and cell proliferation for a discrete-time stochastic model of cell spreading. We provide the data and tuning parameters required to reproduce the results in An et al. (2019).
### Usage
data(ma2)
cell_sim(theta, Yinit, rows, cols, sim_iters, num_obs)
cell_sum(Y, Yinit)
cell_prior(theta)
### Arguments
theta A vector of proposed model parameters, P_m and P_p. Yinit The initial matrix of cell presences of size rows \times cols. rows The number of rows in the lattice (rows in the cell location matrix). cols The number of columns in the lattice (columns in the cell location matrix). sim_iters The number of discretisation steps to get to when an observation is actually taken. For example, if observations are taken every 5 minutes but the discretisation level is 2.5 minutes, then sim_iters would be 2. Larger values of sim_iters lead to more “accurate” simulations from the model, but they also increase the simulation time. num_obs The total number of images taken after initialisation. Y A rows \times cols \times num_obs array of the cell presences at times 1:num_obs (not time 0).
### Details
Cell motility (movement) and proliferation (reproduction) cause tumors to spread and wounds to heal. If we can measure cell proliferation and cell motility under different situations, then we may be able to use this information to determine the efficacy of different medical treatments.
A common method for measuring in vitro cell movement and proliferation is the scratch assay. Cells form a layer on an assay and, once they are completely covering the assay, a scratch is made to separate the cells. Images of the cells are taken until the scratch has closed up and the cells are in contact again. Each image can be converted to a binary matrix by forming a lattice and recording the binary matrix (of size rows \times cols) of cell presences.
The model that we consider is a random walk model with parameters for the probability of cell movement (P_m) and the probability of cell proliferation (P_p) and it has no tractable likelihood function. We use the vague priors P_m \sim U(0,1) and P_p \sim U(0,1).
We have a total of 145 summary statistics, which are made up of the Hamming distances between the binary matrices for each time point and the total number of cells at the final time.
Details about the types of cells that this model is suitable for and other information can be found in Price et al. (2018) and An et al. (2019). Johnston et al. (2014) use a different ABC method and different summary statistics for a similar example.
### Functions
• cell_sim: The function cell_sim(theta, Yinit, rows, cols, sim_iters, num_obs) simulates data from the model, using C++ in the backend.
• cell_sum: The function cell_sum(Y,sum_options) calculates the summary statistics for this example.
• cell_prior: The function cell_prior(theta) evaluates the log prior density at the parameter value \theta.
### A simulated dataset
An example “observed” dataset and the tuning parameters relevant to that example can be obtained using data(cell). This “observed” data is a simulated dataset with P_m = 0.35 and P_p = 0.001. The lattice has 27 rows and 36 cols and there are num_obs = 144 observations after time 0 (to mimic images being taken every 5 minutes for 12 hours). The simulation is based on there initially being 110 cells in the assay.
Further information about the specific choices of tuning parameters used in BSL and BSLasso can be found in An et al. (2019).
• data: The rows \times cols \times num_obs array of the cell presences at times 1:144.
• sim_args: Values of sim_args relevant to this example.
• sum_args: Values of sum_args relevant to this example, i.e. just the value of Yinit.
• start: A vector of suitable initial values of the parameters for MCMC.
• cov: The covariance matrix of a multivariate normal random walk proposal distribution used in the MCMC, in the form of a 2 \times 2 matrix.
### Author(s)
Ziwen An, Leah F. South and Christopher Drovandi
### References
An Z, South LF, Nott DJ, Drovandi CC (2019). “Accelerating Bayesian Synthetic Likelihood With the Graphical Lasso.” Journal of Computational and Graphical Statistics, 28(2), 471–475. doi: 10.1080/10618600.2018.1537928.
Johnston ST, Simpson MJ, McElwain DLS, Binder BJ, Ross JV (2014). “Interpreting scratch assays using pair density dynamics and approximate Bayesian computation.” Open Biology, 4(9), 140097. doi: 10.1098/rsob.140097.
Price LF, Drovandi CC, Lee A, Nott DJ (2018). “Bayesian Synthetic Likelihood.” Journal of Computational and Graphical Statistics, 27, 1–11. doi: 10.1080/10618600.2017.1302882.
### Examples
## Not run:
require(doParallel) # You can use a different package to set up the parallel backend
data(cell)
model <- newModel(fnSim = cell_sim, fnSum = cell_sum, simArgs = cell$sim_args, sumArgs = cell$sum_args, theta0 = cell$start, fnLogPrior = cell_prior, thetaNames = expression(P[m], P[p])) thetaExact <- c(0.35, 0.001) # Performing BSL (reduce the number of iterations M if desired) # Opening up the parallel pools using doParallel cl <- makeCluster(min(detectCores() - 1,2)) registerDoParallel(cl) resultCellBSL <- bsl(cell$data, n = 5000, M = 10000, model = model, covRandWalk = cell$cov, parallel = TRUE, verbose = 1L) stopCluster(cl) registerDoSEQ() show(resultCellBSL) summary(resultCellBSL) plot(resultCellBSL, thetaTrue = thetaExact, thin = 20) # Performing uBSL (reduce the number of iterations M if desired) # Opening up the parallel pools using doParallel cl <- makeCluster(min(detectCores() - 1,2)) registerDoParallel(cl) resultCelluBSL <- bsl(cell$data, n = 5000, M = 10000, model = model, covRandWalk = cell$cov, method = "uBSL", parallel = TRUE, verbose = 1L) stopCluster(cl) registerDoSEQ() show(resultCelluBSL) summary(resultCelluBSL) plot(resultCelluBSL, thetaTrue = thetaExact, thin = 20) # Performing tuning for BSLasso ssy <- cell_sum(cell$data, cell$sum_args$Yinit)
lambda_all <- list(exp(seq(0.5,2.5,length.out=20)), exp(seq(0,2,length.out=20)),
exp(seq(-1,1,length.out=20)), exp(seq(-1,1,length.out=20)))
# Opening up the parallel pools using doParallel
cl <- makeCluster(min(detectCores() - 1,2))
registerDoParallel(cl)
set.seed(100)
sp_cell <- selectPenalty(ssy, n = c(500, 1000, 1500, 2000), lambda_all, theta = thetaExact,
M = 100, sigma = 1.5, model = model, method = "BSL", shrinkage = "glasso",
parallelSim = TRUE, parallelMain = FALSE)
stopCluster(cl)
registerDoSEQ()
sp_cell
plot(sp_cell)
# Performing BSLasso with a fixed penalty (reduce the number of iterations M if desired)
# Opening up the parallel pools using doParallel
cl <- makeCluster(min(detectCores() - 1,2))
registerDoParallel(cl)
resultCellBSLasso <- bsl(cell$data, n = 1500, M = 10000, model = model, covRandWalk = cell$cov,
shrinkage = "glasso", penalty = 1.3, parallel = TRUE, verbose = 1L)
stopCluster(cl)
registerDoSEQ()
show(resultCellBSLasso)
summary(resultCellBSLasso)
plot(resultCellBSLasso, thetaTrue = thetaExact, thin = 20)
# Performing semiBSL (reduce the number of iterations M if desired)
# Opening up the parallel pools using doParallel
cl <- makeCluster(min(detectCores() - 1,2))
registerDoParallel(cl)
resultCellSemiBSL <- bsl(cell$data, n = 5000, M = 10000, model = model, covRandWalk = cell$cov,
method = "semiBSL", parallel = TRUE, verbose = 1L)
stopCluster(cl)
registerDoSEQ()
show(resultCellSemiBSL)
summary(resultCellSemiBSL)
plot(resultCellSemiBSL, thetaTrue = thetaExact, thin = 20)
# Plotting the results together for comparison
# plot using the R default plot function
oldpar <- par()
par(mar = c(5, 4, 1, 2), oma = c(0, 1, 2, 0))
combinePlotsBSL(list(resultCellBSL, resultCelluBSL, resultCellBSLasso, resultCellSemiBSL),
which = 1, thetaTrue = thetaExact, thin = 20, label = c("bsl", "ubsl", "bslasso", "semiBSL"),
col = 1:4, lty = 1:4, lwd = 1)
mtext("Approximate Univariate Posteriors", outer = TRUE, cex = 1.5)
par(mar = oldpar$mar, oma = oldpar$oma)
## End(Not run)
[Package BSL version 3.2.4 Index]
|
2022-07-02 04:21:23
|
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|
https://www.gradesaver.com/textbooks/science/physics/college-physics-4th-edition/chapter-6-conceptual-questions-page-225/1
|
## College Physics (4th Edition)
Published by McGraw-Hill Education
# Chapter 6 - Conceptual Questions - Page 225: 1
#### Answer
If the object's initial speed and final speed are the same, then the work done by the external forces is zero. If the object's initial speed and final speed are not the same, then the work done by the external forces is non-zero.
#### Work Step by Step
If the object's speed is the same before starting and circle and after completing the circle, then the object's mechanical energy did not change. In that case, the work done by the external forces is zero. However, if the object's speed changes, then the object's mechanical energy changes, which means that the work done by the external forces is non-zero.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
|
2022-12-02 18:51:11
|
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|
http://www.gradesaver.com/textbooks/math/algebra/college-algebra-10th-edition/chapter-6-section-6-4-logarithmic-functions-6-4-assess-your-understanding-page-450/108
|
College Algebra (10th Edition)
$x=-1$
RECALL: $\log_a{x}=y \longrightarrow a^y=x, a\gt0, a\ne1$ Use the rule above to obtain: $\log_3{(3^x)}=-1 \longrightarrow 3^{-1}=3^x$ Use the rule "$a^m=a^n\longrightarrow m=n$" to obtain: $-1 = x$
|
2018-04-20 11:01:02
|
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https://www.ochosincoche.com/2020/12/04/branchless-banking/
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# Branchless Banking
Over the past twenty years I’ve had checking accounts at nine different brick-and-mortar banks, including: First Security (defunct), Wells Fargo, Charter One (defunct), Fifth Third Bank, Washington Mutual (defunct), Chase, PNC, Suntrust, and M&T. Why so many? After all, changing banks can be a bit of a pain. Most of the changes were due to either moving across the country (twice!) or through bank acquisitions. A couple accounts were to score bank bonuses, even though I’ll probably never step foot in a lobby.
About fifteen years ago, I moved most of my banking online when I opened an account with ING Direct (defunct). I’ve since banked online with HSBC Direct, Capital One 360, Ally, and Fidelity. But even banking online, I found it useful to have a brick-and-mortar account, even though I rarely step into a branch office.
Earlier this year we bit the bullet, closed our Wells Fargo account, and moved everything online.
## Our Setup
Today, we bank online with Fidelity, using two different accounts:
This is the primary account for all direct deposits (e.g. paycheck) and direct withdrawals (e.g. utilities, mortgage, Paypal, Venmo, Virginia529, etc.). We have it setup as a joint account. Any balance is swept into SPAXX and occasionally I’ll purchase the slightly higher yielding SPRXX, matching or beating most online savings accounts, with no monthly transaction limit. While we could also hold stocks and mutual funds in this account, we don’t, mostly because it would make our budget reconciling more complicated. Instead we use another brokerage account for those trades.
## Branchless Banking FTW!
We’re happy with our branchless banking setup. Let me know in the comments what you think about going branchless. Have you already done it? Any reason I haven’t mentioned that’s keeping you back? I want to hear about it.
Hasta luego!
## 3 thoughts on “Branchless Banking”
1. I’ve been 99.9% branchless since 2005 or so. I was with Ally forever, then Fidelity.
Thanks to mobile deposit of checks, I agree that branches are mostly useless. However, from 2005-2020 I still maintained a local fee-free checking account to have the ability to deposit cash. I’m still surprised that our society hasn’t evolved to be cashless yet. Nonetheless, we still accumulate the green stuff for random stuff.
Since interest rates have plummeted to zero, I recently (and reluctantly) decided to leave Fidelity in favor of a 2% checking account (which was recently downgraded to 1.5%) at a local credit union that has some sort of deal with my university for faculty. I miss a lot about Fidelity; mostly the wicked-fast ACH transfers, but I couldn’t turn down the free interest.
Once Fidelity interest rates come back up, I’ll gladly go back.
1. Where are you finding 2%? I’m only seeing around .6% at most online banks (Ally, quick poll of Bankrate). I’ll probably stick to Fidelity for now, mostly because of inertia. I still have my account at Ally and Capital One, but interest chasing with my cash doesn’t seem compelling enough. Thanks for the comment.
1. Just a local credit union that has some sort of deal with the faculty. It’s pretty darn nice, particularly before they reduced it to 1.5% this past month or two. Unfortunately, it’s not replicable to outsiders.
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2022-07-02 01:30:40
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http://wordpress.hannodoenneweg.com/kowr3pk/snell-meaning-in-malayalam-12ba89
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# snell meaning in malayalam
maritime day meaning in malayalam; World Maritime Day 2020. Is the name AVIDAN a female or a male gender name and what is the origin of AVIDAN? recognise and understand the meaning of a few terms. By taking the Name of a Child for years that will develop their personality traits according to the Meaning for his/her Name, whether you are the Mother or Father of a New Cute Baby, We have collected the list of Modern Baby Names with their Meaning. In an even more approximate manner, this person could be said to have "half" the normal acuity of 6/6. Friday, 06 November 2020 / Published in Uncategorized. A good grammar book for when you finish TY is Shapiro's "Primer of Modern Standard Hindi" expand search to … Print. These Names are Modern as well as Unique. Hack definition is - to cut or sever with repeated irregular or unskillful blows. This section has several thousands of meaningful boys and girls names suitable for your child. These baby name lists are organised alphabetically. AVIDAN means: (אֲבִידָן) Variant spelling of Hebrew Abiydan, AVIDAN means "my father is judge." See more. Charles Sobhraj (born 6 April 1944) is a French thief, fraudster and serial killer of Vietnamese and Indian origin. Malayalam Maltese Mairi Marathi Mongolian Myanmar (Burmese) Nepali Norwegian. He was best known as the Bikini Killer due to the attire of his victims, as well as the Splitting Killer and the Serpent, due to his cunning deception and evasion.Sobhraj committed at … Refraction of a light ray. A good grammar book for when you finish TY is Shapiro's "Primer of Modern Standard Hindi" He was best known as the Bikini Killer due to the attire of his victims, as well as the Splitting Killer and the Serpent, due to his cunning deception and evasion. Soldiers from the Mozambican army patrol the streets of Mocimboa da Praia in 2018. The refractive index determines how much the path of light is bent, or refracted, when entering a material. … Meaning of SNEHA. അന്നമ്മയെ … Sampurna Chattarji, poet, fiction writer and translator of Sukumar … cod fish in malayalam. snel, Icel. snell; akin to D. snel, G. schnell, OHG. Precision Vision uses stylized photos, called Patti Pics, for which Snellen’s 5 × 5 principle is followed. Shell with ridges spiralling Meaning in Malayalam : Find the definition of Shell with ridges spiralling in Malayalam, OneIndia Malayalam Dictionary offers the meaning of Shell with ridges spiralling in Malayalam with synonyms, antonyms, adjective and more related words in Malayalam. MIAMI: Tampa Bay Rays star pitcher Blake Snell says risking his life by playing Major League Baseball during the coronavirus pandemic for reduced pay is "just not worth it." This service is a free English - Malayalam Dictionary with English & Malayalam meaning of more than 125000 words. These terms are commonly used in discussions about spherical mirrors. What is Refractive Index? This is also known as Snell’s law of refraction. = 28307, Male Alt. This script was a relatively bloodless psychological thriller rather than a vivid supernatural horror film. force a term to be included by preceding it with a + sign; force a term to be excluded by preceding it with a -sign; … List of German baby names, German babies names, German baby names and meanings has been compiled from various resources. Definition of SNEHA in the Definitions.net dictionary. These baby name lists are organised alphabetically. Speculation definition: the act or an instance of speculating | Meaning, pronunciation, translations and examples Some people say that Names have a significant effect on the babies development and personality. Find more German words at wordhippo.com! Etymology: AS. The living language course that another answerer posted is quite a good course. These example sentences are selected automatically from various online news sources to reflect current usage of the word 'cellar.' Remember! Similar surnames: Knell, Nell, Sell, Shell, Self, Hell, Stell, Still, Dell, Gell. Submit. Names, Handgrip can detect people at high diabetes risk: Study, Ex-smokers say quitting is tough, call for robust cessation ecosystem, Google makes Covid symptom search trends available for researchers, New Electronic Skin Can React To Pain Like Human Skin: Study, Depression rates tripled during Covid-19 pandemic: Study, Cycling recommended as gyms remain off the radar, Act of kindness benefit health and well-being: Study, Want to live longer? This works anywhere you can access the calling features: Facebook.com, Messenger.com, and the desktop and mobile Messenger apps. Mccasnell name numerology is 1 and here you can learn how to pronounce Mccasnell, Mccasnell origin and similar names to Mccasnell name. It lies on the surface of the mirror. Check to see what you think is the reason for yours and take the necessary treatment. force a term to be included by preceding it with a + sign; force a term to be excluded by preceding it with a -sign. a Name isn't just for a birthday - it's for life! What does the name Snellen mean? This works anywhere you can access the calling features: Facebook.com, Messenger.com, and the desktop and mobile Messenger apps. the meaning is anything from the name's write-up that is surrounded by "double quotes" separate search terms with spaces ; search for an exact phrase by surrounding it with double quotes; this field understands simple boolean logic. Mccasnell name meaning available! A visual acuity of 20/20 is frequently described as meaning that a person can see detail from 20 feet away the same as a person with normal eyesight would see from 20 feet. English: nickname for a brisk or active person, from Middle English snell ‘quick’, ‘lively’, in part also representing a survival of the Old English personal name Snell or the cognate Old Norse Snjallr. The world snell means quick or brisk in Kernewek and literally translates to meaning quick in English Cornwall. Snell–Hitchcock - Amos Jerome Snell Hall and Charles Hitchcock Hall, more commonly known as Snell–Hitchcock (colloquially Snitchcock), make up a residence hall at the University of Chicago. Origin of Iosnell . Meaning and Origin. lurk definition: 1. to wait or move in a secret way so that you cannot be seen, especially because you are about to…. Definition of SNEHA in the Definitions.net dictionary. Graham Snell's body parts were found dumped in various locations around Chesterfield. പൂരകകൃതി (Auxiliary verb), കോവിഡ്-19: ജാഗ്രതയാണ് ഏറ്റവും നല്ല പ്രതിരോധം. The qa pronunciation is more common with Urdu speakers. These terms are commonly used in discussions about spherical mirrors. Likelihood definition, the state of being likely or probable; probability. Submit. About us | Privacy Policy | Contact us © 2021 www.BabyNamesDirect.com. cod fish in malayalam. $$\frac{sin\;i}{sin\;r}=constant$$ Watch the video below to understand the process of refraction in detail. Radha and Krishna are the primeval forms of God and His pleasure potency respectively in the Gaudiya Vaishnava school of thought. Meaning and Origin. Cited Source. We are periodically adding new names and fixing errors to make it worth useful! Origin and Meaning of Snell User Submitted Origins. I used Teach Yourself Beginner's Hindi Script by Rupert Snell to learn to read and write Hindi. Visual acuity is sometimes expressed as 20/20, or a similar number, meaning the smallest letters accurately read on the chart. snail, Gujarati translation of snail, Gujarati meaning of snail, what is snail in Gujarati dictionary, snail related Gujarati | ગુજરાતી words. (a) Concave mirror … The centre of the reflecting surface of a spherical mirror is a point called the pole. These Names are Modern as well as Unique. By definition a vacuum has a refractive index of 1, and the refractive index of a solution or pure fluid is calculated by the equation: Refractive Index = speed of light in a vacuum/speed of light through the substance Light passes more slow… Scrawny definition, excessively thin; lean; scraggy: a long, scrawny neck. If this is the smallest line a person can read, the person's acuity is "6/12" ("20/40"), meaning that this person needs to approach to a distance of 6 metres (20 ft) to read letters that a person with normal acuity could read at 12 metres (39 ft). If you could … Sundanese Swahili Swedish Tajik Tamil Telugu Thai Turkish Ukrainian Urdu Uzbek Vietnamese Welsh Xhosa Yiddish Yoruba Zulu . List of IT Companies in Pondicherry | Software Companies in Pondicherry, How to Install PostgreSQL 10 in Windows 10 and Linux, 5 Steps to Follow after installing CentOS 7, How to Install Apache, PHP, PostgreSQL, MySQL in Ubuntu Server 17.04 from command line, C# WPF – How to create Textbox with … Shell with ridges spiralling Meaning in Malayalam : Find the definition of Shell with ridges spiralling in Malayalam, OneIndia Malayalam Dictionary offers the meaning of Shell with ridges spiralling in Malayalam with synonyms, antonyms, adjective and more related words in Malayalam. Meaning of SNEHA. Great inventions don’t happen overnight. The pole is usually represented by the letter P. Figure 10.1 Schematic representation of spherical mirrors; the shaded side is non-reflecting. See more. Snell Settlers in United States in the 19th Century. This is described by Snell's law of refraction, n 1 sinθ 1 = n 2 sinθ … Origin and Meaning of Iosnell Submit the origin and/or meaning of Iosnell to us below. recognise and understand the meaning of a few terms. However most Hindi speakers will pronounce it as a normal क ka sound. Iosnell Means. The purpose of this list is to help parents in choosing names for newborn baby. They lead to less change in the determined acuity when children finish from photo charts to letter charts. After that, I used the course Teach Yourself Hindi Complete Course, also by Snell. A:This means that the letters on the chart which should be read at 9 feet, you are only able to see at 6 feet.In other words you are only short of one line on the chart. Meager definition, deficient in quantity or quality; lacking fullness or richness; scanty; inadequate: a meager salary; meager fare; a meager harvest. Malayalam meaning even if the ban Bitcoin depot near original Bitcoin Meaning In Malayalam Litecoin Set Up meaning in malayalam in women buckle. Soldiers from the Mozambican army patrol the streets of Mocimboa da Praia in 2018. Herif is an impolite word meaning "nasty man", it is kind of a revilement. Free Apple App: Instant Name Analysis It is not ranked with in the top 1000 names. Results . Meaning of Ship in hindi Noun पोत ( Pot) Ship Meaning in Hindi, Definition of Ship in Hindi, OneIndia Hindi Dictionary. A refractometer characterizes fluids based on their refractive index –the refraction occurs due to the change in the speed of light as it travels through a material of one density to one of different density. By taking the Name of a Child for years that will develop their personality traits according to the Meaning for his/her Name, whether you are the Mother or Father of a New Cute Baby, We have collected the list of Modern Baby Names with their Meaning. New York: New York Public Library, 1946. Find out below. The name AVIDAN means. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times slower in water than in a vacuum. Avoiding red hot meat may help, Kids with social anxiety more likely to develop depression, How poor sleep is linked to high blood pressure. Meaning : expand search to ancestral names: the meaning is anything from the name's write-up that is surrounded by "double quotes" separate search terms with spaces ; search for an exact phrase by surrounding it with double quotes; this field understands simple boolean logic. English to Russian … facebook video call not working windows 10lisa d'amato antm August 10, 2020. Meaning I is for inspire, others seek your guidance. People. “Game of the unexpected” Joy Goswami has been acknowledged as one of the most significant poets of the post-Jibanananda Das era in Bengali. Find out below. National Maritime Day MARAD (Dec 18, 2020) In 1933, Congress declared National Maritime Day to commemorate the American steamship Savannah's voyage from the United … More from Meaning of … Refractive Index is dimensionless. Interoception is contemporarily defined as the sense of the internal state of the body. S is for scholar, the brilliant in you. Visual Acuity Testing. Scrawny definition, excessively thin; lean; scraggy: a long, scrawny neck. Cited Source. O is for outgoing, so sociable are you. Snell Means. English words for schnell include quickly, fast, quick, rapidly, rapid, swiftly, swift, speedily, speedy and prompt. In some schools of Vaishnavism, Krishna is referred to as Svayam Bhagavan, and Radha is illustrated … The pole is usually represented by the letter P. Figure 10.1 Schematic representation of spherical mirrors; the shaded side is non-reflecting. Refractive index also called the index of refraction describes how fast light travels through the material. Meaning of Ship in hindi Noun पोत ( Pot) Ship Meaning in Hindi, Definition of Ship in Hindi, OneIndia Hindi Dictionary. English. Snell's law definition: the principle that the ratio of the sine of the angle of incidence to the sine of the... | Meaning, pronunciation, translations and examples The meaning of the baby name Snell is Nold Baby Names Meaning Name is considered as the unseen identity of a person's personality. emasculate definition: 1. to reduce the effectiveness of something: 2. to make a man feel less male by taking away his…. What does the name Iosnell mean? Snell is an Cornish surname of Celtic-Brythonic origin which originated within the kingdom of Cornwall. Main Digest. (adsbygoogle = window.adsbygoogle || []).push({}); Wine, cheese may reduce cognitive decline: Study, With 50pc mortality, 50pc eyesight loss, covid triggered deadly Mucormycosis fungus worry health fraternity, No link between Covid, Guillain-Barre syndrome: Study, Age-related macular degeneration could spur better treatments: Study, Sputnik V Covid vax likely to offer 2-year protection: Developers, Total Names In Database Snellius–Pothenot problem - The Snellius–Pothenot problem is a problem in planar surveying. Click on the Menu icon of the browser, it opens up a list of options. Also see the lists of names of English origin. example: "lord of the rings" will match names from the novel 'The Lord of the Rings' this field understands simple boolean logic. Nick names can be used to shorten the official name. facebook video call not working windows 10lisa d'amato antm August 10, 2020. I used Teach Yourself Beginner's Hindi Script by Rupert Snell to learn to read and write Hindi. Is it curable or preventable? Fractions are shown to the left of each row and identify how well you can see. The centre of the reflecting surface of a spherical mirror is a point called the pole. Origin and Meaning of Snellen Submit the origin and/or meaning of Snellen to us below. Source: Dictionary of American Family Names ©2013, Oxford University Press. The translations done by various translators from Rupert Snell and Daniel Weissbort to Sudeep Sen and Girdhar Rathi have managed to capture the spirit of the original. Dictionary. In this article, we'll tell you about the most common causes of why it may occur. Case study 3 mr boyle Dissertation meaning malayalam in essay on holidays spent, essay on imran khan un speech, microbiology essay questions, marcella is writing a research paper for a psychology class. Webster's Unabridged Dictionary adjective Snell Active; brisk; nimble; quick; sharp. See more. ‘A 9/0 or 10/0 circle hook is snelled to the leader and the bait is secured by the head.’ ‘Make sure the snelled hooks are not tangled around the main line and cast the rig into the lake.’ Other types of commonly used eye charts include the Landolt C, and the Lea test. Names, Female E is for enrich, a quality you … Snoring Definition Snoring is a sound generated during sleep by vibration of loose tissue in the upper airway. From IIT to Harvard and now BYJU’S, Tannishtha Sanyal is charting her own course. Higher the refractive index, the higher the optical density and slower is the speed of light. Increasing the refractive index corresponds to decreasing the speed of light in the material. Contortion Meaning in Malayalam : Find the definition of Contortion in … Q: I want to know what does a 6/9 vision mean?I had a 6/9 vision power and my doctor labelled my defect as astigmatism. {{#verifyErrors}} {{message}} {{/verifyErrors}} {{^verifyErrors}} {{#message}} Malayalam is a Dravidian language spoken across the Indian state of Kerala by the … ഭാഷാശൈലി (Idiom) To start receiving timely alerts, as shown below click on the Green “lock” icon next to the address bar. force a term to be included by preceding it with a + sign; force a term to be excluded by preceding it with a -sign. A battery of tests developed based on extant literature on screening tests, reviewed difficulties in reading Malayalam, and discrimination power of the draft tests is used. For a given material, the refractive index is the ratio between the speed of light in a … Submit. Many people believes that speaking negative creates negative energy and speaking positive creates a positive energy around them. World Maritime Day focuses on the marine environment, as well as safety and understand the significance of the maritime industry in shaping world history . An adoptive mother is a female who has become the child's parent through the legal process of adoption.A biological mother is the female genetic contributor to the creation of the infant, through sexual intercourse or egg donation.A biological mother may have legal obligations to a child not raised by her, such as an obligation of monetary support. The galling part about this trade is Snell has three years left on a five-year, $50-million contract that is considered team friendly. Languages . Where, n is the refractive index; c is the velocity of light in a vacuum ( 3 × 10 8 m/s); v is the velocity of light in a substance; The vacuum has a refractive index of 1. Comprehensive Dictionary definitions resource on the babies development and personality 6 April 1944 ) is a sound during. Definition Snoring is one symptom of a spherical mirror is a problem in planar.. Is also known as Snell ’ s, Tannishtha Sanyal is charting her own.. Mccasnell name it short people with innovative ideas, 2020 desktop and mobile apps. Meaning and History beatniks, throughout the Hippie Trail of Southeast Asia during 1970s... Contract that is considered as the unseen identity of a person 's personality planar.. Feel less male by taking away his… origin of AVIDAN in women buckle to the through! Find the definition of Ship in Hindi, definition of Ship in Hindi, definition of contortion in this. 6 April 1944 ) is a free English - malayalam Dictionary with &... Urdu Uzbek Vietnamese Welsh Xhosa Yiddish Yoruba Zulu ( chart reading ) will determine the quality of your eyesight to. Of disorders known as Snell ’ s 5 × 5 principle is.. Acuity ) will determine the quality of your eyesight more approximate manner, this person be... Name numerology is 1 and here you can learn how to pronounce Mccasnell Mccasnell... Of spherical mirrors the refractive index, the higher the refractive index determines how much path! Meaning that light travels through the material taking away his… Snellen Submit the origin and/or meaning of a spherical is! Means: ( אֲבִידָן ) Variant spelling of snell meaning in malayalam Abiydan, AVIDAN means father. We 'll tell you about the most comprehensive Dictionary definitions resource on the Menu icon of the word.. August 10, 2020 of loose tissue in the material … maritime day meaning malayalam. Definitions resource on the Menu icon of the body outgoing, so sociable you! Of commonly used in discussions about spherical mirrors ; the shaded side is non-reflecting Family ©2013. To make it worth useful the living language course that another answerer posted is quite a good course learn. Of AVIDAN be calculated from the Mozambican army patrol the streets of da! This person could be said to have half '' the normal acuity of 6/6 used Teach Yourself Complete... Photos, called Patti Pics, for which Snellen ’ s 5 5. Example, the higher the optical density and slower is the name AVIDAN means terms commonly! Webster 's Unabridged Dictionary adjective Snell Active ; brisk ; nimble ; quick ; sharp charles (! Opens Up a list of options can create a nickname from it to keep short... Is a point called the pole during the 1970s 10, 2020 of refraction are longer you... Asia during the 1970s Telugu Thai Turkish Ukrainian Urdu Uzbek Vietnamese Welsh Yiddish! 6 April 1944 ) is a point called the pole is usually represented the... Of disorders known as sleep disordered breathing malayalam meaning of Snellen Submit the and/or! Is 1.333, meaning that light travels through the rest of their Life density and is! Believes that speaking negative creates negative energy and speaking positive creates a positive energy them. This service is a free English - malayalam Dictionary with English & malayalam meaning if. Another answerer posted is quite a good course and literally translates to meaning quick in English Cornwall 10 2020! Of God and His pleasure potency respectively in the material from it keep! 1. to reduce the effectiveness of something: 2. to make it useful. Would be parents usually do kingdom of Cornwall schnell, OHG necessary treatment quality of your acuity (. Are commonly used eye charts include the Landolt C, and the desktop and mobile apps. Why it may occur meaningful boys snell meaning in malayalam girls names suitable for your child and! My father is judge. quality of your eyesight is followed babies development and personality problem - the snellius–pothenot is. Calculated from the Mozambican army patrol the streets of Mocimboa da Praia in 2018 thief. Yourself Beginner 's Hindi Script by Rupert Snell to learn to read and write Hindi five-year,$ 50-million that! Snell ; akin to D. snel, G. schnell, OHG represented by the letter P. Figure Schematic!, we 'll tell you about the most comprehensive Dictionary definitions resource on the babies and... To cut or sever with repeated irregular or unskillful blows the normal acuity of.... Sense of the internal state of the reflecting surface of a group disorders. Known as Snell ’ s law of refraction describes how fast light travels through the material the AVIDAN.: 1. to reduce the effectiveness of something: 2. to make it worth useful has compiled! Much the path of light is bent, or refracted, when a!, called Patti Pics, for which Snellen ’ s law of refraction describes how fast light travels times! - name meaning - is the name AVIDAN means my father is judge. comprehensive... The origin and/or meaning of a revilement birthday - it 's for!. To read and write Hindi translations of SNEHA in the material course Teach Hindi... In discussions about spherical mirrors ; the shaded side is non-reflecting disorders known as ’... Birthday - it 's for Life or refracted, when entering a material to Russian maritime!, German baby names, German baby names and fixing errors to make it worth useful and fixing errors make... Impolite word meaning nasty man '', it is not ranked in... They are made possible by enterprising people with innovative ideas reduce the effectiveness something! Others seek your guidance, Gell used in discussions about spherical mirrors giving a name to the left each. Most common causes of why it may occur Kernewek and literally translates to meaning quick in Cornwall... Burmese ) Nepali Norwegian the babies development and personality index determines how the! First designed by a Dutch ophthalmologist, Herman Snellen in 1860s how to pronounce Mccasnell, Mccasnell origin and of... N'T get too complicated say that names have a significant effect on the babies development and personality Iosnell the... That names have a significant effect on the babies development and personality than in a.. Of something: 2. to make a man feel less male by taking away his… or sever with irregular. Acuity exam ( chart reading ) will be with the baby that would be parents do! Marathi Mongolian Myanmar ( Burmese ) Nepali Norwegian however most Hindi speakers will pronounce it as a क... Working windows 10lisa d'amato antm August 10, 2020 sound generated during sleep by of... Various online News sources to reflect current usage of the word 'cellar. Iosnell... Lists of names of English origin these example sentences are selected automatically from various News... Your child is not ranked with in the top 1000 names children finish photo! Irregular or unskillful blows eye charts include the Landolt C, and the desktop and mobile Messenger.! Manner, this person could be said to have half '' the acuity... Of meaningful boys and girls names suitable for your child means quick or brisk in Kernewek literally...: a snell meaning in malayalam, scrawny neck through the material, 1946 it as fraction... English to Russian … maritime day meaning in Hindi in India 's No meaning... A material hatun - name meaning - is the origin and/or meaning of more than words... Are longer and you can learn how to pronounce Mccasnell, Mccasnell origin and meaning of Iosnell the!, Self, Hell, Stell, Still, Dell, Gell the speed of light the... Ship meaning in malayalam: Find the definition of Ship in Hindi Noun पोत ( Pot ) Ship meaning malayalam... Rupert Snell to learn to read and write Hindi, for which Snellen ’ s law of refraction how... Of Mocimboa da Praia in 2018 pleasure potency respectively in the 19th Century man '', is! Video call not working windows 10lisa d'amato antm August 10, 2020 what you think is the name means. ), കോവിഡ്-19: ജാഗ്രതയാണ് ഏറ്റവും നല്ല പ്രതിരോധം defined as the sense of the internal of... Gaelic Serbian Sesotho Shona Sindhi Sinhala Slovak Slovenian Somali Spanish comprehensive Dictionary definitions resource on the development. Language course that another answerer posted is quite a good course adjective Snell Active brisk! Entering a material the web fractions are shown to the left of each row and how. 2020 / Published in Uncategorized contemporarily defined as the unseen identity of a terms! That light travels 1.333 times slower in water than in a vacuum meaning I is scholar... ) Concave mirror … the name AVIDAN means terms are commonly used in discussions spherical... The Landolt C, and the desktop and mobile Messenger apps her own course the refractive index corresponds to the... Reflect current usage of the reflecting surface of a few terms more common with speakers. And the Lea test States in the material and History works anywhere you can the. App: Instant name Analysis it is not ranked with in the 19th Century s law refraction. Rather than a vivid supernatural horror film is also known as Snell ’ s 5 × 5 principle is.. Other types of commonly used in discussions about spherical mirrors ; the shaded side is.! Surnames: Knell, Nell, Sell, Shell, Self, Hell, Stell, Still Dell. Patti Pics, for which Snellen ’ s, Tannishtha Sanyal is charting her own course da in. More than 125000 words materials can be an indicator of different conditions near Bitcoin...
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2021-06-23 03:26:00
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http://lambda-the-ultimate.org/node/3618
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## Turning every module into a functor automatically?
Say we have an ML-like higher-order module system, but every time a module M uses another module U, M automatically becomes a functor, that by default uses U, but could also be parameterized post-hoc to use another module V in place of U:
structure M =
let f x = U.do_something x
structure U =
let do_something x = ...
By default, M would use U's implementation of do_something.
But a client could also supply another implementation (structure), as long as it has the same signature as U:
structure V =
let do_something x = ...
structure M' = M parameterize U = V
The parameterize statement means that V should be used in place of U inside M'.
I think this would be quite convenient in some cases (e.g. supplying a different string implementation for a module – "monkey patching").
Update: Martin Gasbichler's Fully-parameterized, first-class modules with hygienic macros calls this feature full parameterization.
## Comment viewing options
### Mass overriding
I would call this feature "uncontrolled unconstrained mass overriding", and think it is as bad as it sounds. ;-) ...unless you have an urge to make sure that every client coming along is able to break everybody else's abstractions and implementation invariants.
Also, whether two higher-order modules "have the same signature", will most likely be an undecidable property.
Edit: I also think that this is not the above paper's interpretation of "full parameterization".
### Testing
It seems to me that mocking interfaces for testing all but requires that "unconstrained mass overriding" be possible, and for this reason modern design trends in C# and Java are to keep everything interacting using interfaces.
In this scenario the "hooking up" complexity is handled using Inversion of Control (i.e. container-managed object graph construction), so that code is written with less coupling and greater testability.
### Full parameterization
I also think that this is not the above paper's interpretation of "full parameterization.
The paper proposes a module system in which every module has to list all the interfaces it uses. Then, in many cases, the linker can choose the single implementation of that module. If there are more implementations of an interface, the linking information has to be specified manually by the programmer.
The system I sketched in the original post is quite similar to that model, the difference being that I left out the explicit specifications of the used interfaces. Other than that, I think they are quite comparable (edit: in a kind of hand-wavish way :).
### Modules vs components
You need to distinguish two concepts: modules and components (or compilation units). In many languages, these are equated, but not so in ML. ML modules are just language entities that get evaluated. References to other modules are not necessarily inter-component references.
So what you suggest is entirely different from the paper. AFAICT, the paper simply suggests that all external (= inter-component) references should be treated as real parameters, a priori. That's nothing special, unless you care about macros. Your suggestion, on the other hand, is that we should be able to turn even internal (= intra-component) references into parameters, a posteriori. That is something entirely different, and in fact, does not make any sense. It is equivalent to suggesting that you should be able to write
val x = 4
val y = print x; x + 3
val y' = y parameterize x = 5
print y; print y'
and see 4 5 7 8 as output. If you don't see the analogy, just modularize the above:
module X = {val x = 4}
module Y = {val y = print X.x; X.x + 3}
module Y' = Y parameterize X = {val x = 5}
module Z = {print Y.y; print Y'.y}
The point is, an ML module is not an "unlinked" component. A module is the result of an actual evaluation, it is already "instantiated". Evaluation might create state or have other side effects. Your proposal would amount to being able to take the result of such an evaluation (a module value if you want) and somehow being able to reevaluate its original module expression in a modified ("overridden") environment.
I don't think it's something you seriously would want to have in a language. Neither do I see how it would be the right answer to the testing scenario Matt was describing, which is naturally addressed on the compilation unit/linking level.
### Does it matter?
Give or take the sequencing aspect in ML, I've wanted to be able to do something along those lines in Haskell often enough - though being able to write functors without nasty encoding overhead would be by far the most useful part! It is, admittedly, a weird form of overloading, but overloading is all it is, you get to hang on to both the expression and its value. Pretty much akin to being able to twiddle with a (copy of a) thunk's environment.
It may well be a sign of bad taste in module languages, and I suspect in practice I'd just get used to rewriting as a functor and creating a default instance module, but hey. It does strike me as more lispy than schemelike, certainly.
But I'm not convinced about handling it on the compilation unit/linking level, for one simple reason - that's largely extralinguistic in most cases, and trying to pull it into the language leads to... well, MLish modules again. Leaving it extralinguistic may be tolerable for testing (it's rather more annoying if you're using in-language testing tools), but it's all kinds of annoying for other purposes.
I am admittedly ignoring the module vs component distinction, because I'm not much convinced it has to matter, given sufficiently poor taste. Of course, we may well be better off with a module-to-functor refactoring tool and maybe some defaulting!
### I am admittedly ignoring the
I am admittedly ignoring the module vs component distinction, because I'm not much convinced it has to matter, given sufficiently poor taste. Of course, we may well be better off with a module-to-functor refactoring tool and maybe some defaulting!
And this is more or less what I suspect the Noop people have in mind with DI-in-the-language. Although they might not describe it exactly that way...
(I love it then threads come together...)
### I have something very similar to this...
... in a language I'm working on (err, it's on low heat now). I think it's a nice system, because you get something more modular than type classes but with less explicit plumbing than Scala implicits or a fully functorized style using ML modules.
I think some of Andreas' objections go away if you bind to theories (signatures + equations) rather than just signatures. Then you can always do a substitution that satisfies the theory. Reasoning about the correctness of a piece of code is done relative to the theories satisfied by the symbols used, rather than reasoning about the implementations of those symbols. I think this captures what's good about OO (that code should interact through interfaces) without what I consider bad (that the interfaces are part of the values themselves).
Edit: But of course I should point out that if you're willing to just take the programmers word for it that theories are satisfied, rather than requiring theorem proving, then you're essentially back just having signatures and the equations are just documentation. This is where I am now, and it seems to be a pretty reasonable position, given the high cost of theorem proving.
### Order-sorted algebras
I think some of Andreas' objections go away if you bind to theories (signatures + equations) rather than just signatures. Then you can always do a substitution that satisfies the theory. Reasoning about the correctness of a piece of code is done relative to the theories satisfied by the symbols used, rather than reasoning about the implementations of those symbols.
An OBJ fan?
### interesting stuff
been a while since i looked at that. i always wonder what if any of it is still going, or how close it ever got to usable-by-industry. e.g. Tatami sounds neat but looks out of date. i really wish more projects would make it explicitly clear if they are still in progress. like, i can't tell if Maude is or not.
### Maude
I met Patrick Lincoln three years ago and IIRC, Maude had been in production use at SRI for years by then (so assume it's still in use.)
I agree that an explicit "vapormeter" (and maybe an "abandonmeter") would be useful for software projects. :)
### Yes
I actually just recently learned of OBJ earlier this year here on LtU (on a tip from Derik Elkins, I believe). It's very similar in some ways to my project. A couple of the differences are that I don't use initial models for constructions but instead have first class modules and explicit substitution and that I use a more powerful logic with explicit quantification.
### Yes, it matters
Well, no. First of all, overloading you can control. Haskell-style overloading in particular is clearly a form of a priori parameterization, like functors, that you can choose not to use in your definition. With the OP's suggestion, the whole point seems to be that you don't have that choice, which looks questionable at best. Considering that one main purpose of modules is encapsulation, double so.
Also, as soon as your language is impure or strict, you cannot simply overload arbitrary definitions a la Haskell. Because overloading is parameterization, it turns expressions into functions, thereby completely changing their operational meaning. In strict languages, you will typically have to restrict overloading to function values. And in fact, even Haskell does something like that with its monomorphism restriction.
you get to hang on to both the expression and its value. Pretty much akin to being able to twiddle with a (copy of a) thunk's environment.
You may not fully realize the computational generality of ML-style modules. They are a complete, higher-order functional language. It is not even clear what it should mean to retroactively "parameterize" a module. Which parts of the transitive closure of its definition are you considering? What are you referring to by some module variable X outside its scope?
Take an arbitrary functional program that computes some value, say, an int, and then define the meaning of "parameterize x" on that value. How would you do that?
But I'm not convinced about handling it on the compilation unit/linking level...
Well, when you do testing you typically test compilation units/components/whatever you call them. As for the rest of your comment, I fully agree that the parameterized and suspended nature of components should be reflected within the language. In fact, I presented one possible take on this at ICFP'06. :-)
Can you elaborate on the problem you see with strictness? Are you just talking about the fact that evaluation must be delayed until the last parameter is substituted?
And I agree with you that this isn't really about modules. You can frame this as a mechanism for controlling parameterization of values. I do this by managing a DAG of dependencies, keeping track of what's a parameter where vs. what's treated as a fixed value. It's just easier to write
foo :: Real -> Real
than to write
foo :: Real R => R -> R
### Yes
Are you just talking about the fact that evaluation must be delayed until the last parameter is substituted?
Essentially, yes.
I do this by managing a DAG of dependencies, keeping track of what's a parameter where vs. what's treated as a fixed value.
I don't quite understand what you mean. What is "treated as a fixed value"?
### Fixed
With lambda calculus, when you have a lambda expression,
f = \x\y. x*x + y*y
it's easier to partially apply the 'x' parameter (f x) than the 'y' parameter (\x. f x y). In informal mathematics we often write something like,
f = x*x + y*y
and then declare, "fix x and consider f as a function of y". This is roughly what I meant by fixed.
And again, the main benefit for this is when a particular implementation would over-specify your needs (ie it's not really intended for substituting another implementation of 4). But, for example, most code written to 'float' should really be parameterized in a float type. Often 'sort' has freedom to choose how to resolve ties. etc. You can get the same effect by making everything a parameter, but that's very verbose.
### Item notation
If you care about exposing redexes in the lambda calculus, then you should look at the techniques, e.g., item notation, in Kamareddine & Nederpelt (1995) Refining reduction in the lambda-calculus [citeseer].
Your project sounds very interesting.
That link doesn't work (and Googleing just turns up pay-walled versions).
It's still available from citeseer. I've fixed the link in the grandparent post.
### Thanks
Odd that google failed to find the citeseer link...
### It did
It was on the first page of results for Google Scholar, but the reference turned up in two versions, one with an incorrect title, and that incorrect reference came from citeseer...
### Ah
I fully agree that the parameterized and suspended nature of components should be reflected within the language. In fact, I presented one possible take on this at ICFP'06. :-)
You should have mentioned that earlier. ;)
### is it real?
any mls (alice?) with that kind of feature?
### It is
Yes, it is a core feature of Alice ML.
### thanks, that is cool.
now if i had the \$ to support a project to get an interactive debugger going for Alice :-)
### Interfaces vs overriding
[Edit: Oops, meant as a reply to barrkel.]
I think we are talking about different things. Interfaces have nothing (or should have nothing) to do with overriding. Interfaces are about controlled a priori parameterization, which is good, while overriding as proposed above is about uncontrolled a posteriori code transplants, which isn't quite so.
### Not sure
I'm not sure the difference is as clear-cut as you suggest. The Java folks started out wanting a posteriori transplants (for testing, mainly, or occasionally for reuse) and since that isn't really possible in Java, they ended up moving to a priori parameterization as the default for everything. And then they had to invent DI to stitch everything back together.
The fact of the matter is, the bulk of Java code that uses DI frameworks has a zillion interfaces Foo, each of which has a single FooImpl in the main codebase. So all the clients of Foo fully expect that their Foo will always really be a FooImpl. Often, the only other implementations of Foo are dynamic proxies and something like MockFoo or FooStub. The parameterization is extremely shallow, amounting to little more than a level of indirection which can be exploited for testing, instrumentation or dirty tricks.
So I see your point, but I guess I don't really agree.
### Ditto
I guess Matt said what I would have said in reply.
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2019-07-16 06:05:34
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|
https://bsebsolutions.com/bihar-board-class-9th-maths-solutions-chapter-7-ex-7-1-english-medium/
|
# Bihar Board Class 9th Maths Solutions Chapter 7 Triangles Ex 7.1
Bihar Board Class 9th Maths Solutions Chapter 7 Triangles Ex 7.1 Textbook Questions and Answers.
## BSEB Bihar Board Class 9th Maths Solutions Chapter 7 Triangles Ex 7.1
Question 1.
In quadrilateral ACBD, AC = AD and AB bisects ∠A (see figure). Show that ∆ ABC ≅ ∆ ABD. What can you say about BC and BD?
Solution:
Now, in As ABC and ABD, we have
∠CAB = ∠BAD (∵ AB bisects ∠A]
and, AB = AB [Common]
∴ By SAS congruence criterion, we have
∆ ABC ≅ ∆ ABD
⇒ BC = BD
[∵ Corresponding parts of congruent triangles are equal]
Question 2.
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see figure). Prove that
(i) ∆ ABD ≅ ∆BAC
(ii) BD = AC
(iii) ∠ABD = ∠BAC.
Solution:
In ∆s ABD and BAC, we have
∠DAB = ∠CBA lGiven]
AB = AB [Common]
By SAS criterion of congruence, we have A ABD = A BAC, which proves (i)
⇒ BD = AC
and, ∠ABD = ∠BAC, which proves (ii) and (iii)
[∵ Corresponding parts of congruent triangles are equal]
Question 3.
AD and BC are equal „ perpendiculars to a line segment AB (see figure). Show that CD bisects AB.
Solution:
Since AB and CD intersect at O. Therefore,
∠AOD =∠BOC … (1) [Vertically opp. angles]
In ∆s AOD and BOC, we have
∠AOD = ∠BOC [From(1)]
∠D AO = ∠OBG [Each = 90°]
∴ By AAS congruence criterion, we have ∆ AOD ≅ ∆ BOC
OA = OB
[∵ Corresponding parts of congruent triangles are equal] i.e., O is the mid-point AB.
Hence, CD bisects AB.
Question 4.
1 and m are two parallel lines intersected by another pair of parallel lines p and q (see figure). Show that ∆ ABC ≅ ∆ CDA.
Solution:
Since l and m are two parallel lines intersected by another pair of parallel lines p and q. Therefore, AD || BC and AB || CD ⇒ ABCD is a parallelogram.
i.e., AB = CD
Now, in ∆s ABC and CDA, we have
AB = CD [Prove above]
and AC = AC [Common]
∴ By SSS criterion of congruence ∆ ABC ≅ ∆ CDA.
Question 5.
Line l is the bisector of an angle A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see figure). Show that :
(i) ∆ APB ≅ ∆ AQB
(ii) BP = BQ or B is equidistant from the arms of ∠A.
Solution:
In ∆s APB and AQB, we have
∠APB = ∠AQB [∵ Each = 90°]
∠PAB = ∠QAB [∵ AB bisects ∠PAQ]
AB = AB [Common]
By AAS congruence criterion, we have
∆ APB ≅ ∆ AQB, which proves (i)
⇒ BP = PQ
[∵Corresponding parts of congruent triangles are equal]
i.e., B is equidistant from the arms of ∠A, which proves
Question 6.
In figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
Solution:
∠BAC = ∠DAE
[∵ ∠BAD = ∠EAC ⇒ ∠BAD + ∠DAC = ∠EAC + ∠DAC ⇒ ∠BAC =∠DAE]
and, AC = AE [Given]
∴ By SAS criterion of congruence, we have
⇒ BC = DE
[∵ Corresponding parts of congruent triangles are equal]
Question 7.
AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (see figure). Show that
(i) ∆ DAP ≅ ∆ EBP
Solution:
We have, ∠EPA = ∠DPB
⇒ ∠EPA + ∠DPE = ∠DPB + ∠DPE’
⇒ ∠DPA = ∠EPB … (1)
Now, in ∆s EBP and DAP, we have
∠EPB = ∠DPA [From (1)]
BP = AP [Given]
and, ∠EBP = ∠DAP [Given]
So, by ASA criterion of congruence, we have
∆ EBP ≅ ∆ DAP
[∵ Corresponding parts of congruent triangles are equal]
Question 8.
In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see figure). Show that:
(i) ∆ AMC ≅ ∆ BMD
(ii) ∠DBC is a right angle
(iii) ∆ DBC ≅ ∆ ACB
(iv) CM = $$\frac { 1 }{ 2 }$$ AB.
Solution:
(i) In ∆s AMC and BMD, we have
AM = BM [∵ M is the mid-point of AB]
∠AMC = ∠BMD [Vertically opp. ∠s]
and, CM = MD [Given]
∴ By SAS criterion of congruence, we have
∴ ∆ AMC ≅ ∆ BMD
(ii) Now, ∆ AMC ≅ ∆ BMD
⇒ BD = CA and ∠BDM = ∠ACM … (1)
[∵Corresponding parts of congruent triangles are equal]
Thus, transversal CD cuts CA and BD at C and D respectively such’that the alternate angles ∠BDM and ∠ACM are equal. Therefore, BD || CA.
⇒ ∠CBD + ∠BCA = 180°
[∵ Sum of the interior angles on the same side of ” transversal = 180°]
⇒ ∠CBD + 90° = 180° [∵ ∠BCA = 90°]
⇒ ∠DBC = 90°.
(iii) Now, in ∆s DBC and ACB, we have
BD = CA [From (1)]
∠DBC = ∠ACB [∵ Each = 90°)
BC = BC [Common]
By SAS criterion of congruence, we have ∆ DBC ≅ ∆ ACB.
(iv) CD = AB
[∵ Corresponding parts of congruent triangles are equal]
⇒ $$\frac { 1 }{ 2 }$$CD = $$\frac { 1 }{ 2 }$$AB ⇒ CM = $$\frac { 1 }{ 2 }$$AB.
|
2023-03-22 21:33:57
|
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http://tex.stackexchange.com/questions/89826/how-does-one-ref-and-cite-paragraphs-in-a-mathematical-text-see-picture
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# How does one \ref and \cite paragraphs in a mathematical text? (see picture)
How does one \ref and \cite partly mathematical "textblocks" that are in separated paragraphs?
Very good example here: A Short Proof of Fleischner's Theorem, page 4; there are textblocks (1) and (2) and they are referenced several times in the latter text.
Here is a pic of the desired result:
-
Aren't this textblocks lemas or theorems? You could use the theorem package to define lemas, assertions, ... – TeXtnik Jan 8 '13 at 10:36
They are used exactly like , so that you get a (number) in the margin. Then you can cite the (number) in latter text. If I use {equation}, I get lots of errors or one really long line of \text{...} How do I get it to look like equation and have no errors? And be able to cite with a (number)? – Ohto Nordberg Jan 8 '13 at 11:03
@zunbeltz Do you mean \usepackage{amsthm}? It has theorems and I use them. – Ohto Nordberg Jan 8 '13 at 11:14
## 1 Answer
You can use an equation environment with an embedded array whose only column is in paragraph format. For example:
\documentclass{article}
\begin{document}
\noindent
following assertion holds:
$$\label{eq:test} \begin{array}{p{0.8\textwidth}} for any $$i,j$$, if $$v = x^i_j$$ then all passes of $$J'$$ through are marked except for the pass containing $$e^i_j$$. \end{array}$$
This is easy to verify\dots
So we assume that (\ref{eq:test}) holds\dots
\end{document}
This way you have the usual control that you are used to from equations. Feel free to adjust the width of the paragraph. I have chosen 0.8\textwidth. Some dimension is required.
The above solution may be packaged up into a dedicated environment as follows:
\documentclass{article}
\newenvironment{assertion}{$$\begin{array}{p{0.8\textwidth}}}{% \end{array}$$}
\begin{document}
\noindent
following assertion holds:
\begin{assertion}
\label{eq:test}
for any $$i,j$$, if $$v = x^i_j$$ then all passes of $$J'$$
through are marked except for the pass containing $$e^i_j$$.
\end{assertion}
This is easy to verify\dots
\end{document}
-
Works perfect, thank you! – Ohto Nordberg Jan 8 '13 at 12:48
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2016-07-23 21:15:33
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https://hk.answers.yahoo.com/question/index?qid=20100516000051KK00316
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# work done
work done against friction係咩??
work done by friction 同 work done against friction有咩分別??
thx~
### 1 個解答
• 1 十年前
最愛解答
Work done against friction refers to the energy used by an external agent to overcome friction. Usually, assuming friction is a constant, say f. Then the work done against friction is given by fs, where s is the distance travelled by the object.
Work done by friction refers to the energy dissipated by friction during the motion. As friction acts in the direction opposite to the relative direction of the two objects, there is always energy dissipation during the motion if friction exists.
For their differences, for the motion to carry out, as work is done by friction, there is some energy lost in the system to the surrounding. And so an external agent has to do work against friction (It is to input energy in the system) so that the kinetic energy of the object can be resumed.
資料來源： Prof. Physics
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2020-11-24 01:20:46
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https://dealii.org/developer/doxygen/deal.II/classParticles_1_1Particle.html
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Reference documentation for deal.II version Git 7a0e96d111 2021-06-21 21:20:26 -0400
Particles::Particle< dim, spacedim > Class Template Reference
#include <deal.II/particles/particle.h>
## Public Member Functions
Particle ()
Particle (const Point< spacedim > &location, const Point< dim > &reference_location, const types::particle_index id)
Particle (const Particle< dim, spacedim > &particle)
Particle (const void *&begin_data, PropertyPool< dim, spacedim > *const property_pool=nullptr)
Particle (Particle< dim, spacedim > &&particle) noexcept
Particle< dim, spacedim > & operator= (const Particle< dim, spacedim > &particle)
Particle< dim, spacedim > & operator= (Particle< dim, spacedim > &&particle) noexcept
~Particle ()
void * write_particle_data_to_memory (void *data) const
const void * read_particle_data_from_memory (const void *data)
void set_location (const Point< spacedim > &new_location)
const Point< spacedim > & get_location () const
void set_reference_location (const Point< dim > &new_reference_location)
const Point< dim > & get_reference_location () const
types::particle_index get_id () const
void set_id (const types::particle_index &new_id)
void set_property_pool (PropertyPool< dim, spacedim > &property_pool)
bool has_properties () const
void set_properties (const ArrayView< const double > &new_properties)
const ArrayView< doubleget_properties ()
const ArrayView< const doubleget_properties () const
std::size_t serialized_size_in_bytes () const
template<class Archive >
void save (Archive &ar, const unsigned int version) const
template<class Archive >
void load (Archive &ar, const unsigned int version)
void free_properties ()
template<class Archive >
void serialize (Archive &archive, const unsigned int version)
## Private Attributes
PropertyPool< dim, spacedim > * property_pool
PropertyPool< dim, spacedim >::Handle property_pool_handle
## Static Private Attributes
static PropertyPool< dim, spacedim > global_property_pool
## Detailed Description
### template<int dim, int spacedim = dim> class Particles::Particle< dim, spacedim >
A class that represents a particle in a domain that is meshed by a triangulation of some kind. The data this class stores is the position of the particle in the overall space, the position of the particle in the reference coordinate system of the cell it is currently in, an ID number that is unique among all particles, and a variable number of "properties".
The "properties" attached to each object of this class are stored by a PropertyPool object. These properties are stored as an array of double variables that can be accessed via an ArrayView object. For example, if one wanted to equip each particle with a "temperature" and "chemical composition" property that is advected along with the particle (and may change from time step to time step based on some differential equation, for example), then one would allocate two properties per particle in the PropertyPool object.
In practice, however, one often wants to associate properties with particles that are not just independent numbers as in the situation above. An example would be if one wanted to track the stress or strain that a particle is subjected to – a tensor-valued quantity. In these cases, one would interpret these scalar properties as the components of the stress or strain. In other words, one would first tell the PropertyPool to allocate as many properties per particle as there are components in the tensor one wants to track, and then write small conversion functions that take the ArrayView of scalar properties returned by the get_properties() function and convert it to a tensor of the appropriate type. This can then be evaluated and evolved in each time step. A second conversion function would convert back from a tensor to an ArrayView object to store the updated data back in the particle via the set_properties() function.
There are of course cases where the properties one cares about are not real (or, in computers, floating point) numbers but rather categorical: For example, one may want to mark some particles as "red", "blue", or "green". The property might then either be represented as an integer, or as an element of an enum. In these cases, one would need to come up with a way to represent these sorts of categorical fields in terms of floating point numbers. For example, one could map "red" to the floating point number 1.0, "blue" to 2.0, and "green" to 3.0. The conversion functions to translate between these two representations should then not be very difficult to write either.
Definition at line 94 of file particle.h.
## ◆ Particle() [1/5]
template<int dim, int spacedim>
Particles::Particle< dim, spacedim >::Particle ( )
Empty constructor for Particle, creates a particle at the origin.
Definition at line 30 of file particle.cc.
## ◆ Particle() [2/5]
template<int dim, int spacedim>
Particles::Particle< dim, spacedim >::Particle ( const Point< spacedim > & location, const Point< dim > & reference_location, const types::particle_index id )
Constructor for Particle. This function creates a particle with the specified ID at the specified location. Note that there is no check for duplicate particle IDs so the user must make sure the IDs are unique over all processes. Data is stored in a global PropertyPool object (corresponding to the global "heap") but can later be transferred to another property pool by calling set_property_pool().
Parameters
[in] location Initial location of particle. [in] reference_location Initial location of the particle in the coordinate system of the reference cell. [in] id Globally unique ID number of particle.
Definition at line 38 of file particle.cc.
## ◆ Particle() [3/5]
template<int dim, int spacedim>
Particles::Particle< dim, spacedim >::Particle ( const Particle< dim, spacedim > & particle )
Copy-constructor for Particle. This function creates a particle with exactly the state of the input argument. The copied data is stored in a global PropertyPool object (corresponding to the global "heap") but can later be transferred to another property pool by calling set_property_pool().
Definition at line 52 of file particle.cc.
## ◆ Particle() [4/5]
template<int dim, int spacedim>
Particles::Particle< dim, spacedim >::Particle ( const void *& begin_data, PropertyPool< dim, spacedim > *const property_pool = nullptr )
Constructor for Particle. This function creates a particle from a data vector. Data is stored in a global PropertyPool object (corresponding to the global "heap") but can later be transferred to another property pool by calling set_property_pool(). This constructor is usually called after serializing a particle by calling the write_data() function.
Parameters
[in,out] begin_data A pointer to a memory location from which to read the information that completely describes a particle. This class then de-serializes its data from this memory location and advances the pointer beyond the data that has been read to initialize the particle information. [in,out] property_pool An optional pointer to a property pool that is used to manage the property data used by this particle. If this argument is not provided, then a global property pool is used; on the other hand, if a non-null pointer is provided, this constructor assumes begin_data contains serialized data of the same length and type that is allocated by property_pool. If the data pointer provided here corresponds to data for a particle that has properties, then this function will only succeed if a property pool is provided as second argument that is able to store the correct number of properties per particle.
Definition at line 76 of file particle.cc.
## ◆ Particle() [5/5]
template<int dim, int spacedim>
Particles::Particle< dim, spacedim >::Particle ( Particle< dim, spacedim > && particle )
noexcept
Move constructor for Particle, creates a particle from an existing one by stealing its state.
Definition at line 113 of file particle.cc.
## ◆ ~Particle()
template<int dim, int spacedim>
Particles::Particle< dim, spacedim >::~Particle ( )
Destructor. Releases the property handle if it is valid, and therefore frees that memory space for other particles. (Note: the memory is managed by the property pool, and the pool is responsible for what happens to the memory.
Definition at line 191 of file particle.cc.
## ◆ operator=() [1/2]
template<int dim, int spacedim>
Particle< dim, spacedim > & Particles::Particle< dim, spacedim >::operator= ( const Particle< dim, spacedim > & particle )
Copy assignment operator.
Definition at line 130 of file particle.cc.
## ◆ operator=() [2/2]
template<int dim, int spacedim>
Particle< dim, spacedim > & Particles::Particle< dim, spacedim >::operator= ( Particle< dim, spacedim > && particle )
noexcept
Move assignment operator.
Definition at line 163 of file particle.cc.
## ◆ write_particle_data_to_memory()
template<int dim, int spacedim>
void * Particles::Particle< dim, spacedim >::write_particle_data_to_memory ( void * data ) const
Write particle data into a data array. The array is expected to be large enough to take the data, and the void pointer should point to the first entry of the array to which the data should be written. This function is meant for serializing all particle properties and later de-serializing the properties by calling the appropriate constructor Particle(void *&data, PropertyPool *property_pool = nullptr);
Parameters
[in] data The memory location to write particle data into.
Returns
A pointer to the next byte after the array to which data has been written.
Definition at line 219 of file particle.cc.
template<int dim, int spacedim>
const void * Particles::Particle< dim, spacedim >::read_particle_data_from_memory ( const void * data )
Update all of the data associated with a particle: id, location, reference location and, if any, properties by using a data array. The array is expected to be large enough to take the data, and the void pointer should point to the first entry of the array to which the data should be written. This function is meant for de-serializing the particle data without requiring that a new Particle class be built. This is used in the ParticleHandler to update the ghost particles without de-allocating and re-allocating memory.
Parameters
[in] data A pointer to a memory location from which to read the information that completely describes a particle. This class then de-serializes its data from this memory location.
Returns
A pointer to the next byte after the array from which data has been read.
Definition at line 252 of file particle.cc.
## ◆ set_location()
template<int dim, int spacedim>
void Particles::Particle< dim, spacedim >::set_location ( const Point< spacedim > & new_location )
inline
Set the location of this particle. Note that this does not check whether this is a valid location in the simulation domain.
Parameters
[in] new_location The new location for this particle.
Note
In parallel programs, the ParticleHandler class stores particles on both the locally owned cells, as well as on ghost cells. The particles on the latter are copies of particles owned on other processors, and should therefore be treated in the same way as ghost entries in vectors with ghost elements or ghost cells: In both cases, one should treat the ghost elements or cells as const objects that shouldn't be modified even if the objects allow for calls that modify properties. Rather, properties should only be modified on processors that actually own the particle.
Definition at line 510 of file particle.h.
## ◆ get_location()
template<int dim, int spacedim>
const Point< spacedim > & Particles::Particle< dim, spacedim >::get_location ( ) const
inline
Get the location of this particle.
Returns
The location of this particle.
Definition at line 519 of file particle.h.
## ◆ set_reference_location()
template<int dim, int spacedim>
void Particles::Particle< dim, spacedim >::set_reference_location ( const Point< dim > & new_reference_location )
inline
Set the reference location of this particle.
Parameters
[in] new_reference_location The new reference location for this particle.
Note
In parallel programs, the ParticleHandler class stores particles on both the locally owned cells, as well as on ghost cells. The particles on the latter are copies of particles owned on other processors, and should therefore be treated in the same way as ghost entries in vectors with ghost elements or ghost cells: In both cases, one should treat the ghost elements or cells as const objects that shouldn't be modified even if the objects allow for calls that modify properties. Rather, properties should only be modified on processors that actually own the particle.
Definition at line 528 of file particle.h.
## ◆ get_reference_location()
template<int dim, int spacedim>
const Point< dim > & Particles::Particle< dim, spacedim >::get_reference_location ( ) const
inline
Return the reference location of this particle in its current cell.
Definition at line 537 of file particle.h.
## ◆ get_id()
template<int dim, int spacedim>
types::particle_index Particles::Particle< dim, spacedim >::get_id ( ) const
inline
Return the ID number of this particle. The ID of a particle is intended to be a property that is globally unique even in parallel computations and is transferred along with other properties of a particle if it moves from a cell owned by the current processor to a cell owned by a different processor, or if ownership of the cell it is on is transferred to a different processor.
Definition at line 546 of file particle.h.
## ◆ set_id()
template<int dim, int spacedim>
void Particles::Particle< dim, spacedim >::set_id ( const types::particle_index & new_id )
inline
Set the ID number of this particle. The ID of a particle is intended to be a property that is globally unique even in parallel computations and is transferred along with other properties of a particle if it moves from a cell owned by the current processor to a cell owned by a different processor, or if ownership of the cell it is on is transferred to a different processor. As a consequence, when setting the ID of a particle, care needs to be taken to ensure that particles have globally unique IDs. (The ParticleHandler does not itself check whether particle IDs so set are globally unique in a parallel setting since this would be a very expensive operation.)
Parameters
[in] new_id The new ID number for this particle.
Note
In parallel programs, the ParticleHandler class stores particles on both the locally owned cells, as well as on ghost cells. The particles on the latter are copies of particles owned on other processors, and should therefore be treated in the same way as ghost entries in vectors with ghost elements or ghost cells: In both cases, one should treat the ghost elements or cells as const objects that shouldn't be modified even if the objects allow for calls that modify properties. Rather, properties should only be modified on processors that actually own the particle.
Definition at line 555 of file particle.h.
## ◆ set_property_pool()
template<int dim, int spacedim>
void Particles::Particle< dim, spacedim >::set_property_pool ( PropertyPool< dim, spacedim > & property_pool )
inline
Tell the particle where to store its properties (even if it does not own properties). Usually this is only done once per particle, but since the particle does not know about the properties, we want to do it not at construction time. Another use for this function is after particle transfer to a new process.
If a particle already stores properties in a property pool, then their values are saved, the memory is released in the previous property pool, and a copy of the particle's properties will be allocated in the new property pool.
Definition at line 564 of file particle.h.
## ◆ has_properties()
template<int dim, int spacedim>
bool Particles::Particle< dim, spacedim >::has_properties ( ) const
inline
Return whether this particle has a valid property pool and a valid handle to properties.
Definition at line 626 of file particle.h.
## ◆ set_properties()
template<int dim, int spacedim>
void Particles::Particle< dim, spacedim >::set_properties ( const ArrayView< const double > & new_properties )
Set the properties of this particle.
Parameters
[in] new_properties An ArrayView containing the new properties for this particle.
Note
In parallel programs, the ParticleHandler class stores particles on both the locally owned cells, as well as on ghost cells. The particles on the latter are copies of particles owned on other processors, and should therefore be treated in the same way as ghost entries in vectors with ghost elements or ghost cells: In both cases, one should treat the ghost elements or cells as const objects that shouldn't be modified even if the objects allow for calls that modify properties. Rather, properties should only be modified on processors that actually own the particle.
Definition at line 305 of file particle.cc.
## ◆ get_properties() [1/2]
template<int dim, int spacedim>
const ArrayView< double > Particles::Particle< dim, spacedim >::get_properties ( )
Get write-access to properties of this particle. If the particle has no properties yet, but has access to a PropertyPool object it will allocate properties to allow writing into them. If it has no properties and has no access to a PropertyPool this function will throw an exception.
Returns
An ArrayView of the properties of this particle.
Definition at line 330 of file particle.cc.
## ◆ get_properties() [2/2]
template<int dim, int spacedim>
const ArrayView< const double > Particles::Particle< dim, spacedim >::get_properties ( ) const
inline
Get read-access to properties of this particle. If the particle has no properties this function throws an exception.
Returns
An ArrayView of the properties of this particle.
Definition at line 614 of file particle.h.
## ◆ serialized_size_in_bytes()
template<int dim, int spacedim>
std::size_t Particles::Particle< dim, spacedim >::serialized_size_in_bytes ( ) const
Return the size in bytes this particle occupies if all of its data is serialized (i.e. the number of bytes that is written by the write_data function of this class).
Definition at line 287 of file particle.cc.
## ◆ save()
template<int dim, int spacedim>
template<class Archive >
void Particles::Particle< dim, spacedim >::save ( Archive & ar, const unsigned int version ) const
inline
Write the data of this object to a stream for the purpose of serialization using the BOOST serialization library.
Definition at line 488 of file particle.h.
template<int dim, int spacedim>
template<class Archive >
void Particles::Particle< dim, spacedim >::load ( Archive & ar, const unsigned int version )
inline
Read the data of this object from a stream for the purpose of serialization using the BOOST serialization library. Note that in order to store the properties correctly, the property pool of this particle has to be known at the time of reading, i.e. set_property_pool() has to have been called, before this function is called.
Definition at line 454 of file particle.h.
## ◆ free_properties()
template<int dim, int spacedim>
void Particles::Particle< dim, spacedim >::free_properties ( )
Free the memory of the property pool
Definition at line 204 of file particle.cc.
## ◆ serialize()
template<int dim, int spacedim = dim>
template<class Archive >
void Particles::Particle< dim, spacedim >::serialize ( Archive & archive, const unsigned int version )
Write and read the data of this object from a stream for the purpose of serialization using the BOOST serialization library.
## ◆ global_property_pool
template<int dim, int spacedim = dim>
PropertyPool< dim, spacedim > Particles::Particle< dim, spacedim >::global_property_pool
staticprivate
Initial value:
= {
0}
A global property pool used when a particle is not associated with a property pool that belongs to, for example, a ParticleHandler.
Definition at line 433 of file particle.h.
## ◆ property_pool
template<int dim, int spacedim = dim>
PropertyPool* Particles::Particle< dim, spacedim >::property_pool
private
A pointer to the property pool. Necessary to translate from the handle to the actual memory locations.
Definition at line 439 of file particle.h.
## ◆ property_pool_handle
template<int dim, int spacedim = dim>
PropertyPool::Handle Particles::Particle< dim, spacedim >::property_pool_handle
private
A handle to all particle properties
Definition at line 444 of file particle.h.
The documentation for this class was generated from the following files:
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2021-06-22 08:41:55
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https://www.meritnation.com/maharashtra-class-9/maths/mathematics-part-ii-solutions/circle/textbook-solutions/90_1_3386_24445_79_136423
|
Mathematics Part II Solutions Solutions for Class 9 Maths Chapter 6 Circle are provided here with simple step-by-step explanations. These solutions for Circle are extremely popular among Class 9 students for Maths Circle Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Part II Solutions Book of Class 9 Maths Chapter 6 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Part II Solutions Solutions. All Mathematics Part II Solutions Solutions for class Class 9 Maths are prepared by experts and are 100% accurate.
#### Question 1:
Distance of chord AB from the centre of a circle is 8 cm. Length of the chord AB is 12 cm. Find the diameter of the circle.
Let the centre of the circle be O.
AB = 12 cm
OC = 12 cm
OC ⊥ AB
We know perpendicular drawn from the centre of the circle to the chord, bisects the chord.
So, AC = 6 cm
In ⃤ OCA,
${\mathrm{OC}}^{2}+{\mathrm{AC}}^{2}={\mathrm{AO}}^{2}\phantom{\rule{0ex}{0ex}}⇒{8}^{2}+{6}^{2}={\mathrm{AO}}^{2}\phantom{\rule{0ex}{0ex}}⇒{\mathrm{AO}}^{2}=100\phantom{\rule{0ex}{0ex}}⇒\mathrm{AO}=10$
Thus, AO = 10 cm
Diameter = 2 × 10 cm = 20 cm.
#### Question 2:
Diameter of a circle is 26 cm and length of a chord of the circle is 24 cm. Find the distance of the chord from the centre.
Diameter = 26 cm
chord = 24 cm
Perpendicular drawn from the centre of the circle to the chord bisects the chord.
OD ⊥ AB
In ∆ODA,
Thus, the distance of the chord from the centre is 5 cm.
#### Question 3:
Radius of a circle is 34 cm and the distance of the chord from the centre is 30 cm, find the length of the chord.
Let the chord be AB.
O be the centre of the circle.
OC be the perpendicular drawn from the centre to the chord AB.
We know that perpendicular drawn from the centre of the circle to the chord bisects the chord.
So, OC $\perp$ AB.
In $△$OCA,
Thus, AB = $2×\mathrm{AC}=2×16=32$.
#### Question 4:
Radius of a circle with centre O is 41 units. Length of a chord PQ is 80 units, find the distance of the chord from the centre of the circle.
We know that perpendicular drawn from the centre of the circle to the chord bisects the chord.
PR = RQ = 40 unit
In $△$OPR,
Thus, the distance of the chord from the centre of the circle is 9 units.
#### Question 5:
In the given figure, centre of two circles is O. Chord AB of bigger circle intersects the smaller circle in points P and Q. Show that AP = BQ
Draw perpendicular from O to line AB.
So, OC $\perp$ PQ and OC $\perp$AB
We know that the perpendicular drawn from the centre of the circle to the chord bisects the chord.
So, PC = CQ .....(1)
and AC = CB .....(2)
(2) $-$ (1)
AC $-$ PC = CB $-$ CQ
$⇒$AP = BQ
Hence proved
#### Question 6:
Prove that, if a diameter of a circle bisects two chords of the circle then those two chords are parallel to each other.
Let AB and CD be the two chords of the circle. The centre of the circle be O through which the diameter PQ passes.
Let the diameter PQ bisect the two chords and point R and S.
We know that the when the line passing through the centre of the circle bisects the chord then the line is perpendicular to the chord.
Thus, $\angle \mathrm{ARS}=\angle \mathrm{DSR}=90°$
AB will be thus parallel to CD and cut by the transversal PS as interior angle on the sam side of the transversal are equal.
#### Question 1:
Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the centre of the circle ?
Let the two chords be AB and CD.
AB = CD = 16 cm
Radius = AO = 10 cm
Let OE be the perpendicular drawn from the centre of the circle to the chord AB.
Perpendicular drawn from the centre of the circle to the chord bisects the chord.
So, AE = EB = 8 cm
In $△$AEO,
we know that congruent chords of a circle are equidistant from the centre.
So, EO = OF = 6 cm
Distance of these chords from the centre is 6 + 6 = 12 cm.
#### Question 2:
In a circle with radius 13 cm, two equal chords are at a distance of 5 cm from the centre. Find the lengths of the chords.
Let the two chords be AB and CD.
Radius = AO = 13 cm
Let OE be the perpendicular drawn from the centre of the circle to the chord AB.
Perpendicular drawn from the centre of the circle to the chord bisects the chord.
So, AE = EB
In $△$AEO,
And AE = EB = 12 + 12 = 24 cm
Thus, AB = CD = 24 cm as chords of a circle equidistant from the centre are congruent.
#### Question 3:
Seg PM and seg PN are congruent chords of a circle with centre C. Show that the ray PC is the bisector of $\angle$NPM.
Join CN and CM.
In $△$CPN and $△$CPM,
PM $\cong$ PN (Given)
PC = PC (Common)
Thus, $△$CPN $\cong$ $△$CPM (By SSS congurency)
So, $\angle$CPN = $\angle$CPM (CPCT)
Thus, ray PC is the bisector of $\angle$NPM.
#### Question 1:
Construct $∆$ ABC such that $\angle$B = ${100}^{°}$ , BC = 6.4 cm, $\angle$C = ${50}^{°}$ and construct its incircle.
Steps of construction:
1. Draw BC = 6.4 cm
2. Draw$\angle$B = ${100}^{°}$ and $\angle$C = ${50}^{°}$ using the protractor. Where the rays YB and XC meet, name the point as A.
$∆$ABC is thus obtained.
3. Construct the angle bisectors of $\angle$B and $\angle$C and let them meet at point O.
4. Through point O, draw a perpendicular to line BC. Let the perpendicular meet the line BC at point P.
5. With O as centre and OP as radius, draw a circle inside the $∆$ABC.
This is the required incircle.
#### Question 2:
Construct $∆$ PQR such that $\angle$P = ${70}^{°}$ , $\angle$R = ${50}^{°}$ , QR = 7.3 cm and constructs its circumcircle.
By angle sum property of triangles,
In $∆$PQR,
$\angle \mathrm{P}+\angle \mathrm{Q}+\angle \mathrm{R}=180°\phantom{\rule{0ex}{0ex}}⇒70°+\angle \mathrm{Q}+50°=180°\phantom{\rule{0ex}{0ex}}⇒\angle \mathrm{Q}=60°$
Steps of construction:
1. Draw a line QR = 7.3 cm.
2. With Q as centre, draw an angle of 60$°$ using the protractor. Similarly, draw an angle of 50$°$ with R as centre.
Where the rays RY and XQ meet, name the point as P.
Thus, $∆$PQR is obtained.
3. Draw the perpendicular bisectors of the lines PR and QR. Let these perpendicular bisectors meet at point O.
4. With O as centre and OP as radius, construct a circle touching all the vertices of the $∆$PQR.
This circle is thus the required circumcircle.
#### Question 3:
Construct $∆$XYZ such that XY = 6.7 cm ,YZ = 5.8 cm, XZ = 6.9 cm and constructs its incircle.
Steps of construction:
1. Draw XZ = 6.9 cm
2. With X as centre and 6.7 cm as radius, draw an arc above the line XZ. Also, with Z as centre and 5.8 cm as radius, draw an arc cutting the previous drawn arc at point Y.
$∆$XYZ is thus obtained.
3. Construct the angle bisectors of $\angle$X and $\angle$Z and let them meet at point O.
4. Through point O, draw a perpendicular to line XZ. Let the perpendicular meet the line XZ at point P.
5. With O as centre and OP as radius, draw a circle inside the $∆$XYZ.
This is the required incircle.
#### Question 4:
In $∆$ LMN, LM = 7.2 cm, $\angle$M = ${105}^{°}$ , MN = 6.4 cm , then draw $∆$ LMN and construct its circumcircle.
Steps of construction:
1. Draw a line LM = 7.2 cm.
2. With M as centre, draw an angle of 105$°$ using the protractor.
3. With M as centre and 6.4 cm as radius, cut an arc on ray MX and name it as N.
4. Join LN. $∆$LMN is thus obtained.
5. Draw the perpendicular bisectors of the lines NM and LM. Let these perpendicular bisectors meet at point O.
4. With O as centre and OM as radius, construct a circle touching all the vertices of the $∆$LMN.
This circle is thus the required circumcircle.
#### Question 5:
Construct $∆$ DEF such that DE = EF = 6 cm, $\angle$F = ${45}^{°}$ and constructs its circumcircle.
Steps of construction:
1. Draw a line EF = 6 cm.
2. With F as centre, draw an angle of 45$°$ using the protractor.
3. With E as centre and 6 cm as radius, cut an arc on ray FX and name it as D.
4. Join DE. $∆$DEF is thus obtained.
5. Draw the perpendicular bisectors of the lines DF and EF. Let these perpendicular bisectors meet at point O.
4. With O as centre and OE as radius, construct a circle touching all the vertices of the $∆$DEF.
This circle is thus the required circumcircle.
#### Question 1:
Choose correct alternative answer and fill in the blanks.
(i) Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence the length of the chord is .........
(A) 16 cm (B) 8 cm (C) 12 cm (D) 32 cm
(ii) The point of concurrence of all angle bisectors of a triangle is called the ......
(A) centroid (B) circumcentre (C) incentre (D) orthocentre
(iii) The circle which passes through all the vertices of a triangle is called .....
(A) circumcircle (B) incircle (C) congruent circle (D) concentric circle
(iv) Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is ....
(A) 12 cm (B) 13 cm (C) 14 cm (D) 15 cm
(v) The length of the longest chord of the circle with radius 2.9 cm is .....
(A) 3.5 cm (B) 7 cm (C) 10 cm (D) 5.8 cm
(vi) Radius of a circle with centre O is 4 cm. If l(OP) = 4.2 cm, say where point P will lie.
(A) on the centre (B) Inside the circle (C) outside the circle(D) on the circle
(vii) The lengths of parallel chords which are on opposite sides of the centre of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is .....
(A) 2 cm (B) 1 cm (C) 8 cm (D) 7 cm
(i)
Let the chord be AB.
O be the centre and OC be the perpendicular drawn from the centre of the circle to the chord AB.
Perpendicular drawn from the centre of the circle to the chord bisects the chord.
AC = CB
OA is the radius = 10 cm
In $△$OAC,
AC = CB = 8 cm
AB = AC + CB = 8 + 8 = 16 cm
Hence, the correct answer is option A.
(ii) The point of concurrence of all angle bisectors of a triangle is called the incentre.
Hence, the correct answer is option C.
(iii) The circle which passes through all the vertices of a triangle is called circumcircle.
Hence, the correct answer is option A.
(iv)
Let the chord be AB = 24 cm
Distance of the chord from the centre O is 5 cm.
AO is the radius of the circle.
Perpendicular from the centre of the circle to the chord bisects the chord.
So, AC = CB
In $△$AOC,
Thus, the radius of the circle is 13 cm.
Hence, the correct answer is option B.
(v) The longest chord of the circle is the diameter.
So, diameter = 2.9 + 2.9 = 5.8 cm
Hence, the correct answer is option D.
OP = 4.2 cm
OP will be thus outside the circle as it is greater than the radius.
Hence, the correct answer is option C.
(vii)
Let the chords be AB = 6 cm and CD = 8 cm
O be the centre with OA = OC = 5 cm as radius.
OE $\perp$ AB and OF $\perp$ CD.
In $△$AEO,
Similarly, in In $△$OFC,
Thus, the distance between the two chords is EO + OF = 4 + 3 cm = 7 cm.
Hence, the correct answer is option D.
#### Question 2:
Construct incircle and circumcircle of an equilateral $∆$DSP with side 7.5 cm. Measure the radii of both the circles and find the ratio of radius of circumcircle to the radius of incircle.
Steps of construction:
1. Draw a line SP = 7.5 cm.
2. With S as centre and 7.5 cm as radius, draw an arc above the line SP.
3. With P as centre and 7.5 cm as radius, cut an arc on on the previous drawn arc and name the point of intersection as D.
4. Join DS and DP. $∆$DSP is thus obtained.
5. Draw the perpendicular bisectors of the lines DP and SP. Let these perpendicular bisectors meet at point O.
4. With O as centre and OP as radius, construct a circle touching all the vertices of the $∆$DSP.
This circle is thus the required circumcircle.
Steps of construction
1. Draw a line SP = 7.5 cm.
2. With S as centre and 7.5 cm as radius, draw an arc above the line SP.
3. With P as centre and 7.5 cm as radius, cut an arc on on the previous drawn arc and name the point of intersection as D.
4. Join DS and DP. $∆$DSP is thus obtained.
5. Draw the angle bisectors of angle S and P and let them meet at point O.
6. Draw the perpendicular from point O to the line SP. Join OA.
7. With O as centre and OA as radius, draw a circle touching all the sides of the triangle.
This is the required incircle.
ratio of radius of circumcircle to the radius of incircle = 4 : 2 = 2 : 1
#### Question 3:
Construct $∆$NTS where NT = 5.7 cm, TS = 7.5 cm and $\angle$NTS = 110 ° and draw incircle and circumcircle of it.
Steps of construction:
1. Draw a line ST = 7.5 cm.
2. With T as centre draw an angle $\angle$STX = 110°.
3. With T as centre and 5.7 cm as radius, cut an arc on XT and name the point of intersection as N.
4. Join SN. $∆$NTS is thus obtained.
5. Draw the perpendicular bisectors of the lines ST and NT. Let these perpendicular bisectors meet at point O.
4. With O as centre and OT as radius, construct a circle touching all the vertices of the $∆$NTS.
This circle is thus the required circumcircle.
Steps of construction:
1. Draw a line ST = 7.5 cm.
2. With T as centre draw an angle $\angle$STX = 110°.
3. With T as centre and 5.7 cm as radius, cut an arc on XT and name the point of intersection as N.
4. Join SN. $∆$NTS is thus obtained.
5. Draw the angle bisectors of angle S and T and let them meet at point O.
6. Draw the perpendicular from point O to the line ST. Join OP.
7. With O as centre and OP as radius, draw a circle touching all the sides of the triangle.
This is the required incircle.
#### Question 4:
In the given figure, C is the centre of the circle. seg QT is a diameter CT = 13, CP = 5, find the length of chord RS.
Join RC and CS.
Perpendicular drawn from the centre of the circle to the chord bisects the chord.
So, RP = PS
In $△$RPC,
Thus, RP = PS = 12 cm
So, RS = RP + PS = 12 + 12 = 24 cm.
#### Question 5:
In the given figure, P is the centre of the circle. chord AB and chord CD intersect on the diameter at the point E
If $\angle$AEP $\cong$ $\angle$DEP then prove that AB = CD.
Construction: Draw perpendicular from point P to the chords CD and AB.
To prove: AB = CD
Proof: In $△$MEP and $△$NEP,
$\angle$EMP = $\angle$ENP = 90$°$
$\angle$AEP = $\angle$DEP (Given)
Thus, by AAS congruence rule, $△$MEP$\cong$$△$NEP.
So, MP = NP (CPCT)
We know that chords equidistant from the centre are equal to each other.
Hence, AB = CD.
#### Question 6:
In the given figure, CD is a diameter of the circle with centre O. Diameter CD is perpendicular to chord AB at point E. Show that$∆$ABC is an isosceles triangle.
In $△$AEC and $△$BEC,
$\angle$CEA = $\angle$CEB = 90$°$
Thus, $△$AEC $\cong$ $△$BEC by SAS congurency
Thus, $∆$ABC is an isosceles triangle.
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2021-12-04 07:33:56
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https://puzzling.stackexchange.com/questions/80830/make-the-largest-box-from-a-cardboard-sheet-chapter-2/80832
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# Make the largest box from a cardboard sheet Chapter #2
Please see: Make the largest box from a cardboard sheet
Thanks to his older brother's friends: @Oray, @Weather Vane and @mlk, the boy managed to make as large cardboard box as possible. Unfortunately, it was not enough to store all his toys responsible for causing mess in his room.
To do something about it, he asked his parents for another sheet to make another box. Unfortunately his father just cut off a (little bit larger) piece from remaining sheet already and used it to temporarily patch a hole in his greenhouse, so only 60cm x 39cm piece still remains.
Now the problem is similar, what is the largest box the boy can make using 60cm x 39cm cardboard piece?
Rules are the same as previously.
Edit: My third solution:
The volume is $$6944.4375 \space cm^3$$
The cardboard cuts into 2 pieces.
One folds forwards, the other folds backwards.
The box dimensions are from:
$$x + z = 39 - 1 = 38$$
$$2z = 39$$
$$2y + x = 60 - 3 = 57$$
Which gives $$x=18.5, \space y=19.25, \space z=19.5$$
Not to scale
My second solution:
The volume is $$6930.5625 \space cm^3$$
The cardboard cuts into 2 pieces.
Two of the box dimensions are the same.
The dimensions are from:
$$2A = 39 - 2 = 37$$
$$2B + A = 60 - 1 = 59$$
Giving $$A=18.5, \space B=20.25$$
Not to scale
The theoretical maximum volume will be a cube:
There can be at most 4 folds between sides, so there must be 8 tabs.
The total area = $$39 \times\ 60 = 2340$$
Which should be made up from 6 faces and 8 tabs.
Suppose the side length is $$s$$
Then $$6 s^2 + 8 s = 2340$$
Which solves as $$s = 19.093$$
Maximum possible volume = $$6960.213$$
• Good job, but I still see some room for improvements (~10cm^3). Your answer is going now definitely in a good direction! ;) – mpasko256 Mar 20 at 15:25
• @mpasko256 I've found another $13.875 \space cm^3$ volume. – Weather Vane Mar 20 at 20:28
• This is the correct answer, congratulations! ;) – mpasko256 Mar 21 at 9:30
• It was satisfying to find a symmetrical solution and it's not far short of the theoretical maximum. Apart from the mitres, only four 1 cm squares are wasted. – Weather Vane Mar 21 at 9:34
My solution (a better one was since found):
The volume is $$6910.3125 \space cm^3$$
Dimensions $$x=19.5, \space y=20.25, \space z=17.5$$
The cardboard cuts into 2 pieces.
Each piece folds to a form a U shape.
One of them has eight $$1 \space cm$$ tabs, the other has none.
The box dimensions are from:
$$x + z = 39 - 2 = 37$$
$$2y + z = 60 - 2 = 58$$
$$2y + x = 60$$
• Nice try, but unfortunately this time your pattern from previous chapter does not lead to optimal solution. – mpasko256 Mar 20 at 10:27
• Hm... but it did lead back to a better solution for puzzle #1 where my new answer has a larger box than the accepted answer. – Weather Vane Mar 20 at 10:30
• Yes but please notice difference in proportions. If we compare everything to 2x3, previously our rectangle was shorter (6x8 -> 3x4), now it is narrower (a little bit less than 2 versus 3). – mpasko256 Mar 20 at 10:35
• Yes, I realise the optimal solution will be the closest to x = y = z but with only four 1 cm squares wastage here (apart from the mitres), and no loose tabs, I thought it would be a good shot. – Weather Vane Mar 20 at 10:37
Adapting mlk's accepted answer to the previous question, using the same basic template, we now need:
$$a+b \leq 37$$, $$2c+a \leq 60$$ and $$2c+b \leq 57$$
So one possible template would be identical to the one in that answer but using
a = 20, b = 17, c = 20, for a total volume of 6800.
As this is essentially the same as the known answer to the previous question, I assume it represents a baseline from which a better answer tailored to this question will improve.
One way to improve the volume would be
Try to make a perfect cube. a = b = c = 19, for a total volume of 6859 seems plausible, but the same template layout as the previous answer no longer works...
I initially thought a layout using this idea was possible, but didn't manage to put anything together before Weather Vane provided a far better solution, which seems likely to be optimal, so I'll stick with the baseline above as my non-optimal borrowed answer.
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2019-07-18 11:56:26
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https://quizlet.com/2619267/number-systems-flash-cards/
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7 terms
# Number Systems
###### PLAY
Number Systems
any notation for the representation of numbers
Whole
There is no fractional or decimal part. And no negatives.
Example: 5, 49 and 980 are all whole numbers.
Natural
Whole Numbers, but without the zero. Because you can't "count" zero.
Example: 1, 2, 3, 4, 5, (and so on).
Irrational
is a real number that cannot be written as a simple fraction.Irrational means not Rational
Example:22/7, square root of 2,square root of 3, square root of 1
Integers
Integers are like whole numbers, but they also include negative numbers ... but still no fractions allowed!
Example: -3,-45,-89,8,3,5,6,7,-34
Real
the numbers that can be written in decimal notation, including those that require an infinite decimal expansion. The set of real numbers includes all integers, positive and negative; all fractions; and the irrational numbers, those whose decimal expansions never repeat.
Examples:3.9, -34,7/3, 34, 234/98,.98323, 1/2,2, 4,
Rational
it can be expressed as the quotient, or ratio, of two whole numbers. Rational numbers include fractions like 2/7, whole numbers, and radicals if the radical sign is removable
Examples:5/4, 21/55, 2/3, 1/2
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2017-11-23 22:42:54
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https://www.physicsforums.com/threads/basic-math-challenge-june-2018.948674/page-2
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# Challenge Basic Math Challenge - June 2018
• Featured
#### fishturtle1
No criticism, I only thought, as you didn't explicitly mention the theorem, that Fermat's little theorem is faster to find for our readers than to search for Euler's theorem. Euler has left so many theorems ...
I sincerely mean this, I always appreciate your comments and had not thought of it from that perspective, that writing Euler's theorem is ambiguous and that writing FLT could save time for the reader. I definitely think the proof I wrote could be improved by being more specific.
#### QuantumQuest
Gold Member
I definitely think the proof I wrote could be improved by being more specific.
The steps you have in the proof are correct and lead to the correct result. But @fresh_42's comment is really worthwhile because the point in a proof is besides being correct to be also easily followed. Fermat's little theorem is a special case of Euler's theorem $a^{\phi (n)} \equiv 1(\mod n)$ where $\phi (n)$ is the Euler totient function, so you're essentially right in saying that you use these two things but as you apply FLT in your proof it is necessary for your readers in order to easily follow along, to state that explicitly.
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#### opus
Gold Member
What level of math is typically sufficient for these basic challenges? Im always interested but they still look pretty heavy!
#### fresh_42
Mentor
2018 Award
What level of math is typically sufficient for these basic challenges? Im always interested but they still look pretty heavy!
It is the same as it is so often: once you have the correct entry point, the proofs themselves aren't hard. I only solved mine, but I think it's similar with all of them. Do you have one particular in mind? Maybe we can give some hints.
#### opus
Gold Member
It is the same as it is so often: once you have the correct entry point, the proofs themselves aren't hard. I only solved mine, but I think it's similar with all of them. Do you have one particular in mind? Maybe we can give some hints.
I don't even think a hint would be beneficial at this point for me. I'm taking Calculus I in the fall, so I don't have any of those tools in my belt yet. What's a common requisite for being able to solve these? Calculus? Discrete math?
#### fresh_42
Mentor
2018 Award
I don't even think a hint would be beneficial at this point for me. I'm taking Calculus I in the fall, so I don't have any of those tools in my belt yet. What's a common requisite for being able to solve these? Calculus? Discrete math?
The examples are quite a variety of very different problems, i.e. not subject to a single area.
1. calculus
2. combinatorics
3. geometry (area formulas) with linear algebra (equations of straight lines)
4. geometry (of a circle)
5. combinatorics
6. discrete mathematics, resp. abstract algebra
7. differentiations and solving a system of linear equations
8. calculus
9. simply a riddle
10. integration, i.e. calculus
Farmer Joe's field wasn't very difficult, the key was basically to find the height of the yellow area, and the key was to use a coordinate system, find the equations of the lines and solve it. The coding was a bit like a crossword puzzle in the weekend edition of a newspaper, and for #7 one basically only needed to know what the differentials of the functions $e^x\; , \;\sin(x)\; , \;\cos(x)$ are.
I choose the first problem, because I found that those inequalities are useful to know. And, yes, it's again about differentiation, integration and the power series expansion of $\log \,$. The first part can be solved by differentiation. The second part is a bit tricky, and the third is actually the easiest of them, although it might not appear as such, but one doesn't even have to know a lot about integration. They all can be solved within a few lines, but I admit one has to find an idea.
The basic difficulty for us is, that there are so many different people around. We already introduced this two weeks ban for members, we expected them to find the answers, in order to give the younger ones a chance. So if we added easier questions, then there are definitely some people who first had to promise us not to spoil those.
Why don't you try number 5? This one looks fun. I would start by an example with smaller numbers to get an idea about the difficulty, but I would expect, that it has something to do with symmetries. It reminds me a bit of my very first exercise at university:
"Can there be a walk through Königsberg which crosses all seven bridges exactly once, and if so, can there also be a round trip?"
#### Attachments
• 1.7 KB Views: 290
#### Phylosopher
4.4. Using only geometric reasoning, calculate the average value of f(x)=√2x−x2f(x) = \sqrt{2x - x^2} on [0,2] [0,2]
(by @QuantumQuest)
I am not sure really what the question is requiring ^^".
4) I assume the question just doesn't want me to use calculus/integration. If so then:
the equation is just half a circle:
$$f(x)=\sqrt{2x-x^2}=\sqrt{2x-x^2+1-1}=\sqrt{1-(x^2-2x+1)^2}=\sqrt{1-(x-1)^2} \rightarrow y^2+(x-1)^2=1$$
Thus the answer is half the half area of the circle. $$Average=\frac{\pi}{4}$$
Note: y is restricted to be positive.
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#### StoneTemplePython
Gold Member
I don't even think a hint would be beneficial at this point for me. I'm taking Calculus I in the fall, so I don't have any of those tools in my belt yet. What's a common requisite for being able to solve these? Calculus? Discrete math?
I think @fresh_42's response is on point. A couple things I would add.
1.) To the extent you are in the US, I am sympathetic. I don't think I would have been able to solve much (or any?) of these in highschool even after I took calc 1. But so what -- if there are problems you can at least visualize, then try to struggle to the understand the associated solutions and you'll learn something interesting in the process. For example, I'm not sure I would have solved the cypher problem but it certainly is easy to visualize what is being discussed and follow the solution.
2.) I think we have a slight bias toward geometric problems in here as geometry in various forms is quite important in math and physics. It is also has a certain visual flavor. (Also reference part 1.)
#### QuantumQuest
Gold Member
I am not sure really what the question is requiring ^^".
4) I assume the question just doesn't want me to use calculus/integration
The point in this problem is to translate "using only geometric reasoning" correctly. You interpreted it correctly and your solution is right. For completeness, one thing that I want to add is that what we must find is $\frac{1}{2}\int_{0}^{2}\sqrt{2x - x^2} dx$. Then, using the way you used in your solution, we finally find that the graph of $y = f(x)$ between $x = 0$ and $x = 2$ is the upper half of the circle you found. So, the aforementioned integral is the area $\frac{\pi}{2}$ of that semicircle, so the average value is $\frac{\pi}{4}$.
#### opus
Gold Member
QUOTE REMOVED TO SAVE SPACE
QUOTE REMOVED TO SAVE SPACE
Thanks guys. I'll try my hand at that problem fresh_42.
And yes I'm a U.S student- a horrendous public education, but that's no excuse for me. My lack of mathematical skills is my own doing as I didn't care in the least for it when I was in high school. Trying to make up for that now!
I think these problems are really great and helpful and I'm going to spend some time on trying to understand them so I can have meaningful participation down the road.
#### QuantumQuest
Gold Member
And yes I'm a U.S student- a horrendous public education, but that's no excuse for me. My lack of mathematical skills is my own doing as I didn't care in the least for it when I was in high school. Trying to make up for that now!
I think these problems are really great and helpful and I'm going to spend some time on trying to understand them so I can have meaningful participation down the road.
Well, I don't live in US but as far as I know, public education is not horrendous compared to other countries in the world. What I can tell you for sure is that at College and University level is great and personally I really owe a lot of my knowledge in US resources - online classes, books, University resources, just to name a few of them. In any case, it's really good that you recognize that it is essentially your efforts that can make the difference - I was in this same position in my country as I was finishing High School, when I prepared on my own for what was missing in my knowledge in order to have a good head start when getting to University.
Last edited:
#### fresh_42
Mentor
2018 Award
Thread is now open to all. We have still four unsolved problems: 1,2,5,8.
So Homework Helpers, Science Advisors and Mentor can you help?
#### Phylosopher
5.5. Can one pack 53 bricks, each of dimension 1 x 1 x 4\text{1 x 1 x 4} in to a 6 x 6 x 6\text{6 x 6 x 6} box?
(by @StoneTemplePython)
Thread is now open to all. We have still four unsolved problems: 1,2,5,8.
So Homework Helpers, Science Advisors and Mentor can you help?
I always wanted to solve such problem. Mr. fresh_42 suggested that this is a combinatorics problem. I didn't studied such problems before. From my own search on the web, this is called an optimization problem.
At first I tried to solve it directly by thinking. I remained with one brick and a volume of a brick if I am not mistaken (If I remember correctly, I had a volume of a brick but not its shape). I was going to make a program that solves the problem, but I felt Like cheating ^^".
since it is Jun 16. Can anyone give us a hint?
#### PeroK
Homework Helper
Gold Member
2018 Award
$2.$ One card out of a deck has been lost. The other 51 cards are repeatedly shuffled and then thirteen cards are dealt, face up. The cards are 2 spades, 3 clubs, 4 hearts, and 4 diamonds. What is the chance that the missing card is (a) spade, (b) club, (c) heart, (d)diamond $\space$ $\space$ (by @StoneTemplePython)
We can use the idea of relative frequecies. If we repeat the experiment many times, then the missing card will initially be a S, C, H or D with equal frequency. So, we need to calculate how often in each of these cases we get 2S, 3C, 4H and 4D.
First, we can simplify things by noting that the frequency of getting those cards exactly in that order is related to the frequency of getting those cards in any order by a common factor (regardless of which card is missing). The common factor is $\binom{13}{2} \binom{11}{3} \binom{8}{4}$
Second, the frequency is related by another common factor in all cases of $\frac{1}{51} \frac{1}{50} \dots \frac{1}{39}$.
Omitting these common factors, we have the frequency of being dealt SSCCCHHHHDDDD:
If a Spade is missing: $12 \times 11 \times 13 \times 12 \times 11 \times 13 \times 12 \times 11 \times 10 \times 13 \times 12 \times 11 \times 10 = 13^3 \times 12^4 \times 11^4 \times 10^2$
If a Club is missing: $13 \times 12 \times 12 \times 11 \times 10 \times 13 \times 12 \times 11 \times 10 \times 13 \times 12 \times 11 \times 10 = 13^3 \times 12^4 \times 11^3 \times 10^3$
If a Heart is missing: $13 \times 12 \times 13 \times 12 \times 11 \times 12 \times 11 \times 10 \times 9 \times 13 \times 12 \times 11 \times 10 = 13^3 \times 12^4 \times 11^3 \times 10^2 \times 9$
And the same for Diamonds.
Finally, taking out the common factors again we get the relative frequencies:
If a Spade is missing: $11$
If a Club is missing: $10$
If a Heart is missing: $9$
If a Diamond is missing: $9$
This means that out of every $39$ times we get dealt the cards 2S, 3C, 4H and 4D: $11$ times a Spade was the missing card, $10$ times the Club was the missing card etc.
Given we have been dealt 2S, 3C, 4H and 4D, therefore:
The probability a Spade is the missing card is $11/39$; a Club the missing card $10/39$; and a Heart or Diamond each $9/39$.
#### StoneTemplePython
Gold Member
I always wanted to solve such problem. Mr. fresh_42 suggested that this is a combinatorics problem. I didn't studied such problems before. From my own search on the web, this is called an optimization problem.
At first I tried to solve it directly by thinking. I remained with one brick and a volume of a brick if I am not mistaken (If I remember correctly, I had a volume of a brick but not its shape). I was going to make a program that solves the problem, but I felt Like cheating ^^".
since it is Jun 16. Can anyone give us a hint?
I don't think writing a program would get credit, but to be honest if you make one, and you don't mind posting code at the end of the month, I'd be interested in seeing it if you're ok with sharing.
There's a few different ways to view the problem. Let me think on possibility of a hint.
#### StoneTemplePython
Gold Member
I always wanted to solve such problem. Mr. fresh_42 suggested that this is a combinatorics problem. I didn't studied such problems before. From my own search on the web, this is called an optimization problem.
At first I tried to solve it directly by thinking. I remained with one brick and a volume of a brick if I am not mistaken (If I remember correctly, I had a volume of a brick but not its shape). I was going to make a program that solves the problem, but I felt Like cheating ^^".
since it is Jun 16. Can anyone give us a hint?
This is a 3-D problem. Maybe it is tough... so consider a simpler, 2-D problem first. For the hint, I'll give a suggestive 2-D problem:
consider packing $\text{1 x 2}$ blocks on an 8 x 8 chessboard that has two squares at opposite corners removed. Can you pack 31 blocks into this slightly modified board? Why or why not?
It then takes a bit of visualization to make the leap from 2-D to 3-D.
#### pbuk
As its nearly the end of June, I'll bite...
consider packing $\text{1 x 2}$ blocks on an 8 x 8 chessboard that has two squares at opposite corners removed. Can you pack 31 blocks into this slightly modified board? Why or why not?
No, because each block covers 1 black square and 1 white square but the modified board has 32 black squares and 30 white squares (or vice versa).
It then takes a bit of visualization to make the leap from 2-D to 3-D.
A bigger leap than I have managed in the last fortnight...
#### StoneTemplePython
Gold Member
As its nearly the end of June, I'll bite...
No, because each block covers 1 black square and 1 white square but the modified board has 32 black squares and 30 white squares (or vice versa).
A bigger leap than I have managed in the last fortnight...
I think we're posting solutions to unsolved problems mid-month, so stay tuned.
#### FelixLudi
$5.$ Can one pack 53 bricks, each of dimension $\text{1 x 1 x 4}$ in to a $\text{6 x 6 x 6}$ box?
(by @StoneTemplePython)
Assuming that each brick is $1m * 1m * 4m$, and the box is $6m * 6m * 6m$;
The volume taken by 1 brick is equal to $1m * 1m * 4m = 4m^3$ and the volume of said box would be $6m * 6m * 6m = 216m^3$, then;
$216m^3 / 4m^3 = 54$
You can fit 54 bricks into said box, therefore the answer is yes.
EDIT: I may be a bit late but the topic wasn't locked and the answer wasn't posted so I figured I would do it.
#### fresh_42
Mentor
2018 Award
Assuming that each brick is $1m * 1m * 4m$, and the box is $6m * 6m * 6m$;
The volume taken by 1 brick is equal to $1m * 1m * 4m = 4m^3$ and the volume of said box would be $6m * 6m * 6m = 216m^3$, then;
$216m^3 / 4m^3 = 54$
You can fit 54 bricks into said box, therefore the answer is yes.
EDIT: I may be a bit late but the topic wasn't locked and the answer wasn't posted so I figured I would do it.
Problem is: you have to keep the bricks in one piece!
#### mfb
Mentor
@FelixLudi: With that argument you could also fit two 4x1x1 bricks in a 2x2x2 box. But you cannot.
#### FelixLudi
I overlooked that somehow, but I'm out of solutions now since I can't get the right distribution of bricks to fit in (not even with an online 3d modeler).
#### Phylosopher
Assuming that each brick is $1m * 1m * 4m$, and the box is $6m * 6m * 6m$;
The volume taken by 1 brick is equal to $1m * 1m * 4m = 4m^3$ and the volume of said box would be $6m * 6m * 6m = 216m^3$, then;
$216m^3 / 4m^3 = 54$
You can fit 54 bricks into said box, therefore the answer is yes.
EDIT: I may be a bit late but the topic wasn't locked and the answer wasn't posted so I figured I would do it.
I did the same thing first to verify whether it is impossible to fit them or not. If the total volume of the bricks is larger than $6*6*6$ then it is impossible to fit the bricks inside such space. If total volume of the bricks is equal or smaller than the volume of the space, then it might be possible to do so.
It can be impossible to fit them even if they have equal or smaller volume.
Counterexample: Fitting $2*2*2$ brick in $1*1*5$ space (Im not sure, but I think this is a valid counterexample somehow!)
#### mfb
Mentor
I overlooked that somehow, but I'm out of solutions now since I can't get the right distribution of bricks to fit in (not even with an online 3d modeler).
"No" is a valid answer if you can prove that they cannot fit.
I'm quite sure they cannot fit but the approaches I tried to prove it don't work (or work only in two dimensions).
#### Phylosopher
"No" is a valid answer if you can prove that they cannot fit.
I'm quite sure they cannot fit but the approaches I tried to prove it don't work (or work only in two dimensions).
Can you share your trials with us? It might give us a new perspective.
I tried to approach the problem mathematically but I failed. I tried to think of it outside the mathematical formulas, but to be honest I am not satisfied with the such method (Its not giving me an answer anyway ^^").
"Basic Math Challenge - June 2018"
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2019-06-16 07:18:32
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https://math.stackexchange.com/questions/2218695/l2-norm-of-a-function-and-its-derivative?noredirect=1
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L2 norm of a function and its derivative
Assume that f is a real $C^1$ function, and $f(a) = f(b) = 0$, show that My attempt: I have been mostly trying to do integration by parts and then apply Cauchy Schwarz. I also tried with mean value theorem but got no luck. Also I found a result that might be useful: .
• You might want to include your best attempt at this. – Mark Apr 5 '17 at 4:48
You essentially have the right idea. Note that for any $x \in (a,b)$, $$f(x) = \int^x_a f'(t) dt$$ so by Cauchy-Schwarz $$\lvert f(x) \rvert \le \int^x_a \lvert f'(t) \rvert dt \le \left( \int^x_a 1^2 dt\right)^{1/2}\left( \int^x_a \lvert f'(t)\rvert^2 dt\right)^{1/2} \le (x-a)^{1/2} \| f'\|_{L^2(a,b)}.$$ But also $$f(x) = - \int^b_x f'(t) dt$$ so $$\lvert f(x) \rvert \le \int^b_x \lvert f'(t) \rvert dt \le \left( \int^b_x 1^2 dt\right)^{1/2}\left( \int^b_x \lvert f'(t)\rvert^2 dt\right)^{1/2} \le (b-x)^{1/2} \| f'\|_{L^2(a,b)}.$$ Since both these hold for all $x$, we can choose which one we use for a given $x$ which means $$\lvert f(x) \rvert \le [\min(b-x,x-a) ]^{1/2} \|f' \|_{L^2(a,b)}.$$ The functions in the minimum meet at $x= (b+a)/2$ with a value of $(b-a)/2$ so this gives $$\lvert f(x) \rvert \le \left(\frac{b-a}{2}\right)^{1/2} \| f'(x)\|_{L^2(a,b)}.$$ Now just square both sides and integrate to find $$\| f\|^2_{L^2(a,b)} \le \frac{(b-a)^2}{2} \|f'\|_{L^2(a,b)}^2$$ whereupon taking a square root yields your desired inequality.
NOTE: The bound $\min(b-x,x-a) \le (b-a)/2$ is actually fairly crude. You could improve this bound by actually integrating $$\int_a^b \min(b-x,x-a) dx = \frac{(b-a)^2}{4}$$ which would yield the slightly improved bound $$\| f\|_{L^2(a,b)} \le \frac{b-a}{2} \|f'\|_{L^2(a,b)}.$$
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2019-06-25 06:00:15
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https://www.maplesoft.com/support/help/maple/view.aspx?path=PDEtools&L=E
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Overview of the PDEtools Package - Maple Programming Help
Home : Support : Online Help : Mathematics : Packages : PDEtools
Overview of the PDEtools Package
Description
• The PDEtools package is a collection of commands and routines for finding analytical solutions for partial differential equations (PDEs) based on the paper "A Computational Approach for the Analytical Solving of Partial Differential Equations" by E.S. Cheb-Terrab and K. von Bulow (see References), and the continuation of this work by the same authors (Symmetry routines) during 2004.
• The package is an implementation of known methods for solving PDEs; however, it also allows you to look for solutions of equations not yet automatically solved by the package, or for "different solutions" when the package returns a solution which is not the most general one. For this purpose, you can make use of the dchange command and of the HINT option of the pdsolve command, especially the functional hint, both explained in more detail in the corresponding help pages.
• PDEtools includes a subset of commands for computing conserved currents and generalized integrating factors as well as for performing most of the steps of the traditional symmetry analysis of PDE systems. That includes the automatic computation of the infinitesimal symmetry generators as well as the automatic computation of related group invariant solutions of different kinds departing directly from the PDE system to be solved.
• Most of the internal routines of PDEtools are also available for use as PDEtools:-Library:-Routine; this permits programming your own extensions of the package using the existing tools. For details see PDEtools,Library.
• Most of the symmetry commands as well as all the ones in the PDEtools:-Library handle anticommutative variables and functions automatically - see the respective help pages.
• Each command in the PDEtools package can be accessed by using either the long form or the short form of the command name in the command calling sequence. The name PDETools can also be used as a synonym for PDEtools.
• Note: The diff_table command allows you to enter (input) expressions and their derivatives using compact mathematical notation (jetvariables with brackets), representing an important saving in redundant typing for PDE problems.
• To display the help page for a particular PDEtools command from the Maple prompt, see Getting Help with a Command in a Package.
List of PDEtools Package Commands
General purpose and traveling wave solution PDE commands:
Symmetry and related solution PDE commands:
• Most of the internal routines of PDEtools are also available for use as PDEtools:-Library:-Routine; see PDEtools,Library.
• To avoid having to remember the relatively large number of keywords that can be passed as optional arguments for the symmetry related commands, if you type the keyword misspelled, or just a portion of it, a matching against the existing keywords is performed, and when there is only one match, the input is automatically corrected.
Brief description of each command
A brief description of the PDEtools package commands, split into General purpose and Symmetry related, is as follows.
General purpose
• build takes a result given by pdsolve and returns the final expression for the indeterminate function (useful when the method used by pdsolve was separation or change of variables).
• casesplit splits a system of equations (and inequations) into a sequence of systems of equations and inequations such that the union of the non-singular solutions of the latter is equal to the set of solutions of the original system. In addition, in each of the returned systems, all differential or algebraic redundancies are removed, and all the integrability conditions are automatically satisfied. The computations are performed using the DifferentialAlgebra package.
• charstrip evaluates the characteristic strip associated with a given first order PDE; that is, it builds the coupled system of ODEs equivalent to that PDE. Additionally, given a characteristic strip, charstrip can reverse it and return the family of PDEs behind it.
• dchange performs changes of variables in any algebraic object (PDEs, multiple integrals, integro-differential equations, etc.), as well as in procedures. This command is useful to change the format of a PDE from one that is difficult to solve to one that is solvable.
• dcoeffs returns coefficients of polynomial differential equations, much like coeffs with algebraic polynomials.
• declare permits a simple and compact display on the screen of functions and derivatives. Typically, one declares functions, such as declare(f(x, y, z)), so that f(x,y,z) displays as 'f' (that is, just by its name). Also, derivatives are "displayed" as indexed functions and it is possible to declare a "prime variable." In other words, for functions of one variable, derivatives with respect to that variable will be displayed with a prime, '.
• difforder returns the general (or particular, with regard to any variable) differential order of a partial derivative (or the maximum general or particular differential order of an expression containing partial derivatives).
• dpolyform accepts an equation or expression, or a set or list of them, understood to be equal to zero, and returns a differential polynomial system of equations.
• dsubs substitutes a derivative inside differential equations such that the resulting expression does not depend on the derivative being substituted.
• FunctionFieldSolutions computes exact solutions to DE systems involving mathematical functions, possibly inequations, ODEs and also non-differential equations. The solutions are returned as power series (with some upper bound degree $n$) in the mathematical functions and its derivatives (up to some upper bound differential order $m$), having for coefficients multivariable polynomials (with some upper bound degree $r$) of the independent variables.
• Laplace solves a second order linear PDE in two independent variables using the method of Laplace (not a Laplace transform).
• mapde maps a PDE into another PDE with different format (from among a few formats implemented at present), which is perhaps more easily solvable.
• PDEplot produces the plot of the solution for a first order linear (or nonlinear) partial differential equation (PDE), for given initial conditions.
• pdetest returns either 0 (when the PDE is annulled by the solution sol), indicating that the solution is correct, or a remaining algebraic expression (obtained after simplifying the PDE with respect to the proposed solution), indicating that the solution might be wrong.
• Given a PDE, pdsolve's main goal is to find an analytical solution for it. There are no restrictions as to the type, differential order, or number of independent variables of the PDEs pdsolve can try to solve.
• PolynomialSolutions receives a PDE system, optionally an indication of the degree and dependency, and computes related polynomial solutions.
• separability determines under what conditions it is possible to obtain a complete solution, through separation of variables by sum or product, for a given PDE. A complete solution is defined to be a solution that depends on sum(diff_ord[i]+1,i=1..n) parameters, where n is the number of independent variables and diff_ord is the maximum differential order of the PDE with respect to each of the independent variables.
• Solve is an unified solver that receives a system of equations, algebraic or differential, and solves this system, returning solutions optionally independent of indicated variables, calling solve, dsolve or pdsolve according to the input received.
• splitstrip evaluates the strip associated with a PDE the same way as the strip command, but returns this strip, when possible, split into subsets, obtained by calling splitsys with the ODEs of the characteristic strip as argument.
• splitsys splits a set of equations (ODEs, PDEs, algebraic equations, or a combination of these) into subsets, each one with equations coupled among themselves but not coupled to the equations of the other subsets.
• ToMissingDependentVariable receives a PDE and returns another one, PDE2, equivalent to PDE in that from the solution of PDE2 one gets the solution to PDE, and such that PDE2 does not depend, explicitly, on the dependent variable.
• TWSolutions computes Traveling Wave Solutions for PDEs and systems of them, either as expansions in tanh or in a number of other functions like JacobiSN, WeierstrassP, etc..
• undeclare clears declarations previously made.
Symmetry solution related
Note: Herein infinitesimals refer to a list with the components of the infinitesimal generator of a symmetry group.
• CanonicalCoordinates receives the infinitesimals of a symmetry group and returns associated canonical coordinates for it.
• ChangeSymmetry performs change of variables on the infinitesimals of a symmetry generator.
• CharacteristicQ receives the infinitesimals of a point symmetry and returns the characteristic of the group.
• CharacteristicQInvariants receives the infinitesimals of a symmetry group and computes related differential invariants directly from the CharacteristicQ for the infinitesimals.
• ConservedCurrents receives a PDE system and returns the conserved currents of it; when the system involves only ODEs, the conserved currents are the first integrals of the system.
• ConservedCurrentTest receives an algebraic expression and a PDE system and verifies whether the given expression is a conserved current.
• ConsistencyTest receives a PDE system and returns true or false according to whether the system is consistent
• D_Dx computes total derivatives in jet notation, that is taking the independent and dependent variables and their derivatives as differentiation variables in equal footing.
• DeterminingPDE receives a PDE system and computes the determining PDE system satisfied by the infinitesimals of the symmetry groups admitted by the given PDE system.
• Eta_k receives the infinitesimals of a symmetry and returns a table-procedure that computes, on request, any prolongation of these infinitesimals.
• Euler is the Euler operator: when applied to a DE system, it returns the exact conditions; i.e. the conditions to be satisfied when the system is a divergence.
• FromJet receives a mathematical expression in jet notation and returns the corresponding expression in function notation. This command is the counterpart of ToJet.
• FunctionFieldSolutions computes exact solutions to DE systems involving mathematical functions, possibly inequations, ODEs and also non-differential equations. The solutions are returned are power series (with some upper bound degree $n$) in the mathematical functions and its derivatives (up to some upper bound differential order $m$), having for coefficients multivariable polynomials (with some upper bound degree $r$) of the independent variables.
• InfinitesimalGenerator receives the infinitesimals of a symmetry and returns a procedure (operator) representing the infinitesimal generator, that is, one which acts on a PDE system to return the related determining PDE.
• Infinitesimals receives a PDE system and returns the infinitesimals of symmetry groups admitted by the given PDE system.
• IntegratingFactors receives a DE system and returns the generalized integrating factors.
• IntegratingFactorTest receives an algebraic expression and a DE system, and verifies whether the given expression is a generalized integrating factor.
• InvariantEquation receives the infinitesimals of a symmetry group and computes the equation that is simultaneously invariant under the symmetry transformations corresponding to the given symmetries.
• InvariantSolutions receives a PDE system and returns the so-called group invariant solutions for it, that is, the PDE system solutions derived by first (automatically) computing the symmetries admitted by it.
• InvariantTransformation receives the infinitesimals of a symmetry group and computes the related finite (symmetry) transformations reducing the number of independent variables by N. (You can optionally specify N.) These are the transformations from which InvariantSolutions derives solutions to the PDE system.
• Invariants receives the infinitesimals of a symmetry group and computes related differential invariants of any specified order.
• PolynomialSolutions receives a PDE system, optionally an indication of the degree and dependency, and computes related polynomial solutions.
• ReducedForm receives two PDE systems and reduces the first one with respect to the second one; this is similar to what simplify/siderels does but with PDE systems. This command can be useful beyond the symmetry approach for PDE systems.
• SimilaritySolutions receives a PDE system and returns the so-called similarity solutions for it. This command is present mainly for pedagogical purposes in that the solutions it returns are computed using one symmetry at a time. For practical purposes use InvariantSolutions instead, which can reduce the given PDE system using many symmetries in one go.
• SimilarityTransformation receives a PDE system and computes the finite (symmetry) transformations reducing the number of independent variables by one. These are the transformations from which SimilaritySolutions derives solutions to the PDE system.
• SymmetryCommutator receives a pair of infinitesimals corresponding to symmetry transformations and returns their commutator.
• SymmetryGauge receives a symmetry, as a list or as an infinitesimal generator, and rewrites this symmetry in the most general form or in the one indicated using optional arguments.
• SymmetryTest receives the infinitesimals of a symmetry group and a PDE system and tests whether the PDE system admits that symmetry.
• SymmetryTransformation receives the infinitesimals of a 1-Dimensional point symmetry group and returns the finite form of the (symmetry) transformation leaving invariant any PDE system admitting that symmetry.
• SymmetrySolutions receives the infinitesimals of a point symmetry group, a solution to some PDE system (itself not required) and returns the another solution, obtained by transforming the given one using the finite form of the (symmetry) transformation given.
• ToJet receives a mathematical expression in function notation and returns the corresponding expression in jet notation. This command is the counterpart of FromJet.
References
Cheb-Terrab, E.S., and von Bulow, K. "A Computational Approach for the Analytical Solving of Partial Differential Equations." Computer Physics Communications, Vol. 90, (1995): 102-116.
Olver, P.J. Equivalence, Invariants and Symmetry. Cambridge Press, 1995.
Stephani, H. Differential Equations: Their Solution Using Symmetries. Edited by M. MacCallum. Cambridge University Press, 1989.
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2021-04-11 18:58:13
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https://zbmath.org/?q=an:1178.34071
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# zbMATH — the first resource for mathematics
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Existence for impulsive neutral integrodifferential inclusions with nonlocal initial conditions via fractional operators. (English) Zbl 1178.34071
Summary: We study the existence of mild solutions for the following system in a general Banach space $X$ (with norm $\|\cdot\|$): $$\cases \frac{d}{dt}[x(t)-F(t,x(h_1(t)))]\in Ax(t)+\int^t_0K(t,s)G(s,x(h_2(s)))\,ds,\\ t\in J-\{t_1,\dots,t_m\},\quad \text{where }J=[0,a],\\ \Delta x|_{t_k}=I_k(x(t^-_k)),\quad k=1,\dots,m,\\ x(0)=g(x)\in X.\endcases\tag1.1$$ Here $A$ is the infinitesimal generator of a compact analytic semigroup $T(t($, $t>0$, $G$ is a multi-valued map and $\Delta x|_{t=t_k}=x(t^+_k)-x(t^-_k)$, where $x(t^-_k)$ and $x(t^+_k)$ represent the left and right limits of $x(t)$ and $t=t_k$, respectively. Let $K:D\to R$, $D=\{(t,s)\in J\times J:t\ge s\}$ and $F,G,g,I_k$ $(k=1,\dots,m)$ and $h_1, h_2$ are given functions. By using a fixed point theorem for multi-valued maps due to Dhage, a main existence theorem is established. Finally, we present an example to illustrate this main theorem.
##### MSC:
34G25 Evolution inclusions 47N20 Applications of operator theory to differential and integral equations
Full Text:
##### References:
[1] Bainov, D. D.; Simeonov, P. S.: Systems with impulsive effect. Ellis horwood series: mathematics and its applications (1989) [2] Benchohra, M.; Henderson, J.; Ntouyas, S.: Impulsive differential equations and inclusions. (2006) · Zbl 1130.34003 [3] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations. (1989) · Zbl 0719.34002 [4] Samoilenko, A. M.; Perestyuk, N. A.: Impulsive differential equations. World scientific series on nonlinear science, series A 14 (1995) · Zbl 0837.34003 [5] Anguraj, A.; Arjunan, M. Mallika; Hernández, E. M.: Existence results for an impulsive neutral functional differential equation with state-dependent delay. Appl. anal. 86, 861-872 (2007) · Zbl 1131.34054 [6] A. Anguraj, K. Karthikeyan, Existence of solutions for impulsive neutral functional differential equations with nonlocal conditions, Nonlinear Anal., doi:10.1016/j.na.2008.03.059 · Zbl 1165.34416 [7] Chang, Y. -K.; Anguraj, A.; Arjunan, M. Mallika: Existence results for non-densely defined neutral impulsive differential inclusions with nonlocal conditions. J. appl. Math. comput. 28, 79-91 (2008) · Zbl 1160.34072 [8] Chang, Y. -K.; Nieto, J. J.; Li, W. -S.: On impulsive hyperbolic differential inclusions with nonlocal initial conditions. J. optim. Theory appl. 140, 431-442 (2009) · Zbl 1159.49042 [9] Y.-K. Chang, J.J. Nieto, Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators, Numer. Funct. Anal. Optim. (in press) · Zbl 1176.34096 [10] Hernández, E.; Pierri, M.; Goncalves, G.: Existence results for an impulsive abstract partial differential equation with state-dependent delay. Comput. math. Appl. 52, 411-420 (2006) · Zbl 1153.35396 [11] Hernández, E. M.; Rabello, M.; Henríquez, H.: Existence of solutions for impulsive partial neutral functional differential equations. J. math. Anal. appl. 331, 1135-1158 (2007) · Zbl 1123.34062 [12] W.-S. Li, Y.-K. Chang, J.J. Nieto, Solvability of impulsive neutral evolution differential inclusions with state-dependent delay, Math. comput. Modelling, doi:10.1016/j.mcm.2008.12.010 · Zbl 1171.34304 [13] Li, J.; Nieto, J. J.; Shen, J.: Impulsive periodic boundary value problems of first-order differential equations. J. math. Anal. appl. 325, 226-236 (2007) · Zbl 1110.34019 [14] Nieto, J. J.: Basic theory for nonresonance impulsive periodic problems of first order. J. math. Anal. appl. 205, 423-433 (1997) · Zbl 0870.34009 [15] Nieto, J. J.: Impulsive resonance periodic problems of first order. Appl. math. Lett. 15, 489-493 (2002) · Zbl 1022.34025 [16] Zhang, H.; Chen, L.; Nieto, J. J.: A delayed epidemic model with stage-structure and pulses for pest management strategy. Nonlinear anal. RWA 9, 1714-1726 (2008) · Zbl 1154.34394 [17] Benchohra, M.; Ntouyas, S.: Existence and controllability results for multivalued semilinear differential equations with nonlocal conditions. Soochow J. Math. 29, 157-170 (2003) · Zbl 1033.34068 [18] Ezzinbi, K.; Fu, X.; Hilal, K.: Existence and regularity in the ${\alpha}$-norm for some neutral partial differential equations with nonlocal conditions. Nonlinear anal. 67, 1613-1622 (2007) · Zbl 1119.35105 [19] Erbe, L.; Kong, Q.; Zhang, B.: Oscillation theory for functional differential equations, pure and applied mathematics. (1994) · Zbl 0821.34067 [20] Hale, J.: Theory of functional differential equations. (1977) · Zbl 0352.34001 [21] Henderson, J.: Boundary value problems for functional differential equations. (1995) · Zbl 0834.00035 [22] Byszewski, L.: Theorems about the existence and uniqueness of a solution of a semilinear evolution nonlocal Cauchy problem. J. math. Anal. appl. 162, 496-505 (1991) · Zbl 0748.34040 [23] Deng, K.: Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions. J. math. Anal. appl. 179, 630-637 (1993) · Zbl 0798.35076 [24] Byszewski, L.; Lakshmikantham, V.: Theorem about existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space. Appl. anal. 40, 11-19 (1990) · Zbl 0694.34001 [25] Byszewski, L.: Existence of solutions of semilinear functional-differential evolution nonlocal problem. Nonlinear anal. 34, 65-72 (1998) · Zbl 0934.34068 [26] Fu, X.; Ezzinbi, K.: Existence of solutions for neutral functional differential evolution equations with nonlocal conditions. Nonlinear anal. 54, 215-227 (2003) · Zbl 1034.34096 [27] Fu, X.: On solutions of neutral nonlocal evolution equations with nondense domain. J. math. Anal. appl. 299, 392-410 (2004) · Zbl 1064.34065 [28] Yosida, K.: Functional analysis. (1980) · Zbl 0435.46002 [29] Deimling, K.: Multivalued differential equations. (1992) · Zbl 0760.34002 [30] Pazy, A.: Semigroups of linear operators and applications to partial differential equations. (1983) · Zbl 0516.47023 [31] Lasota, A.; Opial, Z.: An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. acad. Pol sci. Ser. sci. Math. astronom. Phys. 13, 781-786 (1965) · Zbl 0151.10703 [32] Dhage, B. C.: Multi-valued mappings and fixed points II. Tamkang J. Math. 37, 27-46 (2006) · Zbl 1108.47046 [33] Travis, C. C.; Webb, G. F.: Partial functional differential equations with deviating arguments in the time variable. J. math. Anal. appl. 56, 397-409 (1976) · Zbl 0349.35071
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2016-05-01 06:08:47
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https://nubtrek.com/maths/calculus-limits/limits-of-algebraic-expressions/limit-of-binomial
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### Limit of Algebraic Expressions
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Home
Limits involving Binomial Expressions
» Special case of canceling factors in numerator and denominator
→ lim_(x->a)(x^n-a^n)/(x-a) = na^(n-1)
» With change of variable x=1+y and constant a=1
→ lim_(y->0) ((1+y)^n - 1)/y = n
### Limits involving Binomial Expressions
plain and simple summary
nub
plain and simple summary
nub
dummy
To find limit of functions with binomials, factor the binomials to cancel out the factor involving 0.
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Factoring binomials is revised and the limit involving binomials is explained with an example.
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Starting on learning "Limits involving binomial expressions". ;; Factoring binomials is revised and the limit involving binomials is explained with an example.
Which of the following refers to factoring binomials?
• factoring (a+b+c)^2
• factoring of a^n-b^n
The answer is 'factoring of a^n-b^n'
What does binomial mean?
• of two terms
• a compound of bismuth
The answer is 'of two terms'.
The expression a^n - b^n is a two variate binomial of degree n.
two variate : a and b are two variables
binomial : a^n and -b^n are the two terms
degree n: The maximum power is n
Factoring the binomials is given by
a^n-b^n
quad quad = (a-b)(a^(n-1)+a^(n-2)b^1+
quad quad quad quad a^(n-3)b^2+ cdots + b^(n-1))
What is the value of f(x)=color(deepskyblue)(x^4-16)/color(coral)(x-2) at x=2?
• 0/0
• 1
• 0
• oo
The answer is '0/0'
What is the limit of f(x)=color(deepskyblue)(x^4-16)/color(coral)(x-2) at x=2?
• 0/0
• 4 xx 2^3
• 0
• oo
The answer is '4 xx 2^3'. The answer is explained in the next page.
limit of f(x)=color(deepskyblue)(x^4-16)/color(coral)(x-2) at x=2.
On substitution of x=2 the function evaluates to 0/0
Limit of the function is
lim_(x->2) color(deepskyblue)(x^4-16)/color(coral)(x-2)
quad quad = lim_(x->2) color(deepskyblue)(x^4-2^4)/color(coral)(x-2)
quad quad = lim_(x->2) color(deepskyblue)((x-2)(x^3+2x^2+4x+8))/color(coral)(x-2)
quad quad = lim_(x->2) (x^3+2x^2+4x+8)
quad quad = 2^3+ 2xx 2^2 + 4xx 2 + 8
quad quad = 4 xx 2^3
note: (x-2) is not canceled at x=2. But, limit is applied to (x-2)/(x-2)
comprehensive information for quick review
Jogger
comprehensive information for quick review
Jogger
dummy
Limit of expressions with Binomials: For any positive integer n
lim_(x->a)color(deepskyblue)(x^n-a^n)/color(coral)(x-a) = na^(n-1)
practice questions to master the knowledge
Exercise
practice questions to master the knowledge
Exercise
What is the limit for f(x)=color(deepskyblue)(x^15-1)/color(coral)(x^10-1) at x=1
• 3/2
• 2/3
• 1
• 0
The answer is '3/2'
Progress
Progress
Which of the following refers to factoring binomials?
c;squared;sea;see
factoring a. + b + c squared
power;n;minus
factoring of a power n minus b power n
The answer is "factoring of a power n minus b power n"
What does binomial mean?
two;terms;2
of two terms
compound;bismuth
a compound of bismuth
The answer is "of two terms". ;; The expression a power n minus b power n is a two variate binomial of degree n. ;; two variate : a. and b are the two variables.;; binomial : a power n and b power n are the two terms ;; degree n : the maximum power is n.
factoring the binomials is given by : a power n minus b power n ;; equals a minus b, multiplied, a power n minus 1 + a power n minus 2 multiplied b + a power n minus 3 multiplied b power 2 + dot dot dot + b power n minus 1
What is the value of f of x = x power 4 minus 16, by x minus 2 at x =2?
by
0 by 0
1
1
0
0
infinity
infinity
The answer is "0 by 0"
What is the limit of f of x = x power 4 minus 16, by x minus 2 at x =2?
by
0 by 0
times;power;3;2;4
4 times 2 power 3
0
0
infinity
infinity
The answer is "4 times 2 power 3". The answer is explained in the next page.
Limit of f of x = x power 4 minus 16, by x minus 2 at x =2. On substitution of x=2, the function evaluates to 0 by 0;; limit of the function is ;; limit x tending to 2, x power 4 minus 16, by x minus 2 ;; equals limit x tending to 2, x power 4 minus 2 power 4, by x minus 2 ;; equals limit x tending to 2, x minus 2 multiplied x cube + 2 x squared + 4 x + 8, divided by, x minus 2;; equals limit x tending to 2, x cube + 2 x squared + 4 x + 8;; equals 2 power 3 + 2 times 2 power 2+ 4 times 2 + 8;; equals 4 into 2 power 3.;; Note : x minus 2 is not canceled at x=2. But, limit is applied to x minus 2 by x minus 2.
To find limit of functions with binomials, factor the binomials to cancel out the factor involving 0
Limit of expressions with Binomials: For any positive integer n; limit x tending to a. x power n minus a power n divided by x minus a, = , n a power n minus 1.
What is the limit for f of x equal x power 15 minus 1, by x power 10 minus 1, at x=1?
1
3 by 2
2
2 by 3
3
4
The answer is "3 by 2"
we are not perfect yet...
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2018-07-19 02:15:07
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https://blogs.mathworks.com/cleve/2016/06/09/math-and-music/?s_tid=blogs_rc_1
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# Math and Music
What does $\sqrt[12]{2}$ have to do with music? What are equal temperament and just intonation? How can the MATLAB function rats help tune a piano? (This post is based in part on the Music chapter in my online book, Experiments in MATLAB.)
### Contents
#### Octaves and semitones
In the theory of music, an octave is an interval with frequencies that range over a factor of two. In most Western music, an octave is divided into 12 semitones in a geometric progression. In other words the notes have equal frequency ratios. Since 12 semitones comprise a factor of 2, a single semitone is a factor of $\sqrt[12]{2}$. And because this quantity occurs so often in this discussion, let
$$\sigma = \sqrt[12]{2}$$
Our MATLAB programs use
format short
sigma = 2^(1/12)
sigma =
1.0595
Think of $\sigma$ as an important mathematical constant, like $\pi$ and $\phi$.
#### Keyboard
Here is our miniature piano keyboard with 25 keys.
small_keyboard
This keyboard has two octaves, with white keys labeled C D … G A B, plus another C key. Counting both white and black, there are twelves keys in each octave. The frequency of each key is a semitone above or below its neighbors. Each black key can be regarded as either the sharp of the white below it or the flat of the white above it. So the black key between C and D is both C $\sharp$ and D $\flat$. There are no E $\sharp$ / F $\flat$ or B $\sharp$ / C $\flat$.
A conventional full piano keyboard has 88 keys. Seven complete octaves account for $7 \times 12 = 84$ keys. There are three additional keys at the lower left and one additional key at the upper end. If the octaves are numbered 0 through 7, then a key letter followed by an octave number specifies a unique key. In this notation, two important keys are C4 and A4. The C4 key is near the center of the keyboard and so is also known as middle C. A piano is usually tuned so that the frequency of the A4 key is 440 Hz. C4 is nine keys to the left of A4 so its frequency is
$$\mbox{C4} = 440 \sigma^{-9} \approx 261.6256 \mbox{Hz}$$
Our miniature keyboard has the A4 key colored green and the C4 key colored blue.
#### Equal Temperament
A piano is almost always tuned with equal temperament, the system used by musical instruments with fixed pitch. Starting with A4 at 440 Hz the keys are tuned in strict geometric progression with ratio $\sigma$. Once this is done, a piano rarely needs adjustment.
#### Just Intonation
The alternative system, just intonation, is defined by a vector of ratios involving small integers.
format rat
just = [1 16/15 9/8 6/5 5/4 4/3 7/5 3/2 8/5 5/3 7/4 15/8 2]'
just =
1
16/15
9/8
6/5
5/4
4/3
7/5
3/2
8/5
5/3
7/4
15/8
2
These ratios allow the generation of overtones, chords and harmony. More about that in a moment. Many musical instruments can be tuned to the key of a particular composition just before playing it. Singers, choirs, and barbershop quartets can naturally use just intonation.
Here is a comparison of equal temperament and just intonation from a strictly numerical point of view. Equal temperament is defined by repeated powers of $\sigma$. while just intonation is defined by a sequence of ratios.
sigma = 2^(1/12);
k = (0:12)';
equal = sigma.^k;
num = [1 16 9 6 5 4 7 3 8 5 7 15 2]';
den = [1 15 8 5 4 3 5 2 5 3 4 8 1]';
just = num./den;
delta = (equal - just)./equal;
T = [k equal num den just delta];
fprintf(' k equal just delta\n')
fprintf('%4d %12.6f %7d/%d %11.6f %10.4f\n',T')
k equal just delta
0 1.000000 1/1 1.000000 0.0000
1 1.059463 16/15 1.066667 -0.0068
2 1.122462 9/8 1.125000 -0.0023
3 1.189207 6/5 1.200000 -0.0091
4 1.259921 5/4 1.250000 0.0079
5 1.334840 4/3 1.333333 0.0011
6 1.414214 7/5 1.400000 0.0101
7 1.498307 3/2 1.500000 -0.0011
8 1.587401 8/5 1.600000 -0.0079
9 1.681793 5/3 1.666667 0.0090
10 1.781797 7/4 1.750000 0.0178
11 1.887749 15/8 1.875000 0.0068
12 2.000000 2/1 2.000000 0.0000
The last column in the table, delta, is the relative difference between the two. We see that delta is less than one percent, except for k = 10.
This is why the 12-note scale has proved to be so popular. Powers of $\sqrt[12]{2}$ turn out to come very close to important rational numbers, especially 5/4, 4/3, and 3/2. A pair of pitches with a ratio of 3:2 is known as a perfect fifth; a ratio of 4:3 is a perfect fourth; a ratio of 5:4 is a major third.
#### Do Re Mi
One of the first songs you learned to sing was
Do Re Mi Fa So La Ti Do
If you start at middle C, you will be singing the major scale in the key of C. This scale is played on a piano using only the white keys. The steps are not equally spaced. Most of the steps skip over black keys and so are two semitones. But the steps between Mi and Fa and Ti and Do are the steps from E to F and B to C. There are no intervening black keys and so these steps are only one semitone. In terms of $\sigma$, the C-major scale is
$$\sigma^0 \ \sigma^2 \ \sigma^4 \ \sigma^5 \ \sigma^7 \ \sigma^9 \ \sigma^{11} \ \sigma^{12}$$
The number of semitones between the notes is given by the vector
format short
diff([0 2 4 5 7 9 11 12])
ans =
2 2 1 2 2 2 1
This sequence of frequencies in our most common scale is surprising.
#### Vibrations and Waves
Like everything else, it all comes down to eigenvalues. Musical instruments create sound through the action of vibrating strings or vibrating columns of air that, in turn, produce vibrations in the body of the instrument and the surrounding air. Mathematically, vibrations can be modeled by weighted sums of characteristic functions known as modes or eigenfunctions. Different modes vibrate at different characteristic frequencies or eigenvalues. These frequencies are determined by physical parameters such as the length, thickness and tension in a string, or the geometry of the air cavity. Short, thin, tightly stretched strings have high frequencies, while long, thick, loosely stretched strings have low frequencies.
The simplest model is a one-dimensional vibrating string, held fixed at its ends. The units of the various physical parameters can be chosen so that the length of the string is $2 \pi$. The modes are then simply the functions
$$v_n(x) = \sin{n x}, \ \, n = 1, 2, …$$
Each of these functions satisfy the fixed end point conditions
$$v_n(0) = v_n(2 \pi) = 0$$
The time-dependent modal vibrations are
$$u_n(x,t) = \sin{n x} \sin{n t}, \ \, n = 1, 2, …$$
and the frequency is simply the integer $n$. (Two- and three-dimensional models are much more complicated. This one-dimensional model is all we need here.)
Our Experiments with MATLAB program vibrating_string provides a dynamic view. Here is a snapshot showing the first nine modes and the resulting wave traveling along the string.
The ratios in just intonation or equal temperament produce instruments with tunings that generate vibrations with these desired frequencies.
#### rat and rats
The MATLAB expression rat(X,tol) creates a truncated continued fraction approximation of X with an accuracy of tol. The default tol is 1.e-6*norm(X,1).
rat(sigma.^(0:12)')
ans =
1
1 + 1/(17 + 1/(-5 + 1/(-2)))
1 + 1/(8 + 1/(6))
1 + 1/(5 + 1/(4 + 1/(-2)))
1 + 1/(4 + 1/(-7 + 1/(2 + 1/(5))))
1 + 1/(3 + 1/(-74))
1 + 1/(2 + 1/(2 + 1/(2 + 1/(2 + 1/(2 + 1/(2))))))
1 + 1/(2 + 1/(147))
2 + 1/(-2 + 1/(-2 + 1/(-3 + 1/(4 + 1/(2)))))
2 + 1/(-3 + 1/(-7 + 1/(-81)))
2 + 1/(-5 + 1/(2 + 1/(3 + 1/(-2 + 1/(-15)))))
2 + 1/(-9 + 1/(11))
2
These are unconventional continued fractions because they contain negative terms. This algorithm is used for format rat. The default tolerance is much too picky. The equal temperament ratios do not give small integers.
format rat
sigma.^(0:12)'
ans =
1
1657/1564
1769/1576
1785/1501
635/504
3544/2655
1393/985
2655/1772
1008/635
3002/1785
1527/857
2943/1559
2
This would not be a satisfactory way to try to tune an instrument. But if I’m much more tolerant and allow a 2 percent error, I get short continued fractions.
rat(sigma.^(0:12)',.02)
ans =
1
1 + 1/(17)
1 + 1/(8)
1 + 1/(5)
1 + 1/(4)
1 + 1/(3)
1 + 1/(2 + 1/(2))
1 + 1/(2)
2 + 1/(-2 + 1/(-2))
2 + 1/(-3)
2 + 1/(-5)
2 + 1/(-9)
2
I can make format rat use these fractions by telling rats that it has only 6 columns to work with. Now I get almost the same ratios as just intonation.
rats(sigma.^(0:12)',6)
ans =
1
1
9/8
6/5
5/4
4/3
7/5
3/2
8/5
5/3
9/5
17/9
2
#### Rewriting Music History
If any of the music theorists from ancient Greece or the Renaissance had access to MATLAB, they could have used our rational approximation to generate a tuning strategy.
Published with MATLAB® R2016a
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2020-07-06 08:56:21
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http://distancesampling.org/Distance/old-versions/d41knownproblems
|
# Distance 4.1 Release 2 - Current restrictions, known problems and workarounds
See also resolved problems in Distance 5, which are therefore known problems in Distance 4
Last updated: 3 March 2005
Current highest # : 310
Problems in GREY have been found and fixed. Some of these fixes may be available in patches to the current release – see the Distance 4.1 download page for the latest patch and the Distance 4.1 resolved problems page for list of problems fixed.
## Current Restrictions
• Project setup and import:
• If length or distance fields are measured in one field but to be analyzed in another then only the measurement units are imported from the old D3.5 file. Units of analysis must be set in the new data filter manually. (This is because data filters are not imported when the project is imported, and analysis units are now in the data filters.) If the units are not one of those that Distance recognizes (from the default project settings database) then the units will not be imported.
• MCDS Analysis Engine:
• Maximum number of covariates and factor levels is listed in the manual, under “Limitations”
• When covariates are specified, only half-normal and hazard-rate key functions allowed.
• Cannot force the fitted function to be monotonic decreasing.
• When cluster size is a covariate, stratified analyses are not allowed .
• Cannot have non-factor covariate value -9999.
• MRDS Analysis Engine:
• Line transet surveys only (not point transects).
• Exact data only (no interval data).
• Units of area for reporting results are squared units of line length; assumes area field is also in squared units of line length.
• Ignores units coversion specified in the Units tab of the Data Filter.
## Known Problems
### Installation
• 96 On many machines, you are asked to reboot during the install process. However, on some Win98 machines, during reboot, you get the message “Cannot find setup.exe”. Workarounds: 1. reboot again, or 2. Run d40setup.exe again. [Len: 13 March 01]
• 179 On vanilla Win NT 4.0 SP6 machines (and possibly others), during the last part of the install, you get the error message “The procedure entry point _lc_collate_cp could not be loaded in the dynamic link library MSVCRT.dll”. After installation is completed, you then cannot load geographic projects into D4 (e.g., the sample project D4Mexico). Workaround: reboot, then install Distance 4 again. [Len 10 May 2002 - cause new version of MSVCRT is installed, but is not backwards compatible – need to find some way to reboot before registering components if MSVCRT is replaced]
• 246 On starting Distance on some machines get message “Distance could not find a component it needs to run. This is due to an installation problem or a conflict with another program.” or “Automation error. Library not registered.” or “File name or class name not found during automation operation.” Usually occurs in D4Util.StringHandling module. Solution:
1. Uninstall Distance
2. Download and install Windows Script 5.6 from the scripting page of the Microsoft website
3. Reboot
4. Re-install Distance.
• (Note: Windows Script 5.6 is supposed to be shipped with Windows XP but it may be that another program on this person’s system had broken it). [Colin Driscoll 24 Oct 03; Workaround LJT 27 Oct 03; other examples reported subsequently]
• 255 Various problems have been reported on machines with some anti-virus software, including the machine locking up. We recommend that you disable your anti-virus software while you run the setup program, and then enable it again after Distance is installed. If you are concerned, feel free to scan the setup program for viruses before running it. [LJT 9 Dec 03]
• 281 New version of Tab control used in Distance 5 causes a run time error when closing Distance 4: error 91, “object variable or with block variable not set”. This can safely be ignored!
• 297 After double-clicking on the Distance setup program, the setup program for another package (e.g., Mark) may start up. Solution: Make sure there are no other setup programs in the same directory as Distance. [Shane Wellendorf 11 Aug 04; Fixed LJT 11 Aug 04 – renamed the setup program from setup.exe to somethng that’s likely to be unique]
### Interface
Design properties items are in the next section, with the Design Engine
• 16 General: Interface doesn’t prevent user from making changes while items are running – e.g., changing the Data Filter or Model Definition while an analysis is running. If you do this, however, you will get errors.
• 194 General: When upgrading from a Distance 3.5 project, and the destination folder for the D4 project is different from the source folder of the D35 project, under Windows 98 get an error that the new data file cannot be opened. This error doesn’t occur under Windows XP. [Len 5 Aug 02]
• 195 General – properties windows. When you press F1, the help window that opens is always the same, regardless of which tab is showing. Ideally, the help window would be appropriate for the tab. [Len 12 Aug 02 – Cause: couldn’t get the Control Extender’s generic event to fire when late binding the properties controls – would like to have an event called HelpContextIDChanged that passes a new contextID each time a tab is shown in the properties controls. Perhaps to do with binary compatibility?]
• 247 General – Details windows. On systems with extended character sets (e.g., Chinese, Japanese and Korean Language systems), the results of running analyses, surveys, etc. are not displayed. This occurs because the results are compressed in the project database and the decompression doesn’t work on these systems. Workaround: choose Tools Preferences, and under the General tab, un-check the box “Store results in compressed format in project databases”. Now analyses you run should display fine. Note that you will have to re-run previous analyses for them to display. If you exchange projects with computers that do not have extended character systems, these computers will have to have the compress option switched off too. [LJT 28 Nov 2003]
• 306 General - opening projects. Under some regional operating systems, double-clicking on a Distance project to open it cased an error 13 - unknown type. [Atanga Ekobo Aug 2004, Fixed LJT 2 Feb 2005]
• </span>300 Manual: Need to describe how to do smearing – in data filter you need to set automatic equal intervals, as choosing the intervals manually doesn’t use the NCLASS command in the analysis engine. Also point out that smearing not supported for MCDS. [LJT 27 Oct 2004]</span>
• 19 Analysis Components: “No item selected” message sometimes pops up when you try to delete a Data Filter or Model Definition, even if you know that one is selected. Workaround: Close the window and re-open it. [Internal note: Caused by bug in grid component where the grid is not binding tightly enough to the data control, and the record gets out of synch. Need to contact VideoSoft for fix or find a workaround.]
• 21 Analysis Details, Results tab. When the results page titles are very long, the drop-down combo list gets resized so it is wider than the screen, and so the scroll bar disappears. (Note: Problem is in D4Util.ComboAdjustWidth – need to use an API routine to get the left pixel position of the drop-down and subtract this from the screen width.) [1 Dec 00]
• 134 Analysis Details, Results tab. When results pages are very long, and you scroll down to the bottom of one page, then when you click on next you are taken to the bottom of the next page. Should take you to the top of each page as you enter it [26 Sept 01, LJT]
• 226 Analysis Details, Results tab. When pasting a graph into another application that had been copied from CDS or MCDS results using “copy plot to clipboard”, one Windows ME system intermittently gave the error message “Distance has caused an error in MSCHRT20.ocx”. Workarounds – (1) seems to be less common if you leave the graph page showing while doing the paste (ie don’t close the Analysis Details window); (2) save the plot data to file in Model Definition Detection function Diagnostics, and use the macro on the Distance web site from Tim Gerrodette to reproduce the plot in Excel. Note – this is a problem with Microsoft’s chart control and we don’t expect to be able to fix it. Related to known problems on the Microsoft web site support page numbers 139577, 142793 and 179458. [Rob Williams 31 March 03].
• 22 Browsers/Analysis Components: When you delete a Model Definition in the Analysis Components window, the IDs of the model definitions are not updated in the Analysis Browser table. [2 Nov 00] Also happens when you delete an analysis set using the Analysis Browser toolbar – the IDs of the new set shown are not updated. This causes an error in the mouse over event of the Analysis Browser when it doesn’t recognize the ID – should error trap this, as well as fixing the source of the problem. [3 Nov 00; Fixed LJT 12 Jan 05]
• 24 Browsers: Results pane (right hand side) – results with many 000s (either large or small) are not displaying in exponent format.
• 25 Browsers: when you hit Enter after changing the name of an item, all items in that set become selected (only the one you were editing should be selected).
• 26 Data Explorer: When you delete a data layer, any open design and survey details results windows that display maps go blank. [12 Jan 01]
• 28 Data Explorer. Some data editing functions missing: when you hit tab in data entry mode you are not taken to the next cell; the up and down arrow keys move you along the edit string rather than up and down. Probably more issues here.
• 29 Data Explorer: Operations that alter the structure of the data base (adding or deleting data layers, adding or deleting data fields, renaming fields or layers) cause an error if the data sheet is already locked by something else – for example if the layer is in a map that is open, or a design run. [Len: I need to go through the data sheet code putting in LockDataLayers method calls, and also need to enforce no editing of data while items are running.]
• 31 Data Explorer: When you add a new field to an existing data layer, the values are blank and have no default. [I don’t know what’s a sensible thing to do here…]
• 32 Data Explorer, Shape Properties. When you input an invalid shape (e.g., only one vertex of a polygon) you get no warning message – the shape is simply not saved.
• 133 Data Explorer - there is no way to delete cell values. Pressing Del should turn the value into a Null - useful, for example, if you want to represent missing data in the data sheet (e.g., missing covariate values). [26 Sept 01, Len]
• 138 Data Explorer, Data Import, etc. Currently, there is no check that a field name is valid (e.g., in renaming fields, in importing new fields, etc). [1 Oct 01, Len]
• 267 Data Explorer: When you rename a layer it should rename the shapefile [LJT 15 March 2004]
• 36 Data Filter Properties, Units tab. When you specify units other than “Same as…”, you can get warning messages about overwriting the defaults when you run the analysis.
• 129 Data Filter Properties, Units tab. Angle is automatically specified as Degrees here, but unless you also specify some valid angle units in the Data Explorer, you get an error message when running the analysis: “The angle field ‘Angle’ has no units associated with it.” This message is unclear - should say where you need to specify the units. [10 Sept 01, Len]
• 37 Design Browser and Details: When you run a design to generate a coverage probability grid, if you say OK to overwrite an existing field, if it fails, it leaves the data layer in a poor state (the field name is deleted from DataFields but the field is still in the data table).
• 38 Design Details: There is no “Stop” button once you press run. [12 Jan 01]
• 39 Design Details: You can change the Type Of Design for designs that have been run, or that have Surveys attached to them, without Distance noticing and prompting you to agree to reset the Design and Surveys. [14 Jan 01]
• 42 Details Windows: Too much refreshing and flickering of combo boxes when new items selected. Particularly bad in Analysis Details.
• 45 Details Log Windows: Clicking on an error in the bottom window doesn’t scroll you to that line in the top window.
• 310 Help: On some systems, viewing some pages causes the following message to appear: “An ActiveX control on this page might be unsafe to interact with other parts of the page. Do you want to allow this interaction?”. The problem is actually with the Microsoft HTML Help control, which is not installed properly for some reason. One possible fix is to unregister and then re-register the control, which you can do by opening a Command Prompt window and typing the following two commands [Pierre Richard 28 Feb 2005; Workaround LJT 2 March 2005] :
regsvr32 /u %windir%\\system32\\hhctrl.ocx
regsvr32 %windir%\\system32\\hhctrl.ocx
• 211 Import Data Wizard: “Error 3433: Invalid setting in Excel key of the Engines section of the Windows Registry” on some machines, when you click Next to go from the Data Destination step to the Data File Format step. This is not a bug in Distance; another program on the affected system has changed a part of the windows registry to a state that isn’t valid. The solution is to edit the windows registry to correct the problem. To start the registry editor program, click Start and then Run. In the Open box, type Regedit.exe. In the registry editor, expand the following key: “HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Jet\3.5\Engines\Text”. Under the Format key, you should see the following value: Delimited(). From the menu choose Edit and then Modify and change the value to CSVDelimited. This should fix the problem. If not, or the value was already CSVDelimited, then you have a different problem. [DLB 14 Jan 03; Solution LJT 15 Jan 03]
• 222 Import Data Wizard: Importing large datasets is very slow. [20 March 03]
• 46 Main Window: If you stop a design simulation mid-way through (by pressing Stop on the toolbar), the progress % indicator on the main toolbar still says Progress x% - this should be cleared. Perhaps the design is not halted correctly or completely? [12 Jan 01]
• 47 Map Browser: Doesn’t allow you to hit enter in the name field in browser grids while editing.
• 184 Map Window: If you use map tips, then when you try to close a project, get a message that it could not compact the project as DB still in use. Possible reference leak in map tips? Message goes away once you’ve exited Distance. [25 June 2002, LJT]
• 49 Model Definition Properties: CDS and MCDS – Multipliers tabs. If you select the CueRate box for any other than the first line in Multipliers, Distance will put them on the first line next time you open the properties
• 125 Model Definition Properties: MCDS. You can get to the position when it thinks cluster size has been added as a covariate when it hasn’t. To get there: add a covariate, tick the cluster size box, then remove the covariate. Clicking on the first tab, shows it thinks cluster size is a covar. [LJT 19 July 2001]
• 50 Properties: When you click on OK, the contents of the current tab are not validated before the contents are saved [7 Dec 00]
• 51 Preferences: Changing options do not seem to have any affect until you restart (e.g., changing default open path; changing timestamp and echo data options for analysis).
### Design Engine and Design Properties
• 55 Design Engine cannot be run out of process (possibly some problem in the NEngineInterface) – gives a “cannot find stratum” error (by “run” I mean generate surveys and assess probability of coverage) [15 Jan 01]
• 40 Design Properties: When you change the properties of a design that has already been run (ie coverage probability results exist), the status is not reset or results deleted [12 Jan 01]
• 41 Design Properties: Pressing Defaults causes an object not found error.
• 87 Design Properties: Problem with the calculator for probability of coverage when it is assumed even. See 87.zip – BajaCalifornia Norte has 87% of the effort, but looking at the results of the probability of coverage it is 0 for almost all the strata except the Sonora one (see Map and Grid1 field New Design). [9 Feb 01, Len]
• 88 Design Properties: Zigzag design, maybe others. Tick allocate effort by sampler length, update effort in real time, percentage from __ sampler length. Now, as you enter values in the sampler length, you get error messages saying that the amount is not enough – I don’t think it should check as you actually change the number, but only when you loose focus from that box. [9 Feb 01, Len]
• 89 Design Properties: Crash in design engine – subscript out of range. See New Survey in 89a.zip. See also 89b.zip – may be the same problem, or a different one. I think in this case it is something to do with the rotation of the design axis for each stratum – when I set them all to 0 it runs no problem. [9 Feb 01, Len]
• 90 Design Properties: Equal spacing zigzag, Effort allocation, Design axis section. The Defined as geographic coordinates tick box is enabled when you start by default. If you click on the radio button Determined by start and end location, and then back on Runs at angle to design axis it is now disabled and I can’t seem to re-enable it. [9 Feb 01, Len]
• 263 Design properties: On some projected shapefiles, selecting options in the design coordinate system part of the General Properties tab causes an error in D4DesEng.GeneralDesignProperties.InitDesignObject when the project is run [Gjermund Bøthun 8 March 04]
• 265 Design Properties: Systematic Random Line Design. Effort allocation, absolute values for line lengths. When you enter a new line length value, the Samplers and Spacing columns don’t update. [LJT: 15 March 04]
• 266 Design Properties: Systematic Random Line Design. Can define design axis by angle, but cannot define them by x-y coordinates as you can with the equal spacing zigzag. Would be nice to add this feature. [LJT: 15 March 04]
• 91 I don’t know if the error messages in the survey for 91.zip are valid nor not – 1,000,000 meters of sampling seems like it should be enough (see last bug for why its not in kilometers!). Looking at the data sheet, it does seem to have created 2 lines. When I try 1,000,000 meters of effort per stratum, I get lines generated too, but also the same error messages in each stratum. [9 Feb 01, Len]
• 92 Incorrect error messages about lines being too long and reset to 100000 in 92.zip [9 Feb 01, Len]
• 103 Sampler properties are not saved properly if you don’t choose same properties for all strata. This can cause various error messages when running the design or survey, e.g.: (i) No effort, unable to generate survey; (ii) Error 13 (type mismatch) in D4DesEng. ControlDesignProcess. ReadDesignDefinitionString. To reproduce: (i) Open mexico sample project; (ii) create a new design; (iii) on General Properties tab choose Stratum Layer: “MexStrat”; (iv) on Sampler tab, uncheck Same Properties for all strata; (v) click OK to save the sampler properties; (vi) open the properties again, and go to the Sampler tab – the properties for all the strata except the first one are now blank. [20 March 01, Len]
• 120 If don’t define polygon for global stratum, then plots of surveys and designs at the region level have a strange extent [18 June 01, David] [Len to fix].
• 121 Get an error message when you run designs with new layer names that include a “.” or “_”. [18 June 01, David] [Len to fix]
• 122 Adjusted angle design sometimes plots both a straight line and a curved line for some sections of some transects (at least I’ve seen it do it on at least one transect quite frequently). See survey IJHalf2 (and IJHalf1) in 122.zip. [18 June 01, David]
• 123 When using a design to create a new survey, the area and effort field names are not filled in (they are shown as [None] in the Survey Properties Data fields tab. (Internal note: the relevant commands are the Fld part of Area /Lyr= /Fld= and Effort /Lyr= /Fld=). [11 July 01, Len]
• 274 Design engine: Equal angle zigzag. Choosing a design axis angle other than 0 (e.g., 90) causes a subscript out of range error in the engine. Defining the design axis using coordinates works. [LJT 22 April 2004]
• 275 Design engine? Tools Preferences Design Echo commands to log works when you run the design to generate coverage prob, but not to generate a survey. [LJT 22 April 2004]
• 276 Design Properties: Equal angle zigzag. Setting effort to 0 (e.g., line length) in some strata causes a warning message, when it would be useful to be able to use to specify no effort in some strata. Also, if you previously specified a positve line length, then the 0 value doesn’t seem to “take”, in that if you generate the survey there is a non-zero effort for that stratum [LJT 22 April 2004]
• 289 When you specify assume even coverage under Coverage Probability and you have stratum, the coverage probabilities appear to be assigned to the wrong strata – see D4MexioTiago.dst [Tiago Marques 10 June 2004]
### Analysis Engines
• 130 When running an analysis, if units are of the wrong type (e.g., angle field has units “meters”, then the resulting error message isn’t very helpful: “ Internal Error description: “Error reading project or program setting ‘AngUnit.Metre’: Setting not found, and no default supplied.” [10 Sept 01, Len]
• 190 When you specify starting values or bounds on parameters, doesn’t check that the number of starting values does not exceed the number of parameters, and that the number of bounds does not exceed the total number of key functions. (Note – see engine code commented out routine CheckBounds for more info). [LJT 17 July 02]
• 227 On some machines (Windows 2000 and XP only) where the user has a name with accents in it, running any analysis produces the following error message:
** Warning: Analysis engine wrote some output to the console error stream, reproduced below. ** – Start of Console Error Stream – forrtl: severe (43): file name specification error, unit 13, file [there may be a file name or some jibberish here] Image PC Routine Line Source D4.exe 004B0039 Unknown Unknown Unknown [other lines here deleted] D4.exe 00431155 CLRDAT 937 Datcom.for
• The problem is that the FORTRAN analysis engine is not able to cope with TEMP directories that have accents in them. The solution is to rename your TEMP and TMP environment variables. Instructions for Windows XP (something similar should work in other operating systems): (i) Using Windows explorer, create a temp directory e.g., C:\Windows\Temp (or you may have one there already; you can use any other folder you like so long as it doesn’t have an accent in the folder name) (ii) From the control panel, open System Properties; (iii) In the Advanced tab, click on Environment variables; (iv) In the top window, look for the user variables TEMP and TMP. If they are there, change them both to c:\Windows\Temp (click the EDIT button). If they are not there, don’t worry; (v) In the bottom windows, look again for TEMP and TMP. If they are there, change them both to c:\Windows\temp. If they are not there, click on New to create them (one with variable name TEMP and value c:\Windows\Temp, then another with variable name TMP and value c:\Windows\temp); (vi) click OK to confirm the changes and then reboot to get the new environment variables loaded. The analyses should now run without problems. Contact us if it doesn’t. [LJT 14 April 2003; workaround 20 Oct 2003]
• 236 When running an analysis, occasionally get an error from D3NEH.NEngineHost.OpenProjectDatabase. Error number 3260, “Couldn’t update; the database is currently locked by user ‘admin’.”, source D4DbEng.ProjectSettings.Setting. Currently only reported on a Windows 2000 machine. [Charles Paxton 9 May 2003] [I think I’ve fixed this, but will leave as outstanding until confirmed, LJT 9 May 2003]
### MCDS Analysis Engine
• 66 Slow. Generally needs some tuning of estimation. (Can vectorize arrays, etc.) [Aug 2000]
• 162 Bootstrap CV and confidence limit estimates do not include variance due to multipliers. This means that the bootstrap results underestimate variance when multipliers with SEs>0 are specified. [9 Jan 02, LJT]
• 198 On Windows 2000, MCDS example detection function plots do not display properly – they show as two lines (red and blue) and no figure, rather than the expected 3 lines (yellow, orange, red) Solution: Install Windows Script 5.6, available from Microsoft or from the Distance 4.1 download page of the Distance web site. [18 Aug 02, LJT]
• 217 Smearing has not been tested for the MCDS engine – it may produce incorrect results. In any case, qq-plots for MCDS analyses with smearing have been disabled, as they don’t make sense when there are non-integer numbers of observations. [LJT: 3 Feb 03. Disabled smearing interface for MCDS analyses, and added a note to the manual, LJT 1 Jan 05]
• 305 When fitting detection function at a higher level and estimating at a lower one (e.g., fit globally, estimate by stratum) and doing a bootstrap, get the inappropriate warning message ** Bootstrap Warning: Degrees of freedom less than 1.0 for estimating confidence limits on density. Confidence limits not calculated. **. This message should not appear, since bootstrapping is the correct way to obtain variance estimates in this situation. [Tiago Marques 8 Dec 2004; Fixed LJT 6 Jan 2005]
• 308 Same as 305, but message also appears when cluster size is a covariate [Tiago Marques, 17 Feb 2005; Fixed LJT 17 Feb 2005]
• 307 When bootstrapping, with cluster size as a covariate, can get “Internal error 50, mismatched strata” errors, and similar. Problem is caused by Distance trying to report expected cluster size during bootstrap, when this is not estimated when cluster size is a covariate. [Tiago Marques Jan 2005; Fixed LJT Feb 2005]
• 309 When the data structure is complex, with multiple substratum or subsample layers and there are covariates, can encounter an error “Error: Encountered a problem while executing the data creating query”. [Dirk Burhans, 2 March 2005; Fixed LJT 3 March 3005]
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2017-04-30 03:22:45
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|
http://journal.iksrs.or.kr/journal/article.php?code=67430
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ISSN : 2288-3509(Print)
ISSN : 2384-1168(Online)
Journal of Radiological Science and Technology Vol.42 No.3 pp.223-229
DOI : https://doi.org/10.17946/JRST.2019.42.3.223
# Developing Customized Phantom for Korean Bone Density Using 3D Printing
Junho Lee1), Kwan-Yong Choi1), Jae-Ho Choi2)
1)Department of Biomedical Engineering, College of Medical, Chungnam National University
2)Department of Radiological Technology, Ansan College
Corresponding author: Jae-Ho Choi, Department of Radiological Technology, Ansan College, 155, Ansandaehak-ro, Sangnok-gu, Ansan-si, Gyeonggi-do, 15328, Republic of Korea / Tel: +82-31-400-7105 / E-mail: radiogra1@ansan.ac.kr
07/06/2019 24/06/2019 24/06/2019
## Abstract
In order to reduce the radiation exposure dose of the patient and to obtain accurate diagnosis results, the quality control of the diagnostic radiation generator must be conducted periodically In particular, bone density test equipment could be influenced by many factors, and it is far more important because inaccurate measurement would eventually affect the result value. However, the cross-correction phantom of DXA equipment is poorly penetrated due to lack of awareness of the industry and the high cost. Therefore, this study developed a BMD phantom using a 3D printer and Korean BMD phantom with low cost by cross analyzing Korean BMD value from The Korean National Health and Nutrition Examination Survey and evaluated it. The L1, L2, and L3 BMD values of phantoms produced with the 3D printer were measured to be 0.887±0.006 g/cm2, 0.927±0.006 g/cm2, and 0.960±0.005 g/cm2, at 215 mm height and 0.882±0.011 g/cm2, 0.914±0.005 g/cm2, 0.933±0.008 g/cm2 at 155 mm height displaying statistically significant relevance. The result suggests that a proper quality control and cross calibration of DXA device be possible and expected to be an essential data for various medical phantom manufacture development using 3D printer.
# 3D 프린팅을 이용한 한국인 골밀도 맞춤 팬텀 개발
이 준호1), 최 관용1), 최 재호2)
1)충남대학교 일반대학원 의공학과
2)안산대학교 방사선과
## Ⅰ. Introduction
Bone Mineral Density (BMD) is the amount of bone mass in unit area and osteoporosis is bone metabolic disease which alters the bone composition resulting in BMD decrease[1,2]. There are many factors to osteoporosis and it is classified into primary osteoporosis and secondary osteoporosis. The primary osteoporosis is caused by either menopause or aging, however, it is ambiguous to specify because it progresses at almost the same time. Secondary osteoporosis is due to an exposure to a drug or disorder that interferes with the acquisition of the maximal bone mass or reduction of bone mass[3]. In addition, previous research suggests that various factors such as sex, smoking, drinking, and exercise, menopause, calcium, vitamin D and caffeine intake also affected osteoporosis[4-8].
According to the Health Insurance Review and Assessment Service, the number of patients with osteoporosis increased by 12.58% from 805,304 in 2013 to 906,631 in 2017. In 2017, the number of treatment of women in age of 50, the age women normally reach menopause, was significantly higher than that of 40, and the number of men in age of 40 was lower than that of women, but it increased significantly after the age of 50[9].
Osteoporosis and osteopenia are one of the main factors for the diagnosis of bone mineral density, and it is very important to prevent and treat fractures [10-11]. Bone mineral density (BMD) is measured with vrious means such as radiographic absorptiometry, dual energy X-ray absorptiometry (DXA), quantitative ultrasound (QUS), quantitative computed tomography (QCT). DXA displays the multiple level of energy intensities according to the distribution of bone density through two different kinds of energy X-rays passing through the human body. It is the most commonly used measurement device for diagnosis of osteoporosis for used to quantify the bone density and. DXA bone density measurement devices should be its capability to maintain the accuracy and reliability of t he t est[12] . However, s ince t he b one density measurement value requires certain level of periodic maintenance, there is a risk of misdiagnosis by inaccurate result of the test if it is not properly maintained[13]. Moreover, general-purpose phantoms are not easy to secure for with its expensive prices[14].
Therefore, the study developed a bone density phantom using 3D printer for efficient quality control for DXA device. In order to solve the cost problem which is the major issue of the conventional phantom diffusion, 3D printer has been employed to manufacture a cross calibration phantom with FDM 3D printer which is simple and costs less to manufacture, and evaluate the capability of Korean bone mineral density by linear regression analysis of DXA phantom measurements obtained from the Korea National Health and Nutrition Examination Survey (KNHANES).
## Ⅱ. Materials and Methods
### 1. Evaluating Korean Bone Mass Density through The Korea National Health and Nutrition Examination Survey
In this study, the results of the National Health and Nutrition Survey were used to create Korean bone mineral density custom phantom. The National Health and Nutrition Examination Survey was conducted to ascertain the health and nutritional status of the people based on Article 16 of the National Health Promotion Act, the raw data from the first period of 1998 to the seventh periodical data of the year 2017 is open to the public[15]. The study was conducted with the raw data from the fourth period (2008 ~ 2009) and the fifth period (2010 ~ 2011) in which BMD was performed and 21,072 subjects who measured vertebral bone density were selected. The data of 16,906 persons were analyzed as shown in Table 1, except for those who have the double missing value and are younger than 20 years and those older than 80 years.
### 2. Equipment and materials
The phantom was printed with personal FDM 3D printer (3DP-210F, Cubicon, Republic of Korea) of Cubicon. The maximum printer size of the 3D printer is 150 × 150 × 150 mm (W × H × D), and the X and Y positioning accuracy is 12.5 μm, and the Z positioning precision is 2.5 μm.
PLA filaments in a diameter of 1.75 mm and 30% Cu-PLA filaments were used to print out the soft tissue model and the bone tissue model, and the phantom modeling and slicing has been conducted with 123D design (v2.2.14, Autodesk, USA) and Cubicreator (v2.5.3.2, Cubicon, Republic of Korea).
### 3. Phantom production with 3D printer
The study has been conducted with the size of models; the width and depth of the soft tissue model used for phantom production are shown in Fig. 1, 90 mm and 130 mm, and the height was 215 mm and 155 mm. The bone tissue model was placed in the center of the phantom, and it was produced in size of 40 × 30 × 25 mm (W × D × H) to fit into the soft tissue model. Table 2 shows the printing conditions of the soft tissue and bone tissue model. The 30% Cu-PLA used in the bone model was printed by infilling from at beginning 70% and increased by 5% up to 100% in order to evaluate the Hounsfield Unit (HU).
### 4. Evaluation the usability of the phantom
The 30% Cu-PLA was photographed with a 16-ch CT (Alexion, TOSHIBA) to obtain DICOM and the HU was evaluated using Image J 1.52a (National Institutes of Health, USA). Hologic’s Discovery device has was employed and measured 10 times respectively to compute the cross sectional analysis and evaluate the BMD of the National Health and Nutrition Examination Survey and the printed phantom model. Linear regression analysis was performed using SPSS 23.0 (SPSS Inc. Chicago, IL, USA) to determine the relevance of the measured values.
## Ⅲ. Results
### 1. HU Evaluation by bone model infilling
In Fig. 2, HU of 30% Cu-PLA was measured three times to simulate the bone tissue of BMD phantom. As shown in Table 3, 1,011.60 ± 3.80 at 70%, 1,139.55 ± 9.08 at 75%, 1,288.39 ± 6.25 at 80%, 1,376.20 ± 16.33 at 85%, 1,497.51 ± 2.04 at 90%, and 1,624.52 ± 5.52 at 95%, and 1,772.21±11.74 at 100% respectively. The study was conducted with phantom produced with 80%, 85% and 90% infilling rate. In addition, PLA was measured three times with 100% internal filling to simulate soft tissue, and HU was 36.73 ± 0.89.
### 2. Phantom print
Fig. 3(a) is a model with 80%, 85%, and 90% infilling of 30% Cu-PLA, and Fig. 3(b) is a bone mass model stacked with 95 mm a soft tissue phantom top and bottom. Fig. 3(c) is a model with 65 mm a soft tissue phantom.
The total output of time and usage of 215 mm height phantom was about 61 hours 9 minutes for ABS and 3,039.83 g. The total output of time and usage of 155 mm height phantom was 44 hours 11 minutes and 2,160.37 g. 30% Cu-PLA was used for about 2 hours and 26 minutes, 97.27 g.
### 3. Phantom BMD measurement and linear regression analysis
The L1, L2, and L3 BMD values of phantoms produced with the 3D printer were measured to be 3.015±0.049 g/cm2, 3.353±0.047 g/cm2, and 3.631± 0.042 g/cm2 at 215 mm height and 2.973±0.094 g/cm2, 3.247±0.046 g/cm2, 3.405±0.064 g/cm2 at 155 mm height.
BMD values from KNHANES were 0.886±0.146 g/cm2, 0.930±0.157 g/cm2 and 0.958±0.161 g/cm2. Therefore, a linear regression analysis was conduct to examine the relevance with the phantom model. As a result in Fig. 4, R2 was 0.995 at 215 mm height and computed the equation to predict the existing result as Eq. (1), and R2 was 0.9994 at the height of 155 mm and computed the equation as Eq. (2).
$y = 0.1174 × 3 D v a l u e + 0.5333$
(1)
$y = 0.1658 × 3 D v a l u e + 0.3928$
(2)
As Table 4 shows, with Eq (1). the BMD values of L1, L2 and L3 were 0.887 ± 0.006 g/cm2, 0.927±0.006 g/cm2 and 0.960±0.005 g/cm2 respectively, and there are value difference from those of KNHANES which were 0.15% and -0.32% , And 0.16%. In addition, with Eq (2) applied, The BMD values of L1, L2 and L3 were 0.882±0.011 g/cm2, 0.914±0.005 g/cm2 and 0.933± 0.008 g/cm2, respectively, and the values difference were -0.42% and -1.67% % And -2.60% from those of KNHANES.
## Ⅳ. Discussions
In order to reduce dose exposure of patient and obtain accurate diagnosis result, quality control and maintenance of diagnostic radiation generator should be performed periodically. In particular, bone density test equipment could be influenced by many factors, and it is far more important because inaccurate measurement would eventually affect the result value.
The International Society for Clinical Densitometry (ISCD) suggests to conduct cross-analysis of DXA equipment when conducting comparative analysis with BMD values of different facilities or when the same manufacturer or others equipment is introduced[16]. However, the cross-correction phantom of DXA equipment is poorly penetrated due to lack of awareness of the industry and the high cost[17]. Therefore, the study has developed a low-cost cross-calibration phantom using 3D printing technology.
The density of the PLA material is 1.24 g / cm3, which is similar to that of the human tissue. The previous study have used it to produce X-ray dosimetry phantoms for radiotherapy and phantom for diagnostic X-ray devices [18-20]. Moreover, it has the similar density to PMMA which is used for soft tissue and tissue equivalent phantom, and is used for soft tissue mimic material. 30% Cu-PLA whose HU is relatively larger was used as a bone morphogenetic material to effectively display the difference in the radiation transmittance. However, in order to use the phantom as a substitute for the Korean BMD value, a crossover analysis must be performed and the result is shown in Fig 4. In the linear regression analysis, R2 was 0.995 at 215 mm height, and R2 was 0.9994 at 155 mm height, and 215 mm and 155 mm height which displays the statistically significant with the mean value of Korean bone density values. It proves that the produced phantom can be utilized on DXA cross correction by applying Eq (1) and Eq (2) and 3D phantom with a thin 155 mm height soft tissue model had a stronger correlation.
This suggests that the periodical error measurement enable to calibrate the reading and continuous maintenance of the patient’s bone density value by calibrating the measurd value of same models and same BMD value measured from different facilities before and after the measurement. However, the study was performed with the discovery device of Hologic, and the incompatibility between heterogeneous BMD measurement devices should be improved in future studies.
## Ⅴ. Conclusions
This study has produced a DXA cross correction phantom based on Korean BMD with 3D printer. A linear regression analysis of the bone density of the phantom produced by the 3D printer and the Korean bone density displayed a high correlation respectively, and it was slightly higher when using 155 mm height of soft tissue than of 255 mm height.
It would be possible to conduct proper quality control and maintenance and cross - analyze using DXA device, and it is expected to be used as fundamental data for various medical phantom manufacturing using Korean standard numerical value and 3D printer.
## Acknowledgement
This study was supported by the Health Fellowship Foundation.
## Figure
Diagram of phantom
CT scan by infill of 30% Cu-PLA
Completed device in use for examination
Linear regression model
## Table
Number of subjects and BMD density (unit: g/cm2)
Output parameters of phantom
HU measurement result by infill of 30% Cu-PLA
result of BMD Measurement and Apply linear regression model (unit: g/cm2)
## Reference
1. Kim YR, Park SC. Aocnvergence tsudy fo age-related bone loss and peak BMD in Korean. Journal of the Korea Convergence Society. 2018;9(5):77-83.
2. Kanis JA. Assessment of fracture risk and its application to screening for postmenopausal osteoporosis. Osteoporosis International. 1994;4(6):368-81.
3. Chung HY. Osteoporosis diagnosis and treatment 2007. Endocrinology and Metabolism. 2008;23(2): 76-108.
4. Lee HS. The factors influencing the bone mineral density in korean adult men: Based on Korea national health and nutrition examination survey 2010-2011 Data. Korean Journal of Community Nutrition. 2017;22(2):136-44.
5. Kim YR, Lee TY, Park YS, Cheon HK. The effect of lifestyle habits and nutrient intake conditions of female shift workers at general hospitals on bone mineral density values. Journal of Radiological Science and Technology. 2012;35(1):9-15.
6. Kim MS, Koo JO. Comparative analysis of food habits and bone density risk factors between normal and risk women living in the Seoul area. Korean Journal of Community Nutrition. 2008;13(1):125-33.
7. Cho DS, eLe JY. Bone mineral ednsity nad afctors affecting in female college students. Korean Journal of Women Health Nursing. 2008;14(4):297-305.
8. http://opendata.hira.or.kr/op/opc/olapMfrnIntrsDiagBhvInfo.do.
9. Gates BJ, Das S. Management of osteoporosis in elderly men. Maturitas. 2011;69(2):113-9.
10. Dong KR, Kim HS, J ung WK. A study of e quipment accuracy and test precision in dual energy X-ray absorptiometry. Journal of Radiological Science and Technology. 2008;31(1):17-23.
11. Kang BM, Kwon ST, Kim DY, Kim EH, Kim IJ, Kim JG, et al. Manual of bone densitometry. Cheongwoon; 2009.
12. Glüer CC, Blake G, Lu Y, Blunt BA, Jergas M, Genant HK. Accurate assessment of precision errors: How to measure the reproducibility of bone densitometry techniques. Osteoporosis International. 1995;5(4):262-70.
13. Kim HS, Dong KR, Ryu YH. Accurate quality control method of bone mineral density measurement - Focus on dual energy X-ray absorptiometry. Journal of Radiological Science and Technology. 2009;32(4):361-70.
14. https://knhanes.cdc.go.kr/knhanes/main.do.
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2019-09-17 10:55:17
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https://tex.stackexchange.com/questions/444666/unable-to-change-the-numeral-font-format-at-start-of-each-chapter-using-fancyhdr
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# Unable to change the numeral font format at start of each chapter using fancyhdr [closed]
I am facing a strange problem and hope it is a simple trick that I am missing. I am trying to use several custom fancypagestyle using fancyhdr to separate frontmatter,appendix and backmatter and main matter etc.
Now by default, the first page number is at the fancyfoot[c] for every chapter and other front and backmatter. Initially I have not changed the fancyfoot[].
But when for a particular chapter style say appendix style I try to format \thepage style using fancyfoot[CO,CE] and fancyhead[LE,RO] using {\bfseries \sffamily \thepage}, it happens such that excluding first page of each chapter remaining pages font change works fine as per my custom font. How to rectify this.
In short, I want to make the page numbering at the starting of each chapter as \bfseries \sffamily \thepage.
A MWE may be as follows
\documentclass{book}
\usepackage[english]{babel}
\usepackage{fancyhdr}
\usepackage{blindtext}
\fancypagestyle{mystyle}
{
\fancyhf{}
\fancyfoot[CO,CE]{\large \bfseries \sffamily \thepage}
%The first page of each chapter not changing but other pages ok
\renewcommand{\footrulewidth}{0pt}
}
\pagestyle{mystyle}
\begin{document}
\frontmatter
\chapter{Preface}
\Blindtext
\Blindtext
\Blindtext
\Blindtext
\tableofcontents
\mainmatter
\chapter{My Style Chapter}
\blindtext
\Blindtext
\section{My style section}
\Blindtext
\Blindtext
\appendix
\chapter{Appendix My Style}
\blindtext
\section{My Appendix section}
\Blindtext
\Blindtext
\backmatter
\end{document}
## closed as off-topic by Mensch, Raaja, Stefan Pinnow, siracusa, SebastianoMar 11 at 20:46
• This question does not fall within the scope of TeX, LaTeX or related typesetting systems as defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.
• Please help us help you and add a minimal working example (MWE) that illustrates your problem. Reproducing the problem and finding out what the issue is will be much easier when we see compilable code, starting with \documentclass{...} and ending with \end{document}. – albert Aug 5 '18 at 8:34
• @albert, I have now added an MWE where it shows that first page of every new chapter is default style but second page onwards it formats as customized – Deb bijan Aug 5 '18 at 8:45
• Chapter pages uses page style plain by default. So you have to redefine this page style too. – esdd Aug 5 '18 at 9:22
• @esdd, thanks, I have defined \fancypagestyle{plain}{...} for chapter page and it worked. Now format is ok. – Deb bijan Aug 5 '18 at 9:40
• I'm voting to close this question as off-topic because it was solved in comments – Mensch Mar 11 at 17:31
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2019-07-18 01:05:57
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http://bolesnodete.com/kxt6uj/8702b8-right-inverse-matrix-pdf
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# right inverse matrix pdf
0
1
Actually, it seems that A+ depends on the specific choice of U and V in an SVD (U,D,V )forA,butthenext lemma shows that this is not so. 0000025677 00000 n Recall from Definition [def:matrixform] that we can write a system of equations in matrix form, which is of the form $$AX=B$$. /BitsPerComponent 8 Example A = 27 14 is invertible because for B = 4 −7 −12 , we have AB = 27 14 4 −7 −12 = 10 01 = I and likewise BA= 4 −7 −12 27 14 = 10 01 = I. 0000012776 00000 n I A matrix S 2R n cannot have two di erent inverses. 0000012594 00000 n Suppose you find the inverse of the matrix $$A^{-1}$$. 2 The algorithm to test invertibility is elimination: A must have n (nonzero) pivots. Finding an Inverse Matrix by Elementary Transformation. For matrix A= the inverse is: A-1= since we have det A in the denominator, the determinant cannot be equal to 0. 0000012063 00000 n ; A left inverse of a non-square matrix is given by − = −, provided A has full column rank. What about a non-square matrix? 119 0 obj <>stream A Fast Introduction. 0 0000004891 00000 n 0000010688 00000 n Note 2 The matrix A cannot have two different inverses. Step 2 : Swap the elements of the leading diagonal. 0000007930 00000 n 5 For any m n matrix A, we have A i = eT i A and A j = Ae j. P. Sam Johnson (NITK) Existence of Left/Right/Two-sided Inverses May 26, 2017 3 / 29 Here r = n = m; the matrix A has full rank. Given the matrix D we select any row or column. 0000002554 00000 n Next, transpose the matrix by rewriting the first row as the first column, the middle row as the middle column, and the third row as the third column. De &nition 7.1. The remaining four terms make up the minor matrix. I know that the inverse matrix of a square matrix exists iff its determinant isn't 0. {9��,���ŋ��Z��zKp�L��&fSچ@͋*����HΡs�P%����e. Every item of the newly transposed 3x3 matrix is associated with a corresponding 2x2 “minor” matrix. To find the inverse of A using column operations, write A = IA and apply column operations sequentially till I = AB is obtained, where B is the inverse matrix of A. Inverse of a Matrix Formula. Similarly, if A has an inverse it will be denoted by A-1. 0000026780 00000 n As a result you will get the inverse calculated on the right. 446 CHAPTER 11. The concept is the same, we are only creating a different right … Typo around 4:15. pp.. ebook. 0000027678 00000 n given $$n\times n$$ matrix $$A$$ and $$B$$, we do not necessarily have $$AB = BA$$. Theorem 3.3.8 shows that a square matrix is nonsingular if and only if it is invertible. Reduce the left matrix to row echelon form using elementary row operations for the whole matrix (including the right one). Is there any theorem about the existence of a left- or right-inverse matrix of a non-square matrix? The right-quantum algebra was introduced recently by Garoufalidis, Le and Zeilberger in their quantum generalization of the MacMahon master theorem. For R, 1 3 is the multiplicative inverse of 3 since 1(3) = 1. Identity matrix Inverse Matrix Rearranging equations Solving linear systems In fact, the more elementary problem is to find inverses. The reason why we have to define the left inverse and the right inverse is because matrix multiplication is not necessarily commutative; i.e. How else can we solve this … 0000010572 00000 n (x = 13 5,y =− 6 5) Exemple (méthode de Cramer). C. Nazaret Inverse. So it will be A times A inverse on the right, will be I. Point (x,y) in 2-d space can be described as [x y 1] in vector form. the whole inverse matrix) on the right … ” • # another right inverse for EÞ If E has a right inverse, it is not necessarily unique. Two sided inverse A 2-sided inverse of a matrix A is a matrix A−1 for which AA−1 = I = A−1 A. 0000002332 00000 n To determine the inverse of a matrix using elementary transformation, we convert the given matrix into an identity matrix. /Length 9604 0000026910 00000 n On the way, we also rewrote the right-hand side which yielded our solution vector. This preview shows page 18 - 33 out of 72 pages. Free matrix inverse calculator - calculate matrix inverse step-by-step This website uses cookies to ensure you get the best experience. If matrix A can be eigendecomposed, and if none of its eigenvalues are zero, then A is invertible and its inverse is given by − = − −, where is the square (N×N) matrix whose i-th column is the eigenvector of , and is the diagonal matrix whose diagonal elements are the corresponding eigenvalues, that is, =.If is symmetric, is guaranteed to be an orthogonal matrix, therefore − =. 0000018398 00000 n /Filter /FlateDecode %PDF-1.6 %���� [)D*5�oL;�(x*T�c�ʄ4Va��͍�x�*~�(�+�h*����v�Ʀ��I�0���42 [����/���G���h��jq��-*3��������Yڦ�bc+��� -�'���N뺪�����{�Nˋ�q (J�ުq! In fact, if X;Y 2R n are two matrices with XS = I and SY = I, 0000003284 00000 n Also, the relation between inverse and adjoint are given along with their important properties and PDF. Before you work through this leaflet, you will need to know how to find the determinantand cofactorsof a 3× 3 matrix. Abstract. The left and right inverse eigenpairs problem is a special inverse eigenvalue problem. So, a matrix with a determinant of 0 has no inverse and is called a singular matrix. Pages 72. A method for nding inverse matrices. First, adjoin the identity matrix to its right to get an n 2n matrix [AjI]. The underlying idea is very simple: one takes a matrix identity and views 0000025561 00000 n Let A;B;C be matrices of orders m n;n p, and p q respectively. Left inverse 0000001396 00000 n (WesayB is an inverse of A.) Inverse of Matrix Recall that any linear system can be written as a matrix equation A~x =~b: In one dimension case, i.e., A is 1£1; then Ax =b can be easily solved as x = b A = 1 A b =A¡1b provided that A 6= 0: In this lecture, we intend to extend this simple method to matrix equations. Next, convert that matrix to reduced echelon form. /Width 402 3 Pseudo-inverse The SVD also makes it easy to see when the inverse of a matrix doesn’t exist. By using this website, you agree to our Cookie Policy. The inverse matrix … then is a Hilbert inner product space. Let us find the inverse of a matrix by working through the following example: Example: Solution: Step 1 : Find the determinant. xref %%EOF 0000023652 00000 n 1 Introduction Combinatorial linear algebra is a beautiful and underdeveloped part of enumerative com-binatorics. The method is this. It is also known that one can drop the assumptions of continuity and strict monotonicity (even the assumption of Then the matrix has an inverse, and it can be found using the formula ab cd 1 = 1 det ab cd d b ca Left and right inverse eigenpairs problem for -hermitian matrices and its optimal approximate problem are considered.Based on the special properties of -hermitian matrices, the equivalent problem is obtained.Combining a new inner product of matrices, the necessary and sufficient conditions for the solvability of the problem and its general solutions are derived. Matrix inverses Definition AsquarematrixA is invertible (or nonsingular)if∃ matrix B such that AB = I and BA= I. Nicht jede quadratische Matrix besitzt eine Inverse; die invertierbaren Matrizen werden reguläre Matrizen genannt. Here is a matrix of size 2 3 (“2 by 3”), because it has 2 rows and 3 ... (Section 8.1: Matrices and Determinants) 8.05. There is a special matrix, denoted $$I$$, which is called to as the identity matrix. Introduction Définition Méthode de calcul Propriétés et Autres méthodes Soit A une matrice carrée d’ordre n. Définition On dit que A est inversible s’il existe une matrice B telle que AB = BA = I. School National University of Singapore; Course Title MA 1101R; Uploaded By MegaSummerOpossum4. View Inverse of Matrix.pdf from MATHEMATIC 109 at Lahore Garrison University, Lahore. << Earlier, Erik Ivar Fredholm had introduced the concept of a pseudoinverse of integral operators in 1903. (6) Consequently, only l numbers . Inverse Matrices 83 2.5 Inverse Matrices 1 If the square matrix A has an inverse, then both A−1A = I and AA−1 = I. x��yX��Ǜ����*�bEE�ZDq���� q��k�� �-��F�� ��ո�JԈ�RŨTMj5�I���=s�=���~�3g����oO������������o������
���?rrr�Kڞ��۠���@��4��rss����С/����ŋ�n�z����Ǐ�����e��=zt����7o�={����O�Ԁ�s�|Iۻw���\�r��e��h���������_�~��ɿ���L�����+�4�Y~�F��Í7����ɗ����rP v���b.^������ �p:+V����[��������w��wݾ}���+_�EEEyyy۶m�>}z�Ν�W�^�j����7�*U�����k��J��/��\��o���_� ��/�S�*U*��jԨQ�~};;�~�����$''=z��{�� D�^� Next we’ll look at a di erent method to determine if an n n square matrix A is invertible, and if it is what it’s inverse is. /Type /XObject 0000024297 00000 n columns. %PDF-1.5 0000012216 00000 n The first element of row one is occupied by the number 1 … Set the matrix (must be square) and append the identity matrix of the same dimension to it. %���� 0000022059 00000 n 0000025273 00000 n The necessary and su cient conditions, which guarantee that paq have right core inverses are investigated. ?, y = 2 4 1 −1 2 1 1 3 =?? Matrix Multiplication Notation. It turns out that determinants make possible to flnd those by explicit formulas. 3 The algebra test for invertibility is the determinant of A: detA must not be zero. Suppose we are solving a system $$AX = B$$ by the matrix inverse method, but discover $$A$$ has no inverse. That is, for given partial left and right eigenpairs (eigenvalue and corresponding eigenvector) of matrix, and a special matrix … x�bf������������b�,Gb/�Tnľ�n�������\R�:/X6����ٜk�0b�jM]������D�����T>�� A is row-equivalent to the n-by-n identity matrix I n. 0000008813 00000 n 0000033026 00000 n Hence, it could very well be that $$AB = I_n$$ but $$BA$$ is something else. This means that 1 10 0 2 2 l α α λλ + = AA =−∑. ; If = is a rank factorization, then = − − is a g-inverse of , where − is a right inverse of and − is left inverse of . Properties The invertible matrix theorem. Matrix Inverse A square matrix S 2R n is invertible if there exists a matrix S 1 2R n such that S 1S = I and SS 1 = I: The matrix S 1 is called the inverse of S. I An invertible matrix is also called non-singular. If A has rank m, then it has a right inverse: an n-by-m matrix B such that AB = I. A right inverse of a non-square matrix is given by − = −, provided A has full row rank. 0000009110 00000 n If a determinant of the main matrix is zero, inverse doesn't exist. Let $$A=\begin{bmatrix} a &b \\ c & d \end{bmatrix}$$ be the 2 x 2 matrix. In mathematics, and in particular linear algebra, the Moore–Penrose inverse + of a matrix is the most widely known generalization of the inverse matrix. If the determinant is 0, the matrix has no inverse. To find the inverse of a 3x3 matrix, first calculate the determinant of the matrix. Constant third member of the vector (1) is required for simplicity of calculations with 3×3 matrices, described below. What is a matrix -----(One Matrix many matrices) Why do they exist Matrix Terminology Elements Rows Columns Square Matrix Adding/Subtracting Multiplying/ Dividing (Divisions are Multiplications) The Inverse Matrix (equivalent to 1.0) inverse matrix. The inverse exists if and only if elimination produces n pivots (row exchanges.. row operations to reduce the augmented matrix [ A | ej ] as follows: ... obtaining all columns of X (i.e. 0000013221 00000 n A, AB, AT A −1 1st way A B = C 2nd way A B = C 3td way A B = C 4th way A B = C This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. We next develop an algorithm to &nd inverse matrices. 0000010236 00000 n It seems there does not exist a determinant of a non-square matrix as Determinant of a non-square matrix 0000022882 00000 n Recall: The leading diagonal is from top left to bottom right of the matrix. Explain by relating the matrix to a system of equations. Using row reduction to calculate the inverse and the determinant of a square matrix Notes for MATH 0290 Honors by Prof. Anna Vainchtein 1 Inverse of a square matrix An n×n square matrix A is called invertible if there exists a matrix X such that AX = XA = I, where I is the n × n identity matrix. In other words, if a matrix A has any zero singular values (let’s say s … A simple example of finding the inverse matrix of a 4x4 matrix, using Gauss-Jordan elimination Last updated: Jan. 3, 2019 Find the inverse matrix of a 4x4 matrix, The inverse of a matrix The inverse of a squaren×n matrixA, is anothern×n matrix denoted byA−1 such that AA−1 =A−1A =I where I is the n × n identity matrix. A. Note. L’inverse n’existe que si l’hypothese ad−bc 6= 0 est satisfaite. Say we have equation 3x=2 and we want to solve for x.Todoso,multiplybothsidesby1 3 to obtain 1 3 (3 x)= 3 (2) =⇒ = 2 3. DEFINITION The matrix A is invertible if there exists a matrix A. 65 55 Therefore, the reduced Echelon form of A has a non-zero entry in each row and thus has to be the identity matrix. 0000000016 00000 n 0000009968 00000 n OK. 0000011852 00000 n Coordinates in PDF are described in 2-dimensional space. Notion d’inverse d’un application linéaire bijective Dans le cas où f est bijective, on peut lui fabriquer une application inverse notée f 1 f 1: V !U qui à chaque y de V associe l’unique x de U tel que y = f(x). ii Right inverse B with AB I m Left and Right Inverse Let A be a m nmatrix i. Ii right inverse b with ab i m left and right inverse. Namely, if any of the singular values s i = 0, then the S 1 doesn’t exist, because the corresponding diagonal entry would be 1=s i = 1=0. A unique inverse exists if A is square and full rank. A square matrix is singular if and only if its determinant is 0. 0000019057 00000 n ��_�~ԨQ�Z�"hĜ�I���������0;�1�V�1��j�j�jԨ����;Ｓ�@Bɠ^h~.�|�MAAY3p�@KKK&z�ĉ���K��NJ�؊��!k�. Inverse Matrix Questions with Solutions Tutorials including examples and questions with detailed solutions on how to find the inverse of square matrices using the method of the row echelon form and the method of cofactors. Die inverse Matrix, Kehrmatrix oder kurz Inverse einer quadratischen Matrix ist in der Mathematik eine ebenfalls quadratische Matrix, die mit der Ausgangsmatrix multipliziert die Einheitsmatrix ergibt. 0000010004 00000 n We start with the matrix A, and write it down with an Identity Matrix I next to it: (This is called the \\ an n×m matrix, the pseudo-inverse of A is defined as A+ = UD+V$. Selecting row 1 of this matrix will simplify the process because it contains a zero. The induced matrix norm is called Frobenius norm, i.e. There are many definitions of generalized inverses, all of which reduce to the usual inverse when the matrix is square and nonsingular. The identity matrix, when multiplied by any matrix (such that matrix multiplication exists) returns the same matrix. Determinants and inverses A matrix has an inverse exactly when its determinant is not equal to 0. Why is it necessary that a matrix be a square matrix for its inverse to exist? >> This is no accident ! Right inverse ⇔ Surjective Theorem: A function is surjective (onto) iff it has a right inverse Proof (⇐): Assume f: A → B has right inverse h – For any b ∈ B, we can apply h to it to get h(b) – Since h is a right inverse, f(h(b)) = b – Therefore every element of B has a preimage in A – Hence f is surjective <]>> So let me write that as the first column, I'll write as x1 y1, and the second column, I'll write as x2 y2 and that's supposed to be the identity matrix so let me write that out. ***** *** 2⇥2inverses Suppose that the determinant of the 2⇥2matrix ab cd does not equal 0. Left and right inverses; pseudoinverse Although pseudoinverses will not appear on the exam, this lecture will help us to prepare. matrix I. 2 1 1 3 x y = 4 −1 a comme solution : x = 4 1 −1 3 2 1 1 3 =? It was independently described by E. H. Moore in 1920, Arne Bjerhammar in 1951, and Roger Penrose in 1955. Now I wanted to ask about this idea of a right-inverse. Let us consider three matrices X, A and B such that X = AB. 0000025021 00000 n a single variable possesses an inverse on its range. pas d’inverse et qu’on ne sait pas s’il faut multiplier B par l’inverse de A à gauche ou à droite. 3.6) A1=2 The square root of a matrix (if unique), not elementwise (A) ij The (i;j).th entry of the matrix A A ij The (i;j).th entry of the matrix A [A] ij The ij-submatrix, i.e. 0000020721 00000 n stream 0000026052 00000 n 0000010875 00000 n Let A be a square n by n matrix over a field K (e.g., the field R of real numbers). 0000011111 00000 n 0000017999 00000 n So I'm going to have a matrix A, my matrix A, and now there's going to be some inverse on the right that will give the identity matrix. A generalized inverse is an extension of the concept of inverse that applies to square singular matrices and rectangular matrices. 0000030372 00000 n Inverse of a 2×2 Matrix. 0000007121 00000 n One way in which the inverse of a matrix is useful is to find the solution of a system of linear equations. 0000004052 00000 n 6 0 obj /ColorSpace /DeviceRGB Matrix inversion of a 3×3matrix sigma-matrices11-2009-1 Theadjointandinverseofamatrix In this leaflet we consider how to find the inverse of a 3×3 matrix. The determinant of A will be denoted by either jAj or det(A). 0000005349 00000 n To find the right minor matrix for each term, first highlight the row and column of the term you begin with. 0000012947 00000 n 0000006020 00000 n De &nition 7.2 A matrix is called an elementary matrix if it is obtained by performing If necessary you should refer to previous leaflets in this series which cover these topics. Inverse of a Matrix Solving simultaneous equations. 65 0 obj <> endobj Then B D C, according to this “proof by parentheses”: B.AC/D .BA/C gives BI D IC or B D C: (2) This shows that a left-inverse B (multiplying from the left) and a right-inverse C (multi-plying A from the right to give AC D I) must be the same matrix. View Find Inverse Matrix.pdf from CHEMISTRY MISC at Royal University of Phnom Penh. Transformation between two coordinate systems is described as 3×3 matrix. A square matrix that is not invertible is called singular or degenerate. Here are some identity matrices of various sizes. The determinant of a 4×4 matrix can be calculated by finding the determinants of a group of submatrices. Then 1 (AB) ij = A iB j, 2 (AB) i = A iB, 3 (AB) j = AB j, 4 (ABC) ij = A iBC j. 15c48777a1 kunci jawaban workbook english alive yudhistira howbani soft 7.5 12 Bang Bang! Ca sert, à calculer l’inverse de la matrice (si elle existe), résoudre un système sans faire des échelonnements, tester lié ou libre, base ou pas ... Exemple (méthode de Cramer). Lec 17: Inverse of a matrix and Cramer’s rule We are aware of algorithms that allow to solve linear systems and invert a matrix. Adjoint And Inverse Of A Matrix: In this article, you will know how to find the adjoint of a matrix and its inverse along with solved example questions. The right core inverses of a product and a companion matrix Xiaofeng Chen and Jianlong Chen Southeast University Email: xfc189130@163.com, jlchen@seu.edu.cn Abstract: In this paper, characterizations of right core inverse by one-sided invert-ibility are given. Example: Find the inverse of the matrix, if it is defined: A= 1. check to see det ≠0: det A= 8-6=2 2. Intuition from real numbers For real numbers, we can turn division into multiplication as long as we can find the inverse to the denominator. 1 MATH109 – LINEAR ALGEBRA Week-3 Lecture-6 2 Preamble (Past lesson Brief) Definition of matrix and its In base of definition 1, determinant of the forth order (for n=4) can be .... row operations to reduce the augmented matrix [ A | ej ] as follows: ... obtaining all columns of X (i.e. 0000012140 00000 n 0000002987 00000 n Similarly, the rank of a matrix A is denoted by rank(A). 0000011305 00000 n A matrix is called non-invertible or singular if it is not invertible. This is what we’ve called the inverse of A. startxref The following statements are equivalent (i.e., they are either all true or all false for any given matrix): A is invertible, that is, A has an inverse, is nonsingular, or is nondegenerate. If A is a non-singular square matrix, then there exists an inverse matrix A-1, which satisfies the following condition: Solution: Inverse of a Matrix. Free PDF download of RS Aggarwal Solutions Class 12 Maths Chapter-7 Adjoint and Inverse of a Matrix solved by expert teachers on Vedantu.com. 0000019947 00000 n Theorem 3.3.8. n × m matrix A, where n ≤ m, has a right inverse if and only if A is of full row rank n. n × m matrix A, where m ≤ n, has a left inverse if and only if A has full column rank m. Note 3.3.A. So the inverse is the matrix that we don't know, so that's going to be an unknown matrix. J()k the sum of the eigenvalues of the matrix A 0 has to be equal to zero. Since A is a square matrix, this means that r(A)=number of columns = number of rows. That's supposed to equal 1 0 0 1. 0000002429 00000 n Left inverse ⇔ Injective Theorem: A function is injective A bijective proof of this identity due to Konvalinka and Pak, and also the recent proof of the right-quantum Sylvester's determinant identity, make heavy use of a bijection related to the first fundamental transformation on words introduced by Foata. A i denotes the i-th row of A and A j denotes the j-th column of A. ratio theorem, and we use the matrix inverse formula to nd a generalization of the (right-quantum) MacMahon master theorem. 0000012403 00000 n 0000002742 00000 n This should include five terms of the matrix. Step 3: Change the signs of the elements of the other diagonal. 0000021301 00000 n 2.5. If $$AN= I_n$$, then $$N$$ is called a right inverse of $$A$$. If A is m-by-n and the rank of A is equal to n, then A has a left inverse: an n-by-m matrix B such that BA = I. The right inverse tells you where you might have come from, for any possible destination – “All places are reachable, but I can't put you on the return flight because I don't know exactly where you came from” Factoid of the Day #2 Left and right inverses need not exist, and need not be unique Can you come up with some examples? /Subtype /Image trailer 0000006368 00000 n The inverse of a matrix Exploration Let’s think about inverses first in the context of real num-bers. The matrix inverse is defined only for square nonsingular matrices. The identity matrix is always a square matrix, and it has the property that there are ones down the main diagonal and zeroes elsewhere. /Height 51 A+ The pseudo inverse matrix of the matrix A (see Sec. Suppose BA D I and also AC D I. The inverse of a square matrix A, denoted A−1, is a matrix such that A−1A = I = AA−1 where I is the identity matrix of the same dimension as A. 0000018772 00000 n λ 20 ()A, λ 30 ()A, … λ l+10 ()A of the set (4) can be arbitrary; the other eigenvalues are expressed through these … Learn more about how to do elementary transformations of matrices here. Proceeding exactly identically we can also set the identity matrix on the right-hand side which would be transformed in the process into the inverse matrixD −1. left right pseudo-inverse.pdf - Free download as PDF File (.pdf), Text File (.txt) or read online for free. An identity matrix will be denoted by I, and 0 will denote a null matrix. matrix may have a left inverse or right inverse. A superscript T denotes the matrix transpose operation; for example, AT denotes the transpose of A. 1 such that. By any matrix ( such that matrix to a system of equations have (. 2 4 1 −1 2 1 1 3 =? are investigated inverse of from... Calculator - calculate matrix inverse step-by-step this website, you will get the best experience leaflet, will... Matrix besitzt eine inverse ; die invertierbaren Matrizen werden reguläre Matrizen genannt AA =−∑ in leaflet! Two di erent inverses has an inverse it will be denoted by rank ( a.. A field K ( e.g., the field r of real numbers ) Matrizen genannt 1 3 =?! Be calculated by finding the determinants of a 4×4 matrix can be calculated finding. Combinatorial linear algebra, which is called a singular matrix the eigenvalues the. { -1 } \ ) ese ad−bc 6= 0 est satisfaite of RS Aggarwal Solutions Class Maths. 2-D space can be calculated by finding the determinants of a and j. I\ ), which guarantee that paq have right core inverses are investigated if the determinant 0... As a result you will get the best experience to define the left inverse and the right eigenpairs! The given matrix into an identity matrix will be denoted by I, matrix exists. B such that AB = I_n\ ), which guarantee that paq have right core inverses are investigated theorem. Matrix [ AjI ] are only creating a different right … Abstract Moore. Eigenvalue problem is elimination: a must have n ( nonzero ) pivots x, a matrix is singular it. N ( nonzero ) pivots provided a has full column rank to do transformations... 13 5, y = 2 4 1 −1 2 1 1 3 =?... Are only creating a different right … Abstract and SY = I, and 0 will denote a null.. Will not appear on the exam, this lecture will help us prepare! The determinant is 0 download of RS Aggarwal Solutions Class 12 Maths Chapter-7 adjoint and inverse of a matrix ’! Have right core inverses are investigated the determinant of a 3x3 matrix, \! Field K ( e.g., the reduced echelon form using elementary transformation, we the... Paq have right core inverses are right inverse matrix pdf first, adjoin the identity matrix this. Ba\ ) is required for simplicity of calculations with 3×3 matrices, described.! 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Jawaban workbook english alive yudhistira howbani soft 7.5 12 Bang Bang ’ T exist row rank takes a with! ���Ŋ��Z��Zkp�L�� & fSچ @ ͋ * ����HΡs�P % ����e 1101R ; Uploaded by MegaSummerOpossum4 and the one. Or det ( a ) Fredholm had introduced the concept of a 3x3,... ) and append the identity matrix expert teachers on Vedantu.com remaining four terms make up the minor.... Provided a has a right inverse, it could very well be that \ ( AN= I_n\ ) but (... Matrix may have a left inverse of a 4×4 matrix can be described 3×3. Aji ] inverse formula to nd a generalization of the matrix a: a must have n ( )... Conditions, which guarantee that paq have right core inverses are investigated fSچ @ *... ( nonzero ) pivots − = −, provided a has a inverse! Given the matrix a is defined as a+ = UD+V $means that 1 10 0 2 2 α... And append the identity matrix to row echelon form and column of the of. Are two matrices with XS = I, matrix multiplication Notation terms make up the minor matrix for each,. Is the same dimension to it n = m ; the matrix is nonsingular if and only it. It is not necessarily unique is defined as a+ = UD+V$ norm is to! You get the best experience transpose operation ; for example, at denotes the matrix that is invertible! A and B such that matrix multiplication Notation algebra is a special matrix, the matrix transpose ;! Is an extension of the matrix transpose operation ; for example, at denotes the i-th row of group. Ud+V $beautiful and underdeveloped part of right inverse matrix pdf com-binatorics − = −, provided has. We convert the given matrix into an identity matrix of the term you with! X ; y 2R n can not have two different inverses flnd those by explicit formulas to Cookie... Inverse a 2-sided inverse of a is defined as a+ = UD+V$ ; for example, at denotes j-th. Its inverse to exist Title MA 1101R ; Uploaded by MegaSummerOpossum4 Cookie Policy have to define the left matrix a. By E. H. Moore in 1920, Arne Bjerhammar in 1951, p... Its inverse to exist to find the determinantand cofactorsof a 3× 3 matrix transformation, convert. ( ) K the sum of the concept of a matrix a is invertible transformation, we convert the matrix. Echelon form using elementary row operations for the whole matrix ( such that AB I_n\... Described below of rows inverse is because matrix multiplication is not necessarily commutative ; i.e 3×3.. Test invertibility is the right inverse matrix pdf is n't 0 = AA =−∑ 109 at Lahore Garrison University, Lahore 5. Roger Penrose in 1955, the rank of a 3×3 matrix H. Moore 1920! Supposed to equal 1 0 0 1 transpose of a left- or right-inverse matrix of a non-square matrix nd matrices! This idea of a 3×3matrix sigma-matrices11-2009-1 Theadjointandinverseofamatrix in this series which cover these topics Combinatorial linear algebra, which that! Explicit formulas y 1 ] in vector form but \ ( BA\ ) is required for of... Operators in 1903 the given matrix into an identity matrix may have a left inverse of a matrix using row. I and also AC D I ���ŋ��Z��zKp�L�� & fSچ @ ͋ * ����HΡs�P % ����e in row! Die invertierbaren Matrizen werden reguläre Matrizen genannt I a matrix doesn ’ T.! N are two matrices with XS = I, matrix multiplication is not invertible echelon of. Matrix transpose operation ; for example, at denotes the i-th row of a non-square matrix is given by =! A non-zero entry in each row and column of right inverse matrix pdf matrix inverse calculator - calculate matrix calculator. 3 =? of matrices here described below … the induced matrix norm is called a singular matrix −1 comme. Reduced echelon form of a SVD also makes it easy to see when the matrix that we do know! Right to get an n 2n matrix [ AjI ] inversion of a matrix by... Had introduced the concept of inverse that applies to square singular matrices rectangular!
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2021-05-08 23:05:23
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https://www.gamedev.net/forums/topic/691554-what-computer-specs-would-you-recommend-for-taking-on-game-programming/
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# What computer specs would you recommend for taking on game programming?
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I've decided i want to get into game programming as a hobby. Right now I've just been learning my C++, so my laptop has been keeping up, and I'm sure it should be able to handle 2D game development as well. However, I'd like to get an idea of what this hobby might cost me down the line once I start getting into 3D rendering.
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A reasonably modern computer can handle pretty much anything an individual developer can create.
Think of the most advanced games your computer can already run. Those games are developed by enormous teams with hundreds of experts investing tens of thousands of hours writing code that pushes the limits.
Your hobby game may do a lot of things, but your hobby game will be a walk in the park compared to the work required for AAA games your computer is capable of running.
The minimum requirements for the major engines right now (Unreal, Unity) is a 10-year-old machine.
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Well that is great to know lol. I'm primarily a console gamer, so the only specs I've looked for in my computers were to handle photoshop/lightroom/Illustrator. I was mainly worried because I've tried dabbling in video editing, but my laptop couldn't keep up(which was expected).
Well thanks for the input Frob.
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Posted (edited)
I've been doing most of my at-home work on an older laptop, despite having a much better desktop available- and I've been treating it as sort of a benchmark or minimum spec for how well the project performs. If my small project game can't run on this old laptop, then that's a sign that I've made choices/mistakes that are costing me too much in terms of performance.
If what you have now is enough to comfortably use the tools you need, then that's good enough.
Edited by trjh2k2
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Without knowing the specs of your current machine( it could be from the late 90s for all I know )...
If your laptop has its own dedicated graphics card, can run the OS smoothly...yeah, just stick with it. Just about any computer from the last five years will allow you to achieve any level of skill you wish to obtain.
When using 3D/2D packages like Maya/Blender/Photoshop/GIMP then just be mindful of your system and video memory.
Oh, and don't forget to back up your work on separate storage such as a second or external harddrive. All the code you write is your life work - the cost of losing that is far more than the cost of a new laptop...
Hope this helps!
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Posted (edited)
On 18.08.2017 at 10:37 PM, Anri said:
Oh, and don't forget to back up your work on separate storage such as a second or external harddrive. All the code you write is your life work - the cost of losing that is far more than the cost of a new laptop...
This guy devs. This is very important, who knew it could be SO important for me.
Edited by tyhender
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Buy the best for the money you got, that makes easy choise.
New computers are always far better then second hand with these hidden specs you dont think of.
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21 hours ago, the incredible smoker said:
New computers are always far better then second hand with these hidden specs you dont think of.
Care to elaborate on "hidden specs"? I'd almost argue that, at least in terms of laptops, the value you get for something new isn't great right now. I looked around for new laptops maybe 6 months ago and found the current options to be pretty disappointing. Small hard drives, usually-upgradable parts are being soldered in, and specs don't seem to have gone up significantly in the last few years- so a $1k laptop now doesn't get you much more than what that same$1k would have got you 4-5 years ago. Instead, anything less than a "high end" laptop mostly gets you something like a glorified internet browsing machine.
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Usually the most visible things are the CPU chipset, the chipset of the graphics card, the megabytes of memory, and the gigabytes of hard drive space.
Memory chips can make a big difference. They have a wide range of speed, timings, and voltages. Some will automatically overclock to safe limits. Laptops often focus on chips that have less heat and consume less power. As you may suspect, that also typically means worse performance than chips consuming more power and generating more heat.
Hard drive speeds are usually a hidden difference. Sure several computers may all have 1TB drives, but that doesn't mean they're equal. One with a 5400 RPM drive may struggle to reach 50 MB/s reading files. A 7200 RPM drive may comfortably reach just past 110 or 115 MB/s. But it isn't just spindle vs SSD. A cheap SSD may struggle to reach 200 MB/s but a high-quality SSD may read over 2500 MB/s, over ten times faster than a bad SSD drive, and over 50 times faster than a slow spindle drive.
Motherboards are usually a hidden difference. The types of connections between systems, PCIe x16, x8, or x1 can make a huge difference. The interconnections between devices can make a substantial difference.
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Posted (edited)
24 minutes ago, frob said:
Usually the most visible things are the CPU chipset, the chipset of the graphics card, the megabytes of memory, and the gigabytes of hard drive space.
Memory chips can make a big difference. They have a wide range of speed, timings, and voltages. Some will automatically overclock to safe limits. Laptops often focus on chips that have less heat and consume less power. As you may suspect, that also typically means worse performance than chips consuming more power and generating more heat.
Hard drive speeds are usually a hidden difference. Sure several computers may all have 1TB drives, but that doesn't mean they're equal. One with a 5400 RPM drive may struggle to reach 50 MB/s reading files. A 7200 RPM drive may comfortably reach just past 110 or 115 MB/s. But it isn't just spindle vs SSD. A cheap SSD may struggle to reach 200 MB/s but a high-quality SSD may read over 2500 MB/s, over ten times faster than a bad SSD drive, and over 50 times faster than a slow spindle drive.
Motherboards are usually a hidden difference. The types of connections between systems, PCIe x16, x8, or x1 can make a huge difference. The interconnections between devices can make a substantial difference.
This. I just want add to not underestimate the CPU power-section of a motherboard (where the most of MOSFETs, capacitors and inductors lie). One of the predominant price factors between a good and a discount-market piece of silicon is the power section: even if you are not interested on a wide range internal or external device connectors, a decent power-section can make the different between a long-live machine and a piece of garbage you have to recycle in a couple of year. The same applies to the power supply unit: do not save those couple of bucks just to spend them in a pizza.
Edited by Alessio1989
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2017-11-19 12:42:41
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http://physics.stackexchange.com/questions/59970/simulations-of-planetary-motions
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# Simulations of Planetary Motions
I wrote a spreadsheet that simulates the trajectory of 3 planets in 2D space. The method is simple: for each moment in space, calculate the force felt and velocity of each planet, then for the next $\delta$t period, assume that the planet continues to move with the same acceleration. Then recalculate the position, velocity, and acceleration of each object. Proceeds until desired time frame is simulated.
The computation works roughly correct, but there is a problem with it, that is: I can not produce closed curves typical seen in a planet's orbit. Regardless of what velocity and mass I chose, the orbit's radius always gradually increases.
This is probably caused by the approximation method I chose. I am wondering, what are some improvements I can make to the numerical method?
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See related scicomp question: scicomp.stackexchange.com/q/3566/3224 – Chris White Apr 4 '13 at 1:55
Your method is known as the forward Euler method, the simplest DEQ-solver but a really bad one. I suppose it's the approximation everyone tries first, at least I did, too, when I started with such simulations... and soon was troubled by similar "numerical explosions", which can't really be avoided with this algorithm which is why it's virtually never used in real applications.
The most standard, "proper" alternative is the 4th-order Runge-Kutta solver, I suggest you read up on that. It's going to become a little unwieldy in a spreadsheet (you may want to switch to a proper programming language; I'd recommend Python or Haskell for such stuff).
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Be careful - while Runge-Kutta methods have their uses (like non-periodic N-body simulations), they are not entirely stable and will gain or lose energy at least linearly with time in 2-body orbital problems. Still, they are better than forward Euler, and you recommended switching to a proper language, so +1. – Chris White Apr 4 '13 at 2:21
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2014-04-20 03:12:02
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https://nullren.com/blog/2013/05/23/quick-encrypted-folder.html
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## quick encrypted folder
i wanted an encrypted folder that i could throw around like a file to easily backup in different ways. encfs and ecryptfs are usually better solutions for most people. i wanted one file for my entire directory, so this worked out okay.
### set up
first step, create a file suitably large to hold your filesystem
# dd if=/dev/urandom of=derp bs=1M count=10
now mount it with losetup (modprobe loop if not loaded) so that we cna use it as a block device
# losetup -f
/dev/loop0
this just tells me what the next available loop device is.
# losetup /dev/loop0 derp
/dev/loop0 is now like a normal block device. so lets set up dmcrypt on it (modprobe dm_crypt if this is not loaded).
follow the instructions, the defaults should be okay but there are more options you can give it. this command will set up a password used to protect the file.
# cryptsetup luksFormat /dev/loop0
now open it.
# cryptsetup luksOpen /dev/loop0 encstore
enter your password, now we have something like a normal disk device that we can format using whatever fs we want.
# mkfs.ext4 /dev/mapper/encstore
this sets up the encrypted folder. from here i can mount it or whatever.
### mounting
if we had set up a file derp to be an encrypted folder like in the set up, this is how i would mount it.
# losetup -f
/dev/loop0
# losetup /dev/loop0 derp
# cryptsetup luksOpen /dev/loop0 encstore
# mount /dev/mapper/encstore /mnt/sec
now i can put files in /mnt/sec and feel okay about it.
### unmounting
this is how i unmount it
# umount /mnt/sec
# cryptsetup luksClose encstore
# losetup -d /dev/loop0
now i can copy derp to whatever disk i want, write it to a dvd, save to a usb, email it, whatever.
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2019-10-16 10:11:42
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http://clay6.com/qa/6757/if-the-minor-of-an-element-a-is-denoted-by-m-and-the-cofactor-of-an-element
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# If the Minor of an element $a_{ij}$ is denoted by $M_{ij}$ and the cofactor of an element $a_{ij}$ is denoted by $A_{ij}$ then, which of the following is true?
$A) A_{ij} = (–1)^{i+j} M_{ij}$
$B) A_{ij} = 1^{i+j} M_{ij}$
$C) A_{ij} = (–1)^{i-j} M_{ij}$
$D) A_{ij} = 1^{i-j} M_{ij}$
Answer: $A_{ij} = (–1)^{i+j} M_{ij}$
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2017-10-23 20:47:39
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https://blog.kedata.online/perfect-casino-basically-no-downpayment-discount-codes-2022/
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2022-07-01 19:41:15
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http://math.stackexchange.com/questions/218900/average-proportion-for-proportions-with-different-denominators
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# Average proportion for proportions with different denominators
Say I have an experiment in which subjects are asked to respond to some stimulus. Their responses are transcribed and coded, first as "Valid/Invalid", and then for the valid responses, "Correct/Incorrect". I would like to compute the average of the proportion, $\frac{\text{number correct}}{\text{number valid}}$.
There seem to be two different approaches to this. The first is I could use the total proportion correct, $\frac{\sum{Correct_n}}{\sum{Valid_n}}$.
The second would be to find the actual average of the proportions. I cannot straightforwardly compute the average proportion by adding the subject proportions and dividing by the number of subjects, as each subject had a different number of valid responses, and therefore each proportion has a different denominator. So, I end up the the following expression:
$\frac{n*[(Valid_2 \times Valid_3 \times...Valid_n)Correct_1 + (Valid_1 \times Valid_3 \times ... Valid_n)Correct_2... ]}{Valid_1 \times Valid_2 \times...Valid_n}$
While the two approaches seem similar, I can't figure out if they are going to end up being the same thing, and further I can't decided which one makes more sense, or even if either of them do.
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2016-02-06 10:13:46
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